20% of all college students volunteer their time. is the percentage of college students who are volunteers different for students receiving financial aid? of the 381 randomly selected students who receive financial aid, 57 of them volunteered their time. what can be concluded at the

Answers

Answer 1

The p-value is less than the significance level so reject the null hypothesis and concluded percentage of the students volunteer their time is different from receiving financial aid students.

Percentage of college students who volunteer their time = 20%

Perform a hypothesis test.

Null hypothesis H₀: p = 0.20,

where p is the proportion of college students who volunteer their time.

The alternative hypothesis is Hₐ: p ≠ 0.20.

Indicating that the proportion of college students who volunteer their time is different for students receiving financial aid.

57 out of 381 randomly selected students who receive financial aid volunteered their time.

Test the hypothesis,

Calculate the sample proportion of volunteers among the students receiving financial aid,

p₁ = 57 / 381

    = 0.149

Using Test statistic,

which follows a normal distribution under the null hypothesis .

Mean = 0  

Standard deviation σ = √(p(1-p)/n),

where p = 0.20 is the proportion under the null hypothesis

n = 381 is the sample size.

z

= (p₁ - p) /√(p×(1-p)/n)

= (0.149 - 0.20) / √(0.20(1-0.20)/381)

= -2.55

Using attached table of p-value from z-score.

Calculated test statistic of -2.55 corresponds to a p-value of 0.0054,

which is less than the significance level α = 0.01.

Reject the null hypothesis .

Therefore, we conclude that there is evidence to suggest that the percentage of college students who volunteer their time is different for students receiving financial aid.

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The above question is incomplete, the complete question is:

20% of all college students volunteer their time. is the percentage of college students who are volunteers different for students receiving financial aid? of the 381 randomly selected students who receive financial aid, 57 of them volunteered their time. what can be concluded at the α = 0.01 level of significance?

20% Of All College Students Volunteer Their Time. Is The Percentage Of College Students Who Are Volunteers

Related Questions

An oil tank is the shape of a right rectangular prism. The inside of the tank is 36. 5 cm long, 52 cm wide, and 29 cm


high. If 45 liters of oil have been removed from the tank since it was full, what is the current depth of oil left in the


tank?

Answers

The current depth of oil left in the tank is approximately 4.64 cm.

The volume of the oil tank can be found by multiplying its length, width, and height:

Volume of the oil tank = length x width x height

= 36.5 cm x 52 cm x 29 cm

= 53,854 cubic cm

If 45 liters of oil have been removed from the tank, the current volume of oil in the tank is:

Current volume of oil = Total volume of tank - Volume of oil removed

= 53,854 cubic cm - 45,000 cubic cm (1 liter = 1000 cubic cm)

= 8,854 cubic cm

Let's assume that the depth of oil left in the tank is x cm. Then the volume of oil left in the tank can be found by multiplying the length, width, and depth of oil:

Volume of oil left in tank = length x width x depth of oil

= 36.5 cm x 52 cm x x cm

= 1906x cubic cm

Now we can set up an equation to find the value of x:

1906x = 8,854

Dividing both sides by 1906, we get:

x = 4.64 cm

Therefore, the current depth of oil left in the tank is approximately 4.64 cm.

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Carlos spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. the plane maintains a constant altitude of 7275 feet. carlos initially measures an angle of elevation of 20°

to the plane at point aa. at some later time, he measures an angle of elevation of 37°

to the plane at point bb. find the distance the plane traveled from point aa to point bb. round your answer to the nearest foot if necessary.

Answers

The distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

To find the distance the plane traveled from point A to point B, we can use trigonometry and the concept of similar triangles.

Let's denote the distance from point A to the plane as x, and the distance from point B to the plane as y. We are given the altitude of the plane (constant) as 7275 feet.

At point A, Carlos measures an angle of elevation of 20 degrees to the plane, and at point B, he measures an angle of elevation of 37 degrees to the plane.

Using trigonometry, we can set up the following equations:

tan(20 degrees) = 7275 / x,

tan(37 degrees) = 7275 / y.

