the expected payout for each play of a carnival game is $0.15. if each game cost $0.50 to play, what is the carnivals expected gain per play?

The solution of the function, f( )  = -8 is f(1) = -8.

A function relates input to output. A function assigns exactly one output to each input of a specified type.

In other words, a function is a relationship between two or more variables, such that each input has only one output.

Therefore, let's solve the function as follows:

f(x) = -7x - 1

Hence,

f(x)  = -8

Let's find x as follows:

-7x - 1 = - 8

-7x = -8 + 1

-7x = -7

divide both sides by -7

x = -7 / -7

x = 1

Hence,

f(1) = -8

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The birth weight at the 70th percentile is about 3.156 ounces, and the birth weight at the 30th percentile is about 2.844 ounces.

To find the birth weights at the 70th and 30th percentiles, we'll use the properties of a normal distribution, the given mean (3 ounces), and the standard deviation (0.3 ounce).

a. To find the birth weight at the 70th percentile, we first need to find the corresponding z-score, which represents how many standard deviations above or below the mean a value is. Using a z-score table or calculator, we find that the z-score for the 70th percentile is approximately 0.52. Now, we can use the formula:

Weight at 70th percentile = Mean + (Z-score * Standard deviation)
Weight at 70th percentile = 3 + (0.52 * 0.3) ≈ 3.156 ounces

b. To find the birth weight at the 30th percentile, we find the corresponding z-score, which is approximately -0.52. Using the same formula as above:

Weight at 30th percentile = Mean + (Z-score * Standard deviation)
Weight at 30th percentile = 3 + (-0.52 * 0.3) ≈ 2.844 ounces

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The probability that the sample will contain more than 5% defective units is approximately 0.9525 or 95.25%.

To solve this problem, we can use the binomial distribution formula:

P(X > 5) = 1 - P(X ≤ 5)

where X is the number of defective items in a sample of size n = 100, and p = 0.1 is the probability of an item being defective.

To calculate P(X ≤ 5), we can use the binomial cumulative distribution function (CDF) or a binomial probability table. Alternatively, we can use a normal approximation to the binomial distribution, which is valid when np ≥ 10 and n(1-p) ≥ 10, as is the case here (np = 10 and n(1-p) = 90).

Using the normal approximation, we can standardize the distribution of X as follows:

[tex]z = (X - np) / \sqrt{(np(1-p))}[/tex]

Then, we can use a standard normal table or calculator to find the probability of z ≤ z0, where z0 is the standardized value corresponding to X = 5.

Let's use the normal approximation method to solve the problem:

np = 100 x 0.1 = 10

σ = [tex]\sqrt{(np(1-p))} = \sqrt{(9)} = 3[/tex]

z0 = (5 - 10) / 3 = -1.67 (rounded to two decimal places)

Using a standard normal table or calculator, we find that P(Z ≤ -1.67) = 0.0475 (rounded to four decimal places).

Therefore, P(X > 5) = 1 - P(X ≤ 5) = 1 - 0.0475 = 0.9525 (rounded to four decimal places).

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Answer: 7.5 years

Step-by-step explanation: First, we need to calculate your annual savings by multiplying your gross pay by 15% and then subtracting the taxes:

$40,000 x 15% = $6,000 (annual savings before taxes)

$6,000 - $4,000 = $2,000 (annual savings after taxes)

Next, we can calculate how many years it will take to save $15,000 by dividing the goal by the annual savings:

$15,000 ÷ $2,000 = 7.5 years

Therefore, it will take you 7.5 years to achieve your goal of creating a $15,000 emergency fund by saving 15% of your gross pay.

The statement "the sampling distribution of the difference between the two sample means will have a mean of one" is not necessarily true, and neither is the statement "will have a variance of one" or "can be approximated by any distribution."

The sampling distribution of the difference between two sample means from independent populations will have a mean equal to the difference between the population means. However, the variance of the sampling distribution will depend on the sample sizes and the variances of the two populations.

If the sample sizes are large enough (usually considered to be greater than or equal to 30) and the population variances are known or assumed to be equal, then the sampling distribution of the difference between two sample means can be approximated by a normal distribution.

Therefore, the statement "the sampling distribution of the difference between the two sample means will have a mean of one" is not necessarily true, and neither is the statement "will have a variance of one" or "can be approximated by any distribution." However, the statement "can be approximated by a normal distribution" is generally true if the sample sizes are large enough and the population variances are known or assumed to be equal.

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The probability that the driver has no accidents in the next 365 days, but then has at least one accident in the 365-day period that follows this initial 365-day period, is approximately 0.204.

