Is -9 a real or imaginary number?

To find the z-score for a sales associate who earns $37,500, we can use the formula:

z = (x - μ) / σ

Where:

x is the value we want to convert to a z-score (in this case, $37,500),

μ is the mean of the distribution (in this case, $32,500), and

σ is the standard deviation of the distribution (in this case, $2,500).

Substituting the given values into the formula, we have:

z = (37,500 - 32,500) / 2,500

z = 5,000 / 2,500

z = 2

Therefore, the z-score for a sales associate who earns $37,500 is 2.

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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.

The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.

We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:

Z = (Value - Mean) / Standard Deviation

So, the z-score for an associate earning $37,500 would be:

Z = ($37,500 - $32,500) / $2,500

This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.

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To have the same cost at both companies, the number of stickers will have to be 40

Company A :

Design Fee = $30

Costvper sticker = $0.80

Company B :

Design Fee = $14

Cost per sticker = $1.20

Let the number of stickers = p

Total cost of company A = 30 + 0.80p

Total cost of company B = 14 + 1.20p

For the cost to be the same :

Company A = Company B

30 + 0.80p = 14 + 1.20p

Collect like terms :

30 - 14 = 1.20p - 0.80p

16 = 0.40p

Divide both sides by 0.40

p = 16/0.40

p = 40 stickers

Therefore, to have the same price, 40 stickers will have to be ordered.

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Answer:

D

Step-by-step explanation:

The statement is constructed so that, if the machine were to determine that the statement is provable, it would be false.

The statement is not provable by definition.

Here is the answer to your question:

Let F(a,b) be a decidable problem.

G(x) = {“yes”, “no”, ∃yF(y,x) = “yes” otherwise} is recognizable.

It can be shown in the following way:

If F(a,b) is decidable, then we can build a Turing machine T that decides F.

If G(x) accepts “yes,” then we can return “yes” right away.

If G(x) accepts “no,” we know that F(y,x) is “no” for all y.

Therefore, we can simulate T on all possible inputs until we find a y such that F(y,x) = “yes,” and then we can accept G(x).

Since T eventually halts, we are guaranteed that the simulation will eventually find an appropriate y, so G is recognizable.

Gödel’s First Incompleteness

Theorem was proven by creating a statement that said,

“This statement is not provable.” The proof was done in two stages.

First, a machine was created to determine whether a given statement is provable or not.

Second, the statement is constructed so that, if the machine were to determine that the statement is provable, it would be false.

Therefore, the statement is not provable by definition.

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The constraint that is NOT valid is " \(y > = 5x + 30\) "

To determine the constraints, we analyze the given information. The farmer has a 500-acre farm, and she wants to optimize her planting strategy for wheat and corn. Each acre of wheat requires 1 person-day of labor and $20 in expenses, while each acre of corn requires 5 person-days of labor and $30 in expenses. The farmer has a budget of $11,400 and 1480 person-days of labor available.

To maximize profit, we consider the profit per acre for each crop, which is $90 for wheat and $120 for corn. Let x represent the acres of wheat and y represent the acres of corn.

The constraints are as follows:

By considering these constraints, the farmer can determine the optimal combination of wheat and corn planting to maximize profit while adhering to resource limitations.

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In the year 2009, the factory produced 5,249,789 bulbs, while in the year 2010, it produced 624,986 bulbs. The factory produced more bulbs in 2009, with a difference of 4,624,803 bulbs.

To determine in which year the factory produced more bulbs and by how much, we compare the number of bulbs produced in 2009 and 2010. In 2009, the factory produced 5,249,789 bulbs, whereas in 2010, it produced 624,986 bulbs.

To calculate the difference, we subtract the number of bulbs produced in 2010 from the number produced in 2009: 5,249,789 - 624,986 = 4,624,803.

Therefore, the factory produced 4,624,803 more bulbs in 2009 compared to 2010. This signifies that the production output was significantly higher in 2009, indicating a more productive year for the factory in terms of bulb production.

