Given the following list of the number of paintings randomly selected art students created during a watercolor class, find the median.
21,28,30,31,17,16,12

Answer:

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha < 0.50

z = -3.16

P value = P(Z<-3.16) =  0.0008

Decision we reject the null hypothesis and accept the alternative hypothesis. That is, there is convincing evidence that fewer than half of adult Americans would favor the drafting of women.

Rule

If;

P-value > significance level  --- accept Null hypothesis

P-value < significance level  --- reject Null hypothesis

Z score > Z(at 95% confidence interval) ---- reject Null hypothesis

Z score < Z(at 95% confidence interval) ------ accept Null hypothesis

Step-by-step explanation:

Given;

n=1000 represent the random sample taken

Null hypothesis: H0 = 0.50

Alternative hypothesis: Ha < 0.50

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 1000

po = Null hypothesized value = 0.50

p^ = Observed proportion = 0.45

Substituting the values we have

z = (0.45-0.50)/√{0.50(1-0.50)/1000}

z = -3.16

z = -3.16

To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.

P value = P(Z<-3.16) =  0.0008

Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = -3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.

Answer: Miles ran by Matt = 6 miles

Step-by-step explanation: Miles ran by Stan = 4 7/10

i.e. 1 3/10 miles less than Matt.

∴ Miles ran by Matt = 4 7/10 + 1 3/10 = 60/10 = 6miles

∴ Miles ran by Matt = 6 miles

Answer:

The answer is A Mollys work

Step-by-step explanation:

I just did the work, and also it says "Fewer" which is subtraction but you need to change the subtraction to addition. And the answer is 6.

I hope this helps! <Dekomori Sanae(Engilish way to say it)/Sane Dekomori(Japanease way to say it)

Answer:

The cutoff score for recruitment by the statistics department is 675.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

[tex]\mu = 500, \sigma = 100[/tex]

Cutoff score for the top 4%.

100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.

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

[tex]1.75 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = 1.75*100[/tex]

[tex]X = 675[/tex]

The cutoff score for recruitment by the statistics department is 675.

The SAT math scores have a mean of 500 and a standard deviation of 100, and using the z-score for the 96th percentile (approximately 1.75), we calculate the cutoff score.

The SAT mathematics exam scores are normally distributed with a mean (μ) of 500 and a standard deviation (σ) of 100. To find the cutoff score for the top 4%, we need to determine the z-score that corresponds to the 96th percentile (since 100% - 4% = 96%).

Using a z-table or calculator, the z-score for the 96th percentile is approximately 1.75. We can use the formula for the z-score:

Z = (X - μ) / σ

Solving for X (the cutoff score), we get:

1.75 = (X - 500) / 100

X - 500 = 1.75 × 100

X - 500 = 175

X = 675

Therefore, the cutoff score for recruitment by the statistics department is approximately 675. This means students need to score about 675 or higher on the SAT mathematics exam to be in the top 4%.

Answer:

(-4, 0)

Step-by-step explanation:

We just need to identify where it is on both the x and y axis!

X Axis - Horizontal middle line.

Y Axis - Vertical middle line.

On the x-axis, you can see it is at -4, therefore we know our x is that.

On the y-axis, you can see it hasn't gone up or down from the vertex, showing us that it has neither gone up or down, so it is 0!

Answer:

a) [tex]46.14-3.707\frac{1.19}{\sqrt{7}}=44.47[/tex]    

[tex]46.14+3.707\frac{1.19}{\sqrt{7}}=47.81[/tex]    

b) For this case the upper limit for the confidence interval is lower than 48 so then at 1% of significance we can't conclude that the claim given is true.

c) [tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]

If we reduce the sample size from 30 to 10 we will have an interval wider since the margin of error would be larger

Step-by-step explanation:

Data given

[tex]\bar X=46.14[/tex] represent the sample mean

[tex]\mu[/tex] population mean

s=1.19 represent the sample standard deviation

n=7 represent the sample size  

Part a

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]

The Confidence level is 0.99 or 99%, the significance would be [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical value for this case is [tex]t_{\alpha/2}=3.707[/tex]

Replacing we got:

[tex]46.14-3.707\frac{1.19}{\sqrt{7}}=44.47[/tex]    

[tex]46.14+3.707\frac{1.19}{\sqrt{7}}=47.81[/tex]    

Part b

For this case the upper limit for the confidence interval is lower than 48 so then at 1% of significance we can't conclude that the claim given is true.

