Hunter needs 12 ounces of a snack mix that is made up of seeds and dried fruit. The seeds cost $1.50 per ounce, and died fruit costs $2.50 per ounce. Hunter has $22 to spend and plans to spend it all.

Let x = the amount of seeds

Let y = the amount of dried fruit

Part 1: Create a system of eqution to represent the senario.

Part 2: Solve your system using any method (Desmos, Linear combination, or subsitution). Write your answer as an orderd pair.
​

a. There is insufficient evidence to conclude that the average age of all lottery players in the county is different from 50 years at the 5% significance level.

b. Referring to the conclusion in part (a), the type of error that may have been made is a type II error, where we fail to reject a false null hypothesis.

(a) To test if the present-day average age of all lottery players in the county is different from 50 years, we can use a one-sample t-test with the null hypothesis:

H0: μ = 50

And the alternative hypothesis:

Ha: μ ≠ 50

Where μ is the population mean age of lottery players.

We have a sample size of n = 81, sample mean x = 48.7, and sample standard deviation s = 8.5. We can calculate the t-statistic as:

t = (x - μ) / (s / √n) = (48.7 - 50) / (8.5 / √81) = -1.29

Using a t-distribution table with 80 degrees of freedom (df = n - 1), we find the critical values to be ±1.990 at a significance level of α = 0.05 (two-tailed test).

Since the calculated t-statistic (-1.29) does not fall outside the critical values, we fail to reject the null hypothesis. There is insufficient evidence to conclude that the average age of all lottery players in the county is different from 50 years at the 5% significance level.

(b) Referring to the conclusion in part (a), the type of error that may have been made is a type II error, where we fail to reject a false null hypothesis. In other words, there may not be enough evidence to conclude that the population mean age is different from 50 years, even if it truly is.

The error in this context means that the lottery official may have missed an opportunity to update their estimate of the average age of all lottery players in the county.

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Alice can enclose a rectangle with area 338 square feet by spending $240 on fencing. The minimum cost to enclose 300 square feet is $476.64.

Let's suppose that the rectangle is x feet wide, so its length is 2x. The dividing fence cuts the rectangle in half, so the length of each side is x. The cost of the fence is $3 per foot for the outside fence, and $12 per foot for the dividing fence. Alice has $240 to spend, so

$3(2x) + $12(x) = $240

Solving for x, we get

6x + 12x = 240

18x = 240

x = 13.33

Since x has to be a whole number, we can use 13 as the width. The length is 2x, or 26 feet. The area of the rectangle is

13 x 26 = 338 square feet

If Alice wants to enclose 300 square feet, we know that the area of the rectangle is

Area = width x length

Since the rectangle is divided in half by the dividing fence, the length of each side is half the total length, or x. So

Area = x²

We can rearrange this to solve for x

x² = 300

x = √(300) = 17.32 (rounded to two decimal places)

Since the width of the rectangle is half the length, the width is:

Width = 17.32 / 2 = 8.66 (rounded to two decimal places)

The total length is twice the width, or 17.32. The perimeter of the rectangle is

2(8.66 + 17.32) = 52.96 feet

The cost of the outside fence is $3 per foot, so the cost of the outside fence is

$3(52.96) = $158.88

The dividing fence is in the middle of the rectangle, so the length is half the perimeter, or 26.48 feet. The cost of the dividing fence is $12 per foot, so the cost is

$12(26.48) = $317.76

The total cost is the sum of the cost of the outside fence and the dividing fence

$158.88 + $317.76 = $476.64.

Therefore, the minimum cost to enclose 300 square feet is $476.64.