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The given equation is of an ellipse, which is written as\(\[ax^2+by^2+2gx+2fy+c=0\]\)

The area of the ellipse is given as\(\[A = πab\]\\where\\= \[a=\sqrt {{{(b^2+c)} / {(1-e^2)}}}\]and \[b\\=\sqrt {{{(a^2+c)} / {(1-e^2)}}}\]\\where \[e^2=1-{{(b^2)} / {(a^2)}}\]\)

So we get the equation in standard form of an ellipse as\(\[{x^2} / {(57/25)^2} + {y^2} / {(\sqrt {23})^2} = 1\]\)

Comparing this with the standard equation of an ellipse, \(\[{x^2} / {a^2} + {y^2} / {b^2} = 1\]we get, \[a = 57/25\]\)

and

\(\[b = \sqrt {23}\]\)Now, using the area of the ellipse,

we get:

\(\[A = π \cdot \frac{{57}} {{25}} \cdot \sqrt {23}\]\[A\\\\ =\frac{{57}}{{25}} \cdot 23\]\)

Therefore, the area of the ellipse is \(\[\frac{{1302}}{{25}}\]\).

The required area of the ellipse is 1302/25 square units.

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Answer:

x= - 8/3

Step-by-step explanation:

1- Multiply the monomials

2- Combine like terms

3- Rearrange variables to the left side of the equation

4- Divide both sides of the equation by the coefficient of the variable

5- Cross out the common factor

So, the percentage of data values represented on a box plot that falls between the lower quartile and the upper quartile is 50%.

In a box plot, the lower quartile (Q1) represents the 25th percentile, and the upper quartile (Q3) represents the 75th percentile. The interquartile range (IQR) is the range between the lower quartile and the upper quartile. To determine the percentage of data values that fall between the lower quartile and the upper quartile, we need to consider the IQR.

The IQR represents the middle 50% of the data. Therefore, the percentage of data values between the lower quartile and the upper quartile is 50%. In other words, half of the data values are within the IQR range, while the remaining 50% are outside this range, including the lower 25% below the lower quartile and the upper 25% above the upper quartile.

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Answer:

A, D

Step-by-step explanation:

EDGE 2021

Answer:

1

Step-by-step explanation:

a. The test at the 5% significance level indicates no significant difference in the incidence rate of GI problems between those who consume olestra chips and the TG control treatment. b.  To detect a difference between the true percentages of 15% and 20% with a probability of 0.90, a sample size of 29 individuals is necessary for each treatment group (m = n).

How to carry out hypothesis test?

To carry out the hypothesis test, we can use a two-sample proportion test. Let p₁ represent the proportion of individuals experiencing adverse GI events in the TG control group, and let p₂ represent the proportion in the olestra treatment group.

Null hypothesis (H₀): p₁ = p₂

Alternative hypothesis (H₁): p₁ ≠ p₂ (indicating a difference)

Given the data, we have:

n₁ = 529 (sample size of TG control group)

n₂ = 563 (sample size of olestra treatment group)

x₁ = 0.176 x 529 ≈ 93.304 (number of adverse events in TG control group)

x₂ = 0.158 x 563 ≈ 89.054 (number of adverse events in olestra treatment group)

The test statistic is calculated as:

z = (p₁ - p₂) / √((\(\hat{p}\)(1-\(\hat{p}\)) / n₁) + (\(\hat{p}\)(1-\(\hat{p}\)) / n₂))

where \(\hat{p}\) = (x₁ + x₂) / (n₁ + n₂)

b. We want to determine the sample size (m = n) necessary to detect a difference between the true percentages of 15% and 20% with a probability of 0.90.

