Evaluate \dfrac p4 +pq
4
p
​
+pqstart fraction, p, divided by, 4, end fraction, plus, p, q when p=8p=8p, equals, 8 and q=6q=6q, equals, 6.

Hello!

Your answer should be 26.85.

We can use the formula of pi d or 2 pi r for the circumference.

You would get 5 pi.

But since its not a full circle you would divide it in half and get 2.5 pi.

2.5 pi is equal to 7.85.

Now we can use the equation 7.85 + 7 + 7 + 5

That would equal our answer... 26.85!

Hope this helps!

Answer:

20

Step-by-step explanation:

as u have to divide the answr and convert it

Answer:

62 is the answer because

15x4=60 + 1/2x4 = 62

The 95% confidence interval for the population mean weight of adult elephants is approximately (11628, 11666) pounds.

To find the 95% confidence interval of the population mean for the weights of adult elephants, we can use the formula:

CI = x ± Z * (σ/√n)

where CI is the confidence interval, x is the sample mean, Z is the z-score corresponding to the desired confidence level (in this case, 95%), σ is the population standard deviation, and n is the sample size.

Using the given values, x = 11,647 lb, σ = 24 lb, and n = 7, we can calculate the confidence interval:

CI = 11647 ± 1.96 * (24/√7)

CI ≈ 11647 ± 19.12

Therefore, the 95% confidence interval for the population mean weight of adult elephants is approximately (11628, 11666) pounds.

https://brainly.com/question/34700241

#SPJ11

Answer:

The length of the rectangle is

12

c

m

and the area of the rectangle is

60

c

m

2

.

Explanation:

By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.

Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

a

2

+

b

2

=

c

2

5

2

+

b

2

=

13

2

25

+

b

2

=

169

25

−

25

+

b

2

=

169

−

25

b

2

=

144

√

b

2

=

√

144

b

=

±

12

Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is

12

cm.

The area of a rectangle is given by multiplying the width by the length.

A

=

(

5

c

m

)

(

12

c

m

)

A

=

60

c

m

2

Answer:

[tex] {5}^{2} + {x}^{2} = {13}^{2} \\ 25 + {x}^{2} = 169 \\ {x}^{2} = 169 - 25 \\ {x}^{2} = 144 \\ x = \sqrt{144} \\ x = 12cm[/tex]

Step-by-step explanation:

use the Pythagorean theorem

hope this helps you

Parameter:

Null hypothesis:  μ = 1.5 (the machines work as needed)

Alternative hypothesis: μ ≠ 1.5 (The machines don't work properly)

Since we don't know the population deviation, we will apply a t-test to compare the actual mean to the reference value

Conditions:

Simple random sample: The problem states the sample was chosen at random.

Independence: You can assume there are more than 10(200) = 2000 screws.

Normality: (200 ≥ 30)  the sample is large enough for sampling distribution to assume Normality

Calculations:

Since the conditions are met we will carry out a T-test using a calculator for μ≠μ0

μ = population mean = 1.5

σ= standard dev = 0.204

xbar = sampe mean = 1.521

n = sample size= 200

After adding all of this data into the calculator in the T-test program we get a p-value of 0.147

Conclusion:

We will assume a 0.05 sig level for our conclusion.

Since 0.147 > 0.05 we will fail to reject the null hypothesis meaning that we have enough evidence to show that the machines work as needed.

Given the average length and standard deviation of the manufactured bolts, the machine might require recalibration since the lengths produced are slightly larger than desired, and there's a wide spread in lengths. Application of the empirical rule can provide further insight about the need for machine repair. A larger sample size might give a more accurate assessment.

Given that the machine is set to manufacture bolts of 1.5 inches and a random sample of 200 bolts showed an average length of 1.521 inches with a standard deviation of 0.204 inches, it seems the machine may not be calibrated correctly. The average length is slightly larger than the desired length, a factor that may be important depending on the tolerances required for these bolts. The standard deviation is also relatively high, implying that there is a wide spread in the lengths of bolts being produced.

