Answer:
Step-by-step explanation:
Since the two cylinders are similar, their corresponding dimensions (radius and height) are proportional. Let the radius of the smaller cylinder be r.
Then, we can write:
r / 6 = R / 30
where R is the radius of the larger cylinder.
Simplifying this equation, we get:
R = 5r
Now, we can use the formula for the volume of a cylinder to find the volume of the larger cylinder:
Volume of smaller cylinder = πr^2h = 90 cm^3
Volume of larger cylinder = πR^2H = π(5r)^2(30) = 750πr^2 cm^3
Substituting R = 5r, we get:
Volume of larger cylinder = 750πr^2 cm^3
Therefore, the volume of the larger cylinder is 750π times the volume of the smaller cylinder:
Volume of larger cylinder = 750π(90 cm^3) = 67,500π/ cm^3 (approx. 211,239.74 cm^3 rounded to five decimal places).
Find all the points that are described by the following statement.
the first number of my ordered pair is 50. fo 20 points hurry!!!!!
The statement "the first number of my ordered pair is 50" implies that all the points are of the form (50, y), where y can be any real number.
Therefore, the set of points that satisfy this statement is infinite, and it is not possible to list all of them.
However, if you need 20 specific points, you can choose any 20 values for y and pair them with 50 to obtain 20 points that satisfy the given condition.
For example, some of the points that satisfy this statement are (50, 0), (50, 1), (50, -2), (50, π), and (50, 10^6).
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Lulu has 10 feet of ribbon she uses 1 1/3 feet ribbon for a project she uses the rest of the ribbon to make bows she uses 8 inches of ribbon for each bowl how many does lulu make?
The number of bows Lulu can make from the remaining ribbon is 13 bows.
To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.
10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.
She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:
(26/3) * 12 = 104 inches of ribbon remaining.
Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:
104 / 8 = 13 bows.
Lulu can make 13 bows with the remaining ribbon.
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How do I do number 3?
Answer:
V = 1,728 mi³
SA = 864 mi²
Step-by-step explanation:
We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.
First, we can solve for the area of one of the triangle sides:
A(triangle) = (1/2) · b · h
A(triangle) = (1/2) · 24 · 18
A(triangle) = 12 · 18
A(triangle) = 216 mi²
Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.
V = A(triangle) · depth
V = 216 · 8
V = 1,728 mi³
__
We can find the surface area by finding the area of each side, then adding all of those areas together.
We already know that the area of each of the triangle sides is 216 mi².
Now, we can solve for the area of the base.
A(base) = length · width
A(base) = 24 · 8
A(base) = 192 cm²
Then, we can find the area of the top side.
A(top) = length · width
A(top) = 30 · 8
A(top) = 240 mi²
Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.
SA = (2 · A(triangle)) + A(base) + A(top)
SA = 2(216) + 192 + 240
SA = 432 + 192 + 240
SA = 624 + 240
SA = 864 mi²
Here is a sequence of numbers 64,49,36,25,16 find the next number in the sequence
The next number in the sequence is 9.
The given sequence of numbers are perfect squares of decreasing numbers in descending order. Specifically, the given sequence consists of the squares of the first five counting numbers in descending order, starting from 8², then 7², 6², 5², and 4².
Therefore, the next number in the sequence should be the square of the next counting number in descending order, which is 3. Thus, the next number in the sequence should be 3², which is equal to 9.
To further explain, the sequence can be written as follows:
64 = 8²
49 = 7²
36 = 6²
25 = 5²
16 = 4²
The next number in the sequence is the square of the next counting number in descending order, which is 3. Therefore, the next number in the sequence should be 3², which is equal to 9. Thus, the next number in the sequence is 9.
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Find all solutions of the equation algebraically.
|x2 + 9x| = 6x + 54
The solutions to the equation are x= -9 and x = 6
How to determine the valueFrom the information given, we have that;
|x2 + 9x| = 6x + 54
To solve the quadratic equation, collect the like terms, we have;
x² + 9x - 6x = 54
subtract the terms
x² + 3x = 54
Put in standard form
x² + 3x - 54 = 0
Find the pair factors of -54 that add up to give 3 and substitute the values
x² + 9x - 6x - 54 = 0
group in pairs
(x² + 9x) - (6x - 54) = 0
factorize the expressions
x(x + 9) - 6(x + 9) = 0
Then, we have;
x- 6 = 0
x = 6
x + 9 = 0
x = -9
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What’s the answer? I need help
The two types of transformations that are produced by the matrix include:
a 90° counter clockwise rotation followed by a reflection in the vertical axis.a 90° clockwise rotation followed by a a reflection in the vertical axis.How to explain the transformationWe can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.
