Assume a simple random sample of 10 BMIs with a standard deviation of 1.186 is selected from a normally distributed population of recent Miss America winners. Use 0.01 significance level to test the claim that the BMI for recent Miss America winners are from a population with standard deviation of 1.34.
A. Identify the null hypothesis and the alternative hypothesis.
B. Find the critical value or values.
C. Find the test statistic.
D. State the conclusion that addresses the original claim.

Answer:

Read below

Step-by-step explanation:

To graph the inequality, place an open circle on -2.5 because there is no line under the > sign. Draw the arrow pointing to the right because the inequality reads "x is greater than -2.5.

As for the check box questions, only B and C should be checked. The arrow points right, and the circle is open.

Answer:

Step-by-step explanation:

no          x                y                   xy                               x²

1           2300         74             170200                      5290000

2          1800          73             131400                      3240000

3          2500         70             175000                     6250000

4          2700         66             178200                     7290000

5          2000         63             126000                     4000000

6          1700          62             105400                     2890000

7           1500         52              78000                      2250000

8           2700        68              183600                    7290000

Total   17200         528           1147800                   38500000

Mean of x is

[tex]\bar x = \frac{17200}{8} =2150[/tex]

Mean of y is

[tex]\bar y = \frac{528}{8} =66[/tex]

From the table above

we find [tex]\hat B_1[/tex]

[tex]\hat B_1=\frac{\sum xy- \bar x \sum y}{\sum x^2- n \barx^2} \\\\=\frac{1147800-2150(528)}{38500000-8(2150)^2} \\\\=\frac{1147800-1135200}{38500000-36980000} \\\\=\frac{12600}{1520000} \\\\=0.008289[/tex]

so [tex]\hat b_0[/tex] is

[tex]\hat b_0=\bar y-\bar B_1 x\\\\=66-0.008289(2150)\\\\=66-17.82135\\\\=48.17865[/tex]

The line of regression is

The price x is 1900

[tex]\hat y =\hat B_0+\hat B_1x\\\\=48.17865+0.008289\times1900\\\\=48.17865+15.7491\\\\=63.928[/tex]

The line of regression is 63.928

Answer:

y=48.2+0.00829x;64

Step-by-step explanation:

Answer: choice B

Step-by-step explanation:

The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x-axis.

Answer: B

Step-by-step explanation:

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

[tex]\mu = 80, \sigma = 6.5[/tex]

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

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

[tex]Z = \frac{90 - 80}{6.5}[/tex]

[tex]Z = 1.54[/tex]

[tex]Z = 1.54[/tex] has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

Answer:

[tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

Step-by-step explanation:

The objective is to find the moment generating  function of  [tex]M_{X+Y}(t) \ of \ X+Y[/tex].

We are being informed that the fair die is rolled twice;

So; X to be the value for the  first roll

Y to be the value of the second roll

The outcomes  of X are:  X = {1,2,3,4,5,6}

Where ;

[tex]P (X=x) = \dfrac{1}{6}[/tex]

The outcomes  of Y are:  y = {1,2,3,4,5,6}

Where ;

[tex]P (Y=y) = \dfrac{1}{6}[/tex]

The outcome of Z = X+Y

[tex]= \left[\begin{array}{cccccc}(1,1)&(1,2)&(1,3)&(1,4)&(1,5)&(1,6)\\ (2,1)&(2,2)&(2,3)&(2,4)&(2,5)&(2,6)\\ (3,1)&(3,2)&(3,3)&(3,4)&(3,5)&(3,6) \\ (4,1)&(4,2)&(4,3)&(4,4)&(4,5)&(4,6) \\ (5,1)&(5,2)&(5,3)&(5,4)&(5,5)&(5,6) \\ (6,1)&(6,2)&(6,3)&(6,4)&(6,5)&(6,6) \end{array}\right][/tex]

= [2,3,4,5,6,7,8,9,10,11,12]

Here;

[tex]P (Z=z) = \dfrac{1}{36}[/tex]

∴ the moment generating function [tex]M_{X+Y}(t) \ of \ X+Y[/tex]is as follows:

[tex]M_{X+Y}(t) \ of \ X+Y[/tex] = [tex]E(e^{t(X+Y)}) = E(e^{tz})[/tex]