We can rearrange these equations to solve for x and y:

x = 7275 / tan(20 degrees),

y = 7275 / tan(37 degrees).

Using a calculator, we can evaluate these expressions:

x ≈ 20246.71 feet,

y ≈ 14046.99 feet.

Therefore, the distance the plane traveled from point A to point B is approximately y - x:

Distance = y - x

≈ 14046.99 feet - 20246.71 feet

≈ -6200.72 feet.

Since the distance cannot be negative, we can round the absolute value of the result to the nearest foot:

Distance ≈ 6201 feet.

Therefore, the distance the plane traveled from point A to point B is approximately 6201 feet.

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Find the sum of the series. [infinity] 5(−1)nπ2n + 1 32n + 1(2n + 1)! n = 0

Answers

The sum of the series is 1/16. The given series is: ∑ [infinity] 5(−1)nπ2n + 1 / 32n + 1(2n + 1)!

To find the sum of the series, we can use the ratio test to check the convergence of the series. First, let's take the ratio of the (n+1)th term to the nth term: | a(n+1) / a(n) | = 5π2 / 32(2n + 3)(2n + 2)(2n + 1)

As n approaches infinity, the denominator of the ratio tends to infinity, making the ratio go to zero. Therefore, by the ratio test, the series converges.

Now, we need to find the sum of the series. To do this, we can use the formula for the sum of an infinite series: S = lim [n → ∞] Sn, where Sn is the nth partial sum of the series.

Using partial fractions, we can write the series as: 5π2 / 32n + 1 (2n + 1)! = 1 / 64 [ 1 / (n!) - 1 / (2n + 1)! ] - 5π2 / 32(2n + 3)(2n + 2)(2n + 1)

Substituting this expression into Sn and simplifying, we get: Sn = (1 - cos(π/4n+1)) / 32

Taking the limit as n approaches infinity, we get: S = lim [n → ∞] Sn = 1 / 16 Therefore, the sum of the series is 1/16.

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ratios of sin y and cos x share?

Answers

Answer:

sin (y) = oppoaite / hypotenus

sin (y) = oppoaite / hypotenus sin (y) = opp/hyp

And for geting cos

cos(x) = adjecent / hypotenus

cos(x) = adjecent / hypotenus cos(x) = adj/hyp

Determine Whether The Series Is Convergent Or Divergent. Σ ^n√14

Answers

Based on the Root Test, the series Σ^n√14 is convergent.

Hi! To determine if the series Σ^n√14 is convergent or divergent, we need to analyze the terms involved. The series can be written as:

Σ (n√14)

This is a sum of terms, where each term is the n-th root of 14, and we want to find out if the sum converges or diverges as n goes to infinity.

In this case, the series is a type of p-series, where the terms follow the general form of 1/n^p. To be a convergent p-series, p must be greater than 1. Here, the terms are in the form of 14^(1/n), which can be rewritten as (14^(1))^(-n) or 14^(-n). This is not a p-series, as the exponent is not in the form of 1/n^p.

To further analyze the series, we can use the Divergence Test. If the limit of the terms as n goes to infinity is not equal to zero, then the series is divergent. So, let's find the limit:

lim (n → ∞) (14^(-n))

As n approaches infinity, the exponent -n becomes increasingly negative, and 14^(-n) approaches 0. However, the Divergence Test is inconclusive in this case, as it only confirms divergence if the limit is not equal to zero.

To determine convergence or divergence, we can use the Root Test. The Root Test states that if the limit of the n-th root of the absolute value of the terms as n goes to infinity is less than 1, then the series converges. Let's find the limit:

lim (n → ∞) |(14^(-n))|^(1/n)

This simplifies to:

lim (n → ∞) 14^(-1)

Since 14^(-1) is a constant value less than 1, the limit is less than 1.

Thus, based on the Root Test, the series Σ^n√14 is convergent.

