Question 12
You are negotiating to make a 7-year loan of $20,000 to Breck Inc. To repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at
the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently unspecified cash flow, X, at the end of each year from
Year 4 through Year 7. Breck is essentially riskless, so you are confident the payments will be made. You regard 8% as an
appropriate rate of return on a low risk but illiquid 7-year loan. What cash flow must the investment provide at the end of each of
the final 4 years, that is, what is X?
(A) $2,520.02
B) $2,831.49
$3,369.47
$2,491.71
0.5 Points
E $2,661.60

In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

The compound interest model is based on the assumption that the initial capital obtain gains continuously in time. This model is represented by the following expression:

C' = C · (1 + r/100)ˣ     (1)

Where:

Please notice that a year consists in four quarters. If we know that C = 1200, r = 5.25 and x = 8, then the current capital is:

C' = 1200 · (1 + 5.25/100)⁸

C' = 1807

In accordance with the compound interest model, the future value if you invest $ 1200 at 5.25 % compounded quarterly for two years is $ 1807.

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It can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

SAS congruency states that  two triangles are said to be congruent if any two sides or angle between the sides of one triangle are equal to the corresponding two sides and also the angle between the sides of the second triangle.

Thus, it can be concluded that ΔWXY is equivalent to ΔBCD by the SAS rule because the corresponding sides and corresponding angle are congruent. Option D

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Answer:

B. No, because the corresponding congruent angles listed are not the included angles.

Step-by-step explanation:

Answer:

d.) 226.2 cubic inches

Step-by-step explanation:

The soup pot is in the shape of a cylindrical.

And

[tex]\sf Volume \ of \ cylinder= \pi (radius)^2 (height)[/tex]

Here given:

So,

[tex]\sf Volume \ of \ pot= \pi (3)^2 (8)[/tex]

[tex]\sf Volume \ of \ pot= 72\pi \ in^3[/tex]

[tex]\sf Volume \ of \ pot= 226.2 \ in^3[/tex]

Answer:

x + 3

Step-by-step explanation:

x = Anna's age

y = John's age

z = Tamara's age

y = x + 1

z = x - 2

the expression for the sum of Anna's and John's age minus Tamara's age is

x + y - z

and when we use the equations above to simplify that :

x + (x + 1) - (x - 2) = x + x + 1 - x + 2 = x + 3

Answer:

y = 6x+9

Step-by-step explanation:

Equations that are parallel have the same slope

y = 6x+7 is written in slope intercept form where the slope is 6 and the y intercept is 7

The lines will have a slope of 6

The point (0,9) is the y intercept because the x value is 0

We can write the equation in slope intercept form y = mx+b

y = 6x+9

Answer:

Hello! The answer is y = 6x + 9.

Step-by-step explanation:

When lines are parallel, they will have the same slope but a different y-intercept.

The y-intercept, in this case, would be (0, 9) since the x-coordinate equals 0. This leaves us with 9 as the y-intercept.

Our slope-intercept form equation will be written as:

y = 6x + 9

[tex]3y \geqslant 13 - 9[/tex]

[tex]3y \geqslant 4[/tex]

[tex]y \geqslant \frac{4}{3} [/tex]

[tex]3y \leqslant 13 - 1[/tex]

[tex]3y \leqslant 12[/tex]

[tex]y \leqslant 4[/tex]

[tex] \frac{4}{3} \leqslant y \leqslant 4[/tex]

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the problem want us to find:

Let's gather the information:

  ⇒ the information given: y = 1/5 x - 8

        ⇒ the line is in slope-intercept form

            ⇒ means:

                     ⇒ coefficient in front of 'x' is the slope

                     ⇒ constant is the y-intercept

Answer:

Hope that helps!

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Hi!

The equation that we're working with is provided to us in Slope-Intercept Form:

        [tex]\diamondsuit~~~\large\boldsymbol{y=mx+b}[/tex]

In the formula, the letter "m" denotes the slope, and it always comes before x; b is the y-intercept, and it's basically a number that is either added or subtracted from x.

