3) Calculate the shaded area for the given figure.
DO
—4—

h = how old the house is right now

so right now Mark and Lynne are paying the house off, the house as we speak is "h" years old, it happens that Mark and Lynne are going to be paying the whole house in 18 years from now, so by then the house will be whatever years is now, or "h", plus 18 years, so when Mark and Lynne are done paying for it, the house will be "h + 18" years old.

Now, if the house in 18 years is going to be 4 times as old as it's right now, well, hell right now is "h" years old, 4 times that much is just "4h" years, so we can say

[tex]\stackrel{\textit{18 years from now}}{h+18}~~ = ~~\stackrel{\textit{18 years from now}}{4h}\implies 18=3h\implies \cfrac{18}{3}=h\implies 6=h[/tex]

Answer: d = 27

Step-by-step explanation:

      To solve, we will isolate the variable d.

Given:

      9 = [tex]\frac{d}{3}[/tex]

Multiply both sides of the equation by 3:

      27 = d

Reflexive property:

      d = 27

The amount of vegetables that your friend cooks each day is the constant of the proportional relationship.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For this problem, the relationship for the amount of vegetables is given as follows:

Vegetables = Constant x Days.

Hence the daily amount of vegetables is given as follows:

Constant = Vegatables/Days.

The problem is incomplete, hence the general procedure to obtain the amount of vegetables that your friend cooks each day is presented.

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The optimal solution is to produce 4 stereo sound bars and 8 flatscreen TVs, which will result in a profit of $1800.

Define profit ?

Profit is the financial gain that is earned by a business or an individual after deducting all the expenses incurred.

Let's represent the number of sound bars produced by "x" and the number of flatscreen TVs produced by "y."

The objective function for profit can be represented as:

Profit = 125x + 100y

The constraints can be represented by the availability of each machine:

Machine A: 1x + 2y ≤ 16

Machine B: 1x + y ≤ 49

Machine C: 4x + y ≤ 24

Also, the number of sound bars and flatscreen TVs produced must be non-negative:

x ≥ 0 and y ≥ 0

To solve the feasible region using graphical method, we need to plot the constraints and find the intersection points.

First, let's plot the constraint equations:

A: x + 2y <= 16

B: x + y <= 49

C: 4x + y <= 24

To plot each constraint, we need to find two points that satisfy the equation. Then, we can draw a straight line passing through those two points.

For constraint A:

When x = 0, y = 8

When y = 0, x = 16

So the line for constraint A passes through (0,8) and (16,0).

For constraint B:

When x = 0, y = 49

When y = 0, x = 49

So the line for constraint B passes through (0,49) and (49,0).

For constraint C:

When x = 0, y = 24

When y = 0, x = 6

So the line for constraint C passes through (0,24) and (6,0).

Now, let's plot these lines on a graph and find the feasible region.

The feasible region is the shaded area that satisfies all three constraints. We can see that it is a triangle with vertices at (0,0), (6,0), and (4,8).

Therefore, the optimal solution will be at one of the vertices.

At vertex (0,0):

Profit = 0

At vertex (6,0):

Profit = 125(6) + 0(0) = 750

At vertex (4,8):

Profit = 125(4) + 100(8) = 1800

So the optimal solution is to produce 4 stereo sound bars and 8 flatscreen TVs, which will result in a profit of $1800.

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Answer: 185

Step-by-step explanation:

231-46=185

Answer: 185

Step-by-step explanation:

231-46

Answer:

$5,149.44

Step-by-step explanation:

To calculate the compound amount and interest on a loan of ​$10800 compounded annually for four years at 10%, we can use the formula:

A = P(1 + r)^t

where A is the compound amount, P is the principal (the initial loan amount), r is the interest rate (as a decimal), and t is the number of years.

In this case, P = $10800, r = 0.10 (10% as a decimal), and t = 4. Substituting these values into the formula, we get:

A = $10800(1 + 0.10)^4

A = $10800(1.10)^4

A = $15,949.44

Therefore, the compound amount after four years is $15,949.44.

To calculate the interest, we can subtract the principal from the compound amount:

Interest = $15,949.44 - $10,800

Interest = $5,149.44

Therefore, the interest on the loan is $5,149.44.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10800\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 10800\left(1+\frac{0.10}{1}\right)^{1\cdot 4} \implies \boxed{A = 15812.28} ~\hfill \underset{ earned~interest }{\stackrel{ 15812~~ - ~~10800 }{\boxed{5012}}}[/tex]

Answer:

The answer should be P'(-3,-7), Q(-9,3), and R'(-4,1) which is D.

