Mark earns $8 per hour at a store.
Part A: Write an equation for this situation.
Part B: Create a table. Use h for hours worked and p for pay in dollars.
Part C: What part of your rule shows the number of hours Mark worked?
Part D: One week Mark earned $168. How many hours did he work that week?
Part E: Explain whether or not the equation is a direct variation.

Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.

Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:

[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]

where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:

[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]

Solving for P, we get:

P = 2,322.06

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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--

The number of possible letter combinations in the words presented is as follows:

CANNON: 2520

BANANA: 120

TOMORROW: 2520

REFERENCE: 20160

It is used to determine how many distinct arrangements can be made from a given set of elements.

1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:

Total number of permutations = 6! / 3!

= (6 x 5 x 4 x 3 x 2 x 1) / 3!

= 120

3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:

Total number of permutations = 8! / 2!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 20160

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The value of 2m + k is 14.

The continuity of a function at a point is a fundamental concept in calculus. A function f(x) is said to be continuous at a point x = a

In other words, a function is continuous at a point if we can draw its graph without lifting the pencil from the paper at that point. This means that there are no jumps, breaks, or holes in the graph of the function at that point.

Here we have

To determine if f(x) is continuous at x = 2, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 2 are equal, and if they are both equal to f(2).

First, let's calculate the left-hand limit of f(x) as x approaches 2:

lim x → 2- f(x) = lim x → 2- (-x² + 2m) = -(2²) + 2m = 2m - 4

Next, let's calculate the right-hand limit of f(x) as x approaches 2:

lim x → 2+ f(x) = lim x → 2+ (5x - k) = 5(2) - k = 10 - k

Now alculate f(2):

f(2) = -2² + 2m = 2m - 4

For f(x) to be continuous at x = 2, the left-hand limit, right-hand limit, and the function value at x = 2 must all be equal. So we have:

2m - 4 = 10 - k = 2m - 4

Simplifying, we get:

10 - k = 2m - 4

k + 2m = 14

Therefore,

The value of 2m + k is 14.

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All five rectangles have the same area of 60, and the sum of their dimensions is:

2 + 30 + 4 + 15 + 6 + 10 + 8 + 7.5 + 10

Let the width of rectangle 1 be w1, the width of rectangle 2 be w2, and so on. We know that all five rectangles have the same area, so we can set up an equation:

[tex]w1 * l1 = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5[/tex]

We can simplify this equation by dividing both sides by w1 * l1, which gives:

[tex]1 = (w2 * l2) / (w1 * l1) = (w3 * l3) / (w1 * l1) = (w4 * l4) / (w1 * l1) = (w5 * l5) / (w1 * l1)[/tex]

Let's define a new variable x = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5. Then we have:

[tex]w1 * l1 = xw2 * l2 = xw3 * l3 = xw4 * l4 = xw5 * l5 = x[/tex]

Now we need to find the least possible value of w1 + l1 + w2 + l2 + w3 + l3 + w4 + l4 + w5 + l5. Since w1 * l1 = x, we can rewrite this as:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to w1, set it equal to zero, and solve for w1:

[tex]d/dw1 (w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)) = 1 - 2 * sqrt(x) / w1^1.5 + 2 * sqrt(x) / w1^2.5 = 0[/tex]

Solving for w1, we get:

[tex]w1 = 2 * x^(1/4)[/tex]

Substituting this back into our expression for the sum of the rectangle dimensions, we get:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x) = 2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x:

[tex]d/dx (2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)) = 1/2 * x^(-3/4) + 3/2 * x^(1/4) + 2 / (2 * x)^(3/4) = 0[/tex]

Solving for x, we get:

x = 4

Therefore, the least possible value of w1 is:

w1 =[tex]2 * x^(1/4) = 2[/tex]

And the dimensions of the rectangles are:

Rectangle 1: 2 x 30

Rectangle 2: 4 x 15

Rectangle 3: 6 x 10

Rectangle 4: 8 x 7.5

Rectangle 5: 10 x 6

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The length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

The side length b is derived using the Pythagoras rule as follows:

b = √(12.2² - 11²)

b = 5.276

Using the sine rule;

12.2/sin90 = 11/sinA

A = sin⁻¹(11 × sin90)/12.2 {cross multiplication}

A = 64.4

12.2/sin90 = 5.3/sinB

B = sin⁻¹(5.276 × sin90)/12.2 {cross multiplication}

B = 25.6

Therefore, the length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

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Answer: w = ±7

Step-by-step explanation:

To get rid of the square on w, we square root both sides of the equation.

The square root of w^2 is w, and the square root of 49 is ±7.

