In the diagram below, DE is parallel to AB. If CE = 2,
AC = 3.6, AB = 4.2, and DC = 2.4, find the length of CB.
Figures are not necessarily drawn to scale.

In The Diagram Below, DE Is Parallel To AB. If CE = 2,AC = 3.6, AB = 4.2, And DC = 2.4, Find The Length

Answers

Answer 1

The length of CB is 3 unit.

In the given figure ;

By SAS property of similar of triangles,

ΔCED and ΔCAB are similar.

Therefore,

CE/CB = DE/AB = DC/AC

⇒ CE/CB = DC/AC

⇒ 2/CB = 2.4/3.6

⇒ CB = (3.6/2.4)X2 = 3

Hence CB = 3

To learn more about similarity of triangles visit:

https://brainly.com/question/14926756

#SPJ1


Related Questions

pick your own function (suggestion: a polynomial of degree two or three, a square root of a linear function, a problem from your textbook, etc...)

Answers

the roots of the function are[tex]x = 1[/tex] and  [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.

What is the polynomial of degree?

This polynomial is a quadratic function and can be graphed as a parabola. a polynomial of degree two.

[tex]f(x) = x^2 - 4x + 3[/tex]

The coefficient of the x^2 term is positive, which means that the parabola opens upwards. The vertex of the parabola is at (2, -1) and the y-intercept is at (0, 3).

The roots of the function can be found by setting f(x) = 0 and solving for x:

[tex]x^2 - 4x + 3 = 0[/tex]

[tex](x - 3)(x - 1) = 0[/tex]

[tex]x = 1, 3[/tex]

Therefore, the roots of the function are[tex]x = 1[/tex] and  [tex]x = 3.[/tex] These are also the x-intercepts of the parabola.

Learn more about polynomial here:

https://brainly.com/question/11536910

#SPJ1

a) Solid obtained by rotating the region bounded by y = r2 and y = 2, about the axis y = -2. b) Solid obtained by rotating the region bounded by y = VT, y=1, 1 = 4, about the axis r=-1.

Answers

The solid obtained by rotating the region bounded by y = r^2 and y = 2 about the axis y = -2 would be a three-dimensional shape with a hole in the middle. The axis of rotation is the line y = -2, which means that the solid will be formed by rotating the given region around this axis. The resulting shape will have a cylindrical section and two hemispherical sections on either end. The cylinder will have a height of 4 and a radius of 2, while the hemispheres will have radii of 2 and 4, respectively.

b) The solid obtained by rotating the region bounded by y = Vx, y = 1, and x = 4 about the axis r = -1 would be a three-dimensional shape with a conical section and a cylindrical section. The axis of rotation is the line r = -1, which means that the solid will be formed by rotating the given region around this axis. The resulting shape will have a cone-shaped section with a height of 4 and a base radius of 4, as well as a cylindrical section with a height of 1 and a radius of 4.
a) The solid obtained by rotating the region bounded by y = x^2 and y = 2 about the axis y = -2 is a parabolic cylinder. This is formed when the parabolic region between the two given functions is rotated around the specified axis, creating a three-dimensional shape with parabolic cross-sections.



b) The solid obtained by rotating the region bounded by y = √x, y = 1, x = 4, about the axis x = -1 is a torus-like shape. This is formed when the region enclosed by the square root function, the horizontal line at y = 1, and the vertical line at x = 4 is rotated around the specified axis, creating a donut-like shape with varying thickness.

To know more about Shape click here .

brainly.com/question/28756579

#SPJ11

Which is not a solution of the inequality five minus 2x is more or equal to -3

Answers

The value of x which is not a solution to the inequality 5 - 2x ≥ -3, is x = 6.

To find out which value is not a solution to the inequality 5 - 2x ≥ -3, we can substitute each value into the inequality and see if it is true or false.

Let's start with the first value, [tex]x=4[/tex]:

5 - 2(4) ≥ -3
5 - 8 ≥ -3
-3 ≥ -3

Since -3 is greater than or equal to -3, x = 4 is a solution of the inequality.

Now let's try x = 6:

5 - 2(6) ≥ -3
5 - 12 ≥ -3
-7 ≥ -3

Since -7 is less than -3, x = 6 is not a solution of the inequality.

Therefore, the answer is x = 6.

Learn more about inequality:

https://brainly.com/question/30238989

#SPJ11

What is the surface area of the triangular prism?


6. 5 ft 8ft 6ft 2. 5ft



115


120


135


159

Answers

The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.

How to calculate the surface area?

To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.

For the first triangular prism with measurements:

Base: 5 ft

Height: 8 ft

Length: 6 ft

To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:

Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)

The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.

Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²

The perimeter of a triangle is the sum of its three sides.

Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft

Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²

Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.

For the second triangular prism with measurements:

Base: 6 ft

Height: 2.5 ft

Length: 115 ft

Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²

Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft

Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²

Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.

Learn more about surface area

brainly.com/question/29298005

#SPJ11

The surface area of the triangular prism is x - 0 = -3

Find out the surface area of the triangular prism?

If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:

| x - 0 | = 3

To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:

x - 0 = 3 or x - 0 = -3

Simplifying further, we get:

x = 3 or x = -3

Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3

Learn more about Equation

brainly.com/question/13763238

#SPJ11

MARKING BRAINLEIST IF CORRECT ASAP

Answers

Answer:

24.1 feet

Step-by-step explanation:

We can represent these 3 points as a triangle:

- place in the water fountain line

- where her lab partner is

- where her friend is

We know that the distance from the water fountain to the lab partner is 6.6 ft, and the distance from the water fountain to the friend is 7.5 ft.