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Every winter, students at Camden Middle School go on a class ski trip.
For every inch of snow that falls, an additional 25 students sign up.
Write an expression showing the total number of students going on the trip, using only a variable to represent the additional students

Now write a different expression to show the total number of students going on the trip, using an expression consisting of a variable and a number to represent the students

Answers

The total number of students going on the trip would be 75 + 50 = 125 according to the first expression, or 325 according to the second expression.

The expression for the total number of students travelling on the trip with only one variable to reflect the extra pupils is:

25x + b

where x is the number of inches of snow that falls and b is the base number of students who sign up regardless of the snowfall.

Now, to write a different expression to show the total number of students going on the trip using an expression consisting of a variable and a number to represent the students, we can use the formula:

N = 25x + 250

where N represents the total number of students going on the trip and 250 represents the base number of students who sign up regardless of the snowfall.

Let's say that 3 inches of snow have fallen. Using the first expression, we would calculate the total number of students as:

25(3) + b = 75 + b

Now, let's say that the base number of students who signed up is 50. Using the second expression, we would calculate the total number of students as:

N = 25(3) + 250 = 325

Therefore, if 3 inches of snow fell and 50 students signed up regardless of the snowfall, the total number of students going on the trip would be 75 + 50 = 125 according to the first expression, or 325 according to the second expression.

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Find (8. 4 × 108) ÷ (1. 5 × 103). Express your answer in scientific notation

Answers

The simplified value of the given expression (8. 4 × 10^8) ÷ (1. 5 × 10^3) in  scientific notation form is given by  5.6 × 10^5.

Expression is equal to ,

(8. 4 × 10^8) ÷ (1. 5 × 10^3)

To divide two numbers in scientific notation, we need to divide their coefficients and subtract their exponents.

(8.4 × 10^8) ÷ (1.5 × 10^3)

Apply law of exponents here,

When m > n

a^m ÷ a^n = a^( m - n )

Here , a = 10 , m = 8 and n = 3

= (8.4 ÷ 1.5) × 10^(8-3)

= 5.6 × 10^5

Therefore, the value of given expression is equal to  5.6 × 10^5 in scientific notation.

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The above question is incomplete , the complete question is:

Find (8. 4 × 10^8) ÷ (1. 5 × 10^3). Express your answer in scientific notation

A scale drawing of a famous statue uses a scale factor of 240:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?

288 feet
241.2 feet
238.8 feet
200 feet

Answers

The height of the statue is 288 feet.

The scale factor is 240:1

Or, the ratio of the height of the statue to the height of the drawing = 240:1.

This means, for 1 unit height of drawing, the height of the statue = 240 units

Or, for 1 feet height of the drawing, the height of the statue = 240 feet.

Let us suppose the actual height of the statue to be x.

The height of the drawing = 1.2 feet    (given)

So, the ratio of the height of the statue to the height of the drawing = x/1.2

But, the scale factor  = 240:1 = 240/1

240/1=x/1.2

⇒x=240×1.2

x=288

Hence, the height of the statue is 288 feet.

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What is the mean of the data set fifth grade jump distance

Answers

The mean of the fifth-grade jump distance data set.

How to calculate the mean of fifth-grade jump distances?

To determine the mean of the data set for fifth-grade jump distances, we need the actual data values. Without the specific data set, it is not possible to calculate the mean.

The mean is the sum of all the values in a data set divided by the number of values. Therefore, we would need the individual jump distances for each fifth-grade student to calculate the mean accurately.

Once we have the complete data set, we can add up all the distances and divide by the total number of students to find the mean. Without the specific data, we cannot provide a numerical answer for the mean of the fifth-grade jump distance.

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Jack starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2. 1% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jack is ready to purchase the vacation home?



$11,000



$11,231



$44,000



$44,924

Answers

The future value of the investment when Jack is ready to purchase the vacation home is $44,924.

To solve this problem, we can use the formula for future value of an annuity:

FV = Pmt x [(1 + r)^n - 1] / r

Where:

Pmt = $1000 (quarterly contribution)
r = 0.021 (annual interest rate)
n = 40 (number of quarters until Jack turns 50)

Plugging in the numbers, we get:

FV = $1000 x [(1 + 0.021)^40 - 1] / 0.021
FV = $44,924.38

Therefore, the future value of Jack's investment, rounded to the nearest dollar, is $44,924. So the correct answer is $44,924.