Let X be the time until the next accident for the driver. We know that X is exponentially distributed with a mean of 200 days, which means that its probability density function (PDF) is:

[tex]$f(x) = \frac{1}{200} e^{-\frac{x}{200}} \text{ for } x > 0$[/tex]

We want to calculate the probability that the driver has no accidents in the next 365 days (i.e., from day 0 to day 365), but then has at least one accident in the 365-day period that follows (i.e., from day 366 to day 730). We can express this probability as:

P(no accidents in first 365 days) * P(at least one accident in next 365 days | no accidents in first 365 days)

The probability of having no accidents in the first 365 days is simply the cumulative distribution function (CDF) of X evaluated at x = 365:

[tex]$F(365) = \int_{0}^{365} f(x) dx = 1 - e^{-\frac{365}{200}} \approx 0.451$[/tex]

The probability of having at least one accident in the next 365 days, given that there were no accidents in the first 365 days, can be calculated using the memoryless property of the exponential distribution:

P(at least one accident in next 365 days | no accidents in first 365 days) = P(X < 365) = F(365) ≈ 0.451

Therefore, the probability we are interested in is:

P(no accidents in first 365 days) * P(at least one accident in next 365 days | no accidents in first 365 days)

= 0.451 * 0.451 ≈ 0.204

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We can conclude that det a = 12 means that the linear transformation t stretches shapes in R2 by a factor of 12 without reflecting them.

We can start by writing out the matrix representation of the linear transformation t, which is given by:

[t(v1) t(v2)] = [3v1 4v2] = [3 0; 0 4][v1 v2]

Here, we have used the fact that t is a linear transformation, which means that it can be represented by a matrix. The matrix [3 0; 0 4] is the matrix representation of t with respect to the standard basis of R2.

Now, we can use the formula for the determinant of a 2x2 matrix to find det a:

det a = ad - bc

where a, b, c, and d are the entries of the matrix a. In this case, we have:

a = 3, b = 0, c = 0, and d = 4

Plugging these values into the formula, we get:

det a = (3)(4) - (0)(0) = 12

So, we can say that det a = 12.

To justify this answer, we can use the fact that the determinant of a matrix represents the factor by which the matrix scales the area of any given shape in R2. Since det a is positive (since it is the product of two positive numbers), we know that the linear transformation represented by a preserves orientation (i.e., it does not reflect shapes). Furthermore, since det a is greater than 1, we know that the transformation stretches shapes by a factor of det a. Specifically, any shape in R2 that has area A under the transformation t will have area det a * A after the transformation. In this case, since det a = 12, we know that t stretches shapes by a factor of 12.

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For a group of 32 pets including 16 puppies and 16 kittens is lined up in random order, the probability that the pet in the 15-th position is a kitten is equals to the 0.20.

Probability is calculated by dividing the favourable outcomes to the total possible outcomes. There is a group of 16 puppies and 16 kittens. It is lined up in random order. Total number of pets = 32

Which means 32 out of 32 are selected for line up and order of selection is important. So, using the permutation, total possible outcomes = ³²P₃₂ = 32!

We have to determine probability that the pet in the 15ᵗʰ position is a kitten.

When 15ᵗʰ position is a kitten, there is 16 ways to select a kitten to be 15ᵗʰ place and there are ³¹P₃₁ ways to line up the remaining 31 pets. So, favourable outcomes = 16.³¹P₃₁ = 16 × 31!

The required probability = [tex]\frac{ 16 × 31! }{32!} [/tex]

= [tex]\frac{ 16 × 31! }{32×31!} [/tex]

= 0.20

Hence, required probability is 0.20.

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The mean of X based on random samples of size 25 taken with replacement is also 75, and the standard deviation of X based on random samples of size 25 taken with replacement is 8/5.

When random samples are taken with replacement, the mean of the sample means is equal to the population mean, and the standard deviation of the sample means is equal to the population standard deviation divided by the square root of the sample size.

So, the mean of the sample means is 75, and the standard deviation of the sample means is:

[tex]standard deviation of sample means = standard deviation of population / \sqrt{(sample size)}[/tex]

[tex]= 8 / \sqrt{(25)}[/tex]

= 8/5

Therefore, the mean of X based on random samples of size 25 taken with replacement is also 75, and the standard deviation of X based on random samples of size 25 taken with replacement is 8/5.

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They are both the points on the sphere that are farthest from the point (1, -1, 1).To find the point on the sphere x^2 + y^2 + z^2 = 4 that is farthest from the point (1, -1, 1), we need to first find the center of the sphere.