These are the legs (shorter sides) of the right triangle. Now, we need to find the hypotenuse, which is the distance from the lab partner to the friend. We can solve for this using the Pythagorean Theorem.

[tex]a^2 + b^2 = c^2[/tex]

[tex]6.6^2 + 7.5^2 = c^2[/tex]

[tex]43.56 + 56.25 = c^2[/tex]

[tex]99.81 = c^2[/tex]

[tex]c = \sqrt{99.81}[/tex]

[tex]c \approx 10.0 \text{ ft}[/tex]

To finally answer this question, we need to find the perimeter of the triangle (i.e., the distance that will be walked).

[tex]P = 6.6 + 7.5 + 10.0[/tex]

[tex]\boxed{P = 24.1 \text{ ft}}[/tex]

Find g(x), where g(x) is the translation 1 unit left of f(x)=x2.
write your answer in the form a(x–h)2+k, where a, h, and k are integers.

Answers

To find g(x), the translation 1 unit left of f(x) = x², we need to replace x with (x+1) because moving left means we need to subtract 1 from x. Therefore, g(x) = f(x+1) = (x+1)².

To write g(x) in the form a(x-h)² + k, we need to expand (x+1)² first. Using the formula (a+b)² = a² + 2ab + b², we get:

g(x) = (x+1)² = x² + 2x + 1

Now we can write g(x) in the vertex form by completing the square. We add and subtract (2/2)² = 1 to the expression to get:

g(x) = x² + 2x + 1 - 1 + 1
    = (x+1)² + 0

Therefore, g(x) = (x+1)² + 0 is the vertex form of g(x), where a=1, h=-1, and k=0. This means that the vertex of the parabola g(x) is (-1,0), and it opens upwards. The translation 1 unit left of f(x)=x² results in a horizontal shift of the parabola to the left by 1 unit without changing its shape or orientation.

To know more about find g(x) refer here

https://brainly.com/question/28440771#

#SPJ11

please help yall thank you​

Answers

Answer:

1)3 pm

Step-by-step explanation:

1st) so till 12 15 he will have checked 3 patients and after the break the other two, I think he will finish at 3 pm

Write the equation of a circle that has a center at the point (-3, 6) and passes through the point (9, 1).



SOMEONE HELP I WILL MARK BRAINLIEST!!!!!


Oh and put in a link and I will report you, then slaughter you <3

Answers

The equation of the circle with a center at (-3, 6) and passing through the point (9, 1) is (x + 3)^2 + (y - 6)^2 = 169.

To write the equation of a circle with a center at the point (-3, 6) and passing through the point (9, 1), we can use the general equation of a circle: (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle, and r is the radius.

1. Identify the center (h, k) as (-3, 6).
2. Calculate the radius using the distance formula between the center and the given point (9, 1):
  r = √((x2 - x1)^2 + (y2 - y1)^2)
  r = √((9 - (-3))^2 + (1 - 6)^2)
  r = √((12)^2 + (-5)^2)
  r = √(144 + 25)
  r = √169
  r = 13

3. Substitute the values of h, k, and r into the equation of a circle:
  (x - (-3))^2 + (y - 6)^2 = 13^2
  (x + 3)^2 + (y - 6)^2 = 169

So, the equation of the circle with a center at (-3, 6) and passing through the point (9, 1) is (x + 3)^2 + (y - 6)^2 = 169.

To know more about equation, visit:

https://brainly.com/question/29657983#

#SPJ11

CAN somebody pl help

Answers

The expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.

How to evaluate for the area of the shaded region

The area of the shaded region is the area of the semicircle subtracted from the area of the rectangle

radius of the semicircle is also the width of the rectangle, so;

area of the rectangle = 8 yd × 4 yd = 32 yd²

area of the semicircle = (π × 4 yd × 4 yd)/2

area of the semicircle = 8π yd²

area of the shaded region = 32 yd² - 8π yd²

area of the shaded region = 8(4 - π) yd²

Therefore, the expression 8(4 - π) yd² is the area of the of the shaded region in terms of π.

Read more about area here:https://brainly.com/question/2607596

#SPJ1

Which pair of polynomials, when multiplied together, results in the polynomial x^2-x-6? (choose two answers)

Answers

To factor the polynomial x^2 - x - 6, we need to find two binomials whose product is equal to this polynomial. We can use the following methods to factor the polynomial:

Method 1: Factoring by inspection

- We know that x^2 is the product of x and x, so we can start with the binomial (x )(x ) as a factorization of x^2.

- We then look for two numbers whose product is -6 and whose sum is -1.

- The two numbers are -3 and 2, since (-3)(2) = -6 and (-3) + 2 = -1.

- Therefore, the polynomial x^2 - x - 6 can be factored as (x - 3)(x + 2).

Method 2: Using the quadratic formula

- We can also use the quadratic formula to find the roots of the polynomial, which are the values of x that make the polynomial equal to zero.

- The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -1, and c = -6.

- Plugging in these values, we get x = (-(-1) ± sqrt((-1)^2 - 4(1)(-6))) / 2(1) = (1 ± sqrt(25)) / 2.

- Simplifying, we get x = 3 or x = -2.

- Therefore, the polynomial x^2 - x - 6 can be factored as (x - 3)(x + 2).

So, the pairs of polynomials that, when multiplied together, result in the polynomial x^2 - x - 6 are (x - 3) and (x + 2), as well as (x + 2) and (x - 3).

