for what real values of $c$ is $x^2 16x c$ the square of a binomial? if you find more than one, then list your values separated by commas.

If this is a sample of 4 scores, then By using the definitional formula, SS equals 5. Your answer: 5.

Using the definitional formula, SS can be calculated as:

SS = ∑(x - X)2

where X is the sample mean.

To find X, we can use the formula:

X = ∑x / n

where n is the sample size.

Given that ∑x = 22 and n = 4, we can calculate X as:

X = 22 / 4 = 5.5

Now, we'll plug these values into the formula:

SS = 126 - (22)² / 4

Calculate (∑x)² / n:

(22)² / 4 = 484 / 4 = 121
Now we can plug in the values into the formula for SS:

SS = ∑(x - X)2
  = (1-5.5)2 + (2-5.5)2 + (3-5.5)2 + (4-5.5)2
  = (-4.5)2 + (-3.5)2 + (-2.5)2 + (-1.5)2
  = 20.5

Therefore, SS equals 20.5.

So, using the definitional formula, SS equals 5. Your answer: 5.

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Answer:

m = - 3 , b = 5

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line

m = [tex]\frac{-1-5}{2-0}[/tex] = [tex]\frac{-6}{2}[/tex] = - 3

the y- intercept b is the value of y on the y- axis where the line crosses

that is b = 5

Answer:

b = 5

m = -3

Step-by-step explanation:

y-intercept is where the line intersects the y-axis. So, the line intersects at (0,5).

So, y-intercept = b = 5

       Choose two points on the line: (0,5) and (1,2)

 x₁ = 0    ; y₁ = 5

  x₂ = 1    ; y₂ = 2

Substitute the points in the below formula to find the slope.

                [tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

                            [tex]= \dfrac{2-5}{1-0}\\\\=\dfrac{-3}{1}[/tex]

                        [tex]\boxed{\bf m = -3}[/tex]

The probability between 2 and 5 is P(2 ≤ X ≤ 5) = 0.285 + 0.296 + 0.179 + 0.066 = 0.826. We can expect around 5 customers out of 50 to qualify for the membership.

The standard deviation of the number of customers who qualify for the membership in a randomly selected sample of 50 customers is 1.5. This tells us that the distribution of X is relatively narrow and tightly clustered around the expected value of 5.

A) To find the probability that between 2 and 5 (inclusive) out of 20 randomly selected customers qualify for the membership, we can use the binomial distribution formula: P(2 ≤ X ≤ 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

where X is the number of customers who qualify for the membership. We can calculate each probability using the binomial distribution formula:

P(X = k) =

[tex]n choose k) * p^k * (1 - p)^(n - k)[/tex]

where n is the sample size, k is the number of successes, and p is the probability of success. In this case, n = 20, k = 2, 3, 4, 5, and p = 0.1. Plugging these values into the formula, we get: P(X = 2) =

[tex](20 choose 2) * 0.1^2 * 0.9^18 = 0.285[/tex]

P(X = 3) =

[tex] (20 choose 3) * 0.1^3 * 0.9^17 = 0.296[/tex]

P(X = 4) =

[tex] (20 choose 4) * 0.1^4 * 0.9^16 = 0.179[/tex]

P(X = 5) =

[tex](20 choose 5) * 0.1^5 * 0.9^15 = 0.066[/tex]

B) To find the expected number and standard deviation of the number who qualify in a randomly selected sample of 50 customers, we can use the binomial distribution again. The expected value of X is given by: E(X) =

[tex]n * p[/tex]

where n = 50 and p = 0.1. Plugging these values in, we get: E(X) =

[tex]50 * 0.1[/tex]

= 5 The standard deviation of X is given by: SD(X) =

[tex] \sqrt{} (n \times p \times (1 - p))[/tex]

Plugging in n = 50 and p = 0.1, we get: SD(X) = sqrt(50 * 0.1 * 0.9) = 1.5

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The surface area of the prism is 200 cm².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 8 cm (15 cm) + (8 cm + 15 cm + 17 cm) x 2cm

S.A = 120 cm² + 80 cm²

S.A = 200 cm²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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The calculated test statistic is 0.571. P 0.5, the null hypothesis.