Part c

For this case we need to take in count that the margin of error is given by:

[tex] ME = t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]

If we reduce the sample size from 30 to 10 we will have an interval wider since the margin of error would be larger

Answer: C

Step-by-step explanation:

The population for the survey is all people who surf at Breakers Point. And Micah will not get a representative sample. Then the correct options are C and D.

In order to gather information about a service, product, or process, a survey is described as an act of looking at a process or questioning a predetermined sample of people. Surveys used to gather data ask a specific set of people about their beliefs, actions, or knowledge.

Surveys are research techniques used to gather data from a designated group of respondents in order to learn more and acquire insights into a range of interesting topics. Depending on the methodology chosen and the objective of the study, they can be conducted in a variety of methods and serve a variety of objectives.

The population for the survey is all people who surf at Breakers Point. And Micah will not get a representative sample. Then the correct options are C and D.

More about the survey link is given below.

https://brainly.com/question/17373064

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Answer:

96 on edg

Step-by-step explanation:

Answer:

96mm2 on Edge 2021

It maybe wrong if your not on edge depends on what the teachers think, lol.

Answer:

The height of tree house is 70.71 feet

Step-by-step explanation:

We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground

Refer the attached figure

Length of rope AC = Hypotenuse =100 feet

The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =[tex]\angle ACB = 45^{\circ}[/tex]

We are supposed to find the height of tree house i.e.AB = Perpendicular

So, Using trigonometric ratio

[tex]Sin \theta = \frac{perpendicular}{Hypotenuse}\\Sin 45= \frac{AB}{AC}\\\frac{1}{\sqrt{2}}=\frac{AB}{100}\\100 \times \frac{1}{\sqrt{2}}=AB\\70.71=AB[/tex]

Hence The height of tree house is 70.71 feet

Answer:

Step-by-step explanation:

the volume of the prism is the amount of space inside the figure.

120 cubes fit inside the prism, so the figure has a volume of 120 square unite

Answer:

1. B 2. C

Step-by-step explanation:

Answer:

7 + x + 4y

(7 + x) + 4y

x + (7 + 4y)

Step-by-step explanation:

the sum of elements does not change, no matter the order.

Answer:

864 square inches

Step-by-step explanation:

To solve this problem, first we need to know the area of each side of the cube(since the shrink wrap will cover these sides) :

The area of each side is A=[tex]L^{2}[/tex] where L is the length of the side. In this case, L= 4 inches.

Thus, the area of each side is [tex]A=L^{2}=4^{2} =16[/tex] square inches.

However, the cube has 6 sides so we have to multiply the area of each side by 6, this gives us [tex](16)(6)= 96[/tex] square inches. Thus, we need 96 square inches of shrink wrap for each cube.

Now, we have nine cubes, so we have to multiply those 96 square inches by 9, [tex](96)(9)= 864[/tex].

Thus, we need 864 square inches of shrink wrap to wrap 9 cubes.

Final answer:

At a 5% significance level, we can conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%. Both the p-value and critical-value approaches lead to the same conclusion.

Explanation:

To determine whether the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%, we will perform a hypothesis test using both the p-value and the critical-value approaches.

P-Value Approach:

Critical-Value Approach:

Answer:

The beach ball can hold 523.33 cubic inches of air

Step-by-step explanation:

Diameter of beach ball = 10 inches

Radius of beach ball =[tex]\frac{10}{2}= 5 inches[/tex]

We are supposed to find  How many cubic inches of air can the beach ball hold

Volume of sphere = [tex]\frac{4}{3} \pi r^3[/tex]

Where r is the radius

So, volume of sphere = [tex]\frac{4}{3} \times 3.14 \times 5^3=523.333 in^3[/tex]

Hence The beach ball can hold 523.33 cubic inches of air

Answer:

523.33

Step-by-step explanation:

9514 1404 393

Answer:

  1/9

Step-by-step explanation:

Carol can roll a total of 7 in two ways: 3 +4 or 4 + 3.

Two of the six faces are marked with 3, so the probability of rolling a 3 is 2/6 = 1/3. One of the six faces is marked with 4, so the probability of rolling a 4 is 1/6.

Then the probability of rolling a 3, then 4 is (1/3)(1/6) = 1/18. Similarly, the probability of rolling a 4, then 3 is (1/6)(1/3) = 1/18. These are presumed independent so the probability of one or the other of these outcomes is ...

