z = 4(x - 1) - ln (y - 4)
Therefore, the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0) is z = 4(x - 1) - ln (y - 4).
To determine the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0), we first need to find the partial derivatives of the surface with respect to x and y.
∂z/∂x = y/x
∂z/∂y = ln x
Then, we can use these partial derivatives along with the point (1, 4, 0) to find the equation of the tangent plane using the formula:
z - z0 = ∂z/∂x(x0, y0)(x - x0) + ∂z/∂y(x0, y0)(y - y0)
where (x0, y0, z0) is the given point.
Plugging in the values, we have:
z - 0 = (4/1)(x - 1) + ln 1(y - 4)
Simplifying:
z = 4(x - 1) - ln (y - 4)
Therefore, the equation of the tangent plane to the surface z = y ln x at the point (1, 4, 0) is z = 4(x - 1) - ln (y - 4).
Learn more about tangent plane here:
https://brainly.com/question/30260323
#SPJ11
Use the given facts about the functions to find the indicated limit.
lim x->3 f(x)=0, lim x->3 g(x)=4 lim x->3 h(x)=2
lim x->3 6h/ 4f+g (x)
*there are no answer choices. Its a prompt*
The value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
Given, [tex]\lim_{x \to 3} f(x)=0[/tex]
[tex]\lim_{x \to 3} g(x)=4[/tex]
[tex]\lim_{x \to 3} h(x)=2[/tex]
We have to find the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex]
[tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)=\lim_{x \to 3} \frac{6h(x)}{4f(x)+g(x)}[/tex]
[tex]= \frac{\lim_{x \to 3}6h(x)}{\lim_{x \to 3}4f(x)+\lim_{x \to 3}g(x)}[/tex]
[tex]=\frac{6\times 2}{4\times0+4}[/tex]
= 12/4
= 3
Hence, the value of [tex]\lim_{x \to 3} \frac{6h}{4f+g} (x)[/tex] is 3
Learn more about Limits here
https://brainly.com/question/30956864
#SPJ4
Below are the steps for copying Line Segment DE using dynamic geometry software. Which sequence has the steps in the correct order?
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Construct a circle centered at the point G with radius Line Segment DE.
3.) Line Segment DE ≅ Line Segment GH
4.) Draw a point and label it G.
~a.) 2,4,1,3
~b.) 4,2,1,3
~c.) 2,1,4,3
~d.) 3,4,2,1
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is in the order of 2,1,4,3. So, correct option is C.
The correct sequence of steps for copying Line Segment DE using dynamic geometry software is:
1.) Draw Line Segment DE with endpoint H on the circle.
2.) Draw a point and label it G.
3.) Construct a circle centered at the point G with radius Line Segment DE.
4.) Line Segment DE ≅ Line Segment GH
Therefore, option c.) 2,1,4,3 is the correct sequence of steps. The first step is to draw the original line segment DE with endpoint H on the circle.
The second step is to draw a point and label it G. The third step is to construct a circle centered at G with the same radius as Line Segment DE. Finally, in the fourth step, the line segment GH is drawn such that it is congruent to Line Segment DE, completing the copy of Line Segment DE.
So, correct option is C.
To learn more about circle click on,
https://brainly.com/question/30947467
#SPJ1
someone help pls!! giving brainlist to anyone who answers
Answer: csc M = [tex]\frac{\sqrt{86} }{8}[/tex]
Step-by-step explanation:
The csc is related to sin
csc x = 1/sin x
find sin M first then flip it to find csc M
sin M= opposite/hypotenuse
sin M= [tex]\frac{8}{\sqrt{86} }[/tex] >flip that
csc M = 1/sin M
csc M = [tex]\frac{\sqrt{86} }{8}[/tex] >root cannot be simplified it breaks down into 2 and 43
which are 2 prime numbers
How do I solve for X with the base numbers on a right triangle. (Please give an explanation and an answer, I need to know how it works.)
Let's label the 3 points as A;B;C, where BC is the hypotenuse and AB is the shortest side, and x as AH.
