Campus athletics is interested in the proportion of registered students living on campus who play basketball recreationally during the semester. They take a random sample of 222 registered students listed as living in campus housing and ask each whether or not they do so. A 95% confidence interval is correctly calculated from this data as (0.12, 0.18). Which of the following is the correct interpretation of this confidence interval?
a. None of these are correct.
b. We are 95% contident that the proportion of the 111 sampled students that actually play basketball is between 0.12 and 0.18
c. The sample proportion of on-campus students that play basketball will be between 0.12 and 0.18 in 95% of samples of size 111
d. We are 95% confident that the proportion of all students that live on campus who play basketball recreationally is between 0.12 and 0.18
e. We are 95% confident that among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18

Answer:

wsfgnjjjj3999878 ixixixisixiixxiix

Answer:

8

Step-by-step explanation:

24 divided by 3 equals 8.

Answer:

x=-8

Step-by-step explanation:

8x-2=3x+5x

1. Combine Like Terms

3x+5x=8x

Now your equation looks like this:

8x-2=8x

+8x   +8x

2. Move Variables to one side

Now this is your equation:

-2=16x

3. Divide to isolate "x"

16/-2

x=-8

Let me know if this helped! :)

A store sells 5 oranges and 10 apples.

What is the cost amount?

The cost of an asset to you often serves as its basis. The cost is the sum that you pay for it using money, debt, other goods, or services. Sales tax and other purchase-related costs are included in the price.

Here, we have

Given: A store sells oranges and apples. Oranges cost $1.00 each and apples cost $2.00 each. In the first sale of the day, 15 fruits were sold in total, and the price was $25.

We have to determine how many of each type of fruit were sold.

We, let the oranges be x.

let the apples be y.

x + y = 15...(1)

1x + 2y = 25...(2)

We subtract equation(2) from equation(1), we get

y = 10

Now we put the value of y in equation (1) and we get

x + 10 = 15

x= 5

Hence, a store sells 5 oranges and 10 apples.

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The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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The cosine function that represents the graph in the question can be presented as follows;

y = 1·cos(1·x) + 0

The general form of the cosine function can be presented as follows;

y = A·cos(B·x + C) + D

Where;

A = The amplitude

B = A function of the period

D = The vertical shift

C = The horizontal shift

The graph of the cosine function indicates;

The y-coordinate of the peak = 1

The y-coordinate of the trough = -1

The amplitude = (1 - (-1))/2 = 1

The maximum value is at theta = 0, therefore, the horizontal shift is 0

The period = The difference between the x-values of two consecutive peaks = 2·π - 0 = 2·π

The period = 2·π/B, therefore;

2·π = 2·π/B

B = 1

The vertical shift is the raising of the midline above the x-axis, which is 0

The equation is therefore; y = 1·cos(x) + 0 = cos(x)

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Answer:

\(y=\boxed{2}\;\cos \left(\;\boxed{1}\;x\right)+\boxed{1}\)

Step-by-step explanation:

The cosine function is periodic, meaning it repeats forever.

The standard form of a cosine function is:

\(\boxed{y = A \cos(B(x + C)) + D}\)

where:

The parameters of the parent function y = cos(x) are:

The midline of the graph is the x-axis, and the range is -1 ≤ y ≤ 1.

From observation of the graph, we can see that the parent function has been stretched vertically and shifted up, since the mid-line is no longer the x-axis.

The maximum value of the graph is 3, and the minimum value is -1.

The mid-line is halfway between these values, so the mid-line is y = 1. This means that the graph has been shifted 1 unit up, so D = 1.

The amplitude is the difference between the midline and the maximum value. Since the mid-line is y = 1 and the maximum value is y = 3, the amplitude is 2. Therefore, A = 2.

The period is unchanged and there has been no horizontal shift, so B = 1 and C = 0.

Therefore, the equation of the graph is:

\(y=2\cos(x)+1\)

So the values you need to put into the boxes are:

\(y=\boxed{2}\;\cos \left(\;\boxed{1}\;x\right)+\boxed{1}\)

Answer:

Step-by-step explanation:

It is correct till 16/15

But after that it is 16/15 × 5/-3 = 80/-45

simplify it to 16/-9

The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

In the given question,

We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.

Since we have to find the image after a dilation.

So we learn about it now,

Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.

So the given point is (-9,12).

Scale factor is 1/3.

So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as

=(-9×1/3,12×1/3)

Simplifying

=(-3,4)

Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).

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Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

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Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=1100\hspace{35px}r=0.051\hspace{35px}t=18

P=1100r=0.051t=18

Given values

A=1100e^{0.051(18)}

A=1100e

0.051(18)

Answer: 2,750

Explanation:

Plug in

A=1100e^{0.918}

A=1100e

0.918

Multiply

A=2754.70450683

A=2754.70450683

Use calculator (with e button)

A\approx 2750

A≈2750

Round to nearest ten dollars

please heart!

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The amount of money after 18 years nearest to ten will be $2,750.

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

\(\rm A=P_o \times e^{r \times t}\\\)

Faith invested $1,100 in an account paying an interest rate of 5.1% compounded continuously.

Then the amount after 18 years is calculated as,

\(\rm A = \$1,100 \times e^{0.051 \times 18}\\A = \$1,100 \times e^{0.918}\)

Simplify the equation further, then we have

A = $1,100 x 2.504

A = $2,754.7

The amount of money after 18 years nearest to ten will be $2,750.