  1/18 +1/18 = 1/9

The probability that the sum is exactly 7 after two rolls is 1/9.

Answer:

We have the function:

r = -3 + 4*cos(θ)

And we want to find the value of θ where we have the maximum value of r.

For this, we can see that the cosine function has a positive coeficient, so when the cosine function has a maximum, also does the value of r.

We know that the meaximum value of the cosine is 1, and it happens when:

θ = 2n*pi, for any integer value of n.

Then the answer is  θ = 2n*pi, in this point we have:

r = -3 + 4*cos (2n*pi) = -3 + 4 = 1

The maximum value of r is 7

(while you may have a biger, in magnitude, value for r if you select the negative solutions for the cosine, you need to remember that the radius must be always a positive number)

Answer:

the correct answer is d.pi

Step-by-step explanation:

I just took the quiz

Answer:

Step-by-step explanation:

The question is incomplete. The missing part is shown in the comment box.

Mean = (697 + 759 + 1266 + 621 + 569 + 432)/6 = 724

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (697 - 724)^2 + (759 - 724)^2 + (1266 - 724)^2+ (621 - 724)^2 + (569 - 724)^2 + (432 - 724)^2 = 415616

Standard deviation = √415616/6 = 263.2

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 1000

For the alternative hypothesis,

µ > 1000

It is a right tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t. The test statistic, t would be calculated with the formula below

Since n = 6

Degrees of freedom, df = n - 1 = 6 - 1 = 5

t = (x - µ)/(s/√n)

Where

x = sample mean = 724

µ = population mean = 1000

s = samples standard deviation = 263.2

t = (724 - 1000)/(263.2/√6) = - 2.57

We would determine the p value using the t test calculator. It becomes

p = 0.025

From the t distribution table, the critical value is 2.571

Since alpha, 0.05 > than the p value, 0.025, then we would reject the null hypothesis.

Therefore, at a 5% level of significance, the results do not suggest that all of the child booster seats meet the specified​ requirement.

The results suggests that the safety requirement for the hic measurement should be more than 1000 hic.

Answer:

3/6

Step-by-step explanation:

there are 6 sides: 3 odd and 3 even numbers

if you need to find the probability of rolling an odd number, take the number of odd possibilities and form a fraction with the number of total sides, 6.

so, 3/6 Or 1/2

Answer:

It would most likely be a 3 out of 6 chance per roll

Step-by-step explanation

With each roll there is a 50% percent chance of getting an odd number

Answer:

$ 63.75

Step-by-step explanation:

Final answer:

The sale price of a $75 iPod with a 15% discount is calculated by determining the discount amount ($11.25) and subtracting it from the original price, resulting in a sale price of $63.75. A similar calculation method is used to find the total cost of an $85 jacket with 7.5% sales tax, totaling $91.38.

Explanation:

To calculate the sale price of an iPod that originally costs $75 with a 15% discount, we first need to calculate the amount of the discount. To do this, multiply the original price of $75 by the discount rate of 15%.

$75 × 0.15 = $11.25

Now, subtract the discount from the original price to find the sale price:

$75 - $11.25 = $63.75

So, the sale price of the iPod is $63.75.

To illustrate using a similar example, let's imagine Emily purchased a jacket for $85 and needs to calculate the total cost including a 7.5% sales tax. First, find the amount of the sales tax by multiplying the cost of the jacket by the tax rate:

$85 × 0.075 = $6.38

Then, add the sales tax to the original price of the jacket to find the total cost:

$85 + $6.38 = $91.38

Therefore, the total cost of the jacket, including tax, is $91.38.

Answer:

x = 30

Step-by-step explanation:

Answer: one third of a chance

Step-by-step explanation:

The probability that she will select a pencil and a cap that is the same color is 1/4 option (C) 1/4 is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Mechanical pencil: 1 red, 1 green, 1 blue

Erase cap: 1 red, 1 green, 1 blue, and 1 yellow.

P(both red) = (1/3)x(1/4) = 1/12

P(both green) = (1/3)x(1/4) = 1/12

P(both blue) = (1/3)x(1/4) = 1/12

P(same colour) = 1/12 + 1/12 + 1/12 = 3/12 = 1/4

Thus, the probability that she will select a pencil and a cap that is the same color is 1/4 option (C) 1/4 is correct.