We can see that triangle AHC is similar to triangle CAB, and triangle ACH is similar to triangle BCA, so therefore triangle AHC is similar to triangle CHA (i might've messed up the order but you get it)
Because they are similar, we get the ratio : x/12 = 40/x, or x^2 = 480.
So, x = [tex]\sqrt{480}[/tex], or 21.9 (1 d.p)
Answer:
21.9 units-----------------------
According to the right triangle altitude theorem:
the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.We see x is the altitude and 12 & 40 are the segments formed on the hypotenuse.
Applied to the given triangle, we get following equation:
[tex]x=\sqrt{12*40} =\sqrt{480} =21.9\ units[/tex]23. A triangular earring has side lengths of 1. 5 centimeters, 2 centimeters, and 3
centimeters. What is the approximate measure, in degrees, of the largest angle of the
triangular earring?
А
36. 3°
B.
45. 8°
C. 117. 3°
D.
134. 2°
Using cosine rule, the largest angle In the triangle is
C. 117. 3°How to find the measure of the largest angleThe angle is found first using cosine rule by the formula
cos A = (b² + c² - a²) ÷ 2bc
Solving for the largest angle
substituting the values
cos γ = (2² + 1.5² - 3²) ÷ 2 * 1.5 * 2
< γ = arc cos ( -0.4583 )
< γ = 117.28 degrees
Learn more about cosine and sine rule at
https://brainly.com/question/29247917
#SPJ1
The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
How to find the avg number of eggs?To calculate the average number of eggs sold per day, add up the total number of eggs sold and divide by the number of days.
Total number of eggs sold = 42 + 49 + 61 + 35 + 27 + 36 + 50 + 34 + 31 + 40 = 405
Number of days = 10
Average number of eggs sold per day = 405 / 10 = 40.5
The shopkeeper sold an average of 40.5 eggs per day during the given interval.
Read more about average here:
https://brainly.com/question/20118982
#SPJ1
The shopkeeper sold every day the number of eggs is recorded. At equal intervals group 42, 49, 61, 35, 27, 36, 50, 34, 31, 40
What is the average number of eggs sold per day by the shopkeeper over the given interval?
The cylinder below has a height of 6 centimeters and a radius of r1. The volume of the cylinder is 302 cubic centimeters.
Find the radius of the cylinder. Round to the nearest whole centimeter.
___ centimeters
Answer:
There is a cylinder with a height of 6 centimeters and a radius of r1, which has a volume of 302 cubic centimeters. It's fascinating to see how the volume of different shapes can vary based on their dimensions.
MARK AS BRAINLIEST!!!
To find the quotient of 4. 082 and 10,000, move the decimal point in 4. 082
Choose. Right left
places to the
Choose. Right-left
The quotient of 4.082 and 10,000 is 0.000004082.
To find the quotient of 4.082 and 10,000, we need to divide 4.082 by 10,000. However, dividing a decimal by another decimal can be tricky, so we need to move the decimal point of the dividend (4.082) and the divisor (10,000) to make the division easier.
We can move the decimal point of 4.082 four places to the left to obtain 0.04082. This is because moving the decimal point to the left makes the number smaller. For example, moving the decimal point in 4.082 one place to the left gives us 0.4082, which is ten times smaller than 4.082. Moving the decimal point four places to the left gives us a number that is 10,000 times smaller than 4.082.
Similarly, we can move the decimal point of 10,000 four places to the right to obtain 100,000,000. This is because moving the decimal point to the right makes the number larger. For example, moving the decimal point in 10,000 one place to the right gives us 1,000, which is ten times larger than 10,000. Moving the decimal point four places to the right gives us a number that is 10,000 times larger than 10,000.
Now we can divide 0.04082 by 100,000,000, which gives us the quotient of 0.000004082. Therefore, to find the quotient of 4.082 and 10,000, we need to move the decimal point in 4.082 four places to the left and move the decimal point in 10,000 four places to the right, and then divide the resulting numbers.