⇒ [tex]\sum \limits^{12}_ {z=2 } et ^z \ P(Z=z)[/tex]

= [tex]\mathbf{\dfrac{e^{2t}}{36} + \dfrac{e^{3t}}{18} + \dfrac{e^{4t}}{12} +\dfrac{e^{5t}}{9} + \dfrac{5e^{6t}}{36} + \dfrac{7e^{7t}}{6} + \dfrac{5e^{8t}}{36} + \dfrac{e^{9t}}{9} + \dfrac{e^{10t}}{12} + \dfrac{e^{11t}}{18} + \dfrac{e^{12t}}{36} }[/tex]

Answer:

3768 mm ^ 3

Step-by-step explanation:

We have that the volume of a cone is given by:

V = 1/3 * Ac * h

Where Ac is the area of the circle, we know that the radius is half the diameter then:

r = d / 2

r = 12/2

r = 6

And Ac is equal to:

Ac = pi * r ^ 2

replacing:

Ac = 3.14 * 6 ^ 2

Ac = 113.04

113.04 mm ^ 2 is the area of the circle, replacing the volume form knowing that h = 100

V = 1/3 * 113.04 * 100

V = 3768

Therefore they fit a total of 3768 mm ^ 3

Answer:

The correct answer is letter c. Josh had 24 games and Peter had 32 by the end of the week.

Step-by-step explanation:

We know that Josh has a total of 32 games, while that value is 133% as many as Peter's, therefore the number of games Peter had at the beginning of the week is:

[tex]josh = \frac{133}{100}*peter\\peter = \frac{josh}{1.33}\\peter = \frac{32}{1.33}\\peter = 24.06[/tex]

At the beginning of the week Peter had 24 games. At the end of the week Josh gave Peter 25% of his games, therefore Peter's total is:

[tex]peter = 24 + 0.25*josh\\peter = 24 + 0.25*32\\peter = 24 + 8 = 32[/tex]

While Josh had:

[tex]josh = 32 - 8 = 24[/tex]

The correct answer is letter c.

Answer:

The 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).

Step-by-step explanation:

The complete question is:

Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.8 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?

Solution:

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

[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]\bar x=24\\\sigma=0.8\\n=49\\\text{Confidence Level}=95\%[/tex]

The critical value of z for 95% confidence level is:

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

*Use a z-table.

Compute the 95% confidence interval for the mean number of ounces of ketchup per bottle as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=24\pm1.96\cdot \frac{0.80}{\sqrt{49}}\\\\=24\pm 0.224\\\\=(23.776, 24.224)\\\\\approx (23.8, 24.2)[/tex]

Thus, the 95% confidence interval for the mean number of ounces of ketchup bottle is (23.8, 24.2).

Answer:

The equation of the plane is

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 7y - 5z + 13 = 0

Step-by-step explanation:

Given 3 points, P(x₁, y₁, z₁), Q(x₂, y₂, z₂), and R(x₃, y₃, z₃).

We can calculate the equation of the plane through those points as

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0, where (x₀, y₀, z₀) are the coordinates of any one of the points P, Q, or R, and <a,b,c> is a vector perpendicular to the plane.

The vector perpendicular to the plane is obtained by writing vector PQ and PR and taking the cross or vector product.

For this question,

P = (5, 4, 5)

Q = (-5, -1, -4)

R = (-2, 1, -2)

PQ = (-5, -1, -4) - (5, 4, 5) = (-10, -5, -9)

= (-10î - 5ĵ - 9ķ)

PR = (-2, 1, -2) - (5, 4, 5) = (-7, -3, -7)

= (-7î - 3ĵ - 7ķ)

PQ × PR is then

| î ĵ ķ |

|-10 -5 -9|

|-7 -3 -7|

= î [(-5×-7) - (-9×-3)] - ĵ [(-10×-7) - (-9×-7)] + ķ [(-10×-3) - (-7×-5)]

= î (35 - 27) - ĵ (70 - 63) + ķ (30 - 35)

= 8î - 7ĵ - 5ķ

Hence, (a, b, c) = (8, -7, -5)

And using point P as (x₀, y₀, z₀) = (5, 4, 5)

The equation of the plane is

a(x - x₀) + b(y - y₀) + c(z - z₀) = 0

8(x - 5) - 7(y - 4) - 5(z - 5) = 0

8x - 40 - 7y + 28 - 5z + 25 = 0

8x - 7y - 5z = 40 - 28 - 25 = -13

8x - 7y - 5z + 13 = 0

Hope this Helps!!!