On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.
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Here is the question...."The magnitude and direction of two forces acting on an object are 80 pound, S58 degree E, and 50 pounds, N76 degree E, repectively. Find the magnitude, to the nearest hundredth of a pound, and the direction angle, to the nearest tenth of a degree, of the resultant force.".....And it has 2 part
The magnitude of the resultant force is approximately 119.89 pounds, and the direction angle is approximately S12.2°W.
To solve the problem, we can use vector addition.
Let F1 be the vector representing the first force, and F2 be the vector representing the second force. Then, we can find the resultant force R by adding the two vectors:
R = F1 + F2
To add two vectors, we need to resolve them into their x and y components. Let's do that first.
For F1:
Magnitude = 80 pounds
Direction = S58°E
To resolve F1 into its x and y components, we can use trigonometry:
Fx1 = 80 cos 58° = 42.57 pounds (east)
Fy1 = 80 sin 58° = 68.13 pounds (south)
For F2:
Magnitude = 50 pounds
Direction = N76°E
To resolve F2 into its x and y components, we can again use trigonometry:
Fx2 = 50 cos (180° - 76°) = -16.92 pounds (east)
Fy2 = 50 sin (180° - 76°) = 48.76 pounds (north)
Note that we used (180° - 76°) for the angle because the direction is N76°E, which means it is 76° east of due north.
Now we can add the x and y components separately:
Rx = Fx1 + Fx2 = 42.57 - 16.92 = 25.65 pounds (east)
Ry = Fy1 + Fy2 = 68.13 + 48.76 = 116.89 pounds (south)
To find the magnitude and direction of the resultant force, we can use trigonometry again:
Magnitude = sqrt(Rx^2 + Ry^2) = sqrt(25.65^2 + 116.89^2) = 119.89 pounds (rounded to the nearest hundredth)
Direction angle = atan(Rx/Ry) = atan(25.65/116.89) = 12.2° (rounded to the nearest tenth)
The direction angle is approximately S12.2°W, and the resultant force has a magnitude of about 119.89 pounds.
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Isabel invests 2000 euros in a bank that offers 4. 3% interests pa compounded biannually. Calculate the value of her investments after 5 years
The value of Isabel's investment after 5 years is 2512.08 euros.
How much will Isabel's investment be worth after 5 years?To calculate the value,
The formula for calculating compound interest is:
A = P (1 + r/n)^(nt)
where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the time (in years)
In this case, we have
P = 2000 euros
r = 0.043 (4.3% as a decimal)
n = 2 (compounded biannually)
t = 5 years
So, the formula becomes:
A = 2000 (1 + 0.043/2)^(2*5) = 2512.08 euros
Therefore, after 5 years, Isabel's investment will be worth 2512.08 euros.
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PLS HELP!
Joanna went school supply shopping. She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each. She bought a total of 15 notebooks and pencils. How many of each did she buy?
Answer: 10 pencils and 5 notebooks.
Step-by-step explanation:
We will create a system of equations using the information given. Let n be equal to the number of notebooks and p be equal to the number of pencils.
She spent $23.25 on notebooks and pencils. Notebooks cost $2.49 each and pencils cost $1.08 each.
$2.49n + $1.08p = $23.25
She bought a total of 15 notebooks and pencils.
n + p = 15
Next, we will solve for p by substituting.
n + p = 15 ➜ n = 15 - p
$2.49n + $1.08p = $23.25
$2.49(15 - p) + $1.08p = $23.25
$37.35 - $2.49p + $1.08p = $23.25
$37.35 - $1.41p = $23.25
-$1.41p = -$14.10
p = 10 pencils
Lastly, we will solve for n by substituting:
n = 15 - p
n = 15 - 10
n = 5
HELP - A strip of uniform width is plowed along all four sides of a 12-km by 9-km rectangular cornfield. How wide is the plowed strip of the cornfield is half plowed?
Answer:
Let's start by drawing a diagram of the cornfield with the plowed strip around it:
markdown
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_____________________________
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|_______|_______________________|
The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.
The total area of the cornfield is:
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12 km x 9 km = 108 km^2
If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:
scss
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(12 + 2w) km x (9 + 2w) km
The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:
scss
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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2
We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:
scss
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108 + 42w + 4w^2 = (1/2)(108)
Simplifying, we get:
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4w^2 + 42w - 54 = 0
We can solve this quadratic equation using the quadratic formula:
css
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w = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 4, b = 42, and c = -54. Substituting these values, we get:
scss
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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8
arduino
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w = (-42 ± sqrt(1936)) / 8
makefile
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w = (-42 ± 44) / 8
So we have two possible solutions:
makefile
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w = 1/2 km (discarded since it does not satisfy the given condition)
or
makefile
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w = 11/2 km
Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.