To know more about quotient, refer to the link below:
https://brainly.com/question/16134410#
#SPJ11
Procter & Gamble reported that an American family of four washes an average of 1
ton (2000 pounds) of clothes each year. If the standard deviation of the distribution
is 187. 5 pounds, find the probability that the mean of a randomly selected sample of
50 families of four will be between 1980 and 1990 lbs.
The required probability is approximately 0.1253 or 12.53%.
We can use the central limit theorem to approximate the sampling distribution of the mean of the weights of clothes washed by 50 families of four. According to the central limit theorem, the sampling distribution of the mean will be approximately normal if the sample size is large enough (n > 30), regardless of the shape of the population distribution.
The mean of the sampling distribution of the mean will be equal to the population mean, which is 2000 lbs
[tex]SEM=\frac{\sigma}{\sqrt{n} }[/tex]
σ = population standard deviation
n = sample size.
[tex]SEM=\frac{187.5}{\sqrt{50} }[/tex]
= 26.5
Now we need to find the z-scores corresponding to the two values of the mean.
[tex]z_1=\frac{1980-2000}{26.5}[/tex]
= -0.75
[tex]z_2=\frac{1990-2000}{26.5}[/tex]
= -0.38
Using a standard normal table, we can find the probability that a z-score is between -0.75 and -0.38.
P(-0.75 < Z < -0.38) = 0.1253
Therefore, the required probability is approximately 0.1253 or 12.53%.
Learn more about z-score here
https://brainly.com/question/15016913
#SPJ4
What is the exact circumference of a circle with a radius of 15 cm?
Responses
10π cm
10 pi, cm
15π cm
15 pi, cm
30π cm
30 pi, cm
60π cm
Answer:
30π cm
Step-by-step explanation:
if r = 15 cm
circumference = π2r
= π × 2 × 15
= 30π cm
#CMIIWtan(x)>(3^1/2)+1 Range for x( 0
Answer:
Step-by-step explanation:
A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6
what is the probability of not rolling a 2?
enter your answer as a fraction, in simplest form, in the box.
a calculator is allowed on this quiz.
question 1 options:
56
16
23
76
A number cube has sides numbered 1 through 6. the probability of rolling a 2 is 1/6. The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form). The correct answer is 5/6.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 can be calculated as follows:
Determine the total number of outcomes, which is 6 (1, 2, 3, 4, 5, and 6).
Determine the number of favorable outcomes, which is 5 (1, 3, 4, 5, and 6), since you're looking for the probability of not rolling a 2.
Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes.
The probability of not rolling a 2 on a number cube with sides numbered 1 through 6 is 5/6 (in simplest form).
So, the correct answer is 5/6.
Read more about probability.
https://brainly.com/question/11234923
#SPJ11
to measure the length of a hiking trail, a worker uses a device with a 2-foot-diameter wheel that counts the number of revolutions the wheel makes. if the device reads 1,100.5 revolutions at the end of
the trail, how many miles long is the trail, to the nearest tenth of a mile?
The length of the trail is determined as 1.3 miles.
What is the length of the trail?The length of the trail is calculated as follows;
The circumference of the circle is calculated as;
S = πd
where;
d is the diameter of the circleS = π x 2 ft
S = 2π ft
I revolution = 1 circumference = 2π ft
1 rev = 2π ft
1,100.5 rev = ?
= 1,100.5 rev/rev x 2π ft
= 6,914.65 ft
5280 ft -------> 1 mile
6,914.65 ft ------> ?
= 1.3 miles
Learn more about circumference of circle here: https://brainly.com/question/20489969
#SPJ1
The volume of a cylinder is twice the volume of a cone. The cone and the
cylinder have the same diameter. The height of the cylinder is 5 meters.
What is the height of the cone?
The height of the cone that the volume of a cylinder is twice the volume of a cone is 7.5 meters.