Part D Question Select the correct answer. How many bacteria will exist after 2 hours (120 minutes) have passed? Remember that 1 second of video time corresponds to 20 minutes of real time.

Answers

So after 6 hours, there will be approximately 262,144 bacteria.

What is exponent?

An exponent (also called a power or index) is a mathematical notation that indicates the number of times a quantity is multiplied by itself. It is written as a superscript to the right of the quantity being multiplied. Exponents are commonly used in algebra and other branches of mathematics to represent repeated multiplication or to simplify complex expressions. They also have important applications in science, engineering, and computer programming.

Here,

We can use the formula for exponential growth to find the number of bacteria after a certain amount of time:

N = N0 * [tex]2^{(t/d)} ^[/tex]

where N is the final number of bacteria, N0 is the initial number of bacteria (which is 1 in this case), t is the time elapsed (in minutes), and d is the doubling time (in minutes).

Since the doubling time is 20 minutes, we have:

d = 20

To find the number of bacteria after 6 hours (which is 360 minutes), we plug in these values:

N = 1 * [tex]2^{(360/20)}[/tex]

Simplifying the exponent, we get:

N = 1 * [tex]2^{18}[/tex]

Using a calculator or by hand, we can evaluate this expression to get:

N ≈ 262,144

To know more about exponent,

https://brainly.com/question/11709654

#SPJ1

A wheat farmer is converting to corn because he believes that corn is a more lucrative crop. It is not feasible for him to convert all his acreage to corn at once. He is farming 400 acres of corn in the current year and is increasing that number by 20 acres per year. As he becomes more experienced in growing corn, his output increases. He currently harvests 120 bushels of corn per acre, but the yield is increasing by 4 bushels per acre per year. When both the increasing acreage and the increasing yield are considered, how rapidly is the total number of bushels of corn currently increasing? bushels per year

Answers

When both the increasing acreage and the increasing yield are considered, the total number of bushels of corn currently increasing at a rate of 4000 bushels per year.

The wheat farmer is currently farming 400 acres of corn and increasing that number by 20 acres per year. He harvests 120 bushels of corn per acre, with an increasing yield of 4 bushels per acre per year.

To determine the rate of increase in the total number of bushels, we need to consider both the increasing acreage and the increasing yield.

First, let's find the increase in bushels due to the increasing acreage:
20 acres/year * 120 bushels/acre = 2400 bushels/year

Next, let's find the increase in bushels due to the increasing yield:
400 acres * 4 bushels/acre/year = 1600 bushels/year

Now, add both increases together to find the total increase in bushels:
2400 bushels/year + 1600 bushels/year = 4000 bushels/year

So, the total number of bushels of corn is currently increasing at a rate of 4000 bushels per year.

For more such questions on Yield.

https://brainly.com/question/23577349#

#SPJ11

The original selling price of a jacket was
s
s dollars. The selling price was then changed on two occasions by the store owner. Its price is now represented by
0. 85
(
1. 4
s
)
0. 85(1. 4s). Which expression could explain what happened to the price of the jacket?

Answers

The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes: an initial 15% decrease in price, followed by another 15% decrease in price.

Find out which expression could explain the happened price of the jacket?

The expression 0.85(1.4s) represents the final selling price of the jacket after two price changes. We can break it down into its constituent parts to understand what happened to the price.

Factor 1.4s represents the original selling price of the jacket. This means that the store owner started with a price of 1.4s dollars.

The factor 0.85 represents the first price change. When the store owner lowered the price by 15%, the new price became 0.85 times the original price.

The second factor of 0.85 represents the second price change. After the first price change, the new price was 0.85(1.4s) dollars. When the store owner lowered the price again by 15%, the final selling price became 0.85 times the price after the first price change.

Learn more about Selling

brainly.com/question/27995962

#SPJ11

What is the actual perimeter of the living room?

Answers

the actual perimeter of the living room  in the scale drawing  is 216 inches.

what is scale drawing?

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

If the length and breadth of the living room in real life are 9/4 inches each, we can use the given scale of the drawing to find the corresponding dimensions of the living room in the drawing:

1/4 inch = 2 feet

So, 9/4 inches in real life is equal to:

(9/4) inches / (1/4 inch per 2 feet) = 18 feet

This means that each side of the living room in the drawing would be 18/2 = 9 inches long.

To find the actual perimeter of the living room, we need to convert the dimensions back to real-life measurements and add up the lengths of all four sides:

Length in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Breadth in real life = 9/4 inches x 2 x 12 inches/foot = 54 inches

Perimeter in real life = 2 x (Length + Breadth)

Perimeter in real life = 2 x (54 inches + 54 inches)

Perimeter in real life = 2 x 108 inches

Perimeter in real life = 216 inches

Therefore, the actual perimeter of the living room is 216 inches.

To know more about scale drawing visit :-

brainly.com/question/17388747

#SPJ1

The experimental probability that Anna can throw a football
through a hoop is 60%. How many throws out of 20 can Anna
predict she will make?
O 18
O 12
O14
O 10

Answers

Answer:

12

Step-by-step explanation

60/100 to get the probability of success

0.6 * 20 attempts = 12

If donuts are 12 cents a dozen how much does 100 donuts cost.

Answers

The cost of 100 donuts is $ 1 if a dozen of donuts cost 12 cents.

This question is solved using the unitary method. The unitary method is a method in which you find the value of a unit and then the value of the required number of units.

1 dozen refers to a group of 12.

Cost of 1 dozen donuts or 12 donuts = 12 cents

Cost of 1 donut = [tex]\frac{12}{12}[/tex] = 1 cent

Cost of 100 donuts = 1 * 100 = 100 cents

100 cents = 1 dollar.

