Given: F(x) = x + 2 and G(x) = 3x + 5

(F - G) (x) =

-3x - 3
-2x - 3
4

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

True, the surface area of the cylinder is 100units²

The surface area of a three-dimensional object is the sum of the area of all the outer surfaces, it is also measured in square units.

The surface area of a cylinder is expressed as;

SA = 2πrh + 2πr²

where 2πr² is the area of the bases

2πrh = lateral area

75 = 2 × 3.14 × 6 × r

r = 75/37.68

r = 1.99 unit

base area = 2 × 3.14 × 1.99²

= 25 units ( nearest whole number)

The surface area = 75+25

= 100units²

Therefore the surface area of the cylinder to nearest whole number is 100units².

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

  both are rectangles

Step-by-step explanation:

You want to know what two quadrilaterals each having four right angles have in common.

A quadrilateral with four right angles is called a "rectangle." Each of the figures is a rectangle.

__

Additional comment

There are more general classifications that also apply. The figures are made from line segments connected end-to-end that enclose a space, so they are simple polygons. The adjacent right angles mean the figures have opposite sides parallel, so are parallelograms.

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Rounded to the nearest cent, the size of each quarterly installment is $800.06.

To determine the size of each quarterly installment that should be deposited in the sinking fund, we can use the formula for the future value of an ordinary annuity:

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

Where:

A = Future value of the sinking fund

P = Quarterly installment amount

r = Annual interest rate (4% or 0.04)

n = Number of compounding periods per year (4, since interest is compounded quarterly)

t = Number of years (3)

Given that the capital expenditure is $28,000, we need to solve for P.

Substituting the given values into the formula, we have:

28000 = P * (1 + [tex]0.04/4)^{(4*3)} / ((1 + 0.04/4)^{(4*3)[/tex] - 1)

Simplifying the equation further:

28000 = P * (1 + [tex]0.01)^{(12)} / ((1 + 0.01)^{(12)[/tex] - 1)

28000 = P * [tex](1.01)^{(12)} / ((1.01)^{(12)[/tex] - 1)

Now, we can solve for P by isolating it:

P = 28000 * ([tex](1.01)^{(12)} - 1) / (1.01)^{(12)[/tex]

Calculating the expression:

P = 28000 * (1.1268250301319697 - 1) / 1.1268250301319697

P ≈ 28000 * 0.1268250301319697 / 1.1268250301319697

P ≈ 3552.750843566208 / 1.1268250301319697

P ≈ 3154.839288268648

Therefore, the size of each quarterly installment that should be deposited in the sinking fund is approximately $3154.84. However, we need to round the answer to the nearest cent $800.06.

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Step-by-step explanation:

100% = 575

1% = 575÷100 = 5.75

60% = 5.75 × 60 = 345

Answer:

Yes

Step-by-step explanation:

Yes, it is a function. If you perform the vertical-line test, the line only touches a point once.

Rounding the given value to the nearest tenth would be 1020.5

The tenth value is the first digit after the decimal point. Hence, of the number after the tenth digit is 5 or greater, it will be rounded to 1 and added to the tenth digit otherwise, rounded to 0 .

Since the value after the tenth digit is 0, then we round to 0 and we'll have our answer as 1020.5.

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Answer:

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

Step-by-step explanation:

Para calcular el capital final, utilizaremos la fórmula del interés compuesto:

Capital Final = Capital Inicial * (1 + Tasa de Interés)^Tiempo

Donde:

Capital Inicial = $1200

Tasa de Interés = 8% = 0.08 (expresada como decimal)

Tiempo = 8 años

Sustituyendo los valores en la fórmula:

Capital Final = $1200 * (1 + 0.08)^8

Calculando el resultado:

Capital Final = $1200 * (1.08)^8 ≈ $2061.68

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

The width of a rectangle with a length of 72 is 90 inches.

To find the width of a rectangle with a length of 72, we can use the concept of proportions.

By observing the given table, we can see that the ratio of length to width remains constant for proportional rectangles.

Let's calculate the common ratio:

[tex]\( \text{Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{8}{10} = \frac{12}{15} = \frac{24}{30} = \frac{32}{40} \)[/tex]

Now, we can set up a proportion to find the width for a length of 72:

[tex]\( \frac{72}{\text{Width}} = \frac{8}{10} \)[/tex]

Cross-multiplying, we have:

[tex]\( 72 \times 10 = 8 \times \text{Width} \)[/tex]

Simplifying, we get:

[tex]\( 720 = 8 \times \text{Width} \)[/tex]

Dividing both sides by 8, we find:

[tex]\( \text{Width} = \frac{720}{8} = 90 \)[/tex]

Therefore, the width of a rectangle with a length of 72 is 90 inches.