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Let's use "a" to represent the length of the equal sides of the isosceles triangle, and let's use "b" to represent the length of the third side. We're told that one of the equal sides is 2x + 1ft long, so we can set up an equation:

2a + b = 55

We're also told that the other two sides are both 3x - 14ft long, so we can set up another equation:

a = 3x - 14

Now, we can substitute the second equation into the first equation and solve for "b":

2a + b = 55

2(3x-14) + b = 55

6x - 28 + b = 55

b = 83 - 6x

Now, we can substitute both equations into the equation a = 3x - 14 and solve for "x":

3x - 14 = 2x + 1 + 3x - 14

6x - 27 = 0

x = 4.5

Finally, we can substitute "x" into our equations to find the lengths of the sides:

a = 3x - 14 = 3(4.5) - 14 = 0.5

b = 83 - 6x = 83 - 6(4.5) = 55

So the length of the equal sides is 0.5ft, and the length of the third side is 55ft. Therefore, the lengths of the sides of the isosceles triangle are 0.5ft, 0.5ft, and 55ft.

The area of the shaded region in term of π is 6.22π cm²

A sector is a region or space bounded by two radii and an arc. There are two types of sector, the major sector and the minor sector. The of the sector is determined by the angle formed the two radii.

Area of sector = tetha/ 360 × πr²

where r is the radius of the circle.

= 140/360 × π × 4²

= 2240π/360

Area = 6.22 πcm²

Therefore the area of the shaded part is 6.22π cm²

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For the function,

-number of complex zeros: four

-possible # of imaginary zeros: two pairs

-possible # of positive real zeros: zero

-possible # negative real zeros: 0 or 2

-possible rational zeros:  ±1, ±3, ±5, ±9, ±15, ±45

-factors to: (x + 3i)(x - 3i)(x + √5i)(x - √5i)

-zeros: x = ±3i, x = ±√5i.

The function is: F(x) = x⁴ +14x²+45.

Number of complex zeros: By the Fundamental Theorem of Algebra, the function has at most four complex zeros.

Possible number of imaginary zeros: If the complex zeros are not real, then there are at most two pairs of imaginary zeros.

Possible number of positive real zeros: The function has no positive real zeros since F(x) is always positive for x>0.

Possible number of negative real zeros: By Descartes' Rule of Signs, the function has either 0 or 2 negative real zeros.

Possible rational zeros: The rational zeros can be found using the Rational Root Theorem. They are of the form ±(a factor of 45) / (a factor of 1), which gives the following possible rational zeros: ±1, ±3, ±5, ±9, ±15, ±45.

To factor the polynomial:

F(x) = x⁴ +14x²+45

= (x² + 9)(x² + 5)

So the factors to linear factors are: (x + 3i)(x - 3i)(x + √5i)(x - √5i), where i is the imaginary unit.

Therefore, the zeros are: x = ±3i, x = ±√5i.

Note that all zeros are complex since there are no real roots.

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Answer:

x = 14°

t = 12.367 ~ 12.4

r = 2.999 ~ 3

Step-by-step explanation:

1st we can find x by sum theory which is the sum of all side equal to 180° .

x + 90° + 76° = 180 °

x + 166° = 180°

x= 180° - 166°

x = 14° ... So the unknown angle is 14°

and we also can solve hypotenus t and adjecent r by using sin amd cos respectively by angle 76° .

sin(76) = 12/t

sin(76) t = 12 ....... criss cross it

t = 12 / sin(76) ....... divided both side by sin(76)

t = 12.367 ~ 12.4 ....... result

And

cos(76) = r / 12.4

r = cos(76) × 12.4 .......criss cross

r = 2.999 ~ 3 ....... amswer and i approximate it

The equation of the tangent plane is given by:
20736(x - 3) + 12288(y - 4) + 1(z - (-62188)) = 0

To find the equation of the tangent plane to the surface x⁴y⁴ + z - 20 = 0 at the point (3, 4, z), we first need to find the partial derivatives with respect to x, y, and z.

∂f/∂x = 4x³y⁴
∂f/∂y = 4x⁴y³
∂f/∂z = 1

Now, we evaluate the partial derivatives at the given point (3, 4, z):

∂f/∂x(3, 4, z) = 4(3³)(4⁴) = 20736
∂f/∂y(3, 4, z) = 4(3⁴)(4³) = 12288
∂f/∂z(3, 4, z) = 1

Next, we find the value of z by substituting x = 3 and y = 4 in the equation:

(3⁴)(4⁴) + z - 20 = 0
z = 20 - (3⁴)(4⁴) = 20 - 62208 = -62188

The point on the surface is (3, 4, -62188). The equation of the tangent plane is given by:

20736(x - 3) + 12288(y - 4) + 1(z - (-62188)) = 0

This simplifies to:

20736x + 12288y + z = 1885580

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The values of the variables x and y area 42 and 12 respectively

We can see that the quadrilateral that is inscribed in the circle is a parallelogram.

The properties of a parallelogram includes;

Then, from the information given, we have that;

x + 35 = 77

Now. collect the like terms, we get;

x = 77 - 35

subtract the values, we have;

x = 42

Also,

4y + 46 = 94

collect the like terms

4y = 94 - 46

4y = 48

Divide by the coefficient of y, we have;

y = 12

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In this case, it's important for the librarian to make sure that the sample of patrons who were randomly selected is representative of the larger population of patrons in the children's section, and that any assumptions made in the statistical inference process are valid.

To infer the ages of all patrons in the children's section of the library, the librarian should use statistical inference techniques such as estimation or hypothesis testing.

If the librarian wants to estimate the average age of all patrons in the children's section, they can use a point estimate or an interval estimate. A point estimate would involve calculating the sample mean age of the patrons who were randomly selected and using that as an estimate for the population means age. An interval estimate would involve calculating a confidence interval around the sample mean, which would give a range of likely values for the population means.

Alternatively, if the librarian wants to test a hypothesis about the ages of patrons in the children's section, they can use a hypothesis test. For example, they could test whether the average age of patrons in the children's section is significantly different from a certain value (such as the national average age of children), or whether there is a significant difference in age between male and female patrons.

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Surface area of the box is 304 square inches

Two different methods:

Method 1: Sum of the parts

Method 2: General formula for the Surface Area of a box

Method 1: Sum of the parts

For a box, there are 6 sides, all of which are rectangles:

Each of the above pairs has the same area.

The general formula for the area of a rectangle is [tex]A_{rectangle}=length*width[/tex]

As we look at different rectangles, the length of one rectangle may be considered the "width" of another rectangle, and that's okay as we calculate things separately.  (We'll examine how to calculate everything at once in Method 2).

The area for the front/back side is 8in * 10in = 80 in^2

[tex]A_{front}=A_{back}=80~in^2[/tex]

The area for the left/right side is 4in * 8in = 32 in^2

[tex]A_{left}=A_{right}=32~in^2[/tex]

The area for the top/bottom side is 4in * 10in = 40 in^2

[tex]A_{top}=A_{bottom}=40~in^2[/tex]

So, the total surface area is

[tex]A_{Surface~Area} = A_{front} + A_{back} + A_{left} + A_{right} + A_{top} + A_{bottom}[/tex]

[tex]A_{Surface~Area} = (80in^2) + (80in^2) + (32in^2) + (32in^2) + (40in^2) + (40in^2)[/tex]

[tex]A_{Surface~Area} = 304~in^2[/tex]

Method 2: General formula for the Surface Area of a box

There is a formula for the surface area of a box:[tex]A_{Surface~Area~of~a~box} = 2(length*width + width*height + height*length)[/tex]

This formula calculates the area of one of each of the matching sides from the side pairs discussed in Method 1, adds those areas together (giving 3 of the sides), and doubles the result (bringing in the area for the matching missing 3 sides).

For clarity, let's decide that the "10 in" is the width, the "8 in" is the height, and the left over "4 in" is the length.

[tex]A_{Surface~Area~of~the~box} = 2((4in)(10in) + (10in)(8in) + (8in)(4in))[/tex]

[tex]A_{Surface~Area~of~the~box} = 2(40in^2 + 80in^2 + 32in^2)[/tex]

[tex]A_{Surface~Area~of~the~box} = 2(152in^2)[/tex]

[tex]A_{Surface~Area~of~the~box} = 304in^2[/tex]

Infectious diseases, chronic conditions, mental health, healthcare access, health disparities. Vaccination campaigns, disease prevention, healthcare access, mental health support, social determinants. Increased disease burden, higher costs, reduced quality of life, higher mortality, strained healthcare systems, hindered socio-economic development.

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Applying the arc length formula, the radius of the circle is calculated as: r = 9 units.

In a circle, the measure of an angle in radians is related to the length of the intercepted arc and the radius by the formula:

arc length = radius * angle measure

In this case, we are given that the angle measure is π radians and the arc length is 9π. Substituting these values into the formula, we get:

9π = r * π

where r is the radius of the circle.

Simplifying this equation, we can divide both sides by π:

9 = r

Therefore, the radius of the circle is 9.

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The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,

The formula for the confidence interval of a proportion:

CI = p ± z* (√(p*(1-p)/n))

where:

p is the sample proportion (40/90 = 0.4444)

z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)

n is the sample size (90)

Substituting the  values, we have

CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))

CI = 0.4444 ± 1.96 * (√(0.00245))

CI = 0.4444 ± 1.96 * 0.0495

CI = 0.4444 ± 0.097

Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.

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Answer:

y = (x+5)/3

Step-by-step explanation:

Isolate y

x = 3y - 5

x + 5 = 3y

(x+5)/3 = y

The sum of money shared by both Aziz and Ahmad is $80.

To find the sum of money shared by Aziz and Ahmad, we'll use the given ratio and the difference between their shares.

1. We are given that Aziz and Ahmad share the money in the ratio 3:7. Let's represent Aziz's share as 3x and Ahmad's share as 7x.
2. It's mentioned that Aziz received $32 less than Ahmad. So, we can write an equation as follows: 7x - 3x = $32.
3. Simplify the equation: 4x = $32.
4. Solve for x: x = $32 / 4, x = $8.
5. Now, we can find the shares of Aziz and Ahmad. Aziz's share: 3x = 3 * $8 = $24. Ahmad's share: 7x = 7 * $8 = $56.
6. To find the total sum of money shared, add both shares: $24 + $56 = $80.

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The completed matrix represents the system of equations in a convenient format for solving using matrix operations.

The given system of equations has been represented in a matrix form, where the coefficients of the variables x and y and the constant terms are arranged in a matrix. To solve the system of equations, we can use matrix operations to isolate the variables and find their values. The completed matrix shows that the coefficient of x is 700, the coefficient of y is -200, and the constant term is 0 for the first equation. Similarly, the coefficient of x is -75, the coefficient of y is 200, and the constant term is 5000 for the second equation.

To solve this system using matrix operations, we can perform row operations to eliminate one of the variables. For example, we can multiply the first row by 75 and the second row by 200, and then add the two rows to eliminate x. This gives us a new system of equations with only one variable, which we can solve to find the values of x and y.

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There is no convincing evidence that the proportion of Devon's serves that are good is more than 72%. The data collected does not provide sufficient evidence to support Devon's claim that he has a higher proportion of good serves than what his coach stated.

Based on Devon's hypotheses, H₀ states that p = 72%, while Hₐ states that p > 72%, where p represents the true proportion of Devon's good serves. To test this, 50 of his serves are randomly selected, and 42 are good. A simulation is conducted with 100 trials, resulting in an estimated P-value of 0.06. The significance level (α) is set at 0.05.

In this case, the P-value (0.06) is greater than the significance level (0.05). According to the rules of hypothesis testing, we should fail to reject the null hypothesis (H₀) when the P-value is greater than the significance level. Therefore, Devon should fail to reject H₀.

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Saleem scored 50 on the next test, and his average dropped to 58.

To find Saleem's grade on the next test, we can use the concept of weighted averages.

Since Saleem has an average of 60 in 4 subjects, we can calculate the total marks he has obtained so far. Let's denote the total marks in the 4 subjects as "T."

Average = Total marks / Number of subjects

60 = T / 4

To find T, multiply both sides by 4:

T = 60 * 4

T = 240

Now, Saleem's total marks after attempting the next test would be (240 + X), where X is the score he gets on the next test.

The new average after attempting the next test is 58.

Average = Total marks / (Number of subjects + 1)

58 = (240 + X) / 5

To find X, first multiply both sides by 5:

58 * 5 = 240 + X

290 = 240 + X

Now, isolate X:

X = 290 - 240

X = 50

So, Saleem scored 50 on the next test.

To summarize, Saleem scored 50 on the next test, and his average dropped to 58.

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[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 5.1\%\to \frac{5.1}{100}\dotfill &0.051\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 25000[1+(0.051)(4)] \implies A=25000(1.204)\implies A = 30100[/tex]

The length of the string needed is 65 meters

An equation is an expression that shows how numbers and variables using mathematical operators.

Pythagoras theorem shows the relationship between the sides of a right angle triangle.

To find the length of string, Mia needs. A triangle is formed with hypotenuse (l) represent the length of string. The height of the kite (h) = 33 m which is the triangle height; while the 56 m is the base of the triangle (b). Hence:

l² = b² + h²

l² = 33² + 56²

l = 65 meters

The length of the string needed is 65 meters

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Answer:

The third graph from the top could be the graph of f(x) = (2/5)^x. As x approaches infinity, f(x) approaches 0.

Mrs. Carter used 954 square inches of frosting.

To find the surface area of the rectangular prism cake, we need to find the area of all six sides and then subtract the bottom since frosting was not applied to it.

The area of the top and bottom sides is 24 x 15 = 360 square inches each.

The area of the two side faces is 24 x 3 = 72 square inches each.

The area of the two end faces is 15 x 3 = 45 square inches each.

So, the total surface area of the cake is:

2(360) + 2(72) + 2(45) = 720 + 144 + 90 = 954 square inches.

Since frosting was applied to all sides, including the top, we use this surface area to find the amount of frosting used.

Therefore, Mrs. Carter used 954 square inches of frosting.

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The Perimeter of the Triangle is 20.5. when the AB value is 6 m and the angles are 45°. Option B is the correct answer

Given:

AB = 6 m

∠ACB = 45°

By using Trigonometry formulas,

We can determine the AC length by using the sin 45° formula and it is given as,

sin 45° = opposite / hypothesis

sin 45° = AB /AC

1/√2 = 6/ AC

AC = 6√2

We can determine the BC length by using the tan 45° formula which is given as,

tan 45° = opposite / adjacent

tan 45° =AB/ BC

1 = 6/ BC

BC= 6

Now we can determine the perimeter of the triangle by using the perimeter of the triangle formula which is given as,

[tex]P=a+b+√a²+b²[/tex]

Where:

a = opposite side = AC

b = adjacent side = BC

Substuting the a and b values in the above equation we get,

= 6 + 6 +√ 6²+ 6²

= 6 + 6 + 6√2

= 12 +6√2

= 6(2 + √2)

= 20.48 ≅ 20.5

Therefore, The perimeter of the triangle ABC is 20.5.

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The probability of rolling a number greater than three and an R on the first roll of both objects is 5/48. The answer is C.

What's P(rolling >3 and R on the first roll of both objects)?

The probability of rolling a number greater than three on the eight-faced object is 5/8 because there are five numbers greater than three (4, 5, 6, 7, and 8) out of eight possible outcomes. The probability of rolling an R on the six-faced object is 1/6 because there is only one R out of six possible outcomes.

To find the probability of both events occurring simultaneously, we multiply the probabilities together:

P(rolling a number > 3 and rolling an R) = P(rolling a number > 3) x P(rolling an R)

= (5/8) x (1/6)

= 5/48

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Answer:

Carlos=1.5041

Mykala=2.6991

William=4.1350

Emily=4.1773

At a significance level of 0.05, the critical value is 2.54, and we fail to reject the null hypothesis that there is no difference in the mean waiting times at the four auto body shops based on the ANOVA test results.

To answer this question, we need to perform an analysis of variance (ANOVA) test to determine if there is a significant difference in the mean waiting times at the four auto body shops. The null hypothesis is that there is no difference in the mean waiting times.

Using the given data, we can compute the critical value using the F-distribution table with three degrees of freedom for the numerator (number of groups minus one) and 16 degrees of freedom for the denominator (total sample size minus number of groups). At a significance level of 0.05, the critical value is 2.54.

Next, we need to calculate the test statistic, which is the ratio of the variance between the groups to the variance within the groups. The output from the statistical software package provides the necessary information to compute the test statistic:

Source | SS   | df | MS     | F    |
------------------------------------
Between| 2.98 | 3  | 0.99   | 1.15 |
Within | 48.28| 16 | 3.02   |      |
Total  | 51.26| 19 |        |      |

The test statistic is F = 1.15, which is less than the critical value of 2.54. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the mean waiting times at the four auto body shops.

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(a) To find the slope of the curve where it meets the right-hand pole, we need to differentiate the given equation with respect to x. y = 17cosh(x/17) - 12.

Using the chain rule, we get dy/dx = (17/17)sinh(x/17) = sinh(x/17). Therefore, at x = 7, the slope of the curve is sinh(7/17) ≈ 0.6968.

(b) To find the angle theta between the line and the pole, we can use trigonometry. The slope of the curve at the right-hand pole is the same as the tangent of the angle theta.

Therefore, tan(theta) = 0.6968. Taking the inverse tangent of both sides, we get theta = arctan(0.6968) ≈ 34.33 degrees. Therefore, the acute angle formed by the right pole and the hanging line is approximately 34.33 degrees.

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The number of Americans to leave a tip of more than 20% in 1500 is 90

If only 6% of Americans leave a tip of more than 20% for satisfactory service in a restaurant, we can assume that the same proportion of restaurant customers will do so.

Therefore, out of 1,500 restaurant customers, we would expect:

6% of 1,500 = (6/100) x 1,500 = 90

So we would expect 90 restaurant customers to leave a tip of more than 20%.

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Hudson Marine experiences the largest seasonal effect in quarter 4.

a. The four-quarter moving average values can be calculated as follows:

Quarter 1: (7 + 9 + 13 + 18) / 4 = 11.75

Quarter 2: (17 + 19 + 28 + 27) / 4 = 22.75

Quarter 3: (9 + 17 + 23 + 23) / 4 = 18

Quarter 4: (2 + 8 + 12 + 17) / 4 = 9.75

Quarter 5: (17 + 8 + 12 + 20) / 4 = 14.25

Quarter 6: (53 + 23 + 17 + 19) / 4 = 28

Quarter 7: (76 + 85 + 105 + 111) / 4 = 94.25

The centered moving average values can be calculated by averaging the adjacent four-quarter moving averages:

Quarter 3: (11.75 + 22.75 + 18 + 9.75) / 4 = 15.06

Quarter 4: (22.75 + 18 + 9.75 + 14.25) / 4 = 16.19

Quarter 5: (18 + 9.75 + 14.25 + 28) / 4 = 17.75

Quarter 6: (9.75 + 14.25 + 28 + 94.25) / 4 = 36.31

Quarter 7: (14.25 + 28 + 94.25 + 28) / 4 = 41.38

Therefore, the centered moving average values are:

Quarter 3: 15.06

Quarter 4: 16.19

Quarter 5: 17.75

Quarter 6: 36.31

Quarter 7: 41.38

b. The seasonal indexes for the four quarters can be calculated by dividing the centered moving average values by the average of all the centered moving average values and then multiplying by 100:

Quarter 1: (15.06 / 20.31) x 100 = 74.18

Quarter 2: (16.19 / 20.31) x 100 = 79.79

Quarter 3: (17.75 / 20.31) x 100 = 87.40

Quarter 4: (36.31 / 20.31) x 100 = 178.63

Therefore, the seasonal indexes for the four quarters are:

Quarter 1: 74.18

Quarter 2: 79.79

Quarter 3: 87.40

Quarter 4: 178.63

c. Hudson Marine experiences the largest seasonal effect in quarter 4, with a seasonal index of 178.63. This means that the sales in quarter 4 are, on average, 178.63% higher than the average sales for all quarters.

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