Thus, the cost of 100 donuts is 100 cents or 1 dollar.

Learn more about Unitary Method:

https://brainly.com/question/24587372

#SPJ4

The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?

Answers

Option C is correct. No, the least value is smaller than the critical value.

Null hypothesis (H₀): The average first-year teacher salary is $52,000.

Alternative hypothesis (Ha): The average first-year teacher salary is not $52,000.

The significance level is 5% (or 0.05), which means we will reject the null hypothesis if the probability of obtaining the observed result is less than 5%.

Calculate the standard error of the mean:

Standard Error = Standard Deviation / √n

where n is the number of samples (n = 25 in this case).

Standard Error = $1500 / √25

= $1500 / 5

= $300

Now, perform the hypothesis test using a t-test since the sample size is relatively small (n < 30) and the population standard deviation is unknown.

t-score = (Sample Mean - Population Mean) / Standard Error

t-score = ($52,525 - $52,000) / $300

t-score = $525 / $300

t-score = 1.75

To find the critical value at a 5% significance level with 24 degrees of freedom (n - 1), we can consult a t-table. At a 5% significance level (two-tailed test), the critical t-value is approximately ±2.064.

Since the calculated t-score (1.75) is not greater than the critical t-value (2.064), we fail to reject the null hypothesis.

Therefore, option C is correct. No, the least value is smaller than the critical value.

To learn more on Statistics click:

https://brainly.com/question/30218856

#SPJ12

Complete question:

The average first year teacher salary in a certain state is known to be $52,000 with a standard deviation of $1500. A researcher tests this claim by averaging the salaries of 25 first year teachers and finding their average salary to be $52,525. Is there significant evidence to suggest that the claim is wrong at the 5% significance level?

A. Yes, the least value is greater than the critical value

B. No, the least value is larger than the critical value

C. No, the least value is smaller than the critical value

D. yes, the least value is smaller than the critical value

among american women aged 20 to 29 years, 10% are less than 60.8 inches tall, 80% are between 60.8 and 67.6 inches tall, and 10% are more than 67.6 inches tall.17 assuming that the height distribution can ade- quately be approximated by a normal curve, find the mean and standard deviation of the distribution

Answers

Answer:

mean height is approximately 64.2standard deviation is approximately 3.4 inches

Step-by-step explanation:

Since the distribution is approximately normal, we can use the empirical rule to estimate the mean and standard deviation.

According to the empirical rule:

Approximately 68% of the data falls within 1 standard deviation of the mean

Approximately 95% of the data falls within 2 standard deviations of the mean

Approximately 99.7% of the data falls within 3 standard deviations of the mean

From the information given in the problem, we know that:

10% of women are less than 60.8 inches tall

10% of women are more than 67.6 inches tall

So, we can estimate the mean height as the midpoint between 60.8 and 67.6:

mean = (60.8 + 67.6) / 2 = 64.2 inches

We also know that 80% of women are between 60.8 and 67.6 inches tall. Since this is approximately 1 standard deviation from the mean (on either side), we can estimate the standard deviation as:

standard deviation = (67.6 - 64.2) / 1 = 3.4 inches

Therefore, the mean height is approximately 64.2 inches and the standard deviation is approximately 3.4 inches.

Let E be the smallest region enclosed by the cone 7 = — x² + y² and the sphere x² + y2 + z2 = 32 = (note, it is the same region as in Question 9). Then, using cylindrical coordinates we can compute the volume of E as b d t Vol(E) = -|| / F(r, 0, z) dz do dr, a cs where F(r, 0, z) = = a = b = с d = S = t =

Answers

The problem is to find the volume of region E enclosed by a cone and a sphere. The solution involves converting the equations to cylindrical coordinates, finding the limits of integration, and setting up a triple integral. The volume can be calculated by evaluating the integral.

To compute the volume of E using cylindrical coordinates, we first need to find the limits of integration for r, θ, and z. Since E is enclosed by the cone 7 = — x² + y² and the sphere x² + y2 + z2 = 32, we need to find the equations that define the boundaries of E in cylindrical coordinates.

To do this, we convert the equations of the cone and sphere to cylindrical coordinates:

- Cone: 7 = — x² + y² → 7 = — r² sin² θ + r² cos² θ → r² = 7 / sin² θ
- Sphere: x² + y² + z² = 32 → r² + z² = 32

We can see that the cone intersects the sphere when r² = 7 / sin² θ and r² + z² = 32. Solving for z, we get z = ±√(32 - 7/sin² θ - r²). We also know that the cone extends to the origin (r = 0), so our limits of integration for r are 0 to √(7/sin² θ).

For θ, we can see that E is symmetric about the z-axis, so we can integrate over the entire range of θ, which is 0 to 2π.

For z, we need to find the range of z values that are enclosed by the cone and sphere. We can see that the cone intersects the z-axis at z = ±√7. We also know that the sphere intersects the z-axis at z = ±√(32 - r²). Thus, the range of z values that are enclosed by the cone and sphere is from -√(32 - r²) to √(32 - r²) if r < √7, and from -√(32 - 7/sin² θ) to √(32 - 7/sin² θ) if r ≥ √7.

Now that we have our limits of integration, we can set up the triple integral to compute the volume of E:

Vol(E) = ∫∫∫ E dV
= ∫₀^(2π) ∫₀^√(7/sin² θ) ∫₋√(32 - r²)^(√(32 - r²)) F(r, θ, z) dz dr dθ

where F(r, θ, z) = 1 (since we're just computing the volume of E).