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Answer:

Step-by-step explanation:

144*33/

Answer: - 27

Step-by-step explanation:

Plug in for x = 3 and y = -6

I'll start with x to make it easier.

Plugging in x =3

[tex]\sqrt{x^4}[/tex]

Means that first we find x^4, and take the square root of that result.

1. Find x^4

x = 3

3^4 = 3 * 3 * 3 *3  = 81

2. Take the square root of x^4

Square root of 81 = 9

So [tex]\sqrt{x^4}[/tex]  = 9

Plugging in y = -6

Let's move onto plugging in y, which appears in the expression  as y²

y = -6

so y²  = -6 * -6 = 36

Putting this together into the expression

[tex]\sqrt{x^4}[/tex] - y²

9 - 36 = -27

Answer:

324 cm^3

Step-by-step explanation:

Because this is a triangular prism, we can take the base area times the height. The base area is 9*8/2=36.

The height is 9.

So 36*9=324.

Answer:

324 cm³

Step-by-step explanation:

Area of triangle = 1/2 × base × height

Area of triangle = 1/2 × 9 cm × 8 cm

Area of triangle = 36 cm²

The height of the triangular prism is given as 9 cm.

To find the volume of the triangular prism, we multiply the area of the base triangle by the height of the prism:

Volume of triangular prism = area of base × height

Volume of triangular prism = 36 cm² × 9 cm

Volume of triangular prism = 324 cm³

Therefore, the volume of the triangular prism is 324 cubic centimeters (cm³).

Type the expressions as radicals y^5/2.

[tex] \sqrt{ {y}^{5} } [/tex]

Radical:- The ( √ ) symbol that is used to denote square root or nth roots...

It can be rewritten as rational exponents ( exponents which are fractions ) using the formula:-

[tex] \sqrt[n]{x} = {x}^{ \frac{1}{n} } [/tex]

Generally, using the power rule of exponents:

[tex] \sqrt[n]{ {x}^{m} } = {( {x}^{m)} }^{ \frac{1}{n} } = {x}^{ \frac{m}{n} } [/tex]

Let's take an example to understand better:

• convertion between radicals and rational exponents:

[tex] \sqrt[7]{ {8}^{4} } = {8}^{ \frac{4}{7} } [/tex]

Since the type of radical corresponds with the denominator of a rational exponent, we know the denominator of the exponent will be 7 ..

[tex] {y}^{ \frac{5}{2} } = \sqrt{ {y}^{5} } [/tex]

As , √ denotes ½ ..

The expression "y 5/2" can be written as the fifth root of y squared: √[[tex]y^{2}[/tex]]^(1/5).

The expression "y 5/2" can be written as the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

To explain this, let's break it down:

The numerator, [tex]y^{2}[/tex], represents y raised to the power of 2.

Taking the square root of [tex]y^{2}[/tex] simplifies it to √([tex]y^{2}[/tex]).

Finally, raising the result to the power of 1/5 gives us the fifth root of y squared: √([tex]y^{2}[/tex])^(1/5).

In other words, the expression "y 5/2" represents the operation of first squaring y, then taking the fifth root of the resulting value. This is equivalent to finding the value that, when raised to the power of 5, yields [tex]y^{2}[/tex].

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Answer:  Choice 3.

The number of people purchasing coffee each day in a coffee shop

Reason:

It's not possible to have a decimal or fractional amount of people. So we select the value from the set {0,1,2,3,4,...}

On the other hand, it is possible to have a decimal temperature like 98.6 degrees, which means we rule out choice 1. Choices 2, 4, and 5 are a similar story.

Cinnamon tea costs $1.50 per pound, and spice tea costs $2.75 per pound.

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the cost per pound of the cinnamon tea as C, and the cost per pound of the spice tea as S.

From the first mixture, we know that the total weight is 17 pounds, so we can write the equation:

12C + 5S = 28 ----(Equation 1)

From the second mixture, we know that the total weight is 20 pounds, so we can write the equation:

14C + 6S = 33 ----(Equation 2)

To solve this system of equations, we can use a method like substitution or elimination.

Let's use the elimination method to eliminate the variable C:

Multiply Equation 1 by 2 and Equation 2 by -3 to eliminate the C terms:

24C + 10S = 56 ----(Equation 3)

-42C - 18S = -99 ----(Equation 4)

Add Equation 3 and Equation 4:

-18C - 8S = -43

Solve for S:

8S = 43 - 18C

S = (43 - 18C)/8 ----(Equation 5)

Now substitute Equation 5 into Equation 1:

12C + 5((43 - 18C)/8) = 28

Multiply through by 8 to eliminate the fraction:

96C + 215 - 90C = 224

6C = 9

C = 9/6 = 1.5

Substitute the value of C back into Equation 5 to find S:

S = (43 - 18(1.5))/8 = 2.75

Therefore, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

In summary, the cost per pound of the cinnamon tea is $1.50, and the cost per pound of the spice tea is $2.75.

