Women athletes at a certain university have a long-term graduation rate of 67%. Over the past several years, a random sample of 36 women athletes at the school showed that 23 eventually graduated. Does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? Use a 5% level of significance.
(a) What is the level of significance?
State the null and alternate hypotheses.
A. H0: p = 0.67; H1: p < 0.67
B. H0: p = 0.67; H1: p ≠ 0.67
C. H0: p < 0.67; H1: p = 0.67
D. H0: p = 0.67; H1: p > 0.67
(b) What sampling distribution will you use?
A. The standard normal, since np > 5 and nq > 5.
B. The standard normal, since np < 5 and nq < 5.
C. The Student's t, since np > 5 and nq > 5.
D. The Student's t, since np < 5 and nq < 5.
What is the value of the sample test statistic?
(c) Find the P-value of the test statistic. (Round your answer to four decimal places.)
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
A. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
B. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
C. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
D. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
A. There is sufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.
B. There is insufficient evidence at the 0.05 level to conclude that the true proportion of women athletes who graduate is less than 0.67.

Answer:

This statement would be true.

Step-by-step explanation:

Answer:

(4) 644,000

Step-by-step explanation:

643,581

The 3 is in the thousands place

We look at the hundreds place

5

It is 5 or greater so we round the thousands place up 1

644000

Answer: [tex](\frac{2}{5},0) ; (0,2)[/tex]

Step-by-step explanation:

(to find the x-intercept, plug in 0 for y)

(to find the y-intercept, plug in 0 for x)

[tex]0=-5x+2\\5x=2\\x=\frac{2}{5}\\(\frac{2}{5},0)\\y=-5(0)+2\\y=2 \\(0,2)[/tex]

Answer: so there are 666 multiples of 3 between 2 and 2000.

Step-by-step explanation:

the smallest number = 3 which is 3*1. The largest number is = 1998 = 3*666

multiples of 3 between {2,2000} = 666-1+1 = 666

Answer:

520 feets

Step-by-step explanation:

The height of the building, h can be obtuined using trigonometry ;

From the attached diagram, opposite side = 300 feets ; height, h = adjacent side

Hence,

Tan θ = opposite / Adjacent

Tan 30° = 300 / height

0.5773502 = 300 / height

Height = 300 / 0.5773502

Height = 519.615

Height = 520 feets

Answer:

a. P = 30

b. Y = 40

Step-by-step explanation:

Given the following data;

P = 1.2

Y = 100

First of all, we would have to determine the constant of proportionality;

P = k/Y (inverse proportion or relationship)

1.2 = k/100

k = 1.2 * 100

k = 120

a. To find the value of p when y = 4;

P = k/Y

P = 120/4

P = 30

b. To find the value of y when p = 3;​

P = k/Y

Y = k/P

Y = 120/3

Y = 40

9514 1404 393

Answer:

Step-by-step explanation:

The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.

__

No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.

Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.

Answer:Mark Brainliest please

Answer is 4.86 which is rounded to 5

Step-by-step explanation:

Cos 40 degree = VW/7

0.694 =VW/7

0.694 * 7 =VW

4.858 =VW

VW=4.86 is the answer

I REALLY HOPE THIS HELPS! I’m sorry if this was wrong but I really believe it’s true.

Answer:

The value of P is $6.75.

Step-by-step explanation:

In the diagram to the left, we see 6 apples, and are labeled that the price is $4.50.

If the prices are proportional, that may mean that each apple has the same price. To find the price of apples in the diagram to the right, divide the total price by 6:

4.50/6 = 0.75

So the price per apple is 0.75.

As seen on the diagram, P represents the total price of 9 apples.

Multiply the price per apple by 9:

0.75 x 9 = 6.75

So the value of P is $6.75

Answer:

115

Step-by-step explanation:

You divide 230 by 2 cause there are two peoples. I hope that helps :)

9514 1404 393

Answer:

  C.  because the graphs of the two equations overlap each other

Step-by-step explanation:

When a system of linear equations has an infinite number of solutions, the equations are "dependent." That means they both describe the same line. The graph will appear to be one line because the lines overlap each other.