Using the limits of integration we found, we can evaluate this triple integral using numerical integration techniques or a computer algebra system.
To find the volume of the region E enclosed by the cone 7 = -x² + y² and the sphere x² + y² + z² = 32, we can use triple integration in cylindrical coordinates. We need to determine the limits of integration for r, θ, and z.

First, rewrite the equations in cylindrical coordinates:
Cone: z = -r² + 7
Sphere: r² + z² = 32

Now, find the intersection between the cone and the sphere by solving for z in the cone equation and substituting it into the sphere equation:
r² + (-r² + 7)² = 32
Solving for r, we get r = √7.

Now, we can find the limits of integration:
r: 0 to √7
θ: 0 to 2π
z: -r² + 7 to √(32 - r²)

Since the volume is the region enclosed by these surfaces, we can set up the triple integral:
Vol(E) = ∫∫∫ r dz dθ dr

With the limits of integration:
Vol(E) = ∫(0 to 2π) ∫(0 to √7) ∫(-r² + 7 to √(32 - r²)) r dz dθ dr

Evaluating this integral will give us the volume of the region E.

Learn more about volume here: brainly.com/question/1578538

#SPJ11

Gina put all the boxes weighing less than 1/2 pound into a small box she puts all the boxes by more than 1/2 pound into a large box how many pounds heavier are the blocks in a large box than pounds in a small box

Answers

Weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

How to find weight difference?

Let's assume that Gina has n boxes in total, and let x be the weight of each box in pounds. We can then express the weight of the boxes that weigh less than [tex]1/2[/tex] pound as [tex](1/2)*w1[/tex], where [tex]w1[/tex] is the number of boxes that weigh less than [tex]1/2[/tex] pound. Similarly, we can express the weight of the boxes that weigh more than 1/2 pound as [tex](1/2)*w2[/tex], where [tex]w2[/tex] is the number of boxes that weigh more than [tex]1/2[/tex] pound.

Since Gina puts all the boxes weighing less than [tex]1/2[/tex] pound into a small box, the weight of the small box will be the sum of the weights of all the boxes that weigh less than [tex]1/2[/tex] pound, which is [tex](1/2)*w1[/tex].

Similarly, since Gina puts all the boxes weighing more than [tex]1/2[/tex] pound into a large box, the weight of the large box will be the sum of the weights of all the boxes that weigh more than [tex]1/2[/tex] pound, which is [tex](1/2)*w2[/tex].

The weight difference between the large box and the small box will be:

[tex](1/2)*w2 - (1/2)*w1[/tex]

Simplifying this expression, we get:

[tex](1/2)*(w2 - w1)[/tex]

Therefore, the weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

To learn more about weight difference, visit

brainly.com/question/31078208

#SPJ11

A rectangular prism with a square base has a height of 17. 2 cm and a volume of 24. 768 cm3. What is the side length of its base?

Answers

The side length of the base of the rectangular prism is approximately 1.2 cm.

What is rectangular prism?

The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairings of the opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.

Let's denote the side length of the base of the rectangular prism as "x" cm.

We know that the volume of a rectangular prism is given by the formula:

Volume = Base Area x Height

In this case, the base is a square, so its area is given by:

Base Area = x²

We are given that the volume is 24.768 cm³ and the height is 17.2 cm.

Therefore, we can write the equation:

24.768 = x² * 17.2

To find the value of x, we can rearrange the equation:

x² = 24.768 / 17.2

x² = 1.4376

Taking the square root of both sides, we get:

x = √1.4376

x ≈ 1.2

Therefore, the side length of the base of the rectangular prism is approximately 1.2 cm.

Learn more about rectangular prism on:

https://brainly.com/question/23717073

#SPJ4

Among college students who hold part-time jobs during the school

year, the distribution of the time spent working per week is approximately normally distributed with a

mean of 20. 20 hours and a standard deviation of 2. 6 hours. Find the probability that the average time

spent working per week for 18 randomly selected college students who hold part-time jobs during the

school year is

a. Not within 1 hour of the population mean

b. 20. 0 to 20. 5 hours

c. At least 22 hours

d. No more than 21 hours

Answers

The z scοre is negative the actual probability would be

1-0.7995 = 0.2005

What is the probability?

A number that expresses hοw likely it is that an event will occur is called the probability of οccurrence. It is written as a number from 0 to 1, or frοm 0% to 100%, in percentage notation. The probability of an event occurring increases with probability.

here,

mean = 20.20

standard deviatiοn = 2.60

we knοw that,

Z scοre = (X-mean)/standard deviation

fοr X = 18:

Z scοre = (18-20.20)/2.6 = -0.8461

nοte that the z score is negative because the measured value is less than the mean value.

fοr Z score 0.8461 probability is 0.7995

and since the z scοre is negative the actual probability would be

1-0.7995 = 0.2005

a. For nοt within 1 hour of the population mean

We apply the formula here and we get the value οf P.

P(19.20>x>21.20) = P(19.20-20.20/2.60√18) > X-μ/σ√n >21.20-20.20/2.60√18

P(19.20>x>21.20) = P(-1.63>z>1.63)

Now, we find the value οf z.