±7 is your answer.

2(x+4)

hope this helps!!!

Step-by-step explanation:

+ 1.25

every new term is the previous term + 1.25.

with starting value -1.75

f(n) = 1.25n - 1.75

The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.

We are told that each liter of pineapple juice yields the same amount of drink. This is referred to as the "r" ratio. Then:

r = d/p

We can use the provided data to get a table of r values shown in below image form.

The ratio for the first two data points is the same, but it is different for the third. This suggests the drink's recipe changed between the second and third batches.

We can calculate the ratio using the first two data points:

r = d/p = 2/1 = 6/3

So the ratio is 2, which means that we obtain 2 liters of drink for every liter of pineapple juice.

This ratio can be used to calculate the estimated amount of drink for the third batch:

d = r*p = 25 = 10

The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.

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Answer:

the angle of depression is approx 22 degrees

Step-by-step explanation:

Model drawn below to visualize

I represented the angle of depression as x

Since two side lengths are given, we can use tangent to find the angle of depression

tan x= 3/7.5

We then use inverse tangent to find the angle measure:

m<x=[tex]tan^{-1}[/tex](3/7.5)

m<x is approx 21.8 or 22 when rounded to the nearest degree

(when using tan, inverse tan, sin, cos, inv... use deg on calculator when finding angle of depression, solving triangles, etc.)

Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.

Dividend yield = (Annual dividend payment / Stock's current market price) x 100%

In this case:

Annual dividend payment = $1.98

Stock's current market price = $41.68

Dividend yield = ($1.98 / $41.68) x 100% = 4.75%

Therefore, the dividend yield for AT&T is 4.75%.

Step-by-step explanation:

Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.

The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.

Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.

Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.

Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.

Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.

The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.

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--The given question is incomplete, the complete question is given

" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.

(a) Event "X or Y":

(b) Event "X and Y":

(c) The complement of the event X: "--

An equation uses two operations is equal to C = n × p + T.

Relationship between variables is C represents total cost where as 'n × p' is cost of meal per person and T is additional cost.

Total cost of a meal at a restaurant is a function of the number of people and the price per dish.

Represent the variables as follows,

Let us use the variable 'C' to represent the total cost of the meal.

Let us use the variable 'n' to represent the number of people at the table.

Let us use the variable 'p' to represent the price per dish.

An equation that uses two operations, use multiplication and addition.

C = n × p + T

'n × p' represents the cost of the meal per person,

'T' represents any additional costs, such as taxes or tips.

By adding these two values together, total cost of the meal.

Relationship between the variables is as follows,

Total cost of the meal C is directly proportional to both the number of people n and the price per dish p.

Increase either n or p, total cost of the meal will increase proportionally.

For example,

Double number of people at the table n,

Total cost of meal C will also double,

Assuming price per dish p remains constant.

Similarly,

Double the price per dish p,

Total cost of the meal C will also double,

Assuming number of people at the table n remains constant.

Constant term T represents any additional costs.

That are independent of n and p, such as taxes or tips.

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Answer:

To write the equation of the line that passes through the points (2, -4) and (0, -4), we can use the point-slope form of a linear equation, which is:

y - y1 = m(x - x1)

Where (x1, y1) is one of the points on the line, and m is the slope of the line.

In this case, both points have the same y-coordinate, which means that the line is horizontal and has a slope of 0. We can choose either point to use in the equation, so let's use (2, -4):

y - (-4) = 0(x - 2)

Simplifying this equation, we get:

y + 4 = 0

y = -4

So the equation of the line that passes through the points (2, -4) and (0, -4) is y = -4, which is a horizontal line at y-coordinate -4.

The lower and upper control limits that the manufacturer should use in the resulting control chart are LCL = 0.023,UCL = 0.043

To calculate the lower and upper control limits for the control chart, we need to use the following formula:
Lower control limit (LCL) = average proportion of defects - 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Upper control limit (UCL) = average proportion of defects + 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Using the given information, we can plug in the values to get:
LCL = 0.01 - 3 x square root of [(0.01 x 0.99) / 30] = -0.023
UCL = 0.01 + 3 x square root of [(0.01 x 0.99) / 30] = 0.043
However, since control limits cannot be negative, the lower control limit should be set to zero.

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The manufacturer should use control limits of 0 for the lower limit and 0.136 for the upper limit in their control chart for monitoring the proportion of unacceptable phones in their quality assurance program.