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The absolute maximum and minimum values obtained from the graph of the functions are;

Absolute maximum of g; [1, 4]

Absolute minimum of g; [4, -3]

Absolute maximum h; [4, 3]

Absolute minimum of h; (-4, -5)

The absolute maximum and minimum of a function are the coordinates of the highest and lowest points on the graph of the function, within the specified domain.

The points on the graph of the functions indicates that the maximum and minimum values of the functions are;

Graph of g; Absolute maximum of g = (1, 4)

Absolute minimum of g ; [4, -3]

Graph of h

Absolute maximum of h; [4, 3]

Absolute minimum of h; (-4, -5)

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Answer:

Therefore, the correct answer is: x < 23.

Step-by-step explanation:

To solve the inequality x - 5 + 2 < 20, we can simplify it step by step:

x - 5 + 2 < 20

Combine like terms:

x - 3 < 20

Add 3 to both sides of the inequality:

x - 3 + 3 < 20 + 3

Simplify:

x < 23

The solution to the inequality is x < 23.

Therefore, the correct answer is: x < 23.

Answer and Step-by-step explanation:

Please see the photo for the solution :)

Answer:

180 marbles in a 7-pound bag.

Answer:

w(25) = 96

There are 96 wolves in the year 2020

Step-by-step explanation:

Given:

[tex]w(x)=14\cdot 1.08^{x}[/tex]

w(25) =

[tex]w(25)=14\cdot 1.08^{25}\\\\= 14 * (6.848)\\\\=95.872\\\\\approx 96[/tex]

Number of years : 1995 + 25 = 2020

In 2020, there are 96 wolves

The hourly wage, the number of hours and the number of days Jaxon works indicates that the amount Jaxon gets paid is $192

The formula for hourly wage can be presented as follows;

Hourly wage  = Total earnings/Total hours worked

The question in the link is presented as follows;

Jaxon gets paid $6 an hour. He works for 8 hours each day for four days. How much will Jaxon get paid

The amount Jaxon gets paid per hour (his hourly wage) = $6

The number of hours he works each day = 8 hours

The number of days Jaxon works = Four days

The amount Jaxin gets paid = Hourly wage × Hours per day × Number of days

Therefore we get;

Amount he gets paid = $6 per hour × 8 hours/day × 4 days = $192

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The limit of the function As x → - ∞, f(x) → 2.

The limit of a function is the value the function tends to as the independent variable tends to a given value.

Given the graph of the function above, to find the limit of the function As x → -∞, f(x) →? We proceed as follows

Looking at the graph, we see that f(x) has a horizontal asymptote at y = 2. Now, we see that As x → -∞, f(x) approaches 2.

So, As x → - ∞, f(x) → 2.

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Answer:

The word "ENTERTAIN" has 9 letters, but it contains repeated letters. Specifically, it has 3 E's, 2 N's, and 2 T's.

To find the number of distinct permutations, we can use the formula for permutations with repeated elements.

The number of distinct permutations is given by:

n! / (n1! * n2! * ... * nk!)

where n is the total number of elements and n1, n2, ..., nk are the frequencies of each repeated element.

In this case, we have:

n = 9

n1 = 3 (for E)

n2 = 2 (for N)

n3 = 2 (for T)

Plugging these values into the formula, we get:

9! / (3! * 2! * 2!)

Calculating this expression gives us:

(9 * 8 * 7 * 6 * 5 * 4) / (3 * 2) =

(30240) / (12) =

2520

Therefore, there are a total of 2520 distinct permutations that can be formed using the letters of the word "ENTERTAIN".

The polynomial with real coefficients from the zeros is P(x) = 2x³ - 18x² + 2x + 58

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

zeros =  5+2i, 5-2i, -1

One such polynomial P(x) can be defined as

P(x) = x³ - 9x² + x + 29.

When this polynomial is multiplied by a costant, the roots and zeros remain the same

Let the constant be 2

So, we have

New P(x) = 2(x³ - 9x² + x + 29)

Evaluate

New P(x) = 2x³ - 18x² + 2x + 58

Hence, the function is P(x) = 2x³ - 18x² + 2x + 58

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Answer:

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

Divide 1/6 by 4:

Each piece is 1/24 of a pound.