Now let's identify the slope of the line given to us, that is:

[tex]\boldsymbol{\underline{\underline{y=1/5x-8}}}[/tex]

Slope = number before x,

Y-intercept = number added/subtracted from the slope

Therefore,

[tex]\stackrel{\heartsuit}{\boxed{\boxed{\textsc{Answers:}\begin{cases}\bold{Slope:\displaystyle\frac{1}{5}}\\\bold{Y-intercept:-8}\end{cases}}}}[/tex]

I hope it helped! Let me know if you need any explanation or clarification! I'm always happy to help. :D

To solve this exercise, we apply the rule of three:

Oranges......................Price

 8.................................$4.40

 9.......................................x

We solve as follows:

[tex]\boldsymbol{\sf{x=\dfrac{9\times4.40}{8}=\dfrac{39.6 }{8}=4.9 }}[/tex]

Therefore, 9 oranges would cost $4.9.

The required cost of the amount of 4.95 dollars would be for 9 oranges.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

We have been given that a grocery store sells a bag of 8 oranges for $4.40.

We have to determine the cost for 9 oranges.

Let's assume x dollars would it cost for 9 oranges.

As per the given condition, we can write the ratio as:

8 oranges : $4.40 = 9 oranges : x dollars

⇒ 8 / 4.40 = 9 / x

Cross multiplication and rearrange the terms of the above equation,

⇒ 8x = 4.40×9

Divide by 8 into both sides of the equation,

⇒ x = (4.40×9)/8

⇒ x = (39.6)/8

⇒ x = 4.95

Therefore, the cost of the amount of 4.95 dollars would for 9 oranges.

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Answer: 9

Step-by-step explanation:

    We will use the Order of Operations to solve.

 Given:

4 – 15 ÷ (30 – 33)

 Subtract 33 from 30:

4 – 15 ÷ (– 3)

 Divide -15 by -3:

4 + 5

 Add 4 to 5:

9

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{In order for you to solve for this}\\\huge\textbf{equation, you have to do PEMDAS.}\\\\\\\\\huge\textbf{PEMDAS simply means: }[/tex]

[tex]\bullet\large\textbf{ Parentheses}[/tex]

[tex]\bullet\large\textbf{ Exponents}[/tex]

[tex]\bullet\large\textbf{ Multiplication}[/tex]

[tex]\bullet\large\textbf{ Division}[/tex]

[tex]\bullet\large\textbf{ Addition}[/tex]

[tex]\bullet\large\textbf{ Subtraction}[/tex]

[tex]\huge\textbf{Now, let's answer the given equation.}[/tex]

[tex]\mathbf{4 - 15 \div (30 - 33)}[/tex]

[tex]\mathbf{= 4 - 15 \div 3}[/tex]

[tex]\mathbf{= 4 - (-5)}[/tex]

[tex]\mathbf{= 4 + 5}[/tex]

[tex]\mathbf{= 9}[/tex]

[tex]\huge\textbf{We got the \boxed{\bf +} because double negatives}\\\huge\textbf{equal a positive.}[/tex]

[tex]\huge\textbf{We have found the result to the question}[/tex]

[tex]\huge\textbf{Thus, your answer should be: \boxed{\mathsf{9}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equivalent pair of the given expression is; [4.8] and [3.21]

Floor function states that the greatest integer that is less than or equal to x. It is represented by:  ⌊ x ⌋.

Ceiling function states that the least integer that is greater than or equal to x. It is represented by ⌈ x ⌉.

Kareem wrote the expressions;

[3.2] [2.7] [2.9] [4.8]

By definition above;

[3.2] = 4

[2.7] = 2

[2.9] = 3

[4.8] = 4

Thus, the equivalent pair is [4.8] and [3.2]

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if x is changed by 2 , the y changes by  +3, Option B is the correct answer.