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Solve for q q : 30 + q = 43 30+q=43
The solution to the equation 30 + q = 43 is q = 13.
What is the value of q?Given the equation in the question:
30 + q = 43
To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.
30 + q = 43
q + 30 = 43
Next, we can isolate q by subtracting 30 from both sides of the equation:
q + 30 - 30 = 43 - 30
q = 43 - 30
Subtract 30 from 43
q = 13
Therefore, the value of q is 13.
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Harper uploaded a funny video of her dog onto a website.
The relationship between the elapsed time, ddd, in days, since the video was first uploaded, and the total number of views, V(d)V(d)V, left parenthesis, d, right parenthesis, that the video received is modeled by the following function.
V(d)=4^{{1.25d}}V(d)=4
1.25d
V, left parenthesis, d, right parenthesis, equals, 4, start superscript, 1, point, 25, d, end superscript
How many views will the video receive after 666 days?
After 666 days, the video will receive approximately 33,621,452 views.
We are given the function V(d) = 4^(1.25d), where d represents the number of days since the video was uploaded and V(d) represents the number of views the video has received at that time. To find the number of views the video will receive after 666 days, we need to evaluate V(666).
Plugging in d = 666 into the function, we get V(666) = 4^(1.25*666). Using a calculator, we can simplify this to V(666) ≈ 33,621,452. Therefore, after 666 days, the video will receive approximately 33,621,452 views.
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Amy graphed a function that gives the height of a car on a roller coaster as a function of time. She said her graph is the graph of a step function. Is this possible? Explain your reasoning
It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.
A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.
On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.
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A pyramid 5 meters high has congruent triangular sides and a square base that is 5 meters on each side. Each cross section of the pyramid parallel to the base is a square. What is the volume of the solid in cubic meters?
The volume of the pyramid is approximately 41.67 cubic meters.
How to find the volume?To find the volume of the pyramid, we can use the formula:
V = (1/3) x base area x height
Since the base of the pyramid is a square with side length 5 meters, its area is:
base area = side² = 5² = 25 square meters
The height of the pyramid is also given as 5 meters.
Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.
Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:
5 / 5 = x / 5
where x is the side length of the square cross-section.
Solving for x, we get:
x = 5
Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.
Now, we can substitute the values we have found into the formula for the volume:
V = (1/3) x base area x height
= (1/3) x 25 x 5
= 41.67 cubic meters
Therefore, the volume of the pyramid is approximately 41.67 cubic meters.
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Today, everything at the store is on sale. the store offers a 20% discount.
a.what percentage will you pay when a store offers a 20% discount?
b.if the regular price of a t-shirt is $18. what is the discount price?
c.if the regular price of a gaming system is $360. what is the sale price?
show what you typed into the calculator:
d.the discount price of a hat is $18. what’s the regular price (price before the coupon)?
a. You will pay 80% of the original price.
b. $14.40 is the discount price of the t-shirt.
c. The sale price of the gaming system is $288.
d. $22.50 is the regular price of the hat.
a. When a store offers a 20% discount, you will pay 80% of the original price. This is because the discount is taken off the original price, leaving you to pay the remaining percentage.
b. If the regular price of a t-shirt is $18, the discount price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.
Discount price = Regular price x (1 - Discount percentage)
Discount price = $18 x (1 - 0.20)
Discount price = $18 x 0.80
Discount price = $14.40
Therefore, $14.40 is the discount price of the t-shirt.
c. If the regular price of a gaming system is $360, the sale price can be found by multiplying the regular price by the percentage you will pay after the discount, which is 80%.
Sale price = Regular price x (1 - Discount percentage)
Sale price = $360 x (1 - 0.20)
Sale price = $360 x 0.80
Sale price = $288
Therefore, the sale price of the gaming system is $288.
d. If the discount price of a hat is $18 and the discount percentage is 20%, we can find the regular price by dividing the discount price by the percentage you will pay after the discount, which is 80%.
Regular price = Discount price / (1 - Discount percentage)
Regular price = $18 / (1 - 0.20)
Regular price = $18 / 0.80
Regular price = $22.50
Therefore, the regular price of the hat is $22.50.
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Gabriella decides to estimate the volume of an orange by modeling it as a sphere. She measures its circumference as 50.2 cm. Find the orange's volume in cubic centimeters. Round your answer to the nearest tenth if necessary.
The answer is 2143.6.
