1. Expected value and Bivariate Probability. The Chamber of Commerce of a Canadian city
has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received
a rating of 1-3 on its meal price (1 = least expensive; 3 = most expensive), and quality (1 =
lowest quality; 3 = greatest quality). Below is a crosstabulation of the rating data.
Meal Price (y)
Quality (x) 1 2 3 Total
1 42 39 3 84
2 33 63 54 150
3 3 15 48 66
Total 78 117 105 300
a. Develop a bivariate probability distribution for quality and meal price of a randomly selected
restaurant in this Canadian city. Let x = quality rating and y = meal price.
b. Compute the expected value for quality rating, x.
c. Compute the expected value for meal price, y.
d. The Var(x+y) = 1.6691. The Var(x) = 0.4964. The Var(y) = 0.6019. Compute the covariance
of x and y. What can you say about the relationship between quality and meal price. Is this what
you would expect?
e. Compute the correlation coefficient between quality and meal price. What is the strength of
the relationship? Do you suppose it is likely to find a low-cost restaurant in the city that is also
high quality? Why or why not?

The average rate of change in the cost of the hamburger during the period of 2012 to 2022 is 0.18.

The equation is y = 0.18x + 4.32 and the cost will be $7.02 in 2027.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

(a) Given that,

Cost of hamburger in 2012 = $4.32

Cost of hamburger in 2022 = $6.12

Average rate of change = (6.12 - 4.32) / (2022 - 2012)

                                        = 0.18

(b) Linear equation can be written in slope intercept form as y = mx + c, where m is the slope and c is the y intercept.

Slope of a linear equation is equal to the average rate of change.

m = 0.18

y intercept is the value of the y coordinate when x = 0.

In this case, y intercept is the cost of hamburger in the initial year, 2012.

c = 4.32

So the equation is,

y = 0.18x + 4.32

(c) Price of the hamburger will reach $7.02, when,

7.02 = 0.18x + 4.32

0.18x = 2.7

x = 15

Price will reach $7.02 in the year = 2012 + 15 = 2027

Hence the cost of the hamburger will be $7.02 in the year 2027 using the linear model y = 0.18x + 4.32.

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Therefore, the expansion of log(7x²) using the properties of logarithm is

log 7 + 2log x, expressed in terms of log x.

The mathematical idea of a logarithm illustrates the opposite of a power. It follows that the exponential that must be multiplied by bc to get the value of a number, x, is equal to its ground logarithm. As an illustration, 1000 = 103, so log10 = 3 is 1000's base-10 logarithm, which is 3. As an example, the square of ten is now only one twentieth of the base-10 exponential of ten, which is two. Log 100 = 2. Mathematicians use the logistic (or log) notion to respond to problems like these.

Here,

Using the product rule of logarithms, we can write:

log(7x²) = log 7 + log(x²)

Using the power rule of logarithms, we can write:

log(7x²) = log 7 + log(x²) = log 7 + 2log x

Therefore, the expansion of log(7x²) using the properties of logs is:

log 7 + 2log x, expressed in terms of log x.

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A son earns 62 percent of what his father earns if the son earns $52,000 so, the father earns approximately $83,871.

The word "percent" is used to represent a quantity as a percentage of 100. The Latin term per centum, which means "out of a hundred," is where the word "percent" originates. When working with huge numbers, percentages are frequently employed to convey ratios, proportions, and rates in a more practical way.

A percentage can be expressed as a decimal or as a fraction with a denominator of 100. 25%, for instance, might be written as 0.25 or as 25/100. Similarly, 75% might be written as 0.75 or as 75/100.

Let's denote the father's earnings as "F". We are given that the son earns 62% of what his father earns, which can be expressed as:

Son's earnings = 62% of Father's earnings

$52,000 = 0.62F

To solve for F, we can divide both sides of the equation by 0.62:

F = $52,000 ÷ 0.62

F = $83,870.97

Therefore, to the nearest dollar, the father earns approximately $83,871.

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The angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°. The solution has been obtained using concept of co-terminal angles.

What is co-terminal angle?

Co-terminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). The angles where the difference could be 360 degrees or multiples of 360 degrees are known as co-terminal angles.

The calculation of the two positive angles and the two negative angles, which are co-terminal, is as follows:

(a) For 90°, the two positive angles are

90° + 360° = 450°

450° + 360° = 810°

(b) The two negative angles are

90° - 360° = -270°

-270° - 360° = -630°

Hence, the angles which are co-terminal with the given angle and less than 1080 but greater than -720 are 450°, 810°, -270° and -630°.