Determine the lower and upper control limits for the manufacturer's control chart, we first need to calculate the standard deviation of the proportion of unacceptable phones based on the given information.
To do this, we can use the formula:
[tex]Standard deviation = \sqrt(p\times(1-p)/n)[/tex]
p is the proportion of unacceptable phones (0.01), and n is the sample size (30 phones per day for 7 days = 210 total phones).
Plugging in these values, we get:
[tex]Standard deviation = \sqrt(0.01\times(1-0.01)/210) = 0.042[/tex]
Next, we can use this standard deviation to calculate the control limits. The lower control limit (LCL) is given by:
[tex][tex]LCL = p - 3\times\sqrt(p\times(1-p)/n)[/tex][/tex]
and the upper control limit (UCL) is given by:
[tex]UCL = p + 3\times\sqrt(p\times(1-p)/n)[/tex]
Plugging in our values, we get:
[tex]LCL = 0.01 - 3\times0.042 = -0.075[/tex]
[tex]UCL = 0.01 + 3\times0.042 = 0.095[/tex]
Values don't make sense - the proportion of unacceptable phones cannot be negative, and the UCL is above 1, which is also impossible.
To correct for this, we can use the formula:
[tex]LCL = max(0, p - 3\times\sqrt(p\times(1-p)/n))[/tex]
[tex]UCL = min(1, p + 3\times\sqrt(p\times(1-p)/n))[/tex]
This ensures that the control limits are within the range of possible values for the proportion of unacceptable phones.
Plugging in our values with this formula, we get:
[tex]LCL = max(0, 0.01 - 3\times0.042) = 0[/tex]
[tex]UCL = min(1, 0.01 + 3\times0.042) = 0.136[/tex]

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Natalie used for constructing the bar graph is type of writing utensil.

The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.

Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.

Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.

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The solution is all values of x greater than -9.

The correct graph for the given inequality "Negative 3x - 7 < 20" is:

From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.

To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:

Negative 3x - 7 + 7 < 20 + 7

Negative 3x < 27

Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:

Negative 3x/-3 > 27/-3

x > -9

Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.

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The expression that represents the balance in the account is 375 - 2x

Starting with a balance of $350, the customer makes two withdrawals, one of which is $50 more than the other.

After these two withdrawals, the balance of the account is:

350 - x - (x + 50)

Simplifying this expression, we get:

300 - 2x

Next, the customer makes a deposit of $75, so we can add this to the current balance:

75 + 300 - 2x

So, we have

375 - 2x

Hence, the expression is 375 - 2x

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Therefore , the solution of the given problem of trigonometry comes out to be 2 * sin²(ɵ) * cos²(ɵ)  the claimed identity has been established.

Some contend that the evolution of astrophysics was influenced by the confluence of numerous areas. Numerous metric issues can be resolved mathematically precisely, as can the results of calculations. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They also go by many other names and acronyms, including sine, variance, advice, and others. (csc).

Here,

The identified person is:

=>  cot²(ɵ) * sin²(ɵ) + tan²(ɵ) * cos²(ɵ)

=>  cot(ɵ) = 1/tan(ɵ)

=> tan(ɵ) = 1/cot(ɵ)

=> (1/tan(ɵ))² * sin²(ɵ) + (1/cot(ɵ))² * cos²(ɵ)

We may square the reciprocals by applying the formula (a/b)² = a²/b²:

=> 1/(tan²(ɵ)) * sin²(ɵ) + 1/(co²(ɵ)) * cos²(ɵ)

=> sin²(ɵ) / tan²(ɵ) + cos²(ɵ) / cot²(ɵ)

=> tan²(ɵ) + 1 = sec²(ɵ)

=> cot²(ɵ) + 1 = csc²(ɵ)

=> sin²(ɵ) / sec²(ɵ) + cos²(ɵ) / csc²(ɵ)

=> 1/cos²(ɵ) = sec²(ɵ)

=> 1/sin^2(ɵ) = csc^2(ɵ)

=> sin²(ɵ) * cos²(ɵ) + cos²(ɵ) * sin²(ɵ)

=> sin²(ɵ) * cos²(ɵ) + sin²(ɵ) * cos²(ɵ)

Step 6 is to group similar terms.

=> 2 * sin²(ɵ) * cos²(ɵ)

And since we've found the original expression, the claimed identity has been established.

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Answer:

14 hr 32 min (1,477.7 km)

option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.

Given that a special on a 3-topping pizza.

The topping choices are pepperoni, sausage, bacon, mushrooms, green peppers, and olives.

There are six alternatives for the first topping, five options for the second (since we can't choose the same topping twice), and four options for the third. As a result, the total number of possible 3-topping pizzas is:

6 x 5 x 4 = 120

So option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.