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An initial amount of $600 is invested in a compound savings account with an annual interest rate of 3. 5%.


1. Define variables


2. Substitute into formula


3. Evaluate


Formula=A = P(1+r)t



What is the total amount after 2 years?


What is the total amount after 4 years?

Answers

After 2 years, the total amount is approximately $642.45. After 4 years, the total amount is approximately $690.27.

1. Define variables:
A = total amount after a certain number of years
P = initial amount ($600)
r = annual interest rate (3.5% or 0.035)
t = number of years

2. Substitute into formula:
A = 600(1+0.035)^t

3. Evaluate:

For 2 years (t=2):
A = 600(1+0.035)^2
A = 600(1.035)^2
A ≈ 642.45

The total amount after 2 years is approximately $642.45.

For 4 years (t=4):
A = 600(1+0.035)^4
A = 600(1.035)^4
A ≈ 690.27

The total amount after 4 years is approximately $690.27.

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northview swim club has a number of members on monday. on tuesday, 22 new members joined the swim clun on wednesday 17 members cancled their membership or left the swim clun northview swim club has 33 members on thursday morning the equation m+22-17=33 repersents the situation solve the equation

Answers

There were 28 members in the Northview Swim Club on Monday before any new members joined or any current members left.

What is the solution of the equation?

The equation "m+22-17=33" represents the situation where "m" is the number of members in the Northview Swim Club on Monday.

To solve the equation, we can start by simplifying it:

m + 5 = 33

Next, we can isolate "m" on one side of the equation by subtracting 5 from both sides:

m = 33 - 5

m = 28

Thus, the solution of the equation for the Northview Swim Club on Monday before any new members joined is determined as 28 members.

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1. An enclosure at the zoo holds two squirrel monkeys. The floor of the enclosure is a rectangle that has an area of 36 square feet. Then the zoo gets four more squirrel monkeys. The rules say that the zoo must add 9 square feet to the floor area for each additional monkey. What must the area of the floor be for all six monkeys? Explain

Answers

To find the area of the floor needed for 6 squirrel monkeys, first calculate the additional area needed for 4 monkeys 4 x 9 = 36 square feet. Add this to the initial area of 36 square feet, to get a total area of 72 square feet. Thus, the floor area for all six monkeys should be 72 square feet.

Let's first find the area of the floor required for the additional 4 monkeys

4 additional monkeys * 9 sq ft per monkey = 36 sq ft

So, to accommodate all 6 monkeys, the total floor area required would be

36 sq ft (original area) + 36 sq ft (additional area) = 72 sq ft

Therefore, the area of the floor for all six monkeys must be 72 square feet.

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X is a discrete random variable. The table below defines a probability distribution for X.


What is the expected value of X?

Answers

The expected value of x is given as follows:

E(X) = 1.6.

What is the mean of a discrete distribution?

The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.

The distribution for this problem is given as follows:

P(X = -7) = 0.2.P(X = -3) = 0.1.P(X = 3) = 0.4.P(X = 7) = 0.3.

Hence the expected value is given as follows:

E(X) = -7 x 0.2 - 3 x 0.1 + 3 x 0.4 + 7 x 0.3

E(X) = 1.6.

Missing Information

The table is given by the image presented at the end of the answer.

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The local regional transit authority of a large city was interested in determining the mean commuting time for workers who drove to work. They selected a random sample of 125 residents of the metropolitan region and asked them how long they spent commuting to work (in minutes). A 95% confidence interval was constructed and reported as (27. 74, 30. 06). Interpret the interval in the context of this problem. 2. A long distance telephone company recently conducted research into the length of calls (in minutes) made by customers. In a random sample of 45 calls, the sample mean was minutes and the standard deviation was s 5. 2 minutes. (a) Find a 95% confidence interval for the true mean length of long distance telephone calls made by customers of this company. X 1. 68

Answers

For the first problem, we can interpret the confidence interval as follows:

We are 95% confident that the true mean commuting time for workers who drive to work is between 27.74 and 30.06 minutes.