The center of the sphere is the origin (0, 0, 0) since the equation is in the form x^2 + y^2 + z^2 = r^2 where r is the radius, and r is equal to 2 in this case.

Next, we need to find the vector that connects the center of the sphere to the point (1, -1, 1). This vector is given by (1, -1, 1) - (0, 0, 0) = (1, -1, 1).

To find the point on the sphere that is farthest from the point (1, -1, 1), we need to find the point on the sphere where the vector from the center of the sphere to that point is orthogonal (perpendicular) to the vector that connects the center of the sphere to the point (1, -1, 1).

Since the center of the sphere is the origin, the vector from the center of the sphere to the point we're looking for is simply a scalar multiple of the vector (1, -1, 1).

Let the point we're looking for be (x, y, z). Then, the vector from the center of the sphere to that point is given by (x, y, z), and we need to find a scalar k such that (x, y, z) dot (1, -1, 1) = k * (1, -1, 1) dot (1, -1, 1), where "dot" represents the dot product.

Expanding this equation, we get x - y + z = k * 3.

Since the point (x, y, z) is on the sphere x^2 + y^2 + z^2 = 4, we also have x^2 + y^2 + z^2 = 4.

Substituting x - y + z = k * 3 into x^2 + y^2 + z^2 = 4, we get (k * 3)^2 + 2y^2 = 4.

Solving for y, we get y = +/- sqrt((4 - 9k^2)/2).

Since we want the point on the sphere that is farthest from the point (1, -1, 1), we want the value of k that maximizes the distance between the point (1, -1, 1) and the point (x, y, z) on the sphere.

The distance between two points (x1, y1, z1) and (x2, y2, z2) is given by the formula sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2).

Substituting in our values, we get the distance between the points as sqrt((x - 1)^2 + (y + 1)^2 + (z - 1)^2).

To maximize this distance, we want to minimize the square of the distance, which is given by (x - 1)^2 + (y + 1)^2 + (z - 1)^2.

Substituting in our values for y and simplifying, we get (x - 1)^2 + (4 - 9k^2)/2 + (z - 1)^2 = 9k^2/2 - 3.

Since x^2 + y^2 + z^2 = 4, we also have x^2 + (4 - 9k^2)/2 + z^2 = 4.

Substituting in our value for y, we get x^2 + (4 - 9k^2)/2 + z^2 = 4 - (9k^2/2).

Simplifying, we get x^2 + z^2 = 9/2 - (5k^2/2).

Since we want to maximize the distance between the point on the sphere and the point (1, -1, 1), we want to minimize the value of k^2.

The minimum value of k^2 occurs when y = 0, which means that x - y + z = 0.

Substituting in x^2 + y^2 + z^2 = 4, we get x^2 + z^2 = 2.

To find the point on the sphere that is farthest from the point (1, -1, 1), we need to solve the system of equations x - y + z = 0, x^2 + z^2 = 2.

Solving for x, y, and z, we get (x, y, z) = (sqrt(2)/2, -sqrt(2)/2, sqrt(2)/2) or (-sqrt(2)/2, sqrt(2)/2, -sqrt(2)/2).

Since both of these points are equidistant from the point (1, -1, 1), they are both the points on the sphere that are farthest from the point (1, -1, 1).

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According to data from the Pew Research Center, there were approximately 10.5 million unauthorized immigrants living in the United States in 2017. This number represents around 25% of the total foreign-born population in the country. In conclusion, out of the 41.3 million foreign-born individuals in the U.S., about 10.5 million are considered unauthorized immigrants.

Unauthorized immigrants, also known as undocumented immigrants, are individuals who enter the United States without legal permission or overstay their visas. They are not eligible for most government benefits and are often subject to deportation if caught.

The Pew Research Center estimates that there were 41.3 million foreign-born individuals living in the United States in 2017, which includes both authorized and unauthorized immigrants. Of this population, around 10.5 million were unauthorized immigrants.

Unauthorized immigration is a complex and contentious issue in the United States, with many different opinions on how to address it. Understanding the size and characteristics of this population is an important part of any discussion or policy debate.

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Answer:99

Step-by-step explanation:

The number of people on x tables is 2n + mx

From the question, we have the following parameters that can be used in our computation:

Tables = x

Represent the number of people on the middle tables with m

So, we have

Middle table = (x - 2) * m

Considering the first and the last tables have more people

Represent the additional number of people with n

So, we have

First and last = 2(m + n)

The number of people on x tables is

People = First and last + Middle table

This gives

People = 2(m + n) + (x - 2) * m

Expand

People = 2m + 2n + mx - 2m

Evaluate the like terms

People = 2n + mx

Hence, the number of people is 2n + mx

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Mr. Krumm paid $9.27 for a tie that had a 3% sales tax added on. So, the tie cost $231.75 before the tax was included.