__

Additional comment

The Desmos graphing calculator lets the texture of the graph be varied, so we can see that the two lines overlap. In the attached, one equation is graphed as a dotted red line, the other as a solid blue line.

Answer:

The decision rule is to Reject H0 if Z ≤ -1.282

Step-by-step explanation:

We are given;

Population mean; μ = 409 g

Sample mean; x¯ = 401 g

Sample size; n = 21

Standard deviation; s = 26

Let's define the hypotheses;

Null hypothesis; H0: μ = 409 g

Alternative hypothesis; Ha : μ ≠ 409 g

Formula for test statistic is;

z = (x¯ - μ)/(s/√n)

z = (401 - 409)/(26/√21)

z = -1.410

z-value is negative and thus this is a lower tail test.

At significance level of 0.1, the critical value is -1.282.

Thus, the decision rule is;

Reject H0 if Z ≤ -1.282

Answer:

4.95m

Step-by-step explanation:

Let the length of longer and shorter pipe be x and y respectively..

given,

x/y=9/2...(i)

x-1.65=3y ...(ii)

in eqn ii..

x-1.65=3y

or, x/y - 1.65/y = 3

or, 9/2-1.65/y =3

or, 4.5-3 = 1.65/y

or, y=1.65/1.5

•°• y = 1.1m

now,

x/y = 9/2

or, x/1.1 = 4.5

x= 4.5×1.1

•°• x= 4.95m

thus, the length of the longer pipe is 4.95m

Answer:

B

Step-by-step explanation:

5³.5^×

simply means

5³×5^×

using indices rule,

multiplication is addition

5 is common

so 5(³+×)

hence 5^3+×

Answer:

Sin A = 15 / 17

Step-by-step explanation:

Given a right angled triangle, we are to obtain the Sin of the angle A ;

Using trigonometry, the sin of the angle A, Sin A is the ratio of the angle opposite A to the hypotenus of the right angle triangle.

Hence. Sin A = opposite / hypotenus

Opposite = 15 ; hypotenus = 17

Sin A = 15 / 17

Answer:

(a) 218.6 N

(b) 97.14 N

Step-by-step explanation:

When the system is in equilibrium, the net torque on the system is zero.

AC = 1.5 m, CD = 2.3 m, DB = 5 - 1.5 - 2.3 = 1.2 m

Let the centre of gravity of plank is at G.

AG = 2.5 m, CG = 2.5 - 1.5 = 1 m, GB = 2.5 m

(a) Let the reaction at C is R and at D is R'.

R + R' = 29 x 9.8 = 284.2 N ... (1)

Take the torque about C.

29 x 9.8 x CG = R' x GD

29 x 9.8 x 1 = R' x 1.3

R' = 218.6 N

(b) Take the torque about D.

6 x 9.8 x AD = R x CD

6 x 9.8 x (1.5 + 2.3) = R x 2.3

R = 97.14 N

Answer:

B, D, F

Step-by-step explanation:

In a rational exponent, the numerator is an exponent, and the denominator becomes the index of the root.

[tex]a^{\frac{m}{n}} = \sqrt[n] {a^m}[/tex]

Answer: B, D, F

(-1;2;-3)