This means that if we were to repeat the sampling process many times and construct a 95% confidence interval each time, about 95% of those intervals would contain the true mean commuting time.

For the second problem, we can use the following formula to find a 95% confidence interval for the true mean length of long distance telephone calls:

[tex]CI = X ± t*(s/sqrt(n))[/tex]

Where X is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with n-1 degrees of freedom for a 95% confidence interval.

Plugging in the values given, we get:

[tex]CI = 1.68 ± t*(5.2/sqrt(45))[/tex]

To find the value of t, we can look it up in a t-distribution table or use a calculator. For a 95% confidence interval with 44 degrees of freedom, we get t = 2.015.

Plugging this value in, we get:

[tex]CI = 1.68 ± 2.015*(5.2/sqrt(45)) = (0.86, 2.50)[/tex]

So we can interpret the interval as follows:

We are 95% confident that the true mean length of long distance telephone calls made by customers of this company is between 0.86 and 2.50 minutes longer or shorter than the sample mean of 1.68 minutes.

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CAN SOMEONE HELP ME PLEASEEEEEEEEEEEEEE I NEED HELP :( ​

Answers

Answer:

for the first three, divide the number by 2

for the second three, multiply by 2

9 and 11. divide the number by 2 and plug into the formula 2 * pi * radius, radius is number/2

10. plug 7 into formula 2 * pi * radius, radius = 7

Step-by-step explanation:

radius is half the length of the circle, diameter is the full length, circumference is 2 * pi * radius

A string has a length of 80 cm. It is cut into pieces in the ratio 1: 4: 5. Calculate the length of the longest piece.

Answers

First, we need to find the total number of parts in the ratio 1:4:5:

1 + 4 + 5 = 10

This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:

80 cm ÷ 10 = 8 cm

Now, we can find the length of the longest piece, which is 5 times the size of each part:

8 cm x 5 = 40 cm

Therefore, the length of the longest piece is 40 cm.

AABC DEF. What sequence of transformations will move AABC onto ADEF?


A. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis

B. The translation (x, y) - (x + 7, y), followed by a dilation by a scale
factor of 2 centered at the origin

C. A dilation by a scale factor of 2, centered at the origin, followed by
the translation
(x, y) - (x + 7, y)

D. A dilation by a scale factor of 2, centered at the origin, followed by
the translation (x, y) - (x + 7, y)

Answers

Answer:

D

Step-by-step explanation:

If you dilate the figure with the center at (0,0), the sides of the triangle will be twice as long.  Then You translate the figure 7 units to the right.  

Helping in the name of Jesus.

The correct statement is,

⇒ A dilation by a scale factor of 2, centered at the origin, followed by

the translation (x, y) → (x + 7, y)

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Since, Scale Factor is defined as the ratio of the size of the new image to the size of the old image.

If the scale factor is more than 1, then the image stretches.

If the scale factor is between 0 and 1, then the image shrinks.

If the scale factor is 1, then the original image and the image produced are congruent.

And, The only change in the dilation process is that the distance between the points changes.

It means that the length of the sides of the original image and the dilated image may vary.

Here, By dilation with factor 2 to the small triangle, its sides becomes equal as big triangle.

Now, center the small triangle at origin (0,0).

Then, transform the small triangle to (x + 7, y) i.e., it exactly gets the coordinates of the big triangle.

There are same in terms of sides length and coordinates.

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Miles driven to see a space shuttle launch 19 27 14 28 30 51 28

Answers

For the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.

To analyze this data, let's find the mean (average), median, and mode.

1. Mean (average): Add all the miles together and divide by the total number of data points.
(19 + 27 + 14 + 28 + 30 + 51 + 28) / 7 = 197 / 7 = 28.14

The mean miles driven to see a space shuttle launch is 28.14.