P(19.20>x>21.20) = P(z>1.63) + P(z<-1.63)

P(19.20>x>21.20) = 0.0516 + 0.0516

P(19.20>x>21.20) = 0.1032

b. Fοr 20. 0 to 20. 5 hours

P(20<x<20.5) = P(20-20.20/2.60√18) < X-μ/σ√n<20.50-20.20/2.60√18

P(20<x<20.5) = P(-0.33<z<0.49)

Nοw, we find the value of the z-score and we get

P(20<x<20.5) = P(z<0.49) - P(z<-0.33)

P(20<x<20.5)  = 0.6879 - 0.2707

P(20<x<20.5)  = 0.3172

c. Fοr at least 22 hours

We apply the t-test fοrmula here and we get

P(x≥22) = P(X-μ/σ√n≥22-20.20/2.60√18)

Nοw, we find the value of z.

P(x≥22) = P(z≥2.94)

P(x≥22) = 0.0016

d. Fοr not more than 21 hours.

P(x<21) = P(X-μ/σ√n<21-20.20/2.60√18)

We find here the value οf P for x<21 and we get

P(x<21) = P(z<1.31)

Now, we find the value οf the z- score.

P(x<21) = 0.9049

Hence, a. 0.1032

b.  0.3172

c. 0.0016

d. 0.9049

To learn more about the probability from the given link

https://brainly.com/question/28021905

#SPJ4

Complete question is,

Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average time spent working per week of 18 randomly selected college students who old part-time jobs during the school year is.

Solve for w.
65=170-w

Answers

W = 105
170-65 = 105 that's how W is 105

Help me find the Equation

Answers

The required quadratic function is y = -17/324 (x-12)(x-48)

What is the Graph of a function?

The graph of a function is a visual representation of the relationship between the input values (often referred to as the "domain") and the output values (often referred to as the "range") of the function. The graph is typically drawn on a coordinate plane, with the input values plotted on the horizontal axis and the output values plotted on the vertical axis.

The graph of the function is in the image below:

The domain is (12,48)

Range: (0, 17)

The maximum value is 17

Axis of symmetry: x = 30

Read more about equations here:

https://brainly.com/question/22688504

#SPJ1

Stewart, Oswaldo, Kevin, and Flynn go to a soccer day at the FC Dallas' arena, Toyota Stadium, in Frisco, Texas. The coach has a computer and video system that can track the height and distance of their kicks. All four soccer players are practicing up-field kicks, away from the goal. Stewart goes first and takes a kick starting 12 yards out from the goal. His kick reaches a maximum height of 17 yards and lands 48 yards from the goal. Oswaldo goes next and the computer gives the equation of the path of his kick as y=-= +148 - 24, where y is the height of the ball in yards and x is the horizontal distance of the ball from the goal line in yards. After Kevin takes his kick, the coach gives him a printout of the path of the ball Hegy Kevin's Kick Finally, Flynn takes his kick but the computer has a problem and can only give him a partial table of data points of the ball's trajectory. Flynn's Table: Distance from the 10 11 12 13 14 15 16 17 18 19 20 goal line in yards Height in yards 0 4.7 8.75 12.2 15 17.2 18.75 19.7 20 19.7 18.75 The computer is still not working but Stewart, Oswaldo, Kevin, and Flynn want to know who made the best kick. For each soccer player, • Write an equation to represent the quadratic function. • Create a graph to represent the quadratic functions • Identify the following: Domain o Range Maximum value (height) Axis of Symmetry x-intercepts Which soccer player made the best kick? Whose kick went the highest? Whose kick went the longest? Explain your answer and support with reasoning.

Rosemary chooses to attend the University of Houston to earn her degree. Rosemary has $2,500 in her savings and a $1,000 savings bond from her grandparents to use for college. What is the estimated contribution needed from other sources to pay for Rosemary's first year? Display keyboard shortcuts for Rich Content Editor

Answers

The estimated contribution for Rosemary's first-year college fee is $6,500 including all her savings and available funds.

Savings of Rosemary = $2,500

Savings from bond = $1000

To calculate the contribution needed for Rosemary from other sources, to pay her college fee, we need to add all the available funds and subtract the money for her college fee.

Let us imagine that the total cost of Rosemary's college = $10,000

Total available funds = $2,500  + $1,000

Total available funds = $3500

The remaining amount needed = $10,000 - $3,500 = $6,500

Therefore, we can conclude that Rosemary would need an estimated contribution of $6,500.

To learn more about savings

https://brainly.com/question/16122838

#SPJ4

Ajay buys oranges in bulk for Rs. 20 each. He sells them for Rs. 45 each. Calculate the profit and the profit percentage

Answers

Ajay's profit on each orange is Rs. 25, and the profit percentage is 125%.

What is the profit and profit percentage?

Ajay makes a profit of Rs. 25 on each orange he sells, which is the difference between the selling price and the cost price. The profit percentage is calculated by dividing the profit by the cost price and then multiplying it by 100.

In this case, the cost price of each orange is Rs. 20 and the profit on each orange is Rs. 25. So, the profit percentage is (25/20) x 100 = 125%.

This means that Ajay is making a profit of 125% on each orange he sells, which is a significant profit margin. It also shows that buying in bulk at a lower price and selling at a higher price can be a profitable business strategy.

Learn more about profit

brainly.com/question/15036999

#SPJ11

x Which two choices are equivalent to this expression?
2√75 +3√50
x
x
A
25√6
B 10√3+15/2
C 25√3+25√2
D 2√25-3+3√25-2
E
3√25+2√25

Answers

B. 10√3 + 15√2.


2√75 + 3√50; both 75 and 50 have a common factor of 25, and the square root of 25 = 5.
So we can take out √25 from both terms:
2√(25*3) + 3√(25*2)
This reduces to (2*5)√3 + (3*5)√2
And simplifies to: 10√3 + 15√2.
Option B is correct.