а, b, c

~~~~~~

Answer:

The answer is −3y^2−y.

Steps:

Distribute the Negative Sign:

=−2y2+−1(y2+y)

=−2y2+−1y2+−1y

=−2y2+−y2+−y

Combine Like Terms:

=−2y2+−y2+−y

=(−2y2+−y2)+(−y)

=−3y2+−y

Answer:

-3y^2 - y

Step-by-step explanation:

-2y^2 - (y^2 + y)

Find the opposite of y^2 + y, so distribute the negative sign to the values inside the parentheses to get:

−2y^2 −y^2 − y

Then combine like terms to get:

-3y^2 - y

Answer:

1.083

Step-by-step explanation:

Exact form: 13/12

Decimal form: 1.083 (put a line above the 3)

Mixed number form: 1 1/12

the slope-intercept form of the given equation is y = x/3 + 8.

The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. The coordinate plane describes the slope of the line.

The slope-intercept form of a line is Y = m*X +C.

Given an equation 3x-9y = -72, which we will try to make in the slope-intercept form by using simplification.

3x-9y = -72

9y = 3x + 72

y = 1/3 * x + 8

Therefore y = x/3 + 8 is the slope-intercept form of the given equation.  where its slope is 1/3.

Learn more about slope here:

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Answer in picture

….

Answer:

Step-by-step explanation:

The remainder when f(x) is divided by x + 3 would be 76.

If there is a polynomial p(x), and a constant number 'a', then

[tex]\dfrac{p(x)}{(x-a)} = g(x) + p(a)[/tex]

where g(x) is a factor of p(x).

We have been given a function;

[tex]f(x) = -2x^3 + x^2 - 4x + 1[/tex]

We need to find the remainder when f(x) is divided by x + 3.

So, Let p(x) = x + 3

p(x) = 0

x + 3 = 0

x = -3

Substitute in the given function f(x);

[tex]f(x) = -2x^3 + x^2 - 4x + 1\\\\f(-3) = -2(-3)^3 + (-3)^2 - 4(-3) + 1\\\\f(-3) = 54 + 9 + 12 + 1\\\\f(-3) = 76[/tex]

Thus, the remainder when f(x) is divided by x + 3 would be 76.

Learn more about remainder;

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Answer:

C

Step-by-step explanation:

C is the only function that have a consistent decrease while A is a trigonometric function, B is a non linear function, D is an exponential function

Answer:

0.9099 = 90.99% probability that their mean length is less than 21.9 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 18.2 inches, and standard deviation of 3.9 inches.

This means that [tex]\mu = 18.2, \sigma = 3.9[/tex]

2 itens:

This means that [tex]n = 2, s = \frac{3.9}{\sqrt{2}}[/tex]

What is the probability that their mean length is less than 21.9 inches?

This is the p-value of Z when X = 21.9. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{21.9 - 18.2}{\frac{3.9}{\sqrt{2}}}[/tex]

[tex]Z = 1.34[/tex]

[tex]Z = 1.34[/tex] has a p-value of 0.9099.

0.9099 = 90.99% probability that their mean length is less than 21.9 inches.

Answer:

The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".

Step-by-step explanation:

Given:

[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]

let

[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]

and

[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]

[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]

So,

[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]

         [tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]

OR

[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]

Derivate:  

[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]

Answer:

(1). A = 18 cm² ; (2). TR = 18 units

Step-by-step explanation:

this is a special triangle so v = 17

u = 17√2

Answer:

v = 17

u = 17[tex]\sqrt{2}[/tex]

Step-by-step explanation:

If v = 17 (it is because it is a right triangle, so the pythagorean theorum works, and triangles are 180 degrees, so 180 - 90 = 90, so the other two angles are 45 degrees, meaning that v is the same length as 17.) then

17 ^ 2 = u ^2

289 = u^2

17 root to 2

Answer:

y = 3x - 5

Step-by-step explanation:

Slope = 3

x-intercept (what the value of y is when its 0) = -5 so y = 3x - 5

Answer:

y = 3x - 5

Step-by-step explanation:

Find the slope of the line between (0,−5)(0,-5) and (3,4)(3,4) using m=y2−y1x2−x1m=y2-y1x2-x1, which is the change of yy over the change of xx.

m=3m=3

Use the slope 33 and a given point (0,−5)(0,-5) to substitute for x1x1 and y1y1 in the point-slope form y−y1=m(x−x1)y-y1=m(x-x1), which is derived from the slope equation m=y2−y1x2−x1m=y2-y1x2-x1.

y−(−5)=3⋅(x−(0))y-(-5)=3⋅(x-(0))

Simplify the equation and keep it in point-slope form.

y+5=3⋅(x+0)

Add xx and 00.

y+5=3xy+5=3x

Subtract 55 from both sides of the equation.

y=3x−5