2. Median: Arrange the data points in ascending order and find the middle value.
14, 19, 27, 28, 28, 30, 51
Since there are 7 data points, the median is the 4th value, which is 28.

The median miles driven to see a space shuttle launch is 28.

3. Mode: Identify the most frequently occurring value in the data set.
14, 19, 27, 28, 28, 30, 51
The number 28 appears twice, which is more than any other value.

The mode for miles driven to see a space shuttle launch is 28.

In summary, for the given data set of miles driven to see a space shuttle launch, the mean is 28.14, the median is 28, and the mode is 28.

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There are 7 purple flowers, 9 yellow flowers, and 12 pink flowers in a bouquet. You choose a flower to give to a


friend, then choose another flower for yourself. Is this an independent or dependent event? Explain how you


know.

Answers

Choosing two flowers from a bouquet with 7 purple, 9 yellow, and 12 pink flowers is a dependent event.


This is a dependent event. The reason is that after choosing a flower to give to a friend, the number of flowers left in the bouquet changes, which in turn affects the probability of choosing a specific color for yourself. Since the outcome of the first choice impacts the probability of the second choice, the events are dependent.

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The distance from city a to city b is 256. 8 miles. The distance from city a to city c is 739. 4 miles how much farther is the trip to city c than the trip to city b

Answers

Answer:

482.6 mi

Step-by-step explanation:

a to b = 256.8 mi

a to c = 739.4 mi

(a to c) - (a to b) = 739.4 - 256.8 = 482.6 mi

What is the image of (5,−4) after a dilation by a scale factor of 4 centered at the origin?

Answers

The image of (5,−4) after a dilation by a scale factor of 4 centered at the origin is (20,−16)

What is the image after a dilation centered at the origin?

From the question, we have the following parameters that can be used in our computation:

Point = (5,−4)

Scale factor of 4 centered at the origin

The image after a dilation centered at the origin is

Image = Point  * Scale factor

Substitute the known values in the above equation, so, we have the following representation

image = (5,−4) * 4

Evaluate

image = (20,−16)

Hence, the image after a dilation centered at the origin is (20,−16)

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Chris wants to order DVD's over the internet. Each DVD costs $15. 99 and shipping the entire order costs $9. 99. If he can spend no more than $100, how many DVD's could he buy?

Answers

Since Chris can only buy whole DVDs, he can purchase a maximum of 5 DVDs within his $100 budget.

Each DVD costs $15.99, and the shipping for the entire order is $9.99.

We can use the following inequality to represent Chris's budget constraint:

15.99x + 9.99 ≤ 100

Here, x represents the number of DVDs he can buy.

To find the maximum value of x, we can rearrange the inequality:

x ≤ (100 - 9.99) / 15.99 x ≤ 90.01 / 15.99 x ≤ 5.63

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For a certain company , the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0. 5x^2.

a) set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces (hint: it is a quadratic polynomial)

b) find two values of x that will create a profit of $300

c) is it possible for the company to make a profit of $15,000​

Answers

Answer:

Step-by-step explanation:

a)  Profit = Revenue - Cost = (90x - 0.5x²) - (50x + 300)

= -0.5x² + 90x - 50x - 300

= -0.5x² + 40x - 300

b)  -0.5x² + 40x - 300 = 300

-0.5x² + 40x - 600 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -600):

x = 20, 60

c)  -0.5x² + 40x - 300 = 15000

-0.5x² + 40x - 15300 = 0

use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -15300):

x = 40±10√290i

Not possible to make a profit of $15,000

You babysat your neighbor's children, and they paid you $45 for 6 hours.

What is the rate?

What is the unit rate?

Write a function rule to represent this situation.

Answers

Answer:

The rate is $7.50 per hour.

The unit rate is $7.50 per hour.

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Step-by-step explanation:

To find the rate, divide the total amount earned by the number of hours worked. In this case, you earned $45 for 6 hours.

Rate = Total amount earned / Number of hours worked

Rate = $45 / 6 hours

Rate = $7.50 per hour

The rate is $7.50 per hour.

The unit rate refers to the rate per unit of one. In this case, it would be the rate per hour.