How to determine the height of the coneLet's first define some variables to represent the dimensions of the cone and cylinder. Let's use r for the radius of both shapes, h for the height of the cone, and 5 for the height of the cylinder.
The volume of a cone is given by V_cone = (1/3)πr^2h, and the volume of a cylinder is given by V_cylinder = πr^2h.
We are told that the volume of the cylinder is twice the volume of the cone:
V_cylinder = 2V_cone
Substituting the formulas for the volumes of the cone and cylinder, we get:
πr^2(5) = 2[(1/3)πr^2h]
Simplifying, we can cancel the π and the r^2 terms on both sides:
5 = (2/3)h
Multiplying both sides by 3/2, we get:
h = 7.5
Therefore, the height of the cone is 7.5 meters.
Learn more about volume at https://brainly.com/question/463363
#SPJ1
For f(x)=1/x^2 show there is no c such that f(1)-f(-1)=f'(c)(2).
Explain why the mean value theorem doesnt apply over the interval
[-1,1]"
Prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
Let's first understand the Mean Value Theorem (MVT). The MVT states that if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
Now, consider the function f(x) = 1/x^2. This function is continuous and differentiable for all x ≠ 0. However, in the interval [-1, 1], the function is not continuous nor differentiable at x = 0. Therefore, the Mean Value Theorem does not apply to this interval.
Since the MVT does not apply, we cannot say there exists a c in the interval (-1, 1) such that f'(c) = (f(1) - f(-1)) / (1 - (-1)). This is because the prerequisites for the MVT are not met due to the discontinuity and non-differentiability of f(x) at x = 0 within the interval [-1, 1].
To learn more about mean value theorem, refer below:
https://brainly.com/question/30403137
#SPJ11
Lizzie came up with a divisibility test for a certain number m ≠ 1 : Break a positive integer n into two-digit chunks, starting from the ones place. (For example, the number 354764 would break into the two-digit chunks 35, 47, and 64 ) Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be 35-47+64 = 52 ) Find m and show that this is indeed a divisibility test for n (by showing that n is divisible by m if and only if the result of this process is divisible by m)
If and only if the alternating sum of the two-digit chunks of a number n is divisible by m, then n is divisible by m.
What value of m makes the alternating sum of two-digit chunks of a positive integer n divisible by m?Let's denote the two-digit chunks of n as a₁a₂, a₃a₄, ..., where a₁, a₂, a₃, a₄, ... are the digits from the ones place onward.
The alternating sum of these two-digit numbers is given by a₁a₂ - a₃a₄ + a₅a₆ - a₇a₈ + ...
We can rewrite n as (a₁a₂ × 100) + (a₃a₄ × 10) + (a₅a₆ × 1) + ...
The alternating sum expression can be written as (a₁a₂ × 100) - (a₃a₄ × 10) + (a₅a₆ × 1) - ...
If n is divisible by m, we have n ≡ 0 (mod m).
Rewriting n in terms of the alternating sum, we get (a₁a₂ × 100) - (a₃a₄ × 10) + (a₅a₆ × 1) - ... ≡ 0 (mod m).
Factoring out each two-digit chunk, we have (a₁a₂ - a₃a₄ + a₅a₆ - ...) ≡ 0 (mod m).
This implies that n is divisible by m if and only if the result of the alternating sum process is divisible by m.
m is the value that makes the alternating sum of the two-digit chunks of n a divisibility test for n.
Learn more about divisibility
brainly.com/question/21416852
#SPJ11
A farmer of a large apple orchard would like to estimate the true mean number of suitable apples produced per tree. He selects a random sample of 40 trees from his large orchard and determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520. Which of these statements is a correct interpretation of the confidence level?
The confidence level represents the degree of certainty that the interval contains the true population parameter.
The statement "determines with 95% confidence that the true mean number of suitable apples produced per tree is between 375 and 520" means that if the farmer were to repeat the sampling process many times and calculate the confidence interval each time, 95% of those intervals would contain the true mean number of suitable apples per tree.