A one-tailed z-test can be used to verify the assertion that there is a higher than 50% chance of the home side winning.

p > 0.5, where p is the percentage of football games won by the home team in the population.

The test statistic is calculated as:

(p - p) / (p(1-p) / n) = z

If n = 53 is the sample size, p = 0.5 is the hypothesized population proportion, and p is the sample fraction of football games won by the home team.

The percentage of the sample is p = 27/53 = 0.5094.

The calculated test statistic is:

z = (0.5094 - 0.5) / √(0.5(1-0.5) / 53) = 0.571

We determine the p-value for this test to be 0.2826 using a calculator or a table of the normal distribution as a reference.

We are unable to reject the null hypothesis since the p-value is higher than the significance level of 0.05. Therefore, at the 5% level of significance, we lack sufficient data to draw the conclusion that there is a better than 50% chance of the home team winning.

The calculated test statistic is:

z = (0.5094 - 0.5) / √(0.5(1-0.5) / 53)

= 0.571

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The probability that a randomly selected adult has an IQ greater than 133.2 is 0.0436 or 4.36%.

To find the probability that a randomly selected adult has an IQ greater than 133.2, assuming adults have IQ scores that are normally distributed with a mean of 97.6 and a standard deviation of 20.9, follow these steps:

1. Calculate the z-score: z = (X - μ) / σ, where X is the IQ score, μ is the mean, and σ is the standard deviation.
  z = (133.2 - 97.6) / 20.9
  z ≈ 1.71

2. Use a z-table or a calculator to find the area to the left of the z-score, which represents the probability of having an IQ score lower than 133.2.
  P(Z < 1.71) ≈ 0.9564

3. Since we want the probability of having an IQ greater than 133.2, subtract the area to the left of the z-score from 1.
  P(Z > 1.71) = 1 - P(Z < 1.71) = 1 - 0.9564 = 0.0436

So, the probability that a randomly selected adult has an IQ greater than 133.2 is approximately 0.0436 or 4.36%.

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Answer:

Step-by-step explanation:

1, 3 and 4

The approximate percentage error is 22.1514%.

Formulate:  (427.53−350)÷350

Calculate the sum or difference: 77.53/350

Multiply both the numerator and denominator with the same integer:

7753/35000

Rewrite a fraction as a decimal: 0.221514

Multiply a number to both the numerator and the denominator:

0.221514×100/100

Write as a single fraction: 0.221514×100/100

Calculate the product or quotient: 22.1514/100

Rewrite a fraction with denominator equals 100 to a percentage:

22.1514%

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

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The integral ∫g(x) dv(x) does not converge to a finite value.

To find the integral ∫g(x) dv(x) where g(x) = e^x and v is the measure on (R, B(R)) with respect to the Lebesgue measure:

1. Identify the given density function, g(x) = e^x.
2. Note that we need to find the integral of g(x) with respect to v(x), i.e., ∫g(x) dv(x).
3. Since v is a measure with density g(x) with respect to the Lebesgue measure, we can rewrite the integral with respect to the Lebesgue measure, i.e., ∫g(x) dλ(x), where λ is the Lebesgue measure.
4. Now, we can evaluate the integral ∫e^x dλ(x) on the real line (R).

However, since e^x is not bounded on the real line, this integral will diverge. Therefore, the integral ∫g(x) dv(x) does not converge to a finite value.

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Step-by-step explanation:

Using z-score table the value is    .9793     (97.93 %)

There are 15 children’s tickets were sold.

Given that;

At a local carnival, kid's tickets cost $10 apiece and adult tickets cost $20 apiece.

And, These are the only two types of tickets sold. At the recent show, 29 total tickets were sold for a total revenue of $430.