The equation of a Linear Function is given by

y = mx +c

here m is the slope , c is the intercept on the y axis

The data is given in the table

To determine the relation , a function needs to be established between the variables.

m = ( y2 -y1 )/(x2-x1)

m = (-7 +10) /(-2+4)

m = 3 / 2

y = (3/2)x + c

at x = 0 , y= -4

-4 = 0 + c

c = -4

The function is

y = (3/2) x - 4

if x is changed by 2 , the y changes by  +3

Therefore Option B is the correct answer.

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Answer:

[tex]x \ = \ 10[/tex]

Step-by-step explanation:

Let point [tex]D[/tex] be the point where the straight line drawn from point [tex]A[/tex] meets the straight line [tex]BC[/tex], it is evident that [tex]\triangle ABD[/tex] and [tex]\triangle ACD[/tex] is similar given that both triangles share the same angle, [tex]\angle BAD \ = \ \angle DAC[/tex]. Hence, the ratio of the sides of each triangle is the same. Specifically,

                                              [tex]\displaystyle{\frac{x+4}{8} \ = \ \frac{2x+1}{12}}[/tex].

Performing cross multiplication yields

                                           [tex]12\left(x+4\right) \ = \ 8\left(2x+1\right) \\ \\ \rule{0.15cm}{0cm}12x+48 \ = \ 16x+8 \\ \\ \rule{1.1cm}{0cm} 4x \ = \ 40 \\ \\ \rule{1.3cm}{0cm} x \ = \ 10[/tex].

The triangle formed is a right triangle and the hypotenuse side is 6 ft.

The situation forms a right angle triangle.

A right triangle has one of its angles as 90 degrees.

Therefore, the triangle is represented below

The hypotenuse side of the right triangle is 6 foot, which is the length of the ladder.

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Step-by-step explanation:

tens place is 8 because the first number from the back is the unit

the tenth place is 2

Answer:

17 gallons

Step-by-step explanation:

1 gallon has 16 cups

2 gallons have 32 cups

32-15=17

Answer:

17 cups

Step-by-step explanation:

1 gallon=16 cups

Since he made 2 gallons of soup, multiply 16 x 2 and you will get 32 cups of soup. If he served 15 cups of soup to his guests, he will have 17 cups of soup left over, because 32 - 15 = 17.

I hope i helped!!! :)

Answer:

The Prime Factorization of 220 is 22 × 51 × 111.

Step-by-step explanation:

Factors of 220 are integers that can be divided evenly into 220. It has total 12 factors of which 220 is the biggest factor and the prime factors of 220 are 2, 5, 11. There for, the  Prime Factorization of 220 is 22 × 51 × 111.

Answer: Width = 15cm

              L = 31cm

Step-by-step explanation:

P = 92 cm

L = 1 + 2W

P = 2L + 2W

P = 2(1+2W) + 2W

P = 2+4W+2W

P = 2 + 6W

92cm = 2 + 6W

subtract 2 on both sides to cancel the 2 on the right side.

90cm = 6W

W = 90/6

Width = 15cm

L = 1+2W

L = 1 + 30cm

L = 31 cm

Verification:

P = 2L+2W

P = 2(31)+2(15)

P = 62+30

P = 92cm

Hope I Helped!

Answer:

P = 2(L + W) = 2L + 2W (first part)

L = 2W + 1 (second part)

Step-by-step explanation:

L = length of rectangle
W = width of rectangle
P = perimeter of rectangle = 2 * (L + W)
So P = 2(L + W) = 2L + 2W  (1)

It is also given that length is 2 * width + 1

So we get the equation

L = 2W + 1 for L in terms of W  (2)

This question does not ask you to compute L and W but if you wanted to do that use the following steps
Substitute for L from equation 2 to equation 1 giving
P = 2(2W+1) + 2W = 4W + 2 + 2W = 6W + 2

We know P = 92

So 6W + 2 = 92
Subtracting 2 from both sides we get 6W = 90
Dividing both sides by 6 gives us W = 15
and L = 2 * 15 + 1 = 31

We can check this by finding the perimeter from L and W
perimeter = 2(L+W) = 2(31 + 15) = 2 (46) = 92 which matches the data in the question

Answer:

40 feetI is the correct answer

Using substitution, the result of the indefinite integral is:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

The integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

The substitution is:

[tex]u = 1 + x^{\frac{1}{3}}[/tex]

Then the derivative is:

[tex]du = \frac{1}{3}x^{-\frac{2}{3}} dx[/tex]

ttex]dx = 3dux^{-\frac{2}{3}}[/tex]

Hence the integral is:

[tex]\int \frac{1}{x^{\frac{2}{3}}(1 + x^{\frac{1}{3}})} dx[/tex]

[tex]\int \frac{1}{x^{\frac{2}{3}}u} \times 3dux^{-\frac{2}{3}}[/tex]

[tex]\int \frac{3du}{u}[/tex]

[tex]3\ln{u} + C[/tex]

Returning to x:

[tex]3\ln{(1 + x^{\frac{1}{3}})} + C[/tex]

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The expected profit for the gambler is $4,621

The possible outcomes are:

Then the expected profit is:

P = ($6,500*0.81 + $200*0.08 - $6,000*0.11) = $4,621

The expected profit for the gambler is $4,621

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The topsoil will be 4.05 inches deep

From the question, we are to determine how many inches deep the topsoil will be

From the given information,

The volume of the topsoil = 1 cubic yard

Convert to cubic feet

1 cubic yard = 27 cubic feet

∴ The volume of the topsoil = 27 cubic feet

Then,

The depth of the topsoil will be = 27/(8 ×10)

Depth of topsoil = 27/80

Depth of topsoil = 0.3375 foot

Now, convert to inches

1 foot = 12 inches

∴ 0.3375 foot = 0.3375×12 inches

= 4.05 inches

Hence, the topsoil will be 4.05 inches deep

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The statement that describes a key feature of function g if g(x) = f(x + 4) is C. horizontal asymptote of y = 0.

It should be noted that a function is an expression that shows the relationship between the variables.

In this case, the statement that describes a key feature of function g if g(x) = f(x + 4) is that the horizontal asymptote of y = 0.

The horizontal asymptote is vital for guiding the variables

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Answer:

A. 2 and-6

Step-by-step explanation:

Like terms are terms that contain the same variables raised to the same powers. In other words, they have the same variables with the same exponents.

So in option A, we have the terms 2 and -6. These terms are not like terms because they do not have the same variables.

Answer:where are the options ???

Step-by-step explanation:

Answer:

Product 1

Step-by-step explanation:

Got it

The largest sum of three numbers that meet at a corner is 15

The number cube that completes the question is added as an attachment

The largest number in the number cube is 6.

On the number cube, the next largest numbers share the same corner with the number 6

So, the largest set of numbers on the cube are 6, 5, 4

Add the numbers:

Sum = 6 + 5 + 4

Evaluate

Sum = 15

Hence, the largest sum of three numbers that meet at a corner is 15

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The percentage of data points that are above 27 are; 2.28%

We are given;

Mean; μ = 51

Standard deviation; σ = 12

Sample mean; x' = 27

Thus, formula for z-score is;

z = (x' - μ)/σ

z = (27 - 51)/12

z = -2

Now, from the empirical rule of normal distribution graph attached, we see that at z = -2, the percentage is 95.44%. However, we want to find the percentage that lie above 27. Thus, this is (100% - 95.44%)/2 = 2.28%

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Answer:

:)\

Step-by-step explanation:

Answer:

5621 years

Step-by-step explanation:

Plug everything in first.

[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]

Round to closest amount of years = 5621 years

Answer:

231,000

Step-by-step explanation:

In the ratio of 11:13, if you plug in 13, the corresponding value is 11.

Dividing 11 by 13 shows that if you also multiply 13 by 0.846 (Rounded) it also equals 11.

So multiplying 0.846 by the original price of 273,000, we get 231,000.

The new selling price of the car will be 231,000. Then the correct option is A.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The original selling price of a used automobile is N273,000. The price is dropped by the dealer by a ratio of 11:13.

The new selling price of the car will be given as,

Selling price = 273,000 x 11/13

Selling price = 21,000 x 11

Selling price = 231,000

Thus, the correct option is A.

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