Therefore, we can be 95% confident that the true mean number of suitable apples produced per tree is within the interval of 375 to 520 for this particular sample of 40 trees.
The confidence level represents the degree of certainty that the interval contains the true population parameter.
To know more about population parameter refer here
https://brainly.com/question/31907196#
#SPJ11
Solve 2x(x 0.5) = −(x+2.5)² + 5.5 by graphing. Round to the nearest thousandth.
x≈
and x
we find that the solutions to the equation are:x ≈ -1.283, x ≈ 4.283.
How to solve the equation ?To solve the equation 2x(x+0.5) = -(x+2.5)² + 5.5 by graphing, we can first rearrange it to the standard form:
x² - 3x - 2 = 0.5(x+2.5)²
Then we can plot the two functions y = x² - 3x - 2 and y = 0.5(x+2.5)² - 5.5 on the same graph and find their intersection points, which represent the solutions to the equation.
Enter the two functions in separate equations:
[tex]y_1 = x^2 - 3x - 2[/tex]
[tex]y_2 = 0.5(x+2.5)^2 - 5.5[/tex]
Adjust the zoom level and position of the graph to see the intersection points.
Click on the intersection points to see their coordinates.
Round the coordinates to the nearest thousandth.
After following these steps, we find that the solutions to the equation are:
x ≈ -1.283
x ≈ 4.283
To know more about Equation visit:
brainly.com/question/28243079
#SPJ1
Use Newton's method to obtain the third approximation, X2, of the positive fourth root of 3 by calculating the third approximation of the right 0 of f(x)=x*- 3. Start with Xo = 1. The third approximation of the fourth root of 3 determined by calculating the third approximation of the right 0 of f(x) = x4 - 3, starting with Xo = 1, is (Round to four decimal places.) -
To use Newton's method to find the third approximation, X2, of the positive fourth root of 3, we follow these steps:
1. Define the function f(x) and its derivative, f'(x): f(x) = x^4 - 3 f'(x) = 4x^3
2. Start with an initial guess, X0 = 1.
3. Apply Newton's method formula to find the next approximations:
Xn+1 = Xn - f(Xn) / f'(Xn)
4. Calculate the first approximation, X1: X1 = X0 - f(X0) / f'(X0) X1 = 1 - (1^4 - 3) / (4 * 1^3) X1 = 1 - (-2) / 4 X1 = 1 + 0.5 X1 = 1.5
5. Calculate the second approximation, X2: X2 = X1 - f(X1) / f'(X1) X2 = 1.5 - (1.5^4 - 3) / (4 * 1.5^3) X2 = 1.5 - (5.0625 - 3) / 13.5 X2 = 1.5 - 2.0625 / 13.5 X2 = 1.5 - 0.15296 X2 ≈ 1.3470
So, the third approximation of the positive fourth root of 3, determined by calculating the third approximation of the right 0 of f(x) = x^4 - 3, starting with X0 = 1, is approximately 1.3470 (rounded to four decimal places).
Learn more about Newton's method,
https://brainly.com/question/30763640
#SPJ11
The ratio of Adults to Girls in a tennis club is 5:1
The ratio of Girls to Boys in the same club is 3:4
What is the ratio of adults to boys?
The ratio of adult to boys is 35:24
What is ratio?A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. For example, if the ratio of boys to girls in a class is 4:1. This means that the for every 4 boys therefore is a girl.
Represent the total number of adult, boys and girls in the club by x
This means number of boys = 4/7× x
number of adult = 5/6 × x
Therefore the ratio of adults to boys will be
5x/6 : 4x/7
= 5/6 : 4/7
multiply through by 42
= 35 : 24
therefore the ratio of adult to boys is 35: 24
learn more about ratio from
https://brainly.com/question/12024093
#SPJ1
Find an exponential function that passes through (2,8) and (4,128)
The final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To find an exponential function that passes through the points (2,8) and (4,128), follow these steps:
Step 1: Recall the general form of an exponential function: y = ab^x
Here, 'a' and 'b' are constants that need to be determined using the given points.