To find out how much the tie cost before the tax was included, we need to first calculate how much of the total price was due to the tax. We know that the total price Mr. Krumm paid was $9.27, and that this price included a $3% sales tax.

To calculate the amount of tax that was included in the price, we can start by setting up an equation:

0.03x = 9.27 - x

Here, x represents the cost of the tie before the tax was included. We know that the tax is 3% of this cost, which is why we're multiplying it by 0.03.. We're also subtracting x from 9.27 to get the amount of tax that was added on.

Simplifying this equation, we get:

0.04x = 9.27

Dividing both sides by 0.04, we get:

x = 231.75

So the tie cost $231.75 before the tax was included.

In summary, Mr. Krumm paid $9.27 for a tie that had a 3% sales tax added on. To find out how much the tie cost before the tax was included, we set up an equation and solved for the cost of the tie (x) before the tax was added. The answer is that the tie cost $231.75 before the tax was included.

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Answer: 7

Step-by-step explanation:

Answer: y = -1/2x - 5

Step-by-step explanation: slope intercept form equals y=mx+b you are trying to put it in this form therefore you subtract 2x from each side and you get 4y= -2x-20 you then divide 4 from each side and you get the answer

The calculated value of x in the expression x^(1/12) = 49^(1/24) is 7

From the question, we have the following parameters that can be used in our computation:

x^(1/12) = 49^(1/24)

Express 49 as 7^2

So, we have

x^(1/12) = 7^(2 * 1/24)

Evaluate the products

This gives

x^(1/12) = 7^(1/12)

When both sides of the equations are compared, we have

x = 7

Hence, the value of x in the expression is 7

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Observed frequencies are essential in hypothesis testing for comparing population proportions, as they represent the sample data collected from the populations of interest and serve as the basis for calculating test statistics and drawing conclusions about the hypothesis.

In a hypothesis test comparing two or more population proportions, observed frequencies refer to the sample data collected from a population of interest.

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The equivalent expression is 15a(-2a + 3).

To factor out the common factor of -15a from the given expression -30a^2 + 45a, we can first factor out -15, then factor out a:

-30a^2 + 45a = -15a(2a - 3)

Therefore, the expression -30a^2 + 45a is equivalent to -15a(2a - 3).

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An integer C that will make the polynomial factorable 32 − 8 + C = 24

To make the polynomial 32 - 8 + C factorable,

we must use a quadratic trinomial - ax²+bx+c.

We can rewrite the polynomial as 24 + C.

For it to be factorable, C   should be equal to -24, so that the expression becomes 0 when x = 2.

Therefore, C = -24.

Proof:

32 - 8 + (-24) = 0

Note;

A polynomial is an expression in mathematics that consists of variables and coefficients and includes only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

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Full Question:

a)  Find an integer C that will make the polynomial below factorable
32 − 8 + C = ____

10b) Show that the integer C you found works by factoring the trinomial using the X that we learned in class.

The HDD for the month of January in State College, PA is 930.

To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.

HDD = 65°F - 35°F
HDD = 30°F

Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:

1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.

So, the HDD for the month of January in State College, PA is 930.

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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.

To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:

HDD = (65 - 35) x 31
HDD = 930

So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.

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Answer: A

Step-by-step explanation:

p.s i am emo

The expected time taken for the system to fail is dependent on the specific details of the system in question.

However, if we assume that the three modes have equal probabilities of occurring and that the failure occurs when the system reaches a specific mode, we can use the concept of Markov chains to find the expected time until failure.

In this case, the expected time until failure would be the reciprocal of the probability of the system transitioning to the failure mode.

Therefore, if each mode has an equal probability of 1/3, the expected time until failure would be 3 units of time.

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The sum of the series is [[tex]e^a - 1]/(1+a).[/tex]

For the first question, we have:

(1) (2) () 10).(-1)*(0) = (1) * (2) * (0) * (-10) = 0

Therefore, the answer is 0.

For the second question, the Taylor series of the given expression is:

[tex]f(x) = 1 + x^2/2! + x^3/3! + ... + x^n/(n+1)![/tex]

We want to find the sum of this series evaluated at a particular value of x. Let's call this value a. Then:

[tex]f(a) = 1 + a^2/2! + a^3/3! + ... + a^n/(n+1)![/tex]

To find the sum of this series, we need to take the limit as n approaches infinity. Using the ratio test, we can show that the series converges for all values of x. Therefore:

sum = lim (n -> infinity) f(a)

sum = lim (n -> infinity) [[tex]1 + a^2/2! + a^3/3! + ... + a^n/(n+1[/tex])!]