Step 1: Define the given values:

p₁ = 0.15 (true proportion for the TG control treatment)

p₂ = 0.20 (true proportion for the olestra treatment)

Z₁-β = 1.28 (critical value corresponding to a power of 0.90)

Z₁-α/₂ = 1.96 (critical value corresponding to a significance level of 0.05)

Step 2: Substitute the values into the formula for sample size:

n = (Z₁-β + Z₁-α/₂)² * ((p₁ * (1 - p₁) / m) + (p₂ * (1 - p₂) / n)) / (p₁ - p₂)²

Step 3: Simplify the formula since m = n:

n = (Z₁-β + Z₁-α/₂)² * ((p₁ * (1 - p₁) + p₂ * (1 - p₂)) / n) / (p₁ - p₂)²

Step 4: Substitute the given values into the formula:

n = (1.28 + 1.96)² * ((0.15 * 0.85 + 0.20 * 0.80) / n) / (0.15 - 0.20)²

Step 5: Simplify the equation:

n = 3.24² * (0.1275 / n) / 0.0025

Step 6: Multiply and divide to isolate n:

n² = 3.24² * 0.1275 / 0.0025

Step 7: Solve for n by taking the square root:

n = √((3.24² * 0.1275) / 0.0025)

Step 8: Calculate the value of n using a calculator or by hand:

n ≈ √829.584

Step 9: Round the value of n to the nearest whole number since sample sizes must be integers:

n ≈ 28.8 ≈ 29

The complete question is:

Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms. Among 529 individuals in the TG control group, 17.6% experienced an adverse GI event, whereas among the 563 individuals in the olestra treatment group, 15.8% experienced such an event.

a. Carry out a test of hypotheses at the 5% significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment.

b. If the true percentages for the two treatments were 15% and 20% respectively, what sample sizes (m = n) would be necessary to detect such a difference with probability 0.90?

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To determine the critical value of F for a one-way between-subjects ANOVA with 5 levels and 48 people, we need to find the degrees of freedom for the numerator and the denominator.

The numerator degrees of freedom (df₁) is equal to the number of levels minus 1, which is 5 - 1 = 4.

The denominator degrees of freedom (df₂) is equal to the total number of people minus the number of levels, which is 48 - 5 = 43.

Using these degrees of freedom, we can look up the critical value of F from the F-distribution table or use statistical software.

For an alpha level of 0.01 and df₁ = 4 and df₂ = 43, the critical value of F is approximately 3.737.

Therefore, the correct answer is B. 3.737.

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The properties of radicals to simplify the expression is 2 √22. .

\(\sqrt[3]{6} * \sqrt[3 ]{72} / \sqrt[3]{2}\) =2 √22.

2 √22 = 88 .

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Answer:

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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We find that 28 child tickets were sold on Tuesday.

To determine the number of child tickets that were sold on Tuesday, let x be the number of child tickets that were sold. Then, the number of adult tickets sold was four times the number of child tickets sold. Thus, the number of adult tickets sold is 4x.

The cost of one child ticket is $6.50, and the cost of one adult ticket is $9.80. Therefore, the total sales can be represented by the equation:6.50x + 9.80(4x) = 1279.60

Simplifying this equation gives: 6.50x + 39.20x = 1279.60

Combining like terms, the equation can be further simplified to:

45.70x = 1279.60 Solving for x gives: x = 28

Therefore, 28 child tickets were sold on Tuesday

In conclusion, if we assume that the number of child tickets sold is x, then we can calculate the number of adult tickets sold to be 4x. By multiplying the number of child tickets sold by the price of one child ticket and the number of adult tickets sold by the price of one adult ticket and adding the two values together, we obtain the total sales equation. Using this equation, we solve for x by simplifying and combining like terms.

Therefore, we find that 28 child tickets were sold on Tuesday.

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Answer: The linear demand equation (price function, y) as a function of the quantity, x, sold is y = -0.4x + 91.99.