Step 2: Substitute the first point (2,8) into the equation:
8 = ab^2
Step 3: Substitute the second point (4,128) into the equation:
128 = ab^4
Step 4: Divide the second equation by the first equation to eliminate 'a':
(128 = ab^4) / (8 = ab^2)
16 = b^2
Step 5: Solve for 'b':
b = √16
b = 4
Step 6: Substitute the value of 'b' back into the first equation:
8 = a(4^2)
Step 7: Solve for 'a':
8 = 16a
a = 8/16
a = 1/2
Step 8: Write the final exponential function using the values of 'a' and 'b':
y = (1/2)(4^x)
To learn more about Exponential function
https://brainly.com/question/30127596
#SPJ11
Andre owns a condominium with a value of $155,000. He has a stock portfolio worth $8,100. He owes $3,300 on his car, which is valued at $9,100. He has $7,600 in student loans to repay. He has a credit card balance of $4,327. He also has $2,600 in a bank account. Construct a net worth statement to find Andre's net worth.
Using net worth statement, Andre's net worth is $159,573.
How to Construct a net worth statement to find Andre's net worth.Andre's net worth can be calculated by subtracting his total liabilities from his total assets.
Total assets = $155,000 (condominium) + $8,100 (stock portfolio) + $9,100 (car value) + $2,600 (bank account) = $174,800
Total liabilities = $3,300 (car loan) + $7,600 (student loans) + $4,327 (credit card balance) = $15,227
Net worth = Total assets - Total liabilities = $174,800 - $15,227 = $159,573
Therefore, Andre's net worth is $159,573.
Learn more about net worth statement at https://brainly.com/question/29565790
#SPJ1
What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation? x^2= -16x-37
The intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
To complete the square for the given equation, we need to add a constant value to both sides of the equation such that we can factor the left-hand side as a perfect square.
x^2 + 16x = -37
To determine the constant value we need to add to both sides, we take half the coefficient of x (which is 16/2 = 8) and square it to get 64. Then we add 64 to both sides of the equation:
x^2 + 16x + 64 = 27
Now we can factor the left-hand side as a perfect square:
(x + 8)^2 = 27
So the intermediate step in completing the square for x^2= -16x-37 is (x+8)^2=27.
To learn more about square: https://brainly.com/question/27307830
#SPJ11
Alguien q pueda explicar esto
To add fractions with unlike denominators, we need to find the least common multiple of the denominators. In this case, the least common multiple of 3 and 4 is 12. So, we must find equivalents of each fraction with a denominator of 12.
How to add the fractions?To add fractions with unlike denominators, we need to find the least common multiple of the denominators. In this case, the least common multiple of 3 and 4 is 12. So, we must find equivalents of each fraction with a denominator of 12.
Multiplying the numerator and denominator of 2/3 by 4, we get 8/12. On the other hand, multiplying the numerator and denominator of 1/4 by 3, we get 3/12.
Therefore, we can rewrite the sum as:
8/12 + 3/12
And adding the numerators, we get:
11/12
So, 2/3 + 1/4 = 11/12.
The final answer is a proper fraction, which means that the numerator is less than the denominator, and can be further simplified if necessary.
Learn more about fractions at: https://brainly.com/question/10354322
#SPJ1
A rectangular prism has a square
base with edge length (x + 1). Its
volume is (x + 1)2(x – 3). What
does the expression (x + 1)(x – 3)
represent?
area of the base
area of one side
height of the prism
surface area of the prism
The expression (x + 1)(x - 3) represents the Area of base of the prism.
What is Prism?a crystal is a polyhedron containing a n-sided polygon base, a respectable halfway point which is a deciphered duplicate of the first, and n different countenances, fundamentally all parallelograms, joining relating sides of the two bases. Translations of the bases exist in every cross-section that runs parallel to the bases.