Unit Rate = Rate / Number of units

Unit Rate = $7.50 / 1 hour

Unit Rate = $7.50 per hour

The unit rate is $7.50 per hour.

To write a function rule to represent this situation, let's use "x" to represent the number of hours worked and "y" to represent the amount earned:

y = Rate * x

Since the rate is $7.50 per hour, the function rule can be written as:

y = 7.50x

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Answer:

Step-by-step explanation:

7.5

Proctor & Gamble claims that at least half the bars of Ivory soap they produce are 99. 44% pure (or more pure) as advertised. Unilever, one of Proctor & Gamble's competitors, wishes to put this claim to the test. They sample the purity of 146 bars of Ivory soap. They find that 70 of them meet the 99. 44% purity advertised.



What type of test should be run?


t-test of a mean


z-test of a proportion




The alternative hypothesis indicates a


right-tailed test


two-tailed test


left-tailed test




Calculate the p-value.



Does Unilever have sufficient evidence to reject Proctor & Gamble's claim?


No


Yes

Answers

Unilever should run a z-test of a proportion to test Proctor & Gamble's claim that at least half of the bars of Ivory soap they produce are 99.44% pure or more.

What is the appropriate test that Unilever should conduct to test Proctor & Gamble's claim about Ivory soap's purity?

Unilever should use a z-test of a proportion to test whether Proctor & Gamble's claim that at least 50% of Ivory soap bars are 99.44% pure or more is statistically significant based on a sample of 146 bars, of which 70 meet the purity criteria.

The null hypothesis is that the proportion of Ivory soap bars meeting the purity criteria is 0.50, and the alternative hypothesis is that it is greater than 0.50. The z-test yields a p-value of 0.038, which is less than the significance level of 0.05.

Thus, Unilever has sufficient evidence to reject Proctor & Gamble's claim and conclude that the proportion of Ivory soap bars meeting the purity criteria is significantly different from 50%.

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2 Find the first derivative x^{2/3} + y^{2/3} =14

Answers

The first derivative of the implicit function given by x^(2/3) + y^(2/3) = 14 can be found using implicit differentiation. We take the derivative of both sides with respect to x and use the chain rule to differentiate the terms involving y:(2/3)x^(-1/3) + (2/3)y^(-1/3) * dy/dx = 0Then, we solve for dy/dx:dy/dx = -(x/y)^(1/3)This is the first derivative of the implicit function. To evaluate it at a specific point, we need to substitute the coordinates of that point into the equation above.

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[tex]dy/dx = -x^{-1/3} / y^{-1/3}[/tex]

To find the first derivative of the given equation x^{2/3} + y^{2/3} = 14, we will differentiate both sides of the equation with respect to x and then solve for dy/dx (the first derivative of y with respect to x).

Step 1: Differentiate both sides of the equation with respect to x.
[tex]d/dx (x^{2/3} + y^{2/3}) = d/dx (14)[/tex]

Step 2: Apply the chain rule to differentiate y^{2/3}.
[tex]d/dx (x^{2/3}) + d/dx (y^{2/3}) = 0(2/3)x^{-1/3} + (2/3)y^{-1/3}(dy/dx) = 0[/tex]

Step 3: Solve for dy/dx.
[tex](2/3)y^{-1/3}(dy/dx) = -(2/3)x^{-1/3}dy/dx = -(2/3)x^{-1/3} / (2/3)y^{-1/3}[/tex]

Step 4: Simplify the expression.
[tex]dy/dx = -x^{-1/3} / y^{-1/3}[/tex]

Your answer: [tex]dy/dx = -x^{-1/3} / y^{-1/3}[/tex]

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The revenue from selling q items is R(q)=625q−q2, and the total cost is C(q)=50+6q. Write a function that gives the total profit earned, and find the quantity which maximizes the profit.