Let number of children’s tickets = x

And, Number of adult tickets = y

Hence, We can formulate;

⇒ x + y = 29 .. (i)

And, 10x + 20y = 430

⇒ x + 2y = 43

⇒ x = 43 - 2y

Plug above value in (i);

⇒ x + y = 29

⇒ 43 - 2y + y = 29

⇒ 43 - 29 = y

⇒ y = 14

From (i);

⇒ x + y = 29

⇒ x + 14 = 29

⇒ x = 29 - 14

⇒ x = 15

Thus, There are 15 children’s tickets were sold.

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Answer:

53.125 or 53 dumplings.

Step-by-step explanation:

20 percent of 2.00 is 0.40 so 2.00 minus 0.40 is equal to 1.60. Since 85 dumpling were sold we divide 85 with 1.6 to get 53.125

The two positive numbers with a product of 242 and the smallest possible sum of one number and twice the second number are 11 and 22.

To find two positive numbers with a product of 242, we can start by finding the prime factorization of 242, which is 2 x 11 x 11. From this, we know that the two numbers we're looking for must be a combination of these factors.

To minimize the sum of one number and twice the second number, we need to choose the two factors that are closest in value. In this case, that would be 11 and 22 (twice 11). So the two positive numbers we're looking for are 11 and 22.

To check that these numbers have a product of 242, we can multiply them together: 11 x 22 = 242.

Now we need to check that the sum of 11 and twice 22 is smaller than the sum of any other combination of factors. The sum of 11 and twice 22 is 55. If we try any other combination of factors, the sum will be larger. For example, if we chose 2 and 121 (11 x 11), the sum would be 244.

Therefore, the two positive numbers with a product of 242 and the smallest possible sum of one number and twice the second number are 11 and 22.

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The description of the parabola of the quadratic function is:

It opens downwards and is thinner than the parent function

The general formula for expressing a quadratic equation in standard form is:

y = ax² + bx + c

Quadratic equation In vertex form is:

y = a(x − h)² + k .

In both forms, y is the y -coordinate, x is the x -coordinate, and a is the constant that tells you whether the parabola is facing up ( + a ) or down ( − a ), (h, k) are coordinates of the vertex

In this case, a is negative and as such it indicates that it opens downwards and is thinner than the parent function

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In the given case equation P(A|B) = 0.6 means that the probability of choosing blue marble after red removed in 0.6

Let the event where the second marble chosen is blue be = B

Therefore, the Probability P(B|A) =0.6

Bayes' Theorem states that the likelihood of the second event given the first event multiplied by the probability of the first event equals the conditional probability of an event dependent on the occurrence of another event.

In the given case,

P(A|B) = probability of occurrence of A given B has already occurred.

P(B|A) = probability of occurrence of B given A has already occurred.

Therefore,

P(A|B) = P(B|A) P(A)/ P(B)

The likelihood of selecting a blue marble after removing a red stone is 0.6, which is how the probability P(B|A)=0.6 is defined.

Complete question:

John has a bag of red and blue marbles. John chooses 2 marbles without replacing the first. Let A be the event where the first marble chosen is red. Let B be the event where the second marble chosen is blue. What does equation P(A|B) = 0.6 mean ?

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Answer: 2

Step-by-step explanation:

The coordinate point (8, -15) is lies in fourth quadrant.

The given coordinate point is (8, -15).

Part A: Here, x-coordinate is positive that is 8 and the y-coordinate is negative that is -15.

Quadrant IV: The bottom right quadrant is the fourth quadrant, denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

So, the point lies in IV quadrant.

Part B:

Here r²=x²+y²

r²=8²+(-15)²

r²=64+225

r²=289

r=√289

r=17 units

So, the radius is 17 units

Therefore, the coordinate point (8, -15) is lies in fourth quadrant.