Answer:

y = -2x - 10

Step-by-step explanation:

1. rearrange to find the gradient.

the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.

2. substitute into y - y1 = m (x - x1)

y - (-2) = -2 (x - (-4))

y = -2x - 10

Answer:

y + 6 = -3(x - 1) - Point Slope

y=-x+8 - Slope Intercept

2x - 5y = 9 - Standard

Step-by-step explanation:

Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]

y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.

Slope-intercept form is: [tex]y=mx+b[/tex]

y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.

This only leaves 2x - 5y = 9, which is in standard form.

All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

All the expressions are,

1) y = -x + 8  

2) 2x - 5y = 9  

3) y + 6 = -3(x - 1)

Now, All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

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Answer:

The probability that the student is in high school and has visited a foreign country is 0.18.

Step-by-step explanation:

We are given that in a survey of students, 60% were in high school and 40% were in middle school.

Of the high school students, 30% had visited a foreign country.

Let the Probability that students were in high school = P(H) = 60%

Probability that students were in middle school = P(M) = 40%

Also, let F = event that students had had visited a foreign country

So, Probability that high school students had visited a foreign country = P(F/H) = 30%

Now, probability that the student is in high school and has visited a foreign country is given by = Probability that students were in high school [tex]\times[/tex] Probability that high school students had visited a foreign country  

            =  P(H)  [tex]\times[/tex]  P(F/H)

            =  0.60  [tex]\times[/tex]  0.30

            =  0.18 or 18%

Answer:

Step-by-step explanation:

Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.

Each group is 4 items, so 152/4 = 38 groups were sold.

In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.

114 sodas and 38 hot dogs were sold.

Answer:

Cost of visit = 50 + 100n

Step-by-step explanation:

$50 is the set price of the visit.

$100 is the cost per cavity.

N is the number of cavities.

Since we don't know the number of cavities, 'n' will fill that spot.

100 x n will be the total cavity cost.

Cavity cost + set price of visit will equal the total cost of the visit.

Answer:

y= 2x+1

Step-by-step explanation:

Points:

Form of the line:

Finding the slope:

Line is now:

Using one of the given points to find out the value of b:

So the equation for the line is:

Answer:

a) CI = (113,637.5  ,  124,672.5)

b) CI = (112,581  ,  125,729)

c) CI = (110,501.4  ,  127,808.6)

Step-by-step explanation:

You have the following information:

[tex]\overline{x}[/tex]: mean annual household income = 119,155

σ: standard deviation = 30,000

n: sample = 80

The interval of confidence is given by the following expression:

[tex]\overline{x}\pm Z_{\alpha/s}(\frac{\sigma}{\sqrt{n}})[/tex]

Z_α/2: distribution density factor

where α and Z_α/2 are given by the range of the confidence interval.

a) For a 90% confidence interval you have:

α = 1 - 0.9 = 0.1

Z_0.1/2 = Z_0.05 = 1.645   (found in a table of normal distribution)

You replace in the equation (1) to obtain the confidence interval:

[tex]119,155\pm (1.645)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm5,517.5[/tex]

Then, the confidence interval is (119,155 + 5,517.5 , 119,155 - 5,517.5  )

= (113,637.5  ,  124,672.5)

b) For a 95% confidence interval you have:

α = 1 - 0.95 = 0.05

Z_0.05/2 = Z_0.025 = 1.96

[tex]119,155\pm (1.96)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 6,574.0[/tex]

The confidence interval is (112,581  ,  125,729)

c) For a 99% confidence interval:

α = 1 - 0.99 = 0.01

Z_0.01/2 = Z_0.005 = 2.58

[tex]119,155\pm (2.58)(\frac{30,000}{\sqrt{80}})\\\\=119,155\pm 8,653.6[/tex]

The confidence interval is (110,501.4  ,  127,808.6)

d) When the confidence level increases the width of the confidence increases too. This can be noticed in the normal distribution, when the confidence level is higher, the area of the tails is reduced, and so, the confidence interval is higher.

