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Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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The amount of interest Sai will pay is $312.50.

Interest is the cost associated with borrowing money, or the return earned for lending money. It is typically expressed as a percentage of the principal amount borrowed or lent, and is usually paid periodically over the life of the loan. Interest can also be earned from investments, such as savings accounts, bonds, and other financial instruments. The rate of interest charged or earned varies depending on the nature of the loan or investment, the risk associated with the transaction, and the creditworthiness of the borrower or investor.

This is calculated by multiplying the principal amount of $12,500 by the interest rate of 2.5%, which equals 0.025. Then, the 0.025 is multiplied by the loan period of 24 months to come up with the total interest. Therefore, $12,500 x 0.025 x 24 = $312.50.

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The area of the shaded part of the given figure is 60 square inches'

The given figure is made up of a rectangle and 2 similar triangles

Area of the shaded part = Area of rectangle + area of 2 triangles

From the figure

Area of rectangle = 12 * 4 = 48 square in

Area of one triangle = 0.5(6)(4) = 12 square in

Area  of the figure = 48 + 12

Area  of the figure = 60 square inches'

Hence the area of the shaded part is 60 square inches.

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Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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Answer:

19 minutes in 2 miles is how long it tool her to run it

Step-by-step explanation:

Answer:

9 1/2

Step-by-step explanation:

took test

9514 1404 393

Answer:

  c.  3 to 4

Step-by-step explanation:

There are 3 oranges and 4 apples in the bowl, so the ratio is ...

  oranges/apples = 3/4 or 3 to 4

Given expression,

Solving,

Thus,

The answer is

Answer:

141.37

Step-by-step explanation:

\(v =\pi \: r {}^{2}h = \pi \times 3 {}^{2} \times 5 = 141.37\)

Answer:

1 yard=3 feet

Step-by-step explanation:

If it needs more, then 3 feet=36in.

Answer:

first one is x=-15-2y/5

second one x=y-3

Step-by-step explanation:

The polynomial f(x) = 5x² + 7x - 6 have a roots or zeros of 3/5 and -2

Roots of polynomials are the solutions for any given polynomial for which we need to find the value of the unknown variable. If we know the roots, we can evaluate the value of polynomial to zero.

The roots of a polynomial is also known as zero of a polynomial. Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively. Some of the methods used to find the zeros of polynomial are grouping, factorization, and using algebraic expressions.

The roots or zeros of this polynomial can be given as

f(x) = 5x² + 7x - 6

0 = 5x² + 7x - 6

The zeros of this polynomial are 3/5 and -2

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We will use sine function, and length of the opposite side is \(\frac{25\sqrt{3}}{2}$\) feet.

To solve for the opposite side of the right triangle, we would use the sine function. In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse.

In this problem, we are given that one angle of the right triangle is 60 degrees and the hypotenuse is 25 feet. Let's label the opposite side as x and the adjacent side as y. Then we can use the sine function:

\($\sin 60^\circ = \frac{x}{25}$\)

Simplifying the left side, we have:

\($\frac{\sqrt{3}}{2} = \frac{x}{25}$\)

Multiplying both sides by 25, we get:

\($x = \frac{25\sqrt{3}}{2}$\)

Therefore, the length of the opposite side is \(\frac{25\sqrt{3}}{2}$\) feet.

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Answer:

first you correct like terns

Answer:

Unclear.

To find the perimeter you need all three sides of the triangle. You have only given two.

All you need to do is add up all three sides and you have your perimeter.

Formula: P=a+b+c

Answer:

Unknown unless you give the amount of cm for the last side

We are given that a hose in the front yard can fill the pool in 30 minutes and a hose in the back yard can fill it in half the time (so 15 minutes). We are asked to find the time, we'll call "t," it takes for both hoses together to fill up the pool.