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The word “element” is defined as the items in a set

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

The word “element”

By definition, the word “element” is defined as the items in a set

Take for instance, we have

A = {1, 2, 3}

The set is set A and the elements are 1, 2 and 3

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Step-by-step explanation:

Total cost will be

$ 73.56   + 7% of 73.56

$ 73.56 + .07 * $73.56

(1.07) ( 73.56) = $ 78 . 71

The answers are:

(a) f is decreasing on (-∞, 0) and increasing on (0, ∞).

(b) f is concave up on (-∞, ∞).

(c) Local minimum value at x = 0, local maximum value DNE.

(d) Global minimum value is -2 at x = -1, global maximum value is 22 at x = 2.

(e) There are no points of inflection.

(a) To find where the function is increasing or decreasing, we need to find the critical points and test the intervals between them:

[tex]f(x) = x^4 + 3x^3 + 3x^2\\f'(x) = 4x^3 + 9x^2 + 6x[/tex]

Setting f'(x) = 0, we get:

[tex]0 = 2x(2x^2 + 3x + 3)[/tex]

The quadratic factor has no real roots, so the only critical point is x = 0.

We can test the intervals (-∞, 0) and (0, ∞) to find where f is increasing or decreasing:

For x < 0, f'(x) is negative, so f is decreasing.

For x > 0, f'(x) is positive, so f is increasing.

Therefore, f is decreasing on (-∞, 0) and increasing on (0, ∞).

(b) To find where the function is concave up or concave down, we need to find the inflection points:

f''(x) =[tex]12x^2 + 18x + 6[/tex]

Setting f''(x) = 0, we get:

0 = [tex]6(x^2 + 3x + 1)[/tex]

The quadratic factor has no real roots, so there are no inflection points.

Since the second derivative is always positive, f is concave up everywhere.

(c) To find the local extreme values, we need to find the critical points and determine their nature:

f'(x) = [tex]4x^3 + 9x^2 + 6x[/tex]

At x = 0, f'(0) = 0 and f''(0) = 6, so this is a local minimum.

There are no local maximum values.

(d) To find the global extreme values on [-1, 2], we need to check the endpoints and the critical points:

f(-1) = -2, f(0) = 0, f(2) = 22

The global minimum value is -2 at x = -1, and the global maximum value is 22 at x = 2.

(e) To find the points of inflection, we need to find where the concavity changes:

Since there are no inflection points, there are no points of inflection.

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The average speed of the train is both greater than or equal to 2.3928 km/minute and less than or equal to 3.3567 km/minute.

To find the average speed of the train, we divide the distance traveled by the time taken:

Average speed = distance / time

= 503 km / 180 minutes

= 2.7944... km/minute

Since the distance is measured correct to the nearest kilometer, the actual distance could be as low as 502.5 km or as high as 503.5 km. Similarly, since the time is measured correct to the nearest minute, the actual time taken could be as low as 2.5 hours or as high as 3.5 hours.

To find the maximum average speed, we assume that the distance traveled is 503.5 km and the time taken is 2.5 hours.

Maximum average speed = 503.5 km / 150 minutes = 3.3567... km/minute

To find the minimum average speed, we assume that the distance traveled is 502.5 km and the time taken is 3.5 hours.

Minimum average speed = 502.5 km / 210 minutes = 2.3928... km/minute

Therefore, the average speed of the train is both greater than or equal to 2.3928 km/minute and less than or equal to 3.3567 km/minute.

Rounding to two decimal places, the average speed of the train is 2.79 km/minute.

Reason: Both 2.79 km/minute and the minimum and maximum average speeds are correct to the nearest hundredth of a kilometer per minute and take into account the maximum possible error in the measurements.

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We can say with 99% confidence that the true mean price of all transactions is between $2,799.16 and $3,000.84.