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Answer:

8(-2)^3= -64

8(-1)^3= -8

8(0)^3= 0

8(3)^3= 216

Hope this helps! Remember PEMDAS (Please forgive My Dear Aunt Sally)

Therefore , the solution of the given problem of inequality comes out to be  ax - b > c, we get ax - b > c or ax - b < -c, which is the same as

|ax - b| > c.

A mathematical inequality is a relationship or group of values without the equal sign. Equity usually comes after equilibrium. When two parameters are not equal, inequality results. Between equality and inequality, there are differences. Because the numbers are not equal or variable it was chosen to use the most common symbol (). Any difference, no matter how little or significant, can be utilised to compare values.

Here,

One possible equivalent compound inequality is:

ax - b > c or ax - b < -c

To see why this is true, consider the two cases:

Case 1: ax - b > c

If we take the absolute value of both sides, we get |ax - b| > c, which is the original inequality.

Case 2: ax - b < -c

If we multiply both sides by -1, we get -ax + b > c.

Adding ax to both sides, we get b > ax + c. If we subtract this inequality from

=> ax - b < -c

=> -2b < -2c, or b > c.

Substituting b > c back into the inequality ax - b < -c, we get ax < 0. Multiplying both sides by -1 (since c >= 0),

we get

-ax > 0, or ax < 0.

Combining this with the inequality ax - b > c, we get ax - b > c or ax - b < -c, which is the same as |ax - b| > c.

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M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The coordinates of the quadrilateral MLJK are M(7, -8), L(9, -8), K(9, -10)

and J(7,-10)

Now we have to find the  coordinates of the vertices after a reflection over the line x = 4

We need to find the coordinates of the vertices after reflecting over the line x = 4, we just need to flip the x-coordinate of each vertex across the line.

M(7, -8)--->M'(7+4, -8)

=M'(11, -8)

L(9, -8)--->L'(9+4, -8)

=L'(13, -8)

K(9, -10)--->K'(9+4, -10)

=K'(13, -10)

J(7,-10)--->J'(7+4, -10)

=J'(11, -10)

Hence, M'(11, -8), L'(13, -8), K'(13, -10) and J'(11, -10) are the coordinates of the vertices after a reflection over the line x = 4

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The equation that shows the number of cookies Beverly has left is n = 6 - 5.

An integer is any positive or negative number, including zero, that has no decimal or fractional parts.

Natural numbers which start at 1, are categorised as whole numbers, along with 0 as well.

We can see that integers are a collection of numbers that include both positive and negative values as well as 0, whereas whole numbers are a set of numbers that include only positive numbers.

Given that, Beverly evenly shared a box of 24 cookies with three friends.

The number of cookies with Beverly = 24 / 4 = 6 cookies.

She ate 5 of her cookies.

Thus, the number of cookies Beverly has left is:

n = 6 - 5

n = 1

Hence, the equation that shows the number of cookies Beverly has left is n = 6 - 5.

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Based on given data, buying from Photo World would result in the lowest total cost for the camera, at $164.99.

To determine the store with the lowest total cost, we need to calculate the total cost for each store, taking into account the price of the camera, the coupon code (if any), the sales tax, and the shipping cost.

For Camera Hut:

Price of camera: $200.00

Coupon code: 15% off

Discounted price: $170.00 (200.00 * 0.15 = 30.00 discount)

Sales tax: 5% of $170.00 = $8.50

Shipping: Free

Total cost: $170.00 + $8.50 + $0.00 = $178.50

For Photo World:

Price of camera: $180.00

Coupon code: 10% off

Discounted price: $162.00 (180.00 * 0.10 = 18.00 discount)

Sales tax: None

Shipping: $2.99

Total cost: $162.00 + $0.00 + $2.99 = $164.99

For Picture Palace:

Price of camera: $169.99

Coupon code: None

Discounted price: $169.99

Sales tax: 5% of $169.99 = $8.50

Shipping: $6.99

Total cost: $169.99 + $8.50 + $6.99 = $185.48

For Vid-Cam Castle:

Price of camera: $205.00

Coupon code: 18% off

Discounted price: $168.10 (205.00 * 0.18 = 36.90 discount)

Sales tax: None

Shipping: Free

Total cost: $168.10 + $0.00 + $0.00 = $168.10

Therefore, buying from Photo World would result in the lowest total cost for the camera, at $164.99.