Which type of sentence error occurs when a sentence is missing a subject or predicate? No error Fragment Subject -verb agreement Run-on
When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.
What is a sentence error?Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.
An example of a sentence error will be "The children re us"
The phrase "re" is the error word in this sentence.
The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.
In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment
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Al has a cylindrical storage container 30 centimeters tall with a diameter of 22 centimeters. How much bird food in cubic centimeters will fit in the container? Use the formula V = Bh and approximate π using 3.14. Round your answer to the nearest tenth.
The amount of bird food in cubic centimeters will fit in the container is
11, 398. 2 cubic centimeters
How to determine the volumeThe formula that is used for calculating the volume of a cylinder is expressed with the equation;
V = π(d/2)²h
Such that the parameters of the given equation are;
V is the volume of the cylinder.d is the diameter of the cylinderh is the height of the cylinderNow, substitute the values into the formula, we have;
Volume = 3.14 (22/2)² 30
divide the values
Volume = 3.14(121)30
Now, multiply the values and expand the bracket
Volume = 11, 398. 2 cubic centimeters
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If a cup of coffee has temperature 95 C in a room where theremperature is 20 C, then, according to Newon's Law of Cooling, thetemperature of the coffee after t minutes is T(t) = 20+ 75e-t/50. What is the average temperature of thecoffee during the first half hour?
To find the average temperature of the coffee during the first half hour, we need to find the temperature of the coffee at t = 0 (when the coffee is just brewed) and at t = 30 (after half an hour has passed).
At t = 0, T(0) = 20 + 75e^0/50 = 20 + 75 = 95 C. At t = 30, T(30) = 20 + 75e^-30/50 ≈ 42.5 C.
So, the temperature of the coffee decreases from 95 C to 42.5 C during the first half hour.
The average temperature during this time period can be found by taking the average of the initial and final temperatures:
Average temperature = (95 C + 42.5 C) / 2 = 68.75 C.
Therefore, the average temperature of the coffee during the first half hour is 68.75 C.
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What is the equation of a circle with center (2,3) that passes through the point (5, 3)?
The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.
The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.
Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]
Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]
Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]
So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]
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A cube has a volume of 200cm3. What is the length of one edge?
Give your answer in cm correct to one decimal place
Answer:
The answer is 5.8cm to 1 d.p
Step-by-step explanation:
volume of cube=L³
200=L³
cube root both sides
³√200=³√L³
L=5.8cm to 1 d.p
I NEED HELP WITH THIS ONE AND ANOTHER PLEASE
The missing lengths of BE and IJ using the concept of similar quadrilaterals are:
BE = 32
IJ = 18
How to find the lengths of similar quadrilaterals?Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.
Thus:
GJ/BE = IJ/DE = HI/CD
Thus:
12/BE = 6/16
BE = (16 * 12)/6
BE = 32
Similarly:
IJ/48 = 6/16
IJ = (48 * 6)/16
IJ = 18
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the kendall correlation uses rank values to determine the correlation between two variables. the equation for kendall rank shows that if there are more concordant pairs, then the correlation will be positive. using the definition of concordant and disconcordant pairs, explain why this makes sense.
Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.
In Kendall correlation,
Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.
A concordant pair is when the rank order of the two variables is the same both increase or decrease together.
A discordant pair is when the rank order is different one variable increases while the other decreases.
If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.
Which suggests a positive correlation relationship between them.
Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.
Which suggests a negative relationship between them.
Example ,
two variables, X and Y, that are positively correlated.
If we plot the observations of X and Y on a scatter plot.
Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.
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a manufacturing machine has a 80% defect rate. if 109 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).
Percent of defective rate in manufacturing machine = 80%
Random number of items chosen = 109
The correct wording for the random variable in this situation is,
The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.
Number of defective items is successes.
A common symbol for the number of successes in a binomial distribution is X.
Use X to represent the random variable in this situation.
The notation for the binomial distribution is usually written as,
X ~ B(n, p)
where X is the random variable,
n is the sample size,
and p is the probability of success on each trial.
X ~ B(109, 0.8).
Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to X ~ B(109, 0.8).
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Michae
all your steps.
2x 3x
problem a 60 x
miss chang ordered a pizza to share with some grade 8 students. miss chang
gave michael some slices of pizza. miss chang gave amy twice as many slices of
pizza as michael. miss chang gave mr. au three times the sum of what she gave
to michael and amy. miss chang gave 60 slices of pizza to michael, amy and mr.
au in total. how many slices of pizza miss chang give to each person?
Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.
Let's start by using variables to represent the unknown quantities in the problem. Let m be the number of slices of pizza Michael received, a be the number of slices Amy received, and au be the number of slices Mr. Au received.
