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4 years ago

If the radius of mars is about 13.7% of neptune's radius, what is the radius of neptune?

1 answer:

8 0

You said that M is 13.7% of N

In algebraic notation M = 0.137 N

Divide each side by 0.137 : N = M / 0.137 = 7.3 M (rounded)

Online or in a real book, you can look up the radius of Mars.
Then write it in place of 'M' in this solution, and you'll have
an actual number for the radius of Neptune.

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Find the future value and interest earned if $8704.56 is invested for 8 years at 4% compounded (a) semiannually and (b) continuo

Sliva [168]

a) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded 2 times per year over 8 years is <u>$11,949.50</u>.

b) The future value, principal plus interest, with compound interest on a principal of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

<h3>How is the future value determined?</h3>

The future value can be determined using an online finance calculator.

Data and Calculations:

<h3>a) Compounded Semiannually:</h3>

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Semi-Annually

Time (t in years): 8 years

<u>Result</u>:

A = $11,949.50

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,244.94

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 8,704.56(1 + 0.04/2)(2)(8)

A = 8,704.56(1 + 0.02)(16)

A = $11,949.50

<h3>b) Compounded Continuously:</h3>

Using the formula A = Pert

Principal (P): $8,704.56

Annual Rate (R): 4%

Compound (n): Compounding Continuously

Time (t in years): 8 years

<u>Result</u>:

A = $11,987.29

A = P + I where

P (principal) = $8,704.56

I (interest) = $3,282.73

<h3>Calculation Steps:</h3>

First, convert R as a percent to r as a decimal

r = R/100

r = 4/100

r = 0.04 rate per year,

Then solve the equation for A, using the mathematical constant, e = 2.71828

A = Pert

A = 8,704.56(2.71828)(0.04)(8)

A = $11,987.29

Thus, while the future value of $8,704.56 at a rate of 4% per year compounded semiannually over 8 years is <u>$11,949.50</u>, the future value of $8,704.56 at a rate of 4% per year compounded continuously over 8 years is <u>$11,987.29</u>.

Learn more about compounding interest at brainly.com/question/24274034

#SPJ1

8 0

2 years ago

Twelve large bottles of water cost $9.How many bottles can you buy for $3?

Andrej [43]

Answer: 4 large bottles of water for $3.

Step-by-step explanation: To find how many large water bottles you can buy with $3, you’ll have to divide 12 by 3 which equals to 4. You can check your answer by multiplying 4 x 3 which equals to 12, which is the original amount of large water bottles you can buy for $9.

5 0

3 years ago

Please answer the following;

34kurt

The Surface area of the cube will be 433.5 square feet. Then the correct option is C.

<h3>What is a surface area of a cube?</h3>

Suppose that: The side length of the considered cube is L units. Then, we get:

Surface area of that cube = 6L² square units.

Bella is wrapping a cube shape box that measures 8.5 inches along each side.

The edge length of the cube is 8.5 meters.

Then the Surface area of the cube will be

Surface area = 6 x 8.5²

Surface area = 6 x 72.25

Surface area = 433.5 square feet

The Surface area of the cube will be 433.5 square feet.

Then the correct option is C.

More about the surface area of the cube link is given below.

brainly.com/question/13789496

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6 0

2 years ago

A study of the career paths of hotel general managers sent questionnaires to an SRS of 160 hotels belonging to major U.S. hotel

otez555 [7]

Answer:

(10.78483, 12.61517)

Step-by-step explanation:

It is given that the genera mangers of few hotels were sent some questionnaires for conducting a study for the career paths in the major hotel chains of the United States.

Number of hotels = 160

Number of response received = 103

The average number of years these general mangers was in their current hotels, $\bar x$ = 11.7 years

Confidence Interval, CI = 0.99

Therefore,

a = 0.01, |Z(0.005)| (from standard normal table)

∴ 99% of CI = $\bar x \pm Z \times \frac{s}{\sqrt n}$

$= 11.7 \pm 2.58 \times \frac{3.6}{\sqrt {103}}$

$(10.78483, 12.61517)$

3 0

3 years ago

Find the value of x for the following equivalent functions: f(x)=2x^2−3x+4 and f(x)=2x^2−1

masha68 [24]

A) y = 2x – 7 and f(x) = 7 – 2xIncorrect. These equations look similar but are not the same. The first has a slope of 2 and a y-intercept of −7. The second function has a slope of −2 and a y-intercept of 7. It slopes in the opposite direction. They do not produce the same graph, so they are not the same function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. B) 3x = y – 2 and f(x) = 3x – 2Incorrect. These equations represent two different functions. If you rewrite the first equation in terms of y, you’ll find the equation of the function is y = 3x + 2. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5. C) f(x) = 3x2 + 5 and y = 3x2 + 5Correct. The expressions that follow f(x) = and y = are the same, so these are two different ways to write the same function: f(x) = 3x2 + 5 and y = 3x2 + 5. D) None of the aboveIncorrect. Look at the expressions that follow f(x) = and y =. If the expressions are the same, then the equations represent the same exact function. The correct answer is f(x) = 3x2 + 5 and y = 3x2 + 5.

3 0

3 years ago