To obtain a 99% confidence interval for the mean price of all transactions, we can use the formula:

CI =  ± z*(σ/√n)

Where:
= sample mean price = 2900 dollars
σ = population standard deviation = 290 dollars
n = sample size = 30
z = z-score for a 99% confidence level = 2.576 (from the standard normal distribution table)

Substituting these values into the formula, we get:

CI = 2900 ± 2.576*(290/√30)
CI = 2900 ± 100.84
CI = (2799.16, 3000.84)

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The value of the sides are;

CB = 13.8

CD = 6. 9

To determine the value of the sides of the triangle, we need to know the different trigonometric identities are;

From the information given, we have that;

Using the sine identity, we have that;

tan 60 = CD/4

cross multiply the values, we have;

CD = 4(1.73)

multiply the values

CD = 6.9

To determine the value;

sin 30 = 6.9/CB

CB = 13.8

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The probability that the sample mean will be within $500 of the population mean is approximately 0.3982 (or 39.82% when expressed as a percentage) to 4 decimal places.

To find the answers using the z-table, we need to calculate the standard error of the mean and then use it to determine the probability.

a. The standard error of the mean (SE) is calculated using the formula:

SE = σ / sqrt(n),

where σ is the standard deviation and n is the sample size.

Given that the standard deviation is $8,500 and the sample size is 80, we can calculate the standard error of the mean:

SE = 8,500 / sqrt(80) ≈ 950.77.

Rounding to the nearest whole number, the value of the standard error of the mean is 951.

b. To find the probability that the sample mean will be more than $29,000, we need to calculate the z-score and then look up the corresponding probability in the z-table.

The z-score is calculated using the formula:

z = (x - μ) / SE,

where x is the sample mean, μ is the population mean, and SE is the standard error of the mean.

In this case, x = $29,000, μ = population mean (unknown), and SE = 951.

Since the population mean is unknown, we assume that it is equal to the sample mean.

z = (29,000 - 29,000) / 951 = 0.

Looking up the probability in the z-table for a z-score of 0 (which corresponds to the mean), we find that the probability is 0.5000.

However, since we want the probability that the sample mean will be more than $29,000, we need to find the area to the right of the z-score. This is equal to 1 - 0.5000 = 0.5000.

Therefore, the probability that the sample mean will be more than $29,000 is 0.50 (or 50% when expressed as a percentage) to 2 decimal places.

To find the probability that the sample mean will be within $500 of the population mean, we need to calculate the z-scores for the upper and lower limits and then find the area between these z-scores using the z-table.

c. Let's assume the population mean is equal to the sample mean, which is $29,000. We want to find the probability that the sample mean falls within $500 of this value.

The upper limit is $29,000 + $500 = $29,500, and the lower limit is $29,000 - $500 = $28,500.

To calculate the z-scores for these limits, we use the formula:

z = (x - μ) / SE,

where x is the limit value, μ is the population mean, and SE is the standard error of the mean.

For the upper limit:

z_upper = ($29,500 - $29,000) / 951 ≈ 0.526

For the lower limit:

z_lower = ($28,500 - $29,000) / 951 ≈ -0.526

Now, we look up the probabilities associated with these z-scores in the z-table. The area between the z-scores represents the probability that the sample mean will be within $500 of the population mean.

Using the z-table, we find that the probability corresponding to z = 0.526 is approximately 0.6991, and the probability corresponding to z = -0.526 is approximately 0.3009.

The probability that the sample mean will be within $500 of the population mean is the difference between these two probabilities:

Probability = 0.6991 - 0.3009 ≈ 0.3982.

Therefore, the probability that the sample mean will be within $500 of the population mean is approximately 0.3982 (or 39.82% when expressed as a percentage) to 4 decimal places.

To determine how the probability would change if the sample size were increased to 120, we need the population standard deviation (σ). Unfortunately, the value of the population standard deviation was not provided.

The population standard deviation is a crucial parameter for calculating the standard error of the mean (SE) and determining the probability associated with the sample mean falling within a certain range around the population mean.

Without knowing the population standard deviation, we cannot calculate the new standard error of the mean or determine the exact change in the probability. The population standard deviation is necessary to estimate the precision of the sample mean and quantify the spread of the population values.

In general, as the sample size increases, the standard error of the mean decreases, resulting in a narrower distribution of sample means. This reduction in standard error typically leads to a higher probability of the sample mean falling within a specific range around the population mean.