One way to determine if the machine needs to be repaired or not is to apply the empirical rule, also known as the 68-95-99.7 rule, which says approximately 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations in a normal distribution. In this case, it means 95% of the bolts should fall between 1.113 inches (1.521 - 2*0.204) and 1.929 inches (1.521 + 2*0.204). If these lengths are acceptable for the operation, the machine can continue working. If not, it might need to be shut down for repair.

Also, it's also worth noting that a larger sample size could provide a more accurate assessment of whether the machine is working correctly or not. While a sample size of 200 is decent, a larger sample size would reduce the margin of error from sample to population.

https://brainly.com/question/33812621

#SPJ3

Answer:

Distribute the  

1

4

 to the quantity to get:

✔ x – 6 + x = 14

Combine the like terms to get:

✔ 2x – 6 = 14

Add 6 to both sides to get:

✔ 2x = 20

x =

✔ 10

Step-by-step explanation:

i got is right so i hope it helps :)

The required solution is [tex]x=10[/tex].

Important equation:

We need to find the value of [tex]x[/tex].

The given linear equation can be written as:

[tex]\dfrac{1}{4}(4x)-\dfrac{1}{4}(24)+x=14[/tex]

[tex]x-6+x=14[/tex]

[tex]2x=14+6[/tex]

[tex]2x=20[/tex]

Divide both sides by 2.

[tex]x=\dfrac{20}{2}[/tex]

[tex]x=10[/tex]

Thus, the required solution is [tex]x=10[/tex].

Find more about 'Linear equation' here:

https://brainly.com/question/13097570

Answer:

35 miles

Step-by-step explanation:

70miles per hour x1/2 hour =35distance the car travels

Answer: The answer is C

Answer:

i assume 20 dollars per haircut

Step-by-step explanation:

i do not know what the bottom numbers stand for because there is no label

Answer:

The Answer is B. $20 per haircut.

Step-by-step explanation:

Answer:

59 inches

Step-by-step explanation:

a square has 4 equal sides

if the sum of all sides(perimeter) is 236 you can do the inverse of that and divide by 4

so your answer should be 59

Answer:

59 inches

Step-by-step explanation:

All of the 4 sides in a square are equal, and the perimeter is all the sides added together.

s+s+s+s=236

4s=236

Divide both sides by 4

s=59

Each side is 59 inches

Answer:

Correct option: (b).

Step-by-step explanation:

Effect size (η) is a statistical measure that determines the strength of the association (numerically) between two variables.  For example, if we have data on the weight of male and female candidates and we realize that, on average, males are heavier than females, the difference between the weight of male and the weight of female candidates is known as the effect size.

The larger the effect size, the larger the weight difference between male and female will be.  

Statistic effect size helps us in analyzing if the difference is factual or if it is affected by a change of factors.  

In hypothesis testing, effect size, power, sample size, and critical significance level are related to each other.

The effect size formula for a hypothesis test of mean difference is:

[tex]\eta =\frac{\bar x_{1}-\bar x_{2}}{\sqrt{s^{2}}}[/tex]

The denominator s² is combined sample variance.

[tex]s^{2}=\frac{n_{1}s_{1}^{2}+n_{2}s_{2}^{2}}{n_{1}+n_{2}-2}[/tex]

The effect size is affected by two components:

As the sample mean difference is directly proportional to the effect size, on increasing the sample mean difference value the effect size will also increase.

Ans the sample variance is inversely proportional to the the effect size, on decreasing the sample variance value the effect size will increase and vice-versa.

Thus, the correct option is (b).

sin S = [tex]$\frac{48}{73}[/tex] is the ratio found.

Step-by-step explanation:

It is given that m∠U = 90°

TS is the hypotenuse = 73 units

UT is the adjacent side of the right angle = 48 units

SU is the base of the triangle = 55 units

Now we have to find the ratio as,

sin S = [tex]$\frac{opp}{hyp}[/tex]

sin S = [tex]$\frac{UT}{TS}[/tex]

Plugin the values, we will get,

sin S = [tex]$\frac{48}{73}[/tex]

So the ratio was found.