We know that Miss Chang gave Michael 60 slices of pizza in total, so we can write:
m = 60
We also know that Amy received twice as many slices of pizza as Michael, so we can write:
a = 2m
Finally, we know that Mr. Au received three times the sum of what Miss Chang gave to Michael and Amy, so we can write:
au = 3(m + a)
We also know that Miss Chang gave 60 slices of pizza in total, so we can write:
m + a + au = 60
Now we can substitute the expressions we found for a and au into the last equation to get:
m + 2m + 3(m + 2m) = 60
Simplifying this equation, we get:
m + 2m + 3m + 6m = 60
12m = 60
m = 5
So Michael received 5 slices of pizza, and we can use the equations we found for a and au to determine how many slices Amy and Mr. Au received:
a = 2m = 2(5) = 10
au = 3(m + a) = 3(5 + 10) = 45
Therefore, Amy received 10 slices of pizza and Mr. Au received 45 slices of pizza.
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The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters, how long is the gauge needle? Round to the nearest centimeter.
a.) 2cm
b.) 3cm
c.) 4cm
d.) 5cm
The value of the gauge needle is, 9.01 cm
Given that;
The fuel gauge of a car represents how much gasoline is left in the tank. If the area of the sector represented by the fuel gauge is 10.6 square centimeters.
Now, We can formulate;
A = θ/360 πr
10.6 = (135/360) 3.14 x r
3816 = 423.5r
r = 9.01
Thus, The value of the gauge needle is, 9.01 cm
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What percent of the customers at the book sale spent less than 20 dollars? Show or explain how you got your answer
Prove that U(1, 1), Q(4,4), and A(6, 2) are the vertices of a right triangle. Â Use the following as a guide. Find the slopes of sides UQ, QA, and UA. Which segments are perpendicular? How do you know the segments are perpendicular? What are the lengths of each side? Use the Pythagorean Theorem to show that it is a right triangle. â
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
How do we know that UQ and QA are perpendicular?To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:
Find the slopes of sides UQ, QA, and UA:
Slope of UQ: (4-1)/(4-1) = 1Slope of QA: (2-4)/(6-4) = -1Slope of UA: (2-1)/(6-1) = 1/5Determine which segments are perpendicular and how we know they are perpendicular:
To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.
UQ and QA: Since the slope of UQ is 1 and the slope of QA is -1, we know that UQ and QA are perpendicular.UQ and UA: The slopes of UQ and UA are both positive, so they cannot be perpendicular.QA and UA: The slope of QA is -1, and the slope of UA is 1/5. Their product is -1/5, which is not -1, so QA and UA are not perpendicular.Find the lengths of each side:
Length of UQ: √[(4-1)² + (4-1)²] = √27Length of QA: √[(6-4)² + (2-4)²] = √8Length of UA: √[(6-1)² + (2-1)²] = √26Use the Pythagorean Theorem to show that it is a right triangle:
Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.
(Length of UQ)² + (Length of QA)² = (√27)² + (√8)² = 27 + 8 = 35(Length of UA)² = (√26)² = 26Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.
U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.
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Boris's backyard has cement and grass. Find the area of the part with cement.
(Sides meet at right angles. )
4 m
1 m
2 m
grass
5 m
3 m
cement
5 m
The constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.
To find the area of the part with cement, we need to find the area of the entire rectangle and then subtract the area of the part with grass.
The area of the rectangle is: length x width = 5 m x 4 m = 20 m²
The area of the part with grass is: length x width = 3 m x 2 m = 6 m²
So the area of the part with cement is:
20 m² - 6 m² = 14 m²
Therefore, the area of the part with cement is 14 square meters.
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the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?
The numbers chocolate chip cookie would be assigned to the group is equals to the 40 belongs to 60-100. So, right choice is option(a).
We have a data values for a random number ranges within 1 to 100 need to be assigned for each event.
Probability for the chocolate cookies purchased for a fundraiser = 0.40
Probability for the butter cookies purchased for a fundraiser = 0.15
Probability for the peanuts butter cookies purchased for a fundraiser = 0.15
Probability for the lemon cookies purchased for a fundraiser = 0.30
The number would be assigned to the chocolate chip cookie group = 0.40× 100
= 40%
The difference between 60-100 is 40.
Hence, required number is 60-100.
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Complete question:
The above figure complete the question.
the probability distribution table shows the probability for the type of cookies purchased for a fundraiser. to conduct a simulation to determine the type of cookies purchases, random number ranges within 1 to 100 need to be assigned for each event. what numbers would be assigned to the chocolate chip cookie group?
a) 60-100
b) 71-100
c) 20-100