We can rewrite the series as:

sum = lim (n -> infinity) [[tex]1 + a^2/2! + a^3/3! + ... + a^n/(n+1)![/tex]]

sum = lim (n -> infinity) [tex][(a^(n+1)/(n+1)!) + (a^n/n!) + (a^(n-1)/(n-1)!) + ... + (a^2/2!) + 1][/tex]
Using the formula for the sum of an infinite geometric series, we can simplify this expression to:

sum = lim (n -> infinity) [tex][a^(n+1)/(n+1)!] * [1/(1-a)][/tex]

We can now use the fact that [tex]e^x = 1 + x/1! + x^2/2! + x^3/3![/tex]+ ... to rewrite the expression as:

[tex]sum = [e^a - 1]/(1+a)[/tex]

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The statement A confidence interval for proportions is used to estimate the population proportion not the sample proportion is true.

A confidence interval for proportions is a statistical tool used to estimate the range of values within which the population proportion is likely to lie. It is calculated based on the sample proportion, sample size, and a specified level of confidence.

The sample proportion is only used as a point estimate of the population proportion, but the confidence interval takes into account the variability of the sample proportion and provides a range of values that are likely to include the population proportion with a certain level of confidence.

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The simplified form of the given function f(g(x)) as required to be determined in the task content is; f (g(x)) = 3x² -24x + 50.

It follows from the task content that the expression which represents f (g(x)) as required in the task content is to be determined.

Given; f(x) = 3x^2+2 and g(x) = x - 4.

Therefore; f (g(x)) = 3 (x - 4)² + 2

= 3 (x² - 8x + 16) + 2

= 3x² - 24x + 48 + 2

f (g(x)) = 3x² -24x + 50.

Ultimately, the expression which represents the function f (g(x)) as required is; f (g(x)) = 3x² -24x + 50.

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The function f(x) has a relative minimum at x = 1/7 and a relative maximum at x = 0.To find where the function f(x) = 33° - 873 – 210.x2 + 4 is increasing and decreasing, we need to analyze its derivative function, f'(x), which is equal to 12x(1 - 7x). To determine where f'(x) is positive or negative, we use the VD Test and consider the signs of the factors 12, 1 - 7x, and x.

We first find the critical numbers by solving f'(x) = 0:

12x(1 - 7x) = 0
x = 0 or x = 1/7

These critical numbers divide the real line into three intervals: (-∞, 0), (0, 1/7), and (1/7, ∞). We then test a value from each interval in f'(x) to determine its sign:

f'(-1) = 12(-1)(1 + 7) = -96  (negative)
f'(1/14) = 12(1/14)(1 - 1) = 0  (zero)
f'(2) = 12(2)(1 - 14) = -240  (negative)

Using this information, we can construct a chart:

Interval | Test Value | 12 | 1-7x | x | f'(x)
-----------------------------------------------------
(-∞, 0) | -1 | - | - | - | -
(0, 1/7) | 1/14 | + | + | + | Increasing
(1/7, ∞) | 2 | + | - | + | Decreasing

Based on the chart, we can see that f(x) is increasing on the interval (0, 1/7) and decreasing on the interval (1/7, ∞). Therefore, we can conclude that the function f(x) has a relative minimum at x = 1/7 and a relative maximum at x = 0.

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The value of the test statistic is approximately 2.8

To determine the effectiveness of the advertising campaign at the fast-food restaurant, we can use the sample data and perform a hypothesis test using the test statistic. In this case, the terms you want me to include are: average daily sales, sample size, population standard deviation, and the test statistic.

The average daily sales before the campaign were $6,000 per day. After introducing the advertising campaign, a sample of 49 days of sales was taken, showing an average of $6,400 per day. The population standard deviation is $1,000.

To calculate the test statistic, we can use the following formula:

Test statistic = (Sample mean - Population mean) / (Population standard deviation / sqrt(Sample size))

Test statistic = ($6,400 - $6,000) / ($1,000 / sqrt(49))

Test statistic = $400 / ($1,000 / 7)

Test statistic = $400 / $142.86

Test statistic ≈ 2.8

So, the value of the test statistic is approximately 2.8. This test statistic can be used to determine the effectiveness of the advertising campaign by comparing it to a critical value or finding the p-value, which will help us understand if the observed increase in daily sales is statistically significant.

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