Answer:

73/48

Step-by-step explanation:

he put it backwards

Answer:

D

Step-by-step explanation:

If you work backwards and add everything up it works.

Answer:

D

Step-by-step explanation:

Answer:

No, the citrus grower shouldn't spend the $5000 and thereby reduce the profit to $95,000 as the expected profit from doing nothing to protect the citrus plants ($96,000) is more than the profit that'll be available if $5,000 is spent on protection.

Step-by-step explanation:

First of, we compute the probability distribution of X.

X represents the profit if the citrus grower does nothing to protect the citrus fruits.

If the citrus grower does nothing, there are two possibilities as to what will happen.

1) The temperatures can drop below freezing point at a chance of 10% and the profit plummets to $60,000

2) The temperature can remain mild at a chance of 90% (100%-10%) and the profit stays at $100,000.

The probability distribution will then be

X ||||||||||||||| P(X)

60,000 ||| 0.10

100,000 | 0.90

The expected value of any probability distribution is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

E(X) = (60,000×0.10) + (100,000×0.90)

= 6,000 + 90,000 = $96,000

The expected amount of profits from doing nothing to protect the citrus fruits = $96,000

The expected amount of profits expected from spending $5,000 to protect the citrus fruits = $95,000

$96,000 > $95,000

Hence, the citrus grower is better off doing nothing to protect the citrus fruits.

Hope this Helps!!!

Answer:q(x)=-5(x+10)2-1

t(x)=-2x2-4x-3

Step-by-step explanation:

The functions that have a maximum and are transformed to the left and down of the parent function, f(x) = x2 include:

It should be noted that a function simply means a rule the shows the relationship between the variables. The variables are the dependent and the independent variables.

In order to determine whether the function will have a minimum or a maximum depending on the coefficient of the x² term. When the x² coefficient is positive, the function has a minimum and when it is negative, the function has a maximum.

In this case, the above functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2.

Learn more about functions on:

https://brainly.com/question/2833285

#SPJ2

Answer:(x,y) = (-2,2)

Step-by-step explanation:

Final answer:

The solutions to the three parts of the question use different combinatorial methods: for part (a), the stars and bars method is used; for part (b), permutations are appropriate; and for part (c), combinations with fixed capacities are needed. Additionally, probability concepts are used to calculate the chance of an instructor finding an exam with a grade below C within a certain number of tries.

Explanation:

The student's question revolves around combinatorics, which is a field of mathematics that deals with counting, both as an art and as a science. Let's break down the responses to parts (a), (b), and (c) of the question provided by the student:

Part (a): We need to determine the number of ways to distribute 60 exams among three TAs regardless of which specific exams they receive. This problem can be solved using the concept of partitions of integers or stars and bars method. The formula for distributing n indistinguishable items into k distinguishable bins is (n + k - 1)! / [n!(k - 1)!]. Here, n=60 exams, and k=3 TAs.

Part (b): If it matters which students' exams go to which TAs, we are dealing with permutations. The total ways to distribute the exams in this case is 60!, because each exam is distinct and can be assigned to each TA.

Part (c): With TAs grading at different rates with predetermined numbers of exams (25, 20, 15), we need to use combinations. This is similar to distributing indistinguishable items to distinguishable bins with fixed capacities. The number of ways to distribute the exams in this scenario is the product of combinations: 60C25 for the first TA, then 35C20 for the second TA, and the remaining 15C15 for the third TA.

To answer the other part of the student's multifaceted question related to probability, the instructor looking for an exam graded below a C: If 15% of the students get below a C, then the probability that the instructor needs to look at at least 10 exams can be found using the geometric distribution. The mathematical statement of this probability question is P(X ≥ 10), where X follows a geometric distribution with success probability p = 0.15.

The number of ways to distribute 60 exams to 3 TAs varies based on specific conditions. If only the count of exams per TA matters, there are 1891 ways. If specific exams matter, there are approximately 4.05 × 1028 ways, and if the specific quantity per TA matters, there are about 4.28 × 1016 ways.