We can create a rational equation, \(\frac{1}{30}+\frac{1}{15}=\frac{1}{t}\). Solve to "t"

\(\frac{1}{30}+\frac{1}{15}=\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{1}{15}*\frac{2}{2} =\frac{1}{t} \Longrightarrow \frac{1}{30}+\frac{2}{30} =\frac{1}{t} \Longrightarrow \frac{3}{30} =\frac{1}{t}\)

\(\Longrightarrow \frac{1}{t}=\frac{3}{30} \Longrightarrow \frac{1}{t}=\frac{1}{10} \Longrightarrow \boxed{t=10 \ min}\)

Thus, b is the correct option.

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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Answer:

16.2 feet

Step-by-step explanation:

Reference angle = 62°

Opposite = x

Adjacent = 8.6

Apply trigonometric function, TOA:

Tan 62 = Opp/Adj

Tan 62 = x/8.6

8.6 × Tan 62 = x

16.1742476 = x

x = 16.2 ft (nearest tenth)

Explanation

Part A

We can use the formula below to find the mean.

We will then have;

Mean = 6.2632

Part B

Since the data set is odd.

Answer: From the column of cumulative frequency cf, the median is 7

Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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The correct value of Z for the solution to true system is -2

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

2x + 3y - z = 4

x - 3y + 2z = -3

3x + y - z = 5

Transform the third equation

So we have

2x + 3y - z = 4

x - 3y + 2z = -3

9x + 3y - 3z = 15

Eliminate y in the equations by subtraction

So we have

x - 3z = 7

10x - z = 12

Multiply x - 3z = 7 by 10

10x - 30z = 70

10x - z = 12

Subtract the equations

-29z = 58

So, we have

z = -2

Hence, the correct value of Z  is -2

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It is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a Wide range of factors

As an AI language model, I do not have access to up-to-date information about salaries of coaches in Jacksonville. However, in general, the salaries of coaches vary widely depending on a number of factors, such as the type of sport, the level of competition, the location, the success of the team, and the budget of the institution.

In terms of tennis and football, football is generally considered to be a more popular and high-profile sport than tennis in the United States, which could result in higher salaries for football coaches at the collegiate level. Football also typically generates more revenue and has larger budgets for athletic programs, which could also influence the salaries of coaches.

However, there are also factors that could affect the salaries of tennis coaches. For example, if a tennis program has a particularly successful season or has produced successful players, the coach may negotiate a higher salary. Additionally, some colleges may place a greater emphasis on tennis or have larger budgets for tennis programs, which could also impact the salaries of coaches.

Overall, it is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a wide range of factors. It is also important to note that salaries can vary widely between individual institutions, even within the same sport, and that negotiations between coaches and their institutions can play a significant role in determining salaries.

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3. Given, y = (1/2)x + 5

we need to find its parallel lines. For parallel lines, their slopes are equal If we compare the equation with y = mx + c where m indicates slope and c indicates intercept cut at y axis, then we see that slope of the parallel lines are 1/2. for the x intercept we can take any positive or negative number for example:

two more parallel lines are: y = (1/2)x + 4 & y = (1/2)x - 2

part(1) randomly input values in the equation for x. For example if we take x=2, y becomes, y = (1/2)*2 + 5 = 6. So the point becomes (2,6). In the same way take at least another value to get two point and draw the graph. Here it'd be better to take even numbers for x as in that way you avoid fractional values. Graphing fractional values can be a tedious job.

part(2): I think we covered this at the very beginning

part(3): Let's take the equations from 3.

y = (1/2)x + 4 & y = (1/2)x - 2

here we see that their slope is same when we compare them to y = mx+c

which is 1/2. Thus they are parallel lines

Answer:

Step-by-step explanation:

Answer:

b=a-3

Step-by-step explanation:

seventeen minus three gives 14, 14 minus 3 gives 11 and so on.

Answer:

-18 and -27 ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

Answer:

...

Step-by-step explanation:

Answer:

3n - 6

Step-by-step explanation: