the price of a dvd is 24.00 plus 8% sales tax.what is the sales tax on this dvd in dollar and cents

Answer:

a) p-hat (sampling distribution of sample proportions)

b) Symmetric

c) σ=0.058

d) Standard error

e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Step-by-step explanation:

a) This distribution is called the sampling distribution of sample proportions (p-hat).

b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.

This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.

c) The variability of this distribution, represented by the standard error, is:

[tex]\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058[/tex]

d) The formal name is Standard error.

e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:

[tex]\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667[/tex]

If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Using the Central Limit Theorem, we get that:

a) Sampling distribution of sample proportions of size 40.

b) Symmetric.

c) 0.0580.

d) Standard error.

e) It would decrease.

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean  and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean  and standard erro .

For a skewed variable, we need n of 30 and greater.

For a proportion p in a sample of size n, we have that:  and standard deviation .

In this problem:

Item a:

We are working proportions, and sample of 40, thus:

Sampling distribution of sample proportions of size 40.

Item b:

Item c:

This is the standard error, thus:

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.16(0.84)}{40}} = 0.0580[/tex]

It is of 0.0580.

Item d:

Item e:

The formula is:

[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

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Answer:

A is correct, 7 units. Hope this helps! :)

Answer:

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Step-by-step explanation:

We are given the following information:

We treat people having brown eyes as a success.

P(people have brown eyes) = 41% = 0.41

Then the number of people follows a binomial distribution, where

[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 14

We have to evaluate:

[tex]P(x \geq 12) = P(x = 12) + P(x = 13) + P(X = 14) \\= \binom{14}{12}(0.41)^{12}(1-0.41)^2 + \binom{14}{13}(0.41)^{13}(1-0.41)^1 + \binom{14}{14}(0.41)^{14}(1-0.41)^0\\= 0.0007 + 0.00007 + 0.000003\\= 0.000773[/tex]

0.000773 is the probability that atleast 12 out of 14 will have brown eyes.

Yes, it is an unusual event due to small probability values.

Answer:

315

Step-by-step explanation:

The missing percentages of the given scenario are;

Adventure Games: 22%

Puzzles: 28%

Card Games: 30%

Arcade Games: 9%

Board Games: 11%

So in order to solve the problem, we simply use the pie chart distributions to get the result

Now if look at the percentages, we that card games percentage is 30 while arcade games is 9 so, 21 % of people play more card games.

In terms of number of people = 21/100 x 1500 = 315

Hence out of 1500, 315 people play card games more than arcade

Answer:

The number of more people that played card games than arcade games is 150 people

Step-by-step explanation:

Here  we have a pie chart showing games people play in the following proportions

Assumption; Card games = 49%

Arcade games = 32%

Classic = 15%

Kids = 4%

Therefore. if 49%  played card games, we have 49% of 1500 which is 735 people, while 32% that played arcade games, we have 39% of 1500 = 0.39×1500 = 585

Therefore, the number of more people that played card games than arcade games = 735 - 585 = 150 people.

Answer: The surface is (4*n + 2)*L^2

Step-by-step explanation:

The surface of a cube is equal to 6 times the area of one of the sides.

So if the sides of the cube have a length L, we have that the area of one face is L^2, and the surface of the cube is 6*L^2

Now, if we put n of those cubes in a tower, we will have a shape were the bottom and the top still have an area of L^2, then the total area of the bottom and the top is 2*L^2

But each one of the sides has two sides of length L, and two sides of length n*L (n times the length of one of the sides), then the area of each side is equal to n*L*L = n*L^2

and we have 4 sides, then the total area of the sides is 4*n*L^2

Then the total surface of the tower is:

A = 4*n*L^2 + 2*L^2 = (4*n + 2)*L^2

The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

Now,

Given statement is,  ''9 more than the quotient of 52 divided by 4''

What is Quotient?

A quotient is the answer a division problem. The divisor is the number of parts you divide the dividend by.

Now,

The quotient of 52 divided by 4 is,

52 ÷ 4 = 13

And, 9 more than the quotient of 52 divided by 4 is,

( 52 ÷ 4 )+ 9 = 13 + 9 = 22

Hence, The solution of ''9 more than the quotient of 52 divided by 4'' is 22.

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To solve the expression, divide 52 by 4 to get 13, then add 9 to the quotient, resulting in the final answer of 22.

The question asks to find '9 more than the quotient of 52 divided by 4'.

First, we need to calculate the quotient of 52 divided by 4, which is done by performing the division.

So, 52 ÷ 4 equals 13. Next, we add 9 to this quotient to get the final result.

Adding 9 to 13 gives us 22.

Therefore, 9 more than the quotient of 52 divided by 4 is 22.

Answer:

where are the angles? I can't see anything

Answer:

Please provide pictures!!

Step-by-step explanation:

Answer:

24 feet

Step-by-step explanation:

sorry I'm so late

Answer:

Step-by-step explanation:

Let represent the edge of the tank with x and the radius of the first sphere with x/2;

The amount of the water = Volume of the tank - Volume of the sphere

= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]

on the second cube ; the radius of the sphere = [tex]\frac{x}{4} \ units[/tex] ;

Also the number of sphere here is = 8

The amount of water = [tex]x^3 -8*\frac{4}{3} \pi (\frac{x}{4})^3[/tex]

For the third figure ; the radius of the sphere is = [tex]\frac{x}{8} \ units[/tex]

Also the number of sphere here is = 64

The amount of water = [tex]x^6 -64*\frac{4}{3} \pi (\frac{x}{8})^3[/tex]

= [tex]x^3 - \frac{4}{3} \pi (\frac{x}{2})^3[/tex]

In the fourth tank ; 512 sphere illustrates that in a single row; that more than one 8 sphere is present i.e 8³ = 512

then the radius will be = [tex]\frac{x}{16}[/tex]

The amount of water = [tex]x^3 -512*\frac{4}{3} \pi (\frac{x}{16})^3[/tex]

= [tex]x^3 -\frac{4}{3} \pi (\frac{x}{2})^3[/tex]

This implies that alll the three cube shaped tanks are identical and hold equal amount of water.

Answer:

0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.

Step-by-step explanation:

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

Normal probability distribution

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

In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [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.

Central Limit Theorem

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

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

In this problem, we have that:

[tex]\mu = 1217, \sigma = \sqrt{10414} = 102, n = 116, s = \frac{102}{\sqrt{116}} = 9.475[/tex]

What is the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd?

This is 2 multiplied by the pvalue of Z when X = 1217 - 11 = 1206. So

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

By the Central Limit Theorem

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

[tex]Z = \frac{1206 - 1217}{9.475}[/tex]

[tex]Z = -1.16[/tex]

[tex]Z = -1.16[/tex] has a pvalue of 0.1230

2*0.1230 = 0.2460

0.2460 = 24.60% probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs if 116 cows are sampled at random from the herd.

To calculate the probability, we can use the Central Limit Theorem. Calculate the standard error using the formula: standard error = standard deviation / sqrt(n), then use the z-score formula to find the probability.

To find the probability that the mean weight of the sample of cows would differ from the population mean by more than 11 lbs, we can use the Central Limit Theorem. Since the sample size is large (n > 30), the distribution of sample means will be approximately normally distributed. First, we calculate the standard deviation of the sampling distribution, also known as the standard error, using the formula: standard error = standard deviation / sqrt(n). In this case, the standard error is sqrt(10404)/sqrt(116).

Finally, we can use the z-score formula to calculate the probability. The z-score is given by z = (x - mean) / standard error. We want to find the probability that the mean weight differs from the population mean by more than 11 lbs, so we calculate the z-score for both 11 and -11 and use the z-table or a calculator to find the probability of z being greater than the positive z-score and less than the negative z-score. Adding these two probabilities gives us the final answer.

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The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.

Step-by-step explanation:

The given is,

                 Detailed view or net diagram of the three dimensional diagram.

Step:1

                Three dimensional diagram of the given net diagram is attached.  

                From the three dimensional diagram given net diagram is rectangular prism.

Step:2

                 From the three dimensional diagram

                 Formula for surface area of the rectangular prism,

                                       [tex]A = 2(wl + lh + hw)[/tex]..............................(1)

                 Where, w - Width

                                l - Length

                               h - Height

                 From the attachment,

                               l = 6 cm

                              w = 2 cm

                               h = 3 cm                

                 Equation (1) becomes,

                              [tex]A = 2((6)(2) + (6)(3) + (3)(2))[/tex]

                                   = 2 ( 12 + 18 + 6 )

                                   = 2 ( 36 )

                               A = 72 squared centimeters

                                  ( or )

                 From the net diagram,

                 Surface area, A = ((6×3)+(2×3)+(2×6)+(2×3)+(3×6)+(2×6))

                                            = 18 + 6 + 12 + 6 + 18 + 12

                                            = 72

                Surface area, A = 72 squared centimeters

Result:

          The surface area of the three dimensional solid is 72 square centimeters and its three dimensional diagram is attached.

Answer:72 cm2

Step-by-step explanation:

Answer:

s would be the dependent variable, and g the independent.

Step-by-step explanation:

Whatever the score is, it would depend on how many goals the team has scored.

Final answer:

The independent variable is typically the one that is manipulated, like the number of goals scored (g), and the dependent variable is the one that responds, like the team's score (S). A scatter plot can reveal patterns, and the correlation coefficient indicates the strength of the relationship. The least-squares line represents a best-fit line through the data.

Explanation:

The independent variable is typically the one that is controlled or manipulated, whereas the dependent variable is the one that responds to changes in the independent variable. In the context of a team's score (S) and the number of goals scored (g), the independent variable is usually the number of goals scored (g) because it can be controlled or affected through the team's actions. The dependent variable is the team's score (S), because it depends on the number of goals scored.

In a broader context, such as analyzing the relationship between the ranking of a state and the area of the state, the independent variable could be the ranking (since it is not influenced by the area), and the dependent variable would be the area of the state (since it could be influenced by a variety of factors, including ranking).

When creating a scatter plot, it is common to place the independent variable on the x-axis and the dependent variable on the y-axis. This scatter plot could reveal correlations or trends between the two variables. The correlation coefficient is a statistical measure that describes the strength and direction of a relationship between two variables. A correlation coefficient close to 1 or -1 indicates a strong relationship, while a number close to 0 indicates a weak relationship. The least-squares line is a regression line that minimizes the sum of the squared differences between the observed values and the values predicted by the line.

Answer:

There are many possible solutions. For example,

(2^3)^4 = ((2^5)^12)/((2^6)^8) = 2^10 x 2^2 = (2^19)/(2^7)

(2^2)^5 = ((2^6)^11)/((2^7)^8) = 2^1 x 2^9 = (2^20)/(2^10)

Step-by-step explanation:

You need to fill in boxes with the digits 1 to 20 to create equations where both sides yield the same numerical result. This will involve understanding of basic arithmetic operations and a bit of trial and error.

The subject of this question is Mathematics. Specifically, it relates to the concept of equivalent expressions, which are an essential component of algebra and arithmetic. First, it's crucial to understand the concept of equivalent expressions: two expressions are considered equivalent if they share the same numerical value for each possible value of their variable(s).

Now, let's make an example with the numbers 1 to 10 (just to simplify the explanation). Consider the equations: 1+2+3+4 and 5+3+2+1. Even though the order of operations is different, both expressions yield the final numerical value of 10, making them equivalent expressions.

In the context of the question, you are being asked to fill in boxes with the digits 1-20, such that the expressions on either side of the equation sign are equivalent. This might involve a combination of operations like addition, subtraction, multiplication, and division.

It's a challenging task because it involves a bit of trial and error. Start by deciding on the operations for the expressions and then fill in the numbers. Make sure you check your results by calculating the numerical value of each expression.

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Answer:

Step-by-step explanation:

.01 (subtract confidence level from 100)

Answer:

-8 and 1

Step-by-step explanation:

the x is going by 5 and the y is going by 2

so add 5 to the x and 2 to the y

hope this help <(*__*)>

Answer:

(-7,1)

Step-by-step explanation:

(1+x/2) = -3     (-3+y/2) = -1

2(1+x/2) = -3(2)    2 (-3+y/2) = -1(2)

multiple each side by two to cancel the two's.

1+x= -6   -3+y= -2

x=-7      y= 1

Answer:

-2 and 4

Step-by-step explanation:

When you look for values that make an expression “illegal” the first step is to look for 3 things.

1) a variable in a denominator

- we have b, a variable, in the denominator of this expression

- values in the denominator cannot be 0

2) variables under even roots

- variables under even roots are a restriction because even roots are undefined when there are negative values under them

- there are no roots in this case so we dont have to worry about that

3) the literal letters: “log” in the expression

- there’s no “log” in the expression so we dont have to worry about that

—moving on—

We have a variable in the denominator, b.

The expression is a quadratic:

b^2 - 2b - 8

You have to find values that make this quadratic 0.

So you can make an equation setting the quadratics equal to 0.

b^2 - 2b - 8 = 0

Solve for b

Factor:

(b - 4)(b + 2) = 0

Because of zero product property we can say:

b = -2, b = 4.

If these values are plugged into your expression, it will be “illegal,” or “undefined,”

Answer:

129

Step-by-step explanation:

Answer:

$0.90 per kilogram

Step-by-step explanation:

4.5/5=.9

Answer:

Mean = 2.7

In a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Step-by-step explanation:

We are given that the rate of cancer in children is 37 children in 1 million. So the probability of cancer in a child is P(C) = 0.000037

Poisson distribution is used to approximate the number of cases of diseases and we have to find what will be the mean number of cases for 74,090.

In simple words we have to find the expected number of children with cancer in a group of 74,090 children.

The mean value of expected value can be obtained by multiplying the probability with the sample size. So, in this case multiplying probability of child having a cancer with total group size will give us the expected or mean number of children in the group with cancer.

Mean = E(x) = P(C) * Group size

Mean = 0.000037 x 74090

Mean = 2.7

This means in a group of 74090 we would expect about 3 (rounding to nearest whole number) children with the rare form of cancer.

Final answer:

The mean of the Poisson distribution for the number of cancer cases among 74,090 children in Normalville is approximately 2.7413 cases.

Explanation:

To find the mean of the appropriate Poisson distribution for the number of cases in groups of 74,090 children in Normalville, we multiply the probability of the disease by the number of children. Thus, the mean (μ) is:

μ = probability of one child having the disease × total number of children

μ = 0.000037 × 74,090 = approximately 2.7413

The mean of the Poisson distribution, in this case, indicates the average number of children who would have this rare form of cancer in groups of 74,090 children in Normalville.

Answer:

The percent of juniors whose score is at or above the mean is 50%

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 = 80, \sigma = 8[/tex]

Find the percent of juniors whose score is at least 80.

This is 1 subtracted by the pvalue of Z when X = 80. So

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

[tex]Z = \frac{80 - 80}{8}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a pvalue of 0.5

1 - 0.5 = 0.5

So

The percent of juniors whose score is at or above the mean is 50%

Answer:

78,750 pages

Step-by-step explanation:

225 books each with 350 paged

225 x 350

78,750 pages

Answer:

210.22

Step-by-step explanation:

first you need to divide 3785 divided by 18 which is 210.22222222 then u need to round to the nearest tenth which is equaled to 210.22. I hope this helped

Answer:

The answer is 30% off

Step-by-step explanation:

if you do 21.50 - 30% = 15.05

Answer:

[tex]47.36\%[/tex]

Step-by-step explanation:

The equation that governs how the insect population dies is

[tex]p' = - \mu p[/tex]

We need to solve this differential equation for p.

We separate variables to get:

[tex] \frac{p'}{p} = - \mu[/tex]

We integrate both sides to get:

[tex] \int\frac{p'}{p} dt = - \mu \int \: dt[/tex]

[tex] ln( |p| ) = - \mu \: t + ln(k) [/tex]

[tex]p = c{e}^{ \ - ut} [/tex]

If 1200 insects hatch, and only 70 remain after 6 days,

Then we have:

[tex]70 = 1200 {e}^{ - 6 \mu} [/tex]

[tex] \frac{70}{1200} = {e}^{ - 6 \mu} [/tex]

[tex] - 6 \mu = ln( \frac{7}{120} ) [/tex]

[tex] \mu = \frac{ln( \frac{7}{120} ) }{ - 6} [/tex]

[tex] \mu = 0.4736[/tex]

[tex]47.36\%[/tex]

Answer:

49

Step-by-step explanation:

36 minus -18 is 49

Answer:

-1/2

Step-by-step explanation:

The fraction is not reduced to lowest terms. We can reduce this fraction to lowest

terms by dividing both the numerator and denominator by 18.

Answer:

Probability that a randomly selected bill will be at least $39.10 is 0.03216.

Step-by-step explanation:

We are given that the daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of $6.

Let X = daily dinner bills in a local restaurant

So, X ~ N([tex]\mu=28,\sigma^{2} =6^{2}[/tex])

The z-score probability distribution for normal distribution is given by;

               Z = [tex]\frac{ X -\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean amount = $28

            [tex]\sigma[/tex] = standard deviation = $6

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, the probability that a randomly selected bill will be at least $39.10 is given by = P(X [tex]\geq[/tex] $39.10)

  P(X [tex]\geq[/tex] $39.10) = P( [tex]\frac{ X -\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{ 39.10-28}{6}[/tex] ) = P(Z [tex]\geq[/tex] 1.85) = 1 - P(Z < 1.85)

                                                           = 1 - 0.96784 = 0.03216

Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.85 in the z table which has an area of 0.96784.

Hence, the probability that a randomly selected bill will be at least $39.10 is 0.03216.

The probability that a randomly selected bill will be at least $39.10 is approximately 0.0323.

First, we calculate the z-score for a bill of $39.10 using the formula:

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

where X is the value for which we want to find the probability, [tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

Given:

[tex]\[ \mu = 28 \] \[ \sigma = 6 \] \[ X = 39.10 \][/tex]

Plugging in the values:

[tex]\[ z = \frac{39.10 - 28}{6} \] \[ z = \frac{11.10}{6} \] \[ z \approx 1.85 \][/tex]

Now, we look up the z-score of 1.85 in the standard normal distribution table or use a calculator to find the probability of a z-score being at least 1.85. This gives us the area to the right of the z-score on the standard normal curve.

Using a standard normal distribution table or calculator, we find:

[tex]\[ P(Z \geq 1.85) \approx 0.0323 \][/tex]

Given Information:

Smoothing constant = α = 0.25

Initial forecast salary = F₀ = $55,000

Actual salaries = A = $60,000, $72,000, $84,500, and $96,000

Required Information:

Forecast salaries = F = ?

Answer:

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Step-by-step explanation:

The exponential smoothing model is given by

[tex]F_{n} = \alpha \cdot A_{n - 1} + (1 - \alpha ) F_{n - 1}[/tex]

Where

[tex]F_{n}[/tex] is the forecast salary for nth graduate class

α is the smoothing constant

[tex]A_{n-1}[/tex] is the actual salary of n - 1 graduate class

[tex]F_{n-1}[/tex] is the forecast salary of n - 1 graduate class

For n = 1

[tex]F_{1} = 0.25 \cdot A_0} + (1-0.25) \cdot F_{0}\\F_{1} = 0.25 \cdot 60,000} + (0.75) \cdot 55,000\\F_{1} = 56,250[/tex]

For n = 2

[tex]F_{2} = 0.25 \cdot A_1} + (1-0.25) \cdot F_{1}\\F_{2} = 0.25 \cdot 72,000} + (0.75) \cdot 56,250\\F_{2} = 60,187.5[/tex]

For n = 3

[tex]F_{3} = 0.25 \cdot A_2} + (1-0.25) \cdot F_{2}\\F_{3} = 0.25 \cdot 84,500} + (0.75) \cdot 60,187.5\\F_{3} = 66,265.625[/tex]

For n = 4

[tex]F_{4} = 0.25 \cdot A_3} + (1-0.25) \cdot F_{3}\\F_{4} = 0.25 \cdot 96,000} + (0.75) \cdot 66,265.625\\F_{4} = 73,699.218[/tex]

Therefore, the foretasted starting salaries are

[tex]F_{1} = \$56,250\\F_{2} =\$ 60,187.5\\F_{3} = \$66,265.6\\F_{4} = \$73,699.2\\[/tex]

Using an exponential smoothing model with α = 0.25, we sequentially calculate the forecasted starting salary for each year, then use that to estimate the starting salary for the next graduating class.

To predict the starting salary for the next graduating class using a simple exponential smoothing model with α = 0.25 and an initial forecast of $55,000, we follow these steps:

By applying this model, we will obtain the predicted starting salary for the next class after performing these calculations for each given salary data point in sequence.

If a polynomial "contains", in a multiplicative sense, a factor [tex](x-x_0)[/tex], then the polynomial has a zero at [tex]x=x_0[/tex].

So, you polynomial must contain at least the following:

[tex](x-(-2)),\quad (x-0),\quad (x-3),\quad (x-5)[/tex]

If you multiply them all, you get

[tex]x(x+2)(x-3)(x-5)=x^4 - 6 x^3 - x^2 + 30 x[/tex]

Now, if you want the polynomial to be zero only and exactly at the four points you've given, you can choose every polynomial that is a multiple (numerically speaking) of this one. For example, you can multiply it by 2, 3, or -14.

If you want the polynomial to be zero at least at the four points you've given, you can multiply the given polynomial by every other function.

To find a polynomial with given zeros, each zero can be plugged into the format (x - a). Doing so with the provided zeros in this question, i.e., -2, 0, 3, and 5, represents the zeroes of the polynomial equation x(x + 2)(x - 3)(x - 5) which simplifies to  x4 - 6x3 + 3x2 + 60x.

The subject of this question is polynomial equations in mathematics. In order to find a polynomial equation that has zeroes at x = -2, x = 0, x = 3, and x = 5, you can use the fact that the equation (x - a)(x - b)(x - c)(x - d) will have zeros at a, b, c, and d.

By substituting the values for a, b, c, and d into the equation with the zeroes provided (-2, 0, 3, and 5), the polynomial equation that satisfies these zeroes can be expressed as: (x - (-2))(x - 0)(x - 3)(x - 5). Simplifying, this gives: x(x + 2)(x - 3)(x - 5).

To further simplify, we need to multiply these expressions: x*(x+2)*(-x+15)-(2*x-10),which simplifies to: x4 - 6x3 + 3x2 + 60x. This is the polynomial equation that has zeros at x = -2, x = 0, x = 3, and x = 5.

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