Distribution of Exams Among TAs

Let's break down the problem into three parts:

(a) Distribution Based on Number of Exams Each TA Grades

→ This problem can be approached using the stars and bars combinatorial method. We need to distribute 60 → → indistinguishable exams to 3 TAs.

→ The formula for this is:

C(n + r - 1, r - 1) where n = 60 exams and r = 3 TAs.

C(60 + 3 - 1, 3 - 1) = C(62, 2)

→ Calculating this combination:

C(62, 2) = 62! / (2!(60!))

62! / (2! × 60!) = (62 × 61) / (2 × 1)

                       = 1891

Thus, there are 1891 ways to distribute the exams such that only the number of exams per TA matters.

(b) Distribution Where Specific Exams Matter

Now, we are interested in which specific exams go to which TA.

→ This is a permutations problem with repetition. Each of the 60 exams can go to any of the 3 TAs.

3⁶⁰

→ Calculating this value:

3⁶⁰ ≈ 4.0528564 × 10²⁸

Therefore, there are approximately 4.05 × 10²⁸ ways to distribute the specific exams to the TAs.

(c) Distribution with Specific Numbers and Specific Exams

Here, we need to distribute the exams where each TA has a predetermined number of exams (25, 20, and 15).

→ This scenario uses the multinomial coefficient:

C(60, 25, 20, 15)

→ This is calculated as:

60! / (25! 20! 15!)

→ Finding the exact value:

60! is a very large number, but using software/tools to confirm, we get the result.

Thus, there are 60! / (25! 20! 15!) ≈ 4.28 × 10¹⁶ ways to distribute the exams under these conditions.

Answer:

6

Step-by-step explanation:

3+9=12,

So since there are 2 people,

12 divided by 2 is 6.

Your answer would be 6.

9+3=12

12÷2=6

Dwight and Ellis both have 6 cards equally.

Hope this helps!!!

Answer:

(a) The 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

(b) Not reasonable.

Step-by-step explanation:

The information provided is:

n = 1000

[tex]\hat p[/tex] = 0.37

(a)

The (1 - α)% confidence interval for the population proportion p is:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

Here,

[tex]\hat p[/tex] = sample proportion

n = sample size

[tex]z_{\alpha/2}[/tex] = critical value of z.

Compute the critical value of z for 95% confidence interval as follows:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96[/tex]

*Use a z-table for the value.

Compute the 95% confidence interval for the population proportion p as follows:

[tex]CI=\hat p\pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

     [tex]=0.37\pm 1.96\times\sqrt{\frac{0.37(1-0.37)}{1000}}[/tex]

     [tex]=0.37\pm 0.03\\=(0.34, 0.40)[/tex]

Thus, the 95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

(b)

Now we need to determine whether it is reasonable to believe that the actual percent of people in the United States whose favorite sport to watch on television is American football is 33%.

The hypothesis can be defined as:

H₀: The percentage of people in the United States whose favorite sport to watch on television is American football is 33%, i.e. p = 0.33.

Hₐ: The percentage of people in the United States whose favorite sport to watch on television is American football is different from 33%, i.e. p ≠ 0.33

The hypothesis can be tested based on a confidence interval.

The decision rule:

If the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will not be rejected. And if the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will be rejected.

The 95 confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

The confidence interval does includes the null value of p, i.e. 0.33.

So, the null hypothesis will be rejected.

Hence, concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football.

95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

Concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football

Given that,

A recent survey collected information on television viewing habits from a random sample of 1,000 people in the United States.

Of those sampled, 37 percent indicated that their favorite sport to watch on television was American football.

We have to determine,

Construct and interpret a 95 percent confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football.

According to the question,

Sample proportion p = 37% = 0.37

Sample space n = 1000

[tex]C.I. = P \pm Z_\frac{\alpha}{2} \sqrt{\dfrac{p(1-p)}{n} }[/tex]

To compute the critical value of z for 95% confidence interval as follows:

[tex]z_\frac{ \alpha}{2} = z_\frac{0.05}{2} = 1.96[/tex]

By using a z-table for the value.