Learn more about the probability here:

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Answer:

  B.  More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.

Step-by-step explanation:

In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.

The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches any isosceles trapezoid.

Answer:

  (c)  On a coordinate plane, a dashed straight line has a negative slope and goes through (0, 3) and (2, 0). Everything to the left of the line is shaded.

Step-by-step explanation:

You want a description of the graph of 6x +4y < 12.

The x-intercept will be the solution to ...

  6x = 12   ⇒   x = 2, point (2, 0)

The y-intercept will be the solution to ...

  4y = 12   ⇒   y = 3, point (0, 3)

The form of the inequality ...

  x < ( )

tells you the shading is left of the line, and the line is dashed. That is, solution set values of x are less than those on the line. The "or equal to" case is not included, so the line is not included in the solution set.

Answer: The percentage of adults that have a blodd pressure less than 125 mmHg is 15.87%

Step-by-step explanation:

In a normal distribution, we have that in the range:

(-∞, M) we have a 50%

(M, ∞) we have the other 50%.

(the infinite symbols are for notation, obviusly you can not have negative blood pressure)

where M is the mean.

If SD is the standard deviation, in the range

(M - SD, M) we have a 34.13%

Now, the values we have are: M = 134 mmHg, SD = 9mmHg

Then we can replace those values and get:

(M - SD, M) = (125mmHg, 134mmHg) = 34.13%

The range of blodd presure that is smaller than

Then, the range of blood pressure smaller than 125mmHg is the range between (-∞, 125mmHg)

We can calculate this proportion as:

(-∞. 134mmHg) - ( 125mmHg, 134mmHg) = 50% - 34.13% = 15.87%

The percentage of adults that have a blodd pressure less than 125 mmHg is 15.87%

The percentage of adults in the town of Bridgeport with a systolic blood pressure less than 125 mmHg is approximately 15.87%.

In this question, we are given that the systolic blood pressure of adults in the town of Bridgeport is normally distributed with a mean of 134 mmHg and a standard deviation of 9 mmHg.

We need to find the percentage of adults in the town who have a systolic blood pressure less than 125 mmHg.

To solve this, we can standardize the given value of 125 mmHg using the formula z = (x - μ) / σ, where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

Substituting the given values, we have z = (125 - 134) / 9 = -1. Here, we are interested in finding the area to the left of this z-score on the standard normal distribution curve.

Using a standard normal distribution table or a calculator, we can find that the percentage of adults in the town with a systolic blood pressure less than 125 mmHg is approximately 15.87%.

Learn more about Systolic blood pressure here:

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Answer:

Step-by-step explanation:

We assume you want to compare your expression to the form ...

  a(x -h)² +k

  1/2(x +1)² +k

The multiplier outside parentheses is ...

  a = 1/2

The horizontal offset inside parentheses is ...

  -h = 1

  h = -1

The vertical offset outside parentheses is ...

  k = -3

Answer:21

Step-by-step explanation:

To evaluate 6ab with a = 1/2 and b = 7, you multiply 6 by 1/2 to get 3, and then multiply that by 7 to get 21, which is the final answer.

To evaluate the expression 6ab when a = 1/2 and b = 7, you substitute the given values for a and b into the expression. This means you would multiply 6 by 1/2 and then by 7. The operation looks like this: 6 × (1/2) × 7.

First, simplify 6 × (1/2), which equals 3. Then multiply this result by 7, giving you 3 × 7 = 21.

Therefore, when a = 1/2 and b = 7, the expression 6ab evaluates to 21.

Answer:

The Answer Is D

Step-by-step explanation:

I Juss Took It

Answer:

13.98 degrees

Step-by-step explanation:

Let the airplane be at point A, the airport at point B and the point of overshoot, point C.

If the plane is on path AC and the pilot wants to adjust to the path AB, the angle by which the pilot will adjust the airplane heading is the angle between AB and AC which is A.

Using Cosine Rule

[tex]Cos A=\dfrac{b^2+c^2-a^2}{2bc} \\Cos A=\dfrac{65^2+60^2-16^2}{2(65)(60)} \\Cos A=0.9704\\A=arcCos (0.9704)\\\angle A=13.98^\circ[/tex]

The pilot should adjust the plane's heading by 13.98 degrees.

isolate m by subtracting 110 on both sides.

125=m+110

-110      -110

15=m