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If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees

The point o is the center of the circle

∠COB = 96 degrees

Here we have to apply the circle theorem

The circle theorem is defined as the measure of angles joined to any point on the circumference of the circle from the same arc is equal to the one by two of the angle subtended at the center by the same arc.

Then the equation will be

∠COB = 2 × ∠CAB

Substitute the values in the equation

2 × ∠CAB = 96

∠CAB = 96 / 2

Divide the terms

∠CAB = 48 degrees

Hence, If the point o is the center of the circle, then the measure of ∠CAB = 48 degrees

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The two prime numbers that add up to 100005, based on the properties of prime numbers would be 2 and 100003.

To find the two prime numbers, the relevant relationship would be  the Goldbach's Conjecture. This posits that every even number greater than 2 can be expressed as the sum of two prime numbers.

So, to write an odd number as the sum of two prime numbers, one of the prime numbers has to be 2 because we know that 2 is the only even prime number.

The other number would therefore be:

= 100005 - 2

= 100003

100003 is a prime number so the two prime numbers are 2 and 100003.

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Answer:

26.3%

Step-by-step explanation:

5 is divided by 19

That answer is then multiplied by 100.

You may round your answer to the nearest whole number.

Answer:

See below

Step-by-step explanation:

Alex finally understands how Bob was trying to trick him into winning the bet because of how he puts in the condition for probability being less than 10%. Whichever way the outcome of the coin toss turns out to be, it will be in Bob's favor and Alex will lose the bet. If the coin is flipped 3 times, the probability of having heads exactly twice is \(\frac{4}{9}\)

Answer:

what is the problem? pls type in comments

The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

Here's the parallel line: y = 5x - 4

Answer:

The volume of the region V = 2

Step-by-step explanation:

Given that:

\(z_1 = 3y^2\) ;

where initially;

\(z_o = 0; \ x_o = 0; \ x_1 = 1; \ y_o= -1; \ y_1 = 1\)

The volume of the region is given by a triple which is expressed as:

\(V = \int_x \int_y \int_z \ dz \ dy \ dx\)

\(V = \int \limits ^{x_1 = 1}_{x_o=0} \int \limits ^{y_1 = 1}_{y_o=-1} \int \limits ^{z_1 = 3y^2}_{z_o=0} \ dz \ dy \ dx\)

\(V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \int \limits ^{3y^2}_{0} \ dz \ dy \ dx\)

\(V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [z \Bigg]^{3y^2}_{0} \ dy \ dx\)

\(V = \int \limits ^{1}_{0} \int \limits ^{ 1}_{-1} \Bigg [3y^2 \Bigg] \ dy \ dx\)

\(V = \int \limits ^{1}_{0} \Bigg [\dfrac{3y^3}{3} \Bigg]^1_{-1} \ dx\)

\(V = \int \limits ^{1}_{0} \Bigg [\dfrac{3(1)^3}{3}- \dfrac{3(-1)^3}{3} \Bigg] \ dx\)

\(V = \int \limits ^{1}_{0} \Bigg [1-(-1)\Bigg] \ dx\)

\(V =2 \Bigg [x \Bigg] ^1_0\)

V = 2

Thus, the volume of the region is 2

The solution to the system of equations is x = 1 and y = -3.

To solve the system of equations using the substitution or elimination method, let's start with the substitution method.

Given equations:

y = 4x - 7

4x + 2y = -2

We'll solve equation 1) for y and substitute it into equation 2):

Substituting y from equation 1) into equation 2):

4x + 2(4x - 7) = -2

4x + 8x - 14 = -2

12x - 14 = -2

Now, we'll solve this equation for x:

12x = -2 + 14

12x = 12

x = 12/12

x = 1

Now that we have the value of x, we can substitute it back into equation 1) to find y:

y = 4(1) - 7

y = 4 - 7

y = -3

Therefore, the solution to the system of equations is x = 1 and y = -3.

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Depends on where you stay. Here it costs something around ₹400 - ₹500 per square foot.

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

Y = 28

Step-by-step explanation:

Y=16 + 12 = 24

Therefore the y scored 24 points

Answer: x

=

4

Step-by-step explanation:

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The radius of a sphere is the distance from its center to its surface. Assuming a sphere with a radius r its volume is given by the following formula:

In this case the radius of the sphere is of 4.7 miles. Then we take r=4.7 and we find its volume:

Then the answer is 434.9.

Answer:

$26,179.82  

Step-by-step explanation:

FVA = PMT * n * (1 + i) ^ (n - 1)

FVA = 440 * 48* (1.00458)^(47)

Answer:

A

Step-by-step explanation:

FV=PV(1+i)^t

2500(1+.03)^4

A

Answer:

A

Step-by-step explanation:

It is the only one that shows 3% = 0.03 which is correct.

Answer:

A choice

Step-by-step explanation:

sec is defined as 1/cos.

cos is again defined as adjacent to hypotenuse.

We know that adjacent is x and hypotenuse is r.

Therefore:- cos is x/r

Now sec is 1/cos = 1/(x/r)

1 ÷ x/r is 1•r/x

Thus:-

sec is r/x