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If rectangles S and T are similar then the area of rectangle T is 96 units².

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

Since the rectangles S and T are similar, their corresponding sides are proportional.

Let the length of rectangle T be "x" units. Then -

width of S / width of T = length of S / length of T

Using the given values -

16/9.6 = (√160) / (√x)

Simplifying this equation it is obtained-

x = (9.6/16) × (√160)²

x = 10

Therefore, the length of rectangle T is 10 units.

The area of rectangle T is then -

Area of T = width of T × length of T

Area of T = 9.6 × 10

Area of T = 96 units²

Therefore, the area of rectangle T is 96 units².

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Answer: 0

Step-by-step explanation:

Y2 - Y1

________.

X2 - X1

A linear slope means that the Ys are the same and you can't divide by zero.

You have your points (8,7) and (3,7)

Use the template like I have above.

7 - 7

______

3 - 8

which equals....

0

__

-5

I hope that makes sense for you :)

Answer:

6

Step-by-step explanation:

the numerator of the fraction is

6(t+h) +1 -(6t +1) = 6h

so the fraction is 6h/h =6

Tippah Antiques uses the periodic inventory system to account for its inventory transactions. The net sales = $714740

Inventory that is updated on a regular basis is known as periodic inventory. Contrasted with perpetual inventory systems, which are updated as necessary, this system does not. While using a periodic inventory system, neither inventory nor cost of goods sold records are attempted to be kept up to date.

Businesses that only sell a few products during a given accounting period frequently employ the periodic inventory method. Due to its simplicity of use and low cost of ownership due to the lack of expensive software requirements, these businesses frequently find it advantageous to employ this system.

Given that,

TIPPAH ANTIQUES:

For the year ended December 31, Year 2: (Schedule of Cost of Goods sold)

Beginning balance of inventory:                         $24500

Add: Purchases:                                                   $306,400

Less: Purchase returns allowances:                $12,600

Add: Freight in:                                                      $1,810

Cost of goods available for sale:

(24500+306400-12600+1810)                          $320,110

Less: Ending inventory on hand:                          $24,400

Cost of goods sold:

(320110 - 24400)                                                  $295,710

Next,

For the year ended December 31, Year 2: (Income statement)

Net sales                                                            $714,740

Less: Cost of goods sold                                    $295,710

Gross Profit:

(714740 - 295710)                                                     $419,030

Operating expenses:                                             $51,100

Income from Operations:

(419030 - 51100)                                                     $367,930

Thus,

Computation of Net sales

Sales                                                                         $721000

Less: Sales returns and allowances:                          $6260

Net Sales (721000 - 6260):                                        $714740

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Answer:

[tex]\frac{5}{33}[/tex]

Step-by-step explanation:

1.

2

1 5 is what's repeating, and there are two digits.

2.

10² = 100

I chose 10 to the power of 2 because there are 2 digits repeating.

3.

n × 10² = 0.1515 x 10² (square 10)

100n = 0.1515 × 100 (combine like terms)

100n = 15.15

4.

   100n = 15.1515....

-         n = 0.1515....

-------------------------

99n = 15

5.

99n = 15 (divide both sides by 99)

n = [tex]\frac{15}{99}[/tex]

As it asks for simplified form:

[tex]\frac{15}{99}[/tex] ÷ [tex]\frac{3}{3} = \frac{5}{33}[/tex]

Therefore, the fractional equivalent of the repeating decimal n = 0.1515... is [tex]\frac{5}{33}[/tex].

Answer:

Step-by-step explanation:

The Account receivable turnover for Year 1 is 21.04.

The Account receivable turnover for Year 2 is 20.86.

The average number of the times a company collects its accounts receivable balance is measured by the accounts receivables turnover ratio. It is a measurement of how well a business manages its line of credit process and collects unpaid balances from customers. A company's accounts receivable turnover ratio is higher for an efficient business and lower for an inefficient one.

For year 1:

Account receivable turnover:

= Net sales / Average account receivable

= 13,612 / ((654 + 640)/2)

= 13,612 / 647

= 21.0386398764

= 21.04

For year 2:

Account receivable turnover:

= Net sales / Average account receivable

= 12,808 / ((640+588)/2))

= 12,808 / 614

= 20.8599348534

= 20.86

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The elevator is now on the 6th floor.

Arithmetic operations are the basic part of mathematics which combines the basic operations like addition, subtraction, multiplication and division.

Given that the elevator is now on 9th floor.

First, it goes up 2 floors.

Position of elevator = 9 + 2 = 11th floor

Then, it goes down 5 floors.

Position of elevator = 11 - 5 = 6th floor

Hence the elevator is now on the 6th floor.

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Answer:

A

Step-by-step explanation:

Following the accounting cycle, an accountant would make a worksheet right after making an adjusted trial balance. The worksheet is a tool used by accountants to prepare financial statements and to adjust entries. The worksheet summarizes the data in the trial balance and makes it easier for the accountant to prepare the financial statements. The worksheet includes adjustments for accruals, prepayments, depreciation, and other items that were not recorded in the original journal entries. Once the worksheet is complete and the financial statements have been prepared, the accountant would then close the entries to start a new accounting cycle. Therefore, the correct answer is A. make a worksheet.

The values to put in the box will be:

x

y

x.y

x^2

y^2

4

19

76

16

361

9

46

414

81

2116

7

30

210

49

900

6

31

186

36

961

5

23

115

25

529

5

28

140

25

784

4

21

84

16

441

8

42

336

64

1764

total

48

240

1561

312

7856

The sample size is the number of observations used for determining the estimations of a given population.

The size of the sample has been drawn from the population. Sampling is the process of selection of a subset of individuals from the population to estimate the characteristics of the whole population.

Inthi case, sample size n = 8 and the correlation coefficient is 0.9643.

The appropriate values are given above.

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In the equation 11z=66-11, what is the next step in the equation solving sequence?

Two possibilities: You can subtract 66–11 then divide both sides by 11 OR you can divide both sides by 11 and do the subtraction as 6–1. I would usually do it the first way, but some might prefer the second.

The answer is the expected value is - 2. The equation for expected value is the sum of the values times their probabilities.

The requried volume of the pedestal is 135 cubic inches.

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
The volume of a triangular prism is given by the formula V =base x h, where the base is the area of the base and h is the height of the prism.

In this case, the area of the base is given as 9 in², and the height of the prism is given as 15 inches.

Therefore, the volume of the pedestal is:

V = base x h

V = 9 in² x 15 inches

V = 135 cubic inches

So the volume of the pedestal is 135 cubic inches.

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Answer:

Step-by-step explanation:

36

The other endpoint has its coordinate to be (4, -1).

Represent the coordinates of the other endpoint of the line segment be (x, y).

Since the midpoint of the line segment is (5, 1/2), we can use the midpoint formula to write an equation relating the coordinates of the two endpoints:

((6 + x)/2, (2 + y)/2) = (5, 1/2)

Simplifying this equation, we get:

(6 + x)/2 = 5

(2 + y)/2 = 1/2

Solving for x and y, we get:

x = 4

y = -1

Hence, the coordinates of the other endpoint of the line segment are (4, -1).

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Answer:

1. The amplitude of the function is 12 feet, since it moves from 6 feet above to 6 feet below the average sea level.

2. The period of the function is 12 hours, since it takes 12 hours for the tide to go from high to low and back again.

3. The frequency of the function is 0.5 (1/12), since it takes 12 hours for the function to repeat itself.

4. The midline of the function is the average sea level.

5. There is no vertical shift.

6. The phase shift is 0, since the first high tide occurs at x = 0.

The points are as selected on the graph.

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:

x    f(x)

-2   -9

0    -9

2    -9

7    -9

9    -9

Check the attached image for the points on the graph

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Answer:

Below

Step-by-step explanation:

The dose can be .05 gm  ± .002 gm  =  .048 - .052 gm

The equation is given by 5n + 100n = 210

Peggy has 8 quarters and 2 nickels

Let's call q the number of quarters and n the number of nickels.

If Peggy has four times as many quarters as nickels, we can write the following equation:

q = 4n

Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so

0.25q + 0.05n = 2.10

Because she had $2.10. Now, we can replace the first equation on the second one

0.25(4n) + 0.05n = 2.10

1n + 0.05n = 2.10

Finally, we can multiply both sides by 100, so

100n + 0.05(100)n + 2.10(100)

100n + 5n = 210

Therefore, the equation that can be used to solve the problem is

5n + 100n = 210

Now, we can solve the equation for n

105n = 210

105n/105 = 210/105

n = 2

Then, q is equal to

q = 4n

q = 4(2)

q = 8

It means that Peggy has 8 quarters and 2 nickels.

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complete question is listed below:

Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?

Which of the following equations could be used to solve the problem?

On+4 n=210

5 n+100 n=210

n+4 n=2.10

5n+100 n=2.10.