Compute the 95% confidence interval for the population proportion p as follows:

[tex]C.I. = p\pm Z_\frac{\alpha}{2} \sqrt{\dfrac{p(1-p)}{n} }\\\\C.I. = 0.37\pm 1.96 \sqrt{\dfrac{0.43(1-0.34)}{1000} }\\\\C.I.= 0.03 \pm 0.09\\\\C.I. = (0.34, \ 0.40)[/tex]

Hence,  95% confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

H₀: The percentage of people in the United States whose favorite sport to watch on television is American football is 33%, i.e. p = 0.33.

Hₐ: The percentage of people in the United States whose favorite sport to watch on television is American football is different from 33%, i.e. p ≠ 0.33

The hypothesis can be tested based on a confidence interval.

The (1 - α)% confidence interval includes the null value of the test then the null hypothesis will not be rejected.

And if the (1 - α)% confidence interval includes the null value of the test then the null hypothesis will be rejected.

The 95 confidence interval for the proportion of all people in the United States who would indicate that their favorite sport to watch on television is American football is (0.34, 0.40).

The confidence interval does includes the null value of p, i.e. 0.33.

So, the null hypothesis will be rejected.

Hence, Concluding that is is not reasonable to believe that 33% is the actual percent of people in the United States whose favorite sport to watch on television is American football

To know more about Probability click the link given below.

https://brainly.com/question/15694157

Answer:

740°

Step-by-step explanation:

2 *360° + 20° = 720° + 20° = 740°

Answer:

4×107 = 428

428-(5×4) =

428-20= 408

Answer:

Cross section

Step-by-step explanation:

Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.

It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.

Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.

Answer:

[tex]z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795[/tex]  

[tex]p_v =2*P(Z>2.795)= 0.005[/tex]  

So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.  

Step-by-step explanation:

Data given and notation  

[tex]X_{1}=74[/tex] represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

[tex]X_{2}=70[/tex] represent the number of people suburban residents are in favor

[tex]n_{1}=100[/tex] sample 1 selected

[tex]n_{2}=125[/tex] sample 2 selected

[tex]p_{1}=\frac{74}{100}=0.74[/tex] represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

[tex]p_{2}=\frac{70}{125}=0.56[/tex] represent the proportion of suburban residents are in favor

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the value for the test (variable of interest)

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:  

Null hypothesis:[tex]p_{1} = p_{2}[/tex]  

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]  

We need to apply a z test to compare proportions, and the statistic is given by:  

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64[/tex]

Calculate the statistic

Replacing in formula (1) the values obtained we got this:  

[tex]z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795[/tex]  

Statistical decision

The significance level provided is [tex]\alpha=0.05[/tex] ,and we can calculate the p value for this test.  

Since is a two tailed test the p value would be:  

[tex]p_v =2*P(Z>2.795)= 0.005[/tex]  

So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.  

Answer: 25

Step-by-step explanation:

Answer:

What is the probability that a randomly selected string with exactly ten characters results in a valid password?  = 0.02836

Step-by-step explanation:

CHECK THE ATTACHMENT BELOOW

Final answer:

The probability of a randomly selected string with exactly ten characters resulting in a valid password can be determined using combinatorics. The probability is given by (62! / (52!*10!)) / (62^10)

Explanation:

To find the probability of a randomly selected string with exactly ten characters resulting in a valid password, we need to determine how many valid passwords exist out of all possible strings of length ten. Since the password must contain at least one character from each of the three sets (upper-case letters, lower-case letters, and digits), we can calculate the probability using combinatorics.

There are 26 upper-case letters, 26 lower-case letters, and 10 digits, so the total number of characters in the union of the three sets is 26 + 26 + 10 = 62.

The probability of selecting a valid password is then:

P(valid password) = (Number of valid passwords) / (Total number of passwords)

For a valid password, the first character can be any of the 62 characters, the second character can be any of the remaining 61 characters, and so on. Therefore, the number of valid passwords is: 62 * 61 * 60 * ... * 53.