According to question:The volume of a rectangular prism is given by the formula V = Bh, where B is the area of the base and h is the height of the prism. In this case, the base is a square with edge length (x + 1), so its area is (x + 1)^2. The volume of the prism is given as (x + 1)^2(x - 3).
We can find the height of the prism by dividing the volume by the area of the base:
B = V/h = (x + 1)^2(x - 3)/(x + 1) = (x + 1)(x - 3)
Therefore, the expression (x + 1)(x - 3) represents the Area of base of the prism.
To know more about Area visit:
brainly.com/question/13194650
#SPJ1
Kathleen has a fair die with 6 different-colored sides:red,yellow,blue,green,orange, and purple. She rolls the die 120 times. The die lands on the color green 18 times. Based on Kathleen's results, The experimental probability of rolling the color green is?
The Experimental probability of rolling the color green is 0.15
How to calculate the experimental probability of rolling the color green isThe experimental probability of rolling the color green can be calculated by dividing the number of times the die lands on green by the total number of rolls:
Experimental probability of green = Number of green rolls / Total number of rolls
Experimental probability of green = 18 / 120
Experimental probability of green = 0.15 or 15%
learn more about probability at https://brainly.com/question/25870256
#SPJ1
Find the volume of the solid generated when the rectangle below is rotated about side
LO. Round your answer to the nearest tenth if necessary.
The volume of the obtained solid is 36 units³.
Given that a rectangle of dimension 9 units x 2 units, has been rotated to form a solid we need to find its volume,
So we know that a rectangle rotated to form a rectangular prism.
Volume of a rectangular prism = product of the dimensions.
The dimensions of the obtained solid will be 9 units x 2 units x 2 units,
So the volume = 9 x 2 x 2 = 36 units³
Hence the volume of the obtained solid is 36 units³.
Learn more about volumes click;
https://brainly.com/question/1578538
#SPJ1
The money in Maya's college savings account earns 2 1/5% interest. Which value is less than 2 1/5%?
A. 0. 0215
B. 11/5
C. 0. 022
D. 11/500
A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.
= 2 1/5% / 100
= (2 + (1/5)) / 100
= 0.022
A value that is less than 0.022 from the given data is 0. 0215.
Therefore, a value less than 2 1/5% is 0. 0215.
To learn more about decimal numbers:
https://brainly.com/question/28393353
#SPJ4
The cafeteria staff made sandwiches. Each sandwich had either rye or white bread, either ham or turkey, and either cheese or no cheese. The staff made an equal number of each type of sandwich. The sandwiches were placed on a tray. Without looking, Mary will choose a sandwich. What are the chances that Mary will get a sandwich with cheese?
Responses
one eighth
one sixth
one third
one half
Answer:
Step-by-step explanation:
There are 8 equally likely sandwich options: rye and ham, rye and turkey, white and ham, white and turkey, rye and ham with cheese, rye and turkey with cheese, white and ham with cheese, white and turkey with cheese.
Since each type of sandwich was made in equal number, there are 4 sandwiches with cheese.
Therefore, the chances that Mary will get a sandwich with cheese is 4/8 or 1/2.
Answer: one half
Todd had a piggy bank holding $384. He began taking out money each month. The table shows the amount remaining, in dollars, after each of the first four months
A piggy bank is a small container typically used by children to save money. In this scenario, Todd had a piggy bank holding $384 and began taking out money each month. The table provided shows the amount remaining in the piggy bank, in dollars, after each of the first four months. This information can be used to track Todd's spending and savings habits.
In the first month, Todd took out $60, leaving him with $324 in his piggy bank. In the second month, he took out an additional $48, leaving him with $276. By the third month, Todd had taken out a total of $105, leaving him with $279 in his piggy bank. Finally, in the fourth month, he took out $62, leaving him with $217.
By tracking his spending and savings over the course of these four months, Todd can assess his financial habits and make any necessary adjustments. It is important for individuals to develop good financial habits early on in life, and using a piggy bank can be a fun and effective way to do so.
To know more about piggy bank refer here
https://brainly.com/question/25869418#
#SPJ11
