22. Restaurants At Morgan's Fine Cuisine, meals are served a la carte. That is, each
item on the menu is priced separately. Jackie and Ted Parris went to Morgan's to
celebrate their anniversary. Jackie ordered prime rib, 2 side dishes, and a roll. Ted
ordered prime rib, 3 side dishes, and 2 rolls. Jackie's meal came to $36 and Ted's
meal came to $44. If the prime rib is three times as expensive as a side dish, what
is the cost of each item?

The result is the identity matrix, confirming that our inverse is correct.

We'll perform row operations until we reach the identity matrix. The given matrix is:

[1 0 0]
[0 0 1]
[0 1 0]

Step 1: Swap row 2 and row 3 to get the identity matrix on the left:

[1 0 0]
[0 1 0]
[0 0 1]

Now we have reached the identity matrix. Since we performed one row swap, the inverse matrix will be the same as the initial matrix:

Inverse matrix:
[1 0 0]
[0 0 1]
[0 1 0]

To check the result using (1), we'll multiply the original matrix and its inverse:

Original matrix * Inverse matrix:

[1 0 0]   [1 0 0]
[0 0 1] × [0 0 1]
[0 1 0]   [0 1 0]

Performing the matrix multiplication:

[1×1+0×0+0×0  1×0+0×0+0×1   1×0+0×1+0×0]   [1  0  0]
[0×1+0×0+1×0  0×0+0×0+1×1  0×0+0×1+1×0] = [0  0  1]
[0×1+1×0+0×0  0×0+1×0+0×1  0×0+1×1+0×0]   [0  1  0]

The result is the identity matrix, confirming that our inverse is correct.

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Answer:

y=3x - 8

Step-by-step explanation:

first find slope

10 - 7/6 - 5 = 3

Point - slope

y = 3(x-6)+10

Simplify

y = 3x-18+10

y=3x - 8

The solution of the mathematical statement is 102.5

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

"What is -5/2 times -41"

This means that

-5/2 times -41

Express as numbers

So, we have

-5/2 * -41

Divide 5 by 2

So, we have

-2.5 * -41

Evaluate the product

102.5

Hence, the result is 102.5

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The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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The equation in slope intercept form is \(\frac{x}{7} +\frac{15}{7}\).

Given that the line passes through two points (-1,2) and (6,3)

Slope of the line passing through (x1,y1) and (x2,y2) is

\(\frac{y2-y1_ }{x_{2-x_{1} } }\)

Hence slope of our line =

(3-2)/(6+1) = 1/7

So in slope intercept form the equation would be

y = 1/7 x +C

to find C

Since (-1,2) lies on the line substitute these in the line equation

2 = 1/7(-1)+c

C = 2+1/7 = 15/7

Hence equation in slope intercept form is \(\frac{x}{7} +\frac{15}{7}\).

The slope-intercept form of a  line is one of the most common forms used to represent the equation of a line. The slope-intercept formula can be used to find the equation of a line  given the slope of the  line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis). The equation of a line is an equation that is satisfied by each point  on that line.

There are several methods to find this equation of a  line given as

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Answer:

285

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

2x+3y=6

2(0)+3y=6

0+3y=6

3y=6

y=2

Answer:

Step-by-step explanation:

Here is the complete question.

Maria and Franco are mixing sports drinks for a track meet. Maria uses 2/3 cup of powdered mix for every 2 gallons of water. Franco uses 1 1/4 cups of powdered mix for every 5 gallons of water. Which sports drink is stronger?

For us to get the stronger drink, we will need to calculate the amount of cup  of mix  in one gallon of water for both Maria and Franco.

For Maria:

Maria uses 2/3 cup of powdered mix for every 2 gallons of water

2/3 cup of mix = 2 gallons of water

x cup of mix = 1 gallon of water

cross multiply

2 * x = 2/3 * 1

2x = 2/3

6x = 2

x = 2/6

x = 1/3

Hence Maria mixed 1/3 (33.3%) cup of powdered mix in a gallon of water

For Franco:

Franco uses 1 1/4 cup of powdered mix for every 5 gallons of water

5/4 cup of mix = 5 gallons of water

x cup of mix = 1 gallon of water

cross multiply

5 * x = 5/4 * 1

5x = 5/4

20x = 5

x = 5/20

x = 1/4

Hence Maria mixed 1/4 cup of powdered mix (25%) in a gallon of water.

Based on the percentage per gallon of water, Maria sport drink is stronger.

Answer:

-6

Step-by-step explanation:

Plug in -1/3for t

W(-1/3)=15(-1/3)-1=-5-1=-6

Answer:

-6

Step-by-step explanation:

substitute -1/3 into w(t) = 15t - 1

=>  w(-1/3) = 15(-1/3) - 1

=> w(-1/3) = -6

Answer:

the angle 2 is 45 because it is a angle on a straight line I think

The graph of the inequality is a straight line that passes through point 3 and represents the solution set.

A mathematical statement known as an inequality in mathematics examines two values or quantities and determines whether they are equal or not. Ranges of values or equation solutions can also be described by inequality. Inequality x 10 defines all x values that are less than or equal to 10, whereas inequality x > 3 represents all x values that are more than 3. For a visual representation of the range of values that fulfil an inequality, inequality's can be graphed on a number line.

The given inequality is 4x - 2 < 10

The inequality can be written as:

4x < 10 + 2

4x < 12

x < 3

Hence, the graph of the inequality is a straight line that passes through point 3 and represents the solution set.

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Answer:

Step-by-step explanation:

Given equation:

The first step:

We see right side is same and changes on the left side, similar to:

where the factors are differently grouped, but it doesn't change the product.