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1745 packages of tennis balls can be made from 5235 balls.

Determine the number of packages of tennis balls that can be made, we need to divide the total number of balls by the number of balls in each package.

5235 tennis balls and each package contain 3 balls.

Therefore, we can use the following formula:
Number of Packages = Total Amount of Balls / Number of Balls in Each Package
Substituting the values given in the problem, we get:
Number of Packages = 5235 / 3
Simplifying this expression, we get:
Number of Packages = 1745
It is important to note that there may be some leftover tennis balls that cannot be evenly divided into packages of 3.

Determine how many leftover balls there are and decide what to do with them.

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The position of point S after dilating will be half of the original. The dilated point S' has been shown below.

What is dilation?

Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.

We are given a graph showing position of point S.

Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.

The point has been located and attached in the image below.

Hence, the required solution has been obtained.

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The red line on the graph may also include other lines that represent related data, such as the total amount of solid waste generated by all people in the United States per year, or the period of time in years being measured.

Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.

The red line on the graph is a useful tool for understanding the impact of solid waste on the environment and society as a whole.

It helps us to identify areas where we can make changes to reduce waste and improve our overall environmental performance and serves as a reminder of the importance of responsible consumption and waste management practices.

Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.

This is a key metric in measuring the environmental impact of waste production in the country.
The average amount of solid waste generated per person is an important figure because it provides a more accurate picture of individual behavior and consumption patterns.

It takes into account factors such as population growth, changes in household size, and shifts in lifestyle and consumption habits.

By tracking this metric over time, policymakers and environmental advocates can gain insight into trends and patterns in waste generation and identify opportunities for reducing waste and promoting sustainability.

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Answer:

QR=8

Step-by-step explanation:

When two lines are perpendicular, they form two 90-degree angles. So:

m∠QSR = m∠QSP = 90°

We also know that the line segment PS is congruent to the line segment SR.

Lastly, by the reflexive property, QS is congruent to itself.

Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).

Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).

If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):

[tex]3n-1=5n-7=\\6=2n=\\n=3[/tex]

Plug in n to the length of QR:

[tex]5n-7=\\5(3)-7=\\15-7=\\8[/tex]

So, QR=8.

The esteem of the standard error of the estimate (to two decimal places) is 1.34.

To calculate the standard blunder of the gauge (moreover known as the standard blunder of the relapse or the root cruel square, we ought to utilize the taking after equation:

SE = sqrt [ (Σ(y - yhat)[tex]^{2}[/tex]) / (n - k) ]

yhat = 0.471x + 2.606

We too know that there are 5 perceptions, and there's one free variable (x). Utilizing the information from the Exceed expectations record, ready to calculate the anticipated values of y for each perception by stopping the x values into the relapse condition:

yhat1 = 2.696

yhat2 = 3.638

yhat3 = 4.581

yhat4 = 5.524

yhat5 = 6.466

SE = sqrt [ ( (4.75 - 2.696)[tex]^{2}[/tex] + (5.36 - 3.638)[tex]^{2}[/tex]+ (5.95 - 4.581)[tex]^{2}[/tex] + (6.66 - 5.524)[tex]^{2}[/tex]+ (7.03 - 6.466)[tex]^{2}[/tex]) / (5 - 2) ]

SE = sqrt [ (5.3546) / 3 ]

SE = 1.335

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Answer:

distribute x as 3:

3²+10(3)+24

=63

The question "What are the prices of the computers?" is not a statistical question.

A statistical question is a question that can be answered by collecting and analyzing data. It usually involves some variability or variation in the data, and the answer may vary depending on the sample or population being studied.

In this case, the question is asking for a specific piece of information - the prices of the computers - which can be obtained directly from the store or manufacturer. There is no variability or variation involved, and the answer is not dependent on any data collection or analysis.

Therefore, this question is not a statistical question.

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Mean = 13

Variance = 36.2

The total distinguishable ways can the donors be in line is 362,736.

The total number of distinguishable ways:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

To subtract the number of in-distinguishable arrangements:

(4! x 3!) + (3! x 2!) = 144

There are 362,736 distinguishable ways in which four donors with type O blood, three donors with type A blood, and two donors with type B blood can be in line.

This is calculated by first determining the total number of distinguishable arrangements, which is 9!.

Then,

The number of indistinguishable arrangements is subtracted from the total.

Which is done by multiplying the number of arrangements for each blood type separately and then adding them together.

The result is then subtracted from the total, leaving the number of distinguishable ways.

The total number of distinguishable ways is:

362,880 - 144 = 362,736

For similar question on distinguishable ways:

https://brainly.com/question/7211156

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