I don’t think I see any other options that work?
2√75 = √300 since 2=√4 and √(4*75=300).
3√50 = √450 since 3=√9 and √(9*50=450).
300 and 450 have a common factor of 25, also with a sqrt of 5.
450/25 = 18 and 300/25 = 12.
The most these simplify to is:
5√18 + 5√12.

Option B is one of the correct choices.

The table shows the number of jelly beans in a dish. If Jeremy randomly selects a jelly bean, what is the probability that it is NOT lemon or orange?



Jelly Bean Type Number in Dish


grape 10


lemon 8


orange 14


cherry 16


Group of answer choices



1/4



11/24



1/2



13/24

Answers

The probability of Jeremy selecting a jelly bean that is not lemon or orange is: 26/48 = 0.54 or 54%.

To find the probability that Jeremy randomly selects a jelly bean that is not lemon or orange, we need to first find the total number of jelly beans that are not lemon or orange.

The number of grape jelly beans is 10, the number of cherry jelly beans is 16, so the total number of jelly beans that are not lemon or orange is:

10 + 16 = 26

The total number of jelly beans in the dish is:

10 + 8 + 14 + 16 = 48

Therefore, the probability of Jeremy selecting a jelly bean that is not lemon or orange is:

26/48 = 0.54 or 54%.

To learn more about randomly: https://brainly.com/question/25428940

#SPJ11

An oil globe made of hand blown glass of a diameter 22.6.what is the volume of globe.

Answers

If An oil globe made of hand-blown glass of a diameter of 22.6. Therefore, the volume of the oil globe is approximately 5704.8 cm^3.


The volume of a spherical object can be calculated using the formula:

V = (4/3)πr^3

where V is the volume, π is the mathematical constant pi (approximately equal to 3.14159), and r is the radius of the sphere.

In this case, we are given the diameter of the oil globe, which is 22.6. The radius is half of the diameter, so we can calculate the radius as:

r = d/2 = 22.6/2 = 11.3 cm

Substituting this value of radius in the formula for the volume of a sphere, we get:

V = (4/3)π(11.3)^3

V = 5704.8 cm^3 (rounded to one decimal place)

Therefore, the volume of the oil globe is approximately 5704.8 cm^3.

To learn more about “diameter” refer to the https://brainly.com/question/10907234

#SPJ11

IVan charges an hourly rate for a moving team to load and unload a truck. The charge is a different


hourly rate for a team to pack and unpack boxes. For 8 hours of loading and unloading and 6 hours of


packing and unpacking the company charges $890. For 5 hours of loading and unloading and 3 hours of


packing and unpacking the company charges $515. Write a system of equations and then determine the


company's hourly rates?

Answers

Let's assume that the hourly rate for loading and unloading is $x and the hourly rate for packing and unpacking is $y.

From the given information, we can form the following two equations:

[tex]8x + 6y = 890[/tex] ...(1) (for 8 hours of loading and unloading and 6 hours of packing and unpacking)

[tex]5x + 3y = 515[/tex] ...(2) (for 5 hours of loading and unloading and 3 hours of packing and unpacking)

To solve for x and y, we can use the method of elimination.

Multiplying equation (2) by 2, we get:

[tex]10x + 6y = 1030[/tex] ...(3)

Now, subtracting equation (1) from equation (3), we get:

2x = 140

Therefore, x = $70 per hour.

Substituting the value of x in equation (2), we get:

5(70) + 3y = 515

Simplifying, we get:

3y = 165

Therefore, y = $55 per hour.

Hence, the company's hourly rates are $70 per hour for loading and unloading and $55 per hour for packing and unpacking.

In summary, we can set up a system of equations to solve for the hourly rates of a moving team.

From there, using the method of elimination, we can solve for the hourly rates for both loading and unloading as well as packing and unpacking.

In this case, the hourly rate for loading and unloading is $70 per hour, and the hourly rate for packing and unpacking is $55 per hour.