This property is called:

The matching choice is C

If the value of x was 40, then it would make the equation true.

\(x = 40\)

____________________________________________________

To solve for x, we need to simplify both sides of the equation, then isolate the variable. In this case, the x variable being 40.

Hope this helps!

The probability that a randomly selected muffin will be a banana nut muffin is; P(banana nut muffin) = 0.5

From the table in the question, we are given;

Number of blackberry muffins = 10

Number of banana nut muffins = 25

Number of Chocolate chip muffins = 1

Number of blueberry muffins = 11

Number of pumpkin spice muffins = 3

Total number of muffins = 10 + 25 + 1 + 11 + 3

= 50

Probability = number of successful outcomes/Total number of outcomes

Thus;

P(banana nut muffin) = 25/50

= 0.5

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Answer:

The numerator of the first fraction 8 is greater than the numerator of the second fraction 3 , which means that the first fraction 812 is greater than the second fraction 312 and that 23 is greater than 14 .

Step-by-step explanation:

Answer:

-3/2

Step-by-step explanation:

\(2 \frac{3}{4} - 4 \frac{1}{4} \\ = > \frac{11}{4} - \frac{17}{4} \\ = > \frac{ - 6}{4} \\ = > \frac{ - 3}{2} \)

The satellite should be insured for 98 months (rounded up to the nearest month) to be 96% confident that the microchip will last beyond the insurance date.

To answer this question, we need to find the number of months for which we can be 96% confident that the microchip will not malfunction. This means we want to find the value of x such that P(X > x) = 0.04, where X is the random variable representing the life expectancy of the microchip.

We know that X follows a normal distribution with mean μ = 92 months and standard deviation σ = 3.6 months. Therefore, we can standardize X to the standard normal distribution Z ~ N(0, 1) using the formula

Z = (X - μ) / σ

We can then rewrite the probability P(X > x) as

P(X > x) = P(Z > (x - μ) / σ)

1.75 = (x - 92) / 3.6

Solving for x, we get

x = 98 months

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The given question is incomplete, the complete question is:

A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt.for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date?

ANSWER:

38.46%

STEP-BY-STEP EXPLANATION:

Given:

Problems solved by Thazzie: 5 problems

Problems solved by Zhaniyah: 8 problems

Which means that there are 13 problems in total.

Therefore, those 5 represent the following percent:

Therefore, it represents 38.46% of the problems solved by Thazzie

Answer:

$15

Step-by-step explanation:

Answer

Use division, how many times will 14 go into 210?

210÷14=15

$15

Or you can also multiply 15x14=210

Answer:

\frac{15a+20b}{6}     15a+20b/6

Step-by-step explanation:

\mathrm{Apply\:the\:fraction\:rule}:\quad \:a\cdot \frac{b}{c}=\frac{a\cdot \:b}{c}

The population is growing as the births are more than deaths in an year.

Increases in a population's or a dispersed group's membership are referred to as population growth.

Given:

To find: Is population growing or shrinking?

Finding:

Hence the population is growing as the births are more than deaths in an year.

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Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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Answer:

9 inches

Step-by-step explanation:

Perimeter of equilateral triangle = 3x

Perimeter of square = 4x

3(x + 6) = 9 + 4x

3x + 18 = 9 + 4x

-x = -9

x = 9

Answer:

(i)= 45 KPH, (ii) = 251 miles

Step-by-step explanation:

'Per' essentially means divide. Thus, to find Kilometres per hour, divide 270 by 6= 45. The bus is travelling at 45 KPH.

Then, to see how far a nine hour trip would cover, distance = speed * time =  251 miles.

Sample is a subset of the population used to estimate data about the population without including everyone. It is used in statistics to draw inferences about larger populations or groups and statistical research methods are used to achieve better sample results.

In the given scenario, the population in the study would be Bottles of soda produced in the plant on February 2. While the sample in the study would be The 70 bottles of soda selected in the plant on February 2A population is the complete group of people or things that we are studying. Population is the set of all things under examination, while the sample is a subset of the population, which is used to estimate data about the population.What is Sample?A sample is a subset of the population, and it is a way to investigate the entire population without including everyone. It is used to acquire an estimation of the population, but it is not intended to be an exact representation of the population. Sample data is used in statistics to draw inferences about larger populations or groups. To achieve better sample results, statistical research methods are used.

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Answer:

-1/2

Step-by-step explanation:

2x-y=-8 --> y=2x+8 (slope: 2)

to be perpendicular, the product of two slopes should be -1

thus, the slope of a line perpendicular to this one is -1/2

Answer:

Expand the expression.

x^ 4  −  4 x ^3  +  6 x ^2  −  4 x  +  1

The solutions are;

1) m^6/2

2) a^4b^2/4

3) 27x^5y/4

4) 4x^12/9

5) 8y^9/27

6) x^4y^2/4

The simplify means to write is the lowest possible form of the expression.

Let us now simplify each expression;

1) (-2m^4)^2/8m^2

4m^8/8m^2

m^6/2

2) (2a^3b^4)^3/(2ab^2)^5

2^3a^9b^12/2^5a^5b^10

a^4b^2/4

3) (3x^5y^3)^5/(6x^10y^7)^2

243x^25y^15/36x^20y^14

27x^5y/4

4) (4x^7/6x)^2

16x^14/36x^2

4x^12/9

5) (2y^5/3y^2)^3

8y^15/27y^6

8y^9/27

6) (5x^6y^2/10x^4y)^2

25x^12y^4/100x^8y^2

x^4y^2/4

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Answer:

True

Step-by-step explanation:

You need a place holder in both the dividend and the divisor when dividing polynomials.