Answer:

1, 5, 25, 125, ...

3, 6, 12, 24, ...

Step-by-step explanation:

1, 5, 25, 125, ...

3, 6, 9, 12,...

3, 6, 12, 24, ...

3, 9, 81, 6, 561, ...

10, 20, 40, 60, ...

Answer:

10,16,13

Step-by-step explanation:

got that right

The lengths of the sides of the triangle after the dilation is 13 , 10 and 16 respectively

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be represented as ABC

Now , the dilated triangle is represented as A'B'C'

The dilation scale factor is d = 1/3

The measure of side AC = 39

The measure of side AB = 30

The measure of side BC = 48

Now , after the dilation of 1/3 , we get

The measure of side A'C' = 39 ( 1/3 ) = 13

The measure of side A'B' = 30 ( 1/3 ) = 10

The measure of side B'C' = 48 ( 1/3 ) = 16

Hence , the dilation triangle is having lengths 13 , 10 and 16

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Answer: [tex]y = 121[/tex]

[tex](y+57) = 178[/tex]

[tex]y+57= 178[/tex]

[tex]y = 178 -57[/tex]

[tex]y = 121[/tex]

Answer:

Step-by-step explanation:

155

The number of boxes required by the school to order is 155.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.  If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

We have been given that the school needs 1,860 pencils for its students. Also, the pencils are sold in boxes of 12.

We need to find the school needs to requires boxes to order.

Total number of pencil = 1,860

Number of boxes = 12

Therefore, boxes needed = 1,860 / 12

= 155

Hence, the number of boxes required by the school to order is 155.

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Answer:

8x/5

There’s a 1 in front of the x also remember to always simplify

3/5x + 1x

Answer:8x/5

Step-by-step explanation:

Answer:

Part a

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] \bar X = 69.8[/tex] the sample mean

[tex] n= 140[/tex] represent the sample size

[tex] s = 11.2[/tex] represent the standard deviation

Part a

And we want to test if the true mean is equal to 69.3 so then the system of hypothesis:

Null hypothesis: [tex] \mu = 69.3[/tex]

Alternative hypothesis: [tex]\mu \neq 69.3[/tex]

Part b: Find the statistic

The statistic is given by:

[tex] z= \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And replacing the info we got:

[tex] z = \frac{69.8- 69.3}{\frac{11.2}{\sqrt{140}}}= 0.528[/tex]

Answer:

149.14 [tex]m^{2}[/tex]

Step-by-step explanation:

Area of a circle = π[tex]r^{2}[/tex]

so A = π * 6.89^2 = 149.14 (to 2d.p.)

Answer:

This has multiple answers, A, C, And D

Step-by-step explanation:

Answer:

It is definitely A, C, and D.

Step-by-step explanation:

I just answered this question and got it right. I hope this helps and please mark brainliest!

The answer would be -3 13/81 (simplified)

Answer:

50π cm²

Step-by-step explanation:

In this case we have that the area of the boomerang has been the area of the largest semicircle minus the area of the smaller semicircles.

We know that the radius is half the diameter:

r = d / 2 = 20/2

r = 10

Now we have to:

Alargest = π · r²

Alargest = π · (10 cm) ²

Alargest = 100π cm²

Asmaller = π · r²

Asmaller = π · (5 cm) ²

Asmaller = 25π cm²

Finally, the boomerang area has been:

Aboomerang = 100π cm² - 2 · (25π cm²)

Aboomerang = 50π cm²

[tex]0.84 \div 3 = 84 \div 300 = 0.28[/tex]

Answer:

22.7

Step-by-step explanation:

ok so, First we need to find new values:

       96( 1 + 0.25) =120

       85( 1+0.2)=  102

Boys last year        girls last year      total this year

   96                             85                        181

Boys this year        girls this year        total this year

  120                         102                           222

   Find the overall increase:

181( 1+r)= 1.226519

THEN U SUBTRACT 1

r=0.226519

Multiply by 100 and round to nearest 10th

22.7%

Final Answer: 22.7%

HOPED IT HELPED:)