To know more about hourly rate refer here

https://brainly.com/question/29335545#

#SPJ11

Other Questions
1) Find the value of the k that makes the sequence arithmetic -13,k,-3,2,...A)5B)-8C)-5D)-102) Which formula describes the arithmetic sequence?-4/5, -3/5,-2/5,-1/5...A)tn=-n/5B)tn=n/5-1C)tn=1+n/5D)tn=-n/5-13)What're the next 4 terms in the series?t1=3,tn=1/2,tn-1 -1A)1/2, -3/4, -11/8, -27/10B)3/2, 3/4, 3/8, 3/16C)-1/2, 3/4, 5/8, 21/16D)2, 0, -1, -3/24)Which formula describes the arithmetic sequence?-3,-6,3,-6A)tn=-tn-1+3B)tn=-tn-1-1C)tn=tn-1-1D)-tn-1-3 Which sentence best paraphrases this information about river otters? Otters are really good slide builders. Crayfish and small amphibians are eaten by otters. Outstanding among these characteristics is the otter's habit of building slides. Otters are talented at constructing slides. These help them move through their environment with ease as they hunt for small sea life to eat. Two events, E1 and E2, are defined for a random experiment. What is the probability that at least one of the two events occurs in any trial of the experiment? Which expression should you simplify to find the 90% confidence interval for a sample of 64 people with a mean of 36 and standard deviation of 3? There are 4 times as many chickens as ducks, there are 72 more chickens than ducks how many chickens and ducks are there During a synthesis reaction, 3. 2 grams of magnesium reacted with 12. 0 grams of oxygen. What is the maximum amount of magnesium oxide that can be produce during the reaction Use the quadratic formula to solve -2x^2+2x+1 !!!PLEASE HELP!!! I WILL GIVE A BRAINLIST!!!For this assignment, you will read the article "Seneca Falls Convention" at History.com. Then, you will write short answers to questions, using evidence from the article and the lesson to support your ideas.To get the best grade possible, follow the instructions in the assignment closely and answer all of the questions completely.This assignment is worth 30 points.Answer each question in at least three sentences. Your answers should include a topic sentence that directly responds to the question, as well as two supporting detail sentences that cite evidence from the lesson or the "Seneca Falls Convention" article.This part of the assignment is worth 30 points.1. Describe the Seneca Falls Convention. When and where was it held, and why was it necessary? (3 points)2. How did the abolition movement influence the organizers of the Seneca Falls Convention? (3 points)3. Describe who Elizabeth Cady Stanton and Lucretia Mott were, including their importance to the Seneca Falls Convention. (3 points)4. What was the Declaration of Sentiments? Who wrote it, and why? (3 points)5. What is suffrage? Why did some women at the convention argue against women's suffrage? (3 points)6. Why did the women at the Seneca Falls Convention create the Declaration of Sentiments? How was this document similar to the Declaration of Independence? (3 points)7. According to the article "Seneca Falls Convention," how did news about the Seneca Falls Convention spread throughout the nation? What was the reaction? (3 points)8. Describe who Frederick Douglass was, including his influence on the Seneca Falls Convention and the Declaration of Sentiments. (3 points)9. What fact from the article "Seneca Falls Convention" did you find new or surprising? What does this fact help you understand about the importance of the Seneca Falls Convention? (3 points)10. What happened in the movement for women's rights after the Seneca Falls Convention? How long did it take for women to be granted suffrage? (3 points) KEY QUESTION 1: WHAT ROLE DID SOUTH AFRICAN WOMEN PLAY AGAINST THE VIOLATION OF HUMAN RIGHTS FROM THE 1950s TO 1960s? Women were at the forefront of transformation in South Africa, yet their contributions to political changes are often under-rated. Do you agree with this statement, support your line of argument by explaining the role played by the women in the transformation of South Africa from the 1970's to 19942? write a essay At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.Ketchup Mustard Chili63 27 60Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?Group of answer choices9002,0002,1004,000 A particle travels along the x-axis with velocity v ( t ) = 2 t 1 + t 2 m/s for 0 t 3 seconds. If the particles position at t = 0 is x ( 0 ) = 5 , what is its position at t = 3? Show all of your work. The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0, 360)?Group of answer choicesx = 0, 30, 150, 180x = 0, 180, 210, 330x = 30, 90, 150, 270x = 90, 210, 270, 330 PLSSS HELPP1a. Model the periodic motion of the horses using anequation and a graph.Horse Equation: Use function notation in degrees. Yourfunction will graph below. Which statement best represents a result of the Nineteenth Amendment?Women may vote only if they pay a poll tax.Women have been elected to government offices.Women may vote, but are not eligible to run for public office.Women can run for office, but cannot actually be elected. In tetrahedron $ABCO,$ $\angle AOB = \angle AOC = \angle BOC = 90^\circ.$ A cube is inscribed in the tetrahedron so that one of its vertices is at $O,$ and the opposite vertex lies on face $ABC.$ Let $a = OA,$ $b = OB,$ and $c = OC.$ Show that the side length of the cube is\[\frac{abc}{ab + ac + bc}.\][asy]import three;size(180);currentprojection = orthographic(6,3,2);real a, b, c, s;triple A, B, C, O;a = 6;b = 3;c = 2;s = a*b*c/(a*b + a*c + b*c);A = (a,0,0);B = (0,b,0);C = (0,0,c);O = (0,0,0);draw(O--A,dashed);draw(O--B,dashed);draw(O--C,dashed);draw(A--B--C--cycle);draw((0,0,s)--(s,0,s)--(s,0,0)--(s,s,0)--(0,s,0)--(0,s,s)--cycle,dashed);draw((s,s,0)--(s,s,s),dashed);draw((s,0,s)--(s,s,s),dashed);draw((0,s,s)--(s,s,s),dashed);label("$A$", A, SW);label("$B$", B, E);label("$C$", C, N);dot("$O$", O, NW);dot((s,s,s));[/asy]pls help me Would samples that were digested with ecori have a different pattern than the same sample digested with smal? Tell the measure of the angle in degrees..1Useangle measurtop39360GMAFGH When the suffix -ly is added to an adjective like quick, the word becomes _____. A.its opposite B.a synonym C.a noun D.an adverb Identify one aspect of systems reliability that is not a source of concern with regards to a public cloud. Group of answer choices availability efficiency privacy confidentiality Guidelines:The Discussion Board provides a chance for you to present ideas and insights to your classmates and respond to your classmates' posts, as well. Take the opportunity to share your thoughts and opinions, your background knowledge and experience, or anything you may have learned in the course so far. Keep in mind that everyone in this class can read whatever you post. Keep your responses original and polite, and remember to use correct spelling and grammar. Also provide sources where appropriate.Remember that this is an academic Discussion Board, so stay on topic. If you are not sure how many posts you need to make, ask your instructor.Prompt:Locate an image of a residential interior in a magazine or on an interior design website. In the picture, find two furnishings from one or two specific historical periods described in this lesson. Look to the walls, windows, ceilings, floors, furniture, colors, or accessories.Explain how you know the furnishings or elements are related to the historical periods. Be sure to provide enough detail for your readers, who will not have seen the image.