Step-by-step explanation:

Answer:

$3267

Step-by-step explanation:

$121000 × $2970/$110000

= 11 × 297

= $3267

The taxes on the house with an assessment of $121000 are $3267

Answer:

  $3267

Step-by-step explanation:

You want to know the taxes on a house assessed at $121000 if the taxes on a house assessed at $110000 are $2970.

The taxes are proportional to the house value, so if the house value goes up by a factor of 121000/110000, so do the taxes. The taxes will be ...

  (121000/110000)·$2970 = $3267

The taxes on the house with an assessment of $121,000 are $3267.

__

Additional comment

You could go to the trouble to find the tax rate, which is ...

  rate = $2970/$110000 = 0.027

This can be described as 27 mils, 27‰, or $27 per thousand.

Multiplying this rate by the higher assessed value shows the taxes are ...

  0.027 × $121000 = $3267

We don't really need to know the tax rate. All we need to know is that the house with the 10% higher value will have 10% higher taxes.

Answer:

13.5

Step-by-step explanation:

Answer: 13.5

Step-by-step explanation:

just use the calculator

Answer:

1384.7

Step-by-step explanation:

42/2     21^2x3.14=1384.74

Hope this Helps :)

Answer:

16t⁶ - 192t⁵ + 640t⁴ - 384t³ + 64t²

Step-by-step explanation:

1. Multiply the numbers

2. Combine exponents

3. Combine exponents

4. Expand the square

5. Distribute

6. Distribute

7. Distribute

8. Distribute

9. Combine like terms

10. Combine like terms

11. Combine like terms

12. Distribute

The total surface area of the triangular prism using the net is 640 square meters

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

The net of a triangular prism

The surface area of the triangular prism from the net is calculated as

Surface area = sum of areas of individual shapes that make up the net of the triangular prism

Using the above as a guide, we have the following:

Area = 2 * 8 * 17 + 8 * 16 + 2 * 1/2 * 15 * 16

Evaluate

Area = 640

Hence, the surface area is 640 square meters

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Answer:

23.33

Step-by-step explanation:

The solutions of the inequalities are s≤2 and s>7 respectively

The given inequalities are 2s +3≤7 OR 3s +5> 26

We have to find the solutions

2s +3≤7

Subtract 3 from both sides

2s≤4

Divide both sides by 2

s≤2

Now inequality 3s +5> 26

Subtract 5 from both sides

3s>21

s>7

Hence, the solutions of the inequalities are s≤2 and s>7 respectively.

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Answer:

the vertex form of the given quadratic expression is:

y = 3(x + 8/3)^2 - 4/3

Step-by-step explanation:

To write the given quadratic expression 3x^2+16x+20 in vertex form, we need to complete the square.

Step 1: Factor out the coefficient of x^2:

3(x^2 + (16/3)x) + 20

Step 2: Take half of the coefficient of x and square it:

(16/3)/2 = 8/3

(8/3)^2 = 64/9

Step 3: Add and subtract the result from step 2 inside the parentheses:

3(x^2 + (16/3)x + 64/9 - 64/9) + 20

Step 4: Simplify inside the parentheses and factor:

3[(x + 8/3)^2 - 64/9] + 20

Step 5: Simplify the constant term:

3(x + 8/3)^2 - 4/3

Therefore, the vertex form of the given quadratic expression is:

y = 3(x + 8/3)^2 - 4/3

Answer:

the formula is:

degrees = radians x 180/π

Therefore, to convert π/8 radians to degrees, we have:

degrees = (π/8) x 180/π

degrees = 22.5°

So, π/8 radians is equal to 22.5 degrees.:)

The value of π/8 into degree is, 22.5 degrees.

We have to given that,

Convert pi/8 radian to degrees​

Since, We know that,

the formula is:

Degrees = Radians x 180/π

Hence, to convert π/8 radians to degrees, we have:

Degrees = (π/8) x 180/π

degrees = 22.5°

So, π/8 radians is equal to 22.5 degrees.

Therefore,

The value of π/8 into degree is, 22.5 degrees.

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The solution is, the selection can be made in 593775ways

Combination has to do with selection of r objects from a total number of n objects and this can be done in nCr ways. Generally,

nCr = n!/(n-r)!r!