Answers

To find the total profit earned, we need to subtract the total cost from the revenue. Therefore, the profit function is:

P(q) = R(q) - C(q)
P(q) = 625q - q^2 - (50 + 6q)
P(q) = -q^2 + 619q - 50

To find the quantity which maximizes the profit, we need to take the derivative of the profit function and set it equal to zero:

P'(q) = -2q + 619
0 = -2q + 619
2q = 619
q = 309.5

Therefore, the quantity which maximizes the profit is 309.5. To find the total profit earned at this quantity, we plug it back into the profit function:

P(309.5) = -(309.5)^2 + 619(309.5) - 50
P(309.5) = $95,268.25

So the total profit earned at the quantity which maximizes the profit is $95,268.25.

To find the total profit function, you'll want to subtract the total cost function, C(q), from the revenue function, R(q). So the profit function, P(q), is given by:

P(q) = R(q) - C(q) = (625q - q^2) - (50 + 6q)

Now, simplify the profit function:

P(q) = 625q - q^2 - 50 - 6q = -q^2 + 619q - 50

To find the quantity which maximizes the profit, you can take the first derivative of the profit function with respect to q, set it equal to 0, and solve for q:

P'(q) = -2q + 619

Set P'(q) to 0 and solve for q:

0 = -2q + 619
2q = 619
q = 309.5

Since you can't have a fraction of an item, consider checking q = 309 and q = 310 to find the maximum profit. Evaluate P(q) at both points:

P(309) = -309^2 + 619(309) - 50
P(310) = -310^2 + 619(310) - 50

P(309) = 95441
P(310) = 95439

Thus, the quantity which maximizes the profit is 309 items.

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Due to an unresolved national issue, the popularity of a politician is suspected to have decreased over the past year. his popularity vote percentage used to be 55%. to confirm the suspicion, a sample of 820 adult residents is surveyed. the survey reveals that 405 of the respondents still support him. determine if there exists a significant decrease in his popularity vote percentage. use significance level of 0.10 to conduct a hypothesis testing ​

Answers

Answer:

Step-by-step explanation:

To test if there exists a significant decrease in the popularity vote percentage of the politician, we can conduct a hypothesis test using the significance level of 0.10.

The null hypothesis, denoted by H0, is that there is no significant decrease in the politician's popularity vote percentage. The alternative hypothesis, denoted by H1, is that there is a significant decrease in the politician's popularity vote percentage.

We can use the sample proportion of supporters, which is 405/820 = 0.494, as an estimator of the true proportion of supporters in the population.

Assuming the null hypothesis is true, we can calculate the standard error of the sample proportion using the formula sqrt(p(1-p)/n), where p is the hypothesized proportion (0.55) and n is the sample size (820). This gives us a standard error of sqrt(0.55*0.45/820) = 0.024.

We can then calculate the test statistic using the formula (p - hypothesized proportion)/standard error, where p is the sample proportion. This gives us a test statistic of (0.494 - 0.55)/0.024 = -2.333.

With a significance level of 0.10 and a two-tailed test, the critical values for the test statistic are -1.645 and 1.645. Since the calculated test statistic (-2.333) is outside the range of the critical values, we can reject the null hypothesis.

Therefore, we can conclude that there is sufficient evidence to suggest a significant decrease in the popularity vote percentage of the politician at a significance level of 0.10.

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Evaluate the integral. 8 Vi s dt Vi 8V1 ſ Vi dt=U Help me solve this Ca

Answers

The integral evaluates to (16/3)s³/² + C.

What is power rule of integration?

The power rule of integration is a method for finding the indefinite integral of a function of the form f(x) = x^n, where n is any real number except for -1. The rule states that the indefinite integral of f(x) is (x^(n+1))/(n+1) + C, where C is an arbitrary constant of integration.

To evaluate the integral 8√(s) ds, follow these steps:


1. Rewrite the integral with a rational exponent: ∫8s¹/² ds
2. Apply the power rule for integration: ∫sⁿ ds = (sⁿ⁺¹/(n+1) + C, where n ≠ -1
3. Substitute n=1/2: (s³/²)/(3/2) + C
4. Multiply by 8: 8*(s³/²)/(3/2) + C
5. Simplify the expression: (16/3)s³/² + C

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