Since there are 10 characters in a valid password, the number of valid passwords is:

62 * 61 * 60 * ... * 53 = 62! / (52!*10!).

The total number of passwords of length 10 is: 62^10.

Therefore, the probability of a randomly selected string with exactly ten characters resulting in a valid password is:

P(valid password) = (62! / (52!*10!)) / (62^10).

Answer:

decay

Step-by-step explanation:

Answer:

khan

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Given that M is directly proportional to r³ then the equation relating them is

M = kr³  ← k is the constant of proportion

To find k use the condition when r = 4, M = 160, thus

160 = k × 4³ = 64k ( divide both sides by 64 )

2.5 = k

M = 2.5r³ ← equation of variation

(a)

When r = 2, then

M = 2.5 × 2³ = 2.5 × 8 = 20

(b)

When M = 540, then

540 = 2.5r³ ( divide both sides by 2.5 )_

216 = r³ ( take the cube root of both sides )

r = [tex]\sqrt[3]{216}[/tex] = 6

The task involves summarizing previous answers and reflecting upon them using a paragraph planner to organize and provide clarity to the response. This process aids in addressing the questions effectively and personally.

To approach the task at hand, one must begin by summarizing the answers provided previously. It is essential to distill the content into a coherent summary that accurately represents the experiences and advice shared. Upon doing so, reflection on these insights will lead to a personal understanding that is both informed and enriched by the various perspectives.

An effective strategy for this analysis is to use a paragraph planner. This tool assists in organizing thoughts and structuring the response in a logical and clear manner. By leveraging such a planner, the responses to the posed questions will not only address the directly asked matters but also encapsulate a broader interpretation of the information received.

Tonight's endeavor is to answer critical questions that resonate with the audience's collective curiosity. This act of addressing inquiries serves as a bridge between the speaker and the listener, fostering a shared understanding and grounding the conversation in mutual interests and concerns.

Answer:

Yes. There is enough evidence to support the claim that the GSR for all scholarship athletes in this division differs from 62%.

Step-by-step explanation:

We have to perform a hypothesis test on a proportion.

The claim is that the GSR for all scholarship athletes in this division differs from 62%. Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.62\\\\H_a:\pi<0.62[/tex]

The significance level, named here as Type I error rate, is 0.05.

The sample size is n=500.

The sample proportion is:

[tex]p=X/n=285/500=0.57[/tex]

The standard deviation of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62(1-0.62)}{500}}=\sqrt{0.0004712}=0.022[/tex]

The z-statistic is then:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/500}{0.022}=\dfrac{-0.049}{0.022} = -2.227[/tex]

The P-value for this left tailed test is:

[tex]P-value=P(z<-2.227)=0.013[/tex]

The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

There is enough evidence to support the claim that the GSR for all scholarship athletes in this division differs from 62%.

Answer:

[tex]z=\frac{0.57 -0.62}{\sqrt{\frac{0.62(1-0.62)}{500}}}=-2.303[/tex]  

[tex]p_v =2*P(z<-2.303)=0.0213[/tex]  

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of student athletes who graduate within 6 years is significantly different from 0.62 or 62%

Step-by-step explanation:

Data given and notation

n=500 represent the random sample taken

X=285 represent the student athletes who graduate within 6 years

[tex]\hat p=\frac{285}{500}=0.57[/tex] estimated proportion of student athletes who graduate within 6 years

[tex]p_o=0.62[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that true proportion differs from 0.62.:  

Null hypothesis:[tex]p=0.62[/tex]  

Alternative hypothesis:[tex]p \neq 0.62[/tex]  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.57 -0.62}{\sqrt{\frac{0.62(1-0.62)}{500}}}=-2.303[/tex]  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z<-2.303)=0.0213[/tex]  

So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of student athletes who graduate within 6 years is significantly different from 0.62 or 62%

Answer:

I believe its 84

Step-by-step explanation:

6 multiplied by 14