To determine the specific change in the probability, we would need to know the population standard deviation (σ). Without that information, we cannot provide a precise answer to part (d) of the question.

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The probability of number of 1-2 Children in car and 3 plus children in car is 0.203.

We have,

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

The probability of P(1-2 children| car). P (3 plus children| car) is given by:

P = 63/88 × 25/88

P=0.203

The probability of P(Bus| 1-2 children). P (Bus | 3 plus children) is given by:

P = 38/101 × 49/74

P=0.249

The probability of P(Car |1-2 Children) is given by:

P= 63/101

P=0.624

The probability of P(3 plus children | Bus)is given by:

P=49/87

P=0.563

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complete question:

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

The table shows the mode of transportation to school for families with a specific number of children.

Mode of Transportation

Car

Number of

Children

0.284

1-2

63

38

3+

25

49

Total

88

87

A family from the survey is selected at random. Match the probability to each event.

0.662

Bus

0.203

0.249

101

74

175

0.624

P (3+ Children Bus)

Total

P(1-2 Children Car) - P (3+ Children Car)

Reset

P (Car 1-2 Children)

0.563

P (Bus 1-2 Children) - P (Bus 3+ Children)

▸

The coordinates of S' is (-10, 6).

We have,

Dilation is a transformation in which the size of a figure is changed without altering its shape.

In the coordinate plane, a dilation changes the size of a figure by multiplying the distance between each point and the center of dilation by a scale factor.

The center of dilation is a fixed point in the plane about which the figure is dilated. If the scale factor is greater than 1, the figure is enlarged, and if it is less than 1, the figure is reduced. If the scale factor is negative, the figure is also reflected across the center of dilation.

From the figure,

S = (-5, 3)

Now,

Dilated with a scale factor of 2.

This means,

S' = (-5 x 2, 3 x 2) = (-10, 6)

Thus,

The coordinates of S' is (-10, 6).

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The three pairs of fraction whose sum is 3/5 are

We have to find pairs of fractions that have a sum of 3/5.

First pair:

1/5 + 2/5

= 3/5

Second pair:

= -2/5 + 1

= -2/5+ 5/5

= 3/5

Third pair:

= -6/5 + 9/5

= 3/5

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The probability that at least two of the kittens will be chocolate brown is 0.3087.

We have,

Number of kittens = 5

Each kitten has a 30% chance of being chocolate brown.

So, p = 0.5 and q= 1-0.3 = 0.7

Now, P(X =2) = C( 5, 2) 0.3² (0.7)³

= 5! / 2!3! (0.09) (0.343)

= 10 x 0.03087

= 0.3087

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Answer:

A sample is a subset of the population.

In the given scenario, the nominal variables are Taia's income, the price of a digital movie rental, and the price of an americano. The real variables would be Taia's income adjusted for inflation, the real price of a digital movie rental, and the real price of an americano.

To calculate the real value of a variable, we need to adjust it for inflation using a suitable price index. As the question does not provide any information about inflation, we cannot calculate the real value of any variable.

Therefore, none of the options given in the question would give the real value of a variable.
Hi! I'd be happy to help you with this question. In the context of the classical dichotomy, real variables are quantities or values that are adjusted for inflation, while nominal variables are unadjusted values.

In the given scenario, Taia spends her income on digital movie rentals and americanos. We have the following information for 2016:

1. Hourly wage: $28.00 (nominal variable)
2. Price of a digital movie rental: $7.00 (nominal variable)
3. Price of an americano: $4.00 (nominal variable)

To determine the real value of a variable, we need to adjust these nominal values for inflation. However, the question does not provide any information about the inflation rate or a base year for comparison. Thus, we cannot calculate the real values for these variables in this scenario.

In summary, we do not have enough information to determine the real value of any variable in this case. Please provide the inflation rate or base year if you'd like me to help you calculate the real values.

Learn more about :

Nominal variables : brainly.com/question/13539124

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