Since the math teacher has to select 6 students from a class of 30, this can be done in 30C6 number of ways to have;

30C6 = 30!/(30-6)!6!

30C6 = 30!/24!6!

30C6 = 30×29×28×27×26×25×24!/24!×6×5×4×3×2

30C6 = 30×29×28×27×26×25/6×5×4×3×2

30C6 = 427,518,000/720

30C6 = 593775ways

This means, the selection can be made in 593775ways.

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Answer:

b have a great day today and look in comments

Answer:

Step-by-step explanation:

try adding 18 and 60 the subtracting the answer from 180 :)

Answer:

Single payment Variable annuity

Answer:

$886.47

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the expected value of the game, we need to multiply the value of each outcome by its probability, and then add up the results. Let's first calculate the probabilities of drawing a diamond and not drawing a diamond:

P(diamond) = 13/52 = 1/4

P(not diamond) = 1 - P(diamond) = 3/4

Now we can calculate the expected value of the game:

E = (5)(P(diamond)) + (-2)(P(not diamond))

E = (5)(1/4) + (-2)(3/4)

E = 5/4 - 6/4

E = -1/4

The expected value of the game is -$0.25. This means that, on average, the player can expect to lose 25 cents per game in the long run.

answer:

a. 7/8

b.9

c.9

explanation:

In the figure given, rotation is the only single transformation that takes shape A to shape B.

A function, f, that maps to itself is called the transformation, i.e., f: X → X. The pre-image X becomes the image X after the transformation. This transformation can be any or the combination of operations like translation, rotation, reflection, and dilation. The translation is moving a function in a specific direction, rotation is spinning the function about a point, reflection is the mirror image of the function, and dilation is the scaling of a function. Transformations in Math describe how two-dimensional figures move around a coordinate plane.

In this problem, the only single transformation that will make the figure A turn into figure B is rotation. This is only one of the four transformation techniques which are rotation, reflection, dilation and translation and in this case, only rotation is mentioned.

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Answer:

To simplify 3/27, find the greatest common factor (GCF) of the numerator and denominator and divide both by it123. The GCF of 3 and 27 is 3134. Therefore, 3/27 can be reduced to 1/9 by dividing both 3 and 27 by 312345. This is the simplest form of 3/2715.

Step-by-step explanation:

x√2 is the quotient of √22x⁶÷√11x⁴, √22x⁶ is dividend and √11x⁴ is divisor

The number which is getting divided here is called the dividend.

The number which divides a given number is the divisor.

The number which we get as a result is known as the quotient.

We have to find the quotient of √22x⁶÷√11x⁴

√22x⁶/√11x⁴

√22x⁶ is dividend.

√11x⁴ is divisor

√2√11 x³/√11 x²

x√2 is the quotient.

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Step-by-step explanation:

A:(x+6)^2-36

The rest of the answers are at the top just identify the form your looking for.

This is difficult to estimate exactly without knowing more details about the investment fund and returns, but we can make some reasonable assumptions and calculations:

* Let's assume the fund generates an average annual return of 6% over 40 years. This is a modest but achievable return for a balanced stock/bond fund.

* At a 6% annual return, that amounts to a 0.06 annual return on the money invested.

* Let's also assume an average annual inflation rate of 3% over 40 years. So the returns need to beat inflation by at least 3% to generate real growth.

* $15,000 invested today at 6% annual return for 40 years:

1) $15,000 * (1 + 0.06)^40 = $263,174

2) Inflation adjustment (at 3% for 40 years): $263,174 * (1 - 0.03^40) = $79,378

* So after 40 years, the initial $15,000 investment could be worth around $79,378 in today's dollars.

* As a very rough estimate, if inflation averages out and the nominal returns are decent but not too high, the $15,000 could grow to $100,000 to $200,000 in 40 years. A lot will depend on how the specific fund performs versus the broader market and economy.

* The future value will also depend on whether any money is withdrawn or added over the 40 years. I have assumed the full $15,000 is invested for the entire 40 years.

The probability from the t distribution is 0.8999 and the value of c is 1.77

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

Degrees of freedom = 15

Using a graphing calculator, we have

P(t ≥ -1.34) = 1 - 0.1001

So, we have

P(t ≥ -1.34) = 0.8999

Calculating the value of c, we have

P(-c < t < c) = 0.95

At a degree of freedom of 13, we have

c = 1.77

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