The demand equation represents the relationship between price and quantity demanded of a particular good or service. Through focus groups, Hasbro determined that they could sell 110,000 furbies at a price of $47.99. If they lower the price to $9.99, they can sell 50,000 more furbies. The slope of the demand equation, which represents the change in price with respect to change in quantity sold, can be found using the two given price-quantity pairs. The slope is calculated as follows:

slope = (change in y / change in x) = ((9.99 - 47.99) / (110000 + 50000)) = -0.4

The intercept value of the equation, which represents the price when quantity sold is zero, can be found using either of the two price-quantity pairs. Using the first pair, we have:

y = mx + b
47.99 = -0.4(110000) + b
b = 91.99

Thus, the linear demand equation is y = -0.4x + 91.99, where y is the price of the furbies and x is the quantity sold. The equation shows that as the quantity sold increases, the price decreases. This is in line with the basic economic principle of demand, which states that as the price of a good or service decreases, the quantity demanded increases.

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Answer:

One

Step-by-step explanation:

7x+3x= - 46

10x= - 46

x= - 4.6

one answer

Answer:

A : (146-4b)=(122-1b)

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x9

Answer:

44

Step-by-step explanation:

1/2×2=1

22×2=44

The car is going 44 miles in 1 hour

Answer:

2x-60=180

Step-by-step explanation:

RQS = x-6

the two angles add to make 180 because they are on a straight line

so x + x-6 = 180

therfore, 2x+6 = 180

Answer:

No

Step-by-step explanation:

Both triangles have angle T with measure 99°.

Triangle TUV has angle U with measure 45°, making m<Y = 36°.

Triangle TXY has angle TYX with measure 52°, making m<TXY = 29°.

Since only one pair of angles of the two triangles are congruent, the triangles are not similar.

Answer: No

The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.

This is because the sample means would be expected to be centered around the population mean.

The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:

standard deviation of sample means = standard deviation of population / square root of sample size

In this case, the standard deviation of sample means would be:

6 / square root of 4 = 3

So the answer is 3.

So, the mean of the distribution of the sample means would be 3. Your answer: 3.

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Based on the definition of the the angles on a straight line, we have:

m<B = 40°; m<E = 50°; m<C = 90; m<D = 90°.

When two straight lines intersect, they form four angles. Angles that are formed on a straight line are called "angles on a straight line" or "linear pairs." These angles are also known as supplementary angles because they add up to 180 degrees. Therefore, if two angles are formed on a straight line, the measure of one angle added to the measure of the other angle equals 180 degrees.

m<B = 180 - 140 = 40° [straight angle]

m<E = 180 - 130 = 50°

m<C = 180 - m<B - m<E [triangle sum theorem]

Substitute:

m<C = 180 - 40 - 50

m<C = 90

m<D = 180 - m<C

m<D = 180 - 90 = 90°

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408 students selected either calculus or discrete math.

The stated data in the question-

Therefore,

The number of people who pick calculus or discrete math is equal to the sum of the number of people who select calculus and the number of people who choose discrete math.

Thus,

Discrete maths or calculus is preferred by =  339 + 217 - 148 students.

Discrete maths or calculus is preferred by = 408 students.

Thus, 408 people selected either calculus or discrete math.

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The given function y = 3.28x converts length from x meters to y feet.

To graph the function, we can plot a few points and connect them.

Here are some points that we can plot:

x (meters) y (feet)0 03.28 10.7613.12 42.9456.56 214.5489.14 299.8720 65.6160 524.9340.3048 1

Since y depends on x, x is the independent variable, and y is the dependent variable.

We can see that as the value of x increases, so does the value of y, which means that the graph slopes upward

The domain of a function is the set of all values that the independent variable can take on. Since we can have any positive value of x (in meters), the domain of this function is continuous.

In conclusion, the given function y = 3.28x converts length from x meters to y feet. x is the independent variable, and y is the dependent variable. The graph of the function slopes upward, indicating that as x increases, y also increases. The domain of the function is continuous because x can take on any positive value.

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