please help with the steps

Please Help With The Steps

Answers

Answer 1

9514 1404 393

Answer:

346.1 monthly payments; 28.8 years18.5 years; infinite years

Step-by-step explanation:

Two formulas come into play here. One is the future value of a series of payments. The other is the payment amount available from an ordinary annuity.

  FV = An/r((1 +r/n)^(nt) -1) . . . . future value of payments of A made n times per year for t years

  A = P(r/n)/(1 -(1 +r/n)^(-nt)) . . . . payment from principal P at invested at rate r for t years, compounded n times per year.

__

Problem 1

You want FV = $350,000, A = $400, r = 0.057, n = 12, and we want to find t. We can solve the FV equation for t to get ...

  log(FV·r/(An) +1)/log(1 +r/n) = nt . . . . . number of months

  log(350000·0.057/(400·12) +1)/log(1 +0.057/12) = nt ≈ 346.1

The retirement account can be funded by 346.1 monthly payments. That will take 28.8 years.

__

Problem 2

Again, solving for t, we get ...

  log(1 -Pr/(An))/(-n·log(1 +r/n)) = t

The parameters for this are P = 700,000, A = 5000, n = 12, r = 0.054, so the account can be expected to last for ...

  log(1 -700000·0.054/(5000·12))/(-12·log(1 +0.054/12)) ≈ 18.5 . . . years

Changing the withdrawal to $3000 per month makes the account last forever.  It earns $3150 in interest each month, so the account balance continues to increase.

The account will support withdrawals of $5000 per month for 18.5 years.

The account will support withdrawals of $3000 per month forever.


Related Questions

How much interest will be earned on a $1600 investment at 7.72% compounded
quarterly for 9 years?

Answers

56% interest will be earned

A rectangular piece of paper with length 34cm and width 14cm has two semicircles cut out of it. Find the area of the paper that remains. Use the value 3.14 for PIE , and do not round your answer.

Answers

Answer:

Step-by-step explanation:

322.14 cm²

What is the height of a rectangular prism, if the volume is 750 cm, the length 25 cm, and the width is 5 cm?

Answers

Answer:

6 cm

Step-by-step explanation:

Volume of a prism= Length X Width x height

750 = 25 x 5 x h

750= 125h

750/125 = 125h/125

h= 6

Answered by Gauthmath

If the mean of a normal distribution is 105, what is the median of the distribution? O A 315 OB. 105 O C. 420 D. 210 SUBM​

Answers

Answer:

105

Step-by-step explanation:

A normal or symmetrical distribution where each the distance between each side of the distribution to the midpoint is the same, a normal distribution, also called a symmetrical distribution has the se value for both its median and mean. Hence, if the mean of a normal distribution is x, then it's median will also be x.

For the scenario given,

Since mean = 105 ; then median = 105

A books storevhad 30816 exercise books which were packed in cartons, each carton contains 24exercise books.The mass of an empty carton was 2kg and full was 12kg."what was the total mass of each empty carton, what was the total mass of the books alone?"​

Answers

Step-by-step explanation:

the total mass of each empty carton

1284×2568kg

the total mass of books alone

30816×10=12840kg

what is 2.8436 rounded to the nearest thousandth?​

Answers

Answer:

2.844

Step-by-step explanation:

2.8436 is 2.844 when rounded to the nearest thousandth because the ten thousandth digit is 6, which means you round up for 3. Hope this helps!

Answer:

2.84

Step-by-step explanation:

2.8436 is rounded to the nearest thousands we get 2.84

the equation of a circle C is (x+2)^2+(y-7)^2=36. What is its crnter (h,k)?​

Answers

Answer:

The center is ( -2, 7) and the radius is 6

Step-by-step explanation:

A circle is written in the form

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x+2)^2+(y-7)^2=36

(x -  -2)^2+(y-7)^2=6^2

The center is ( -2, 7) and the radius is 6

factorise fully 16c^4p^2+20cp^3​

Answers

Answer:

4cp^2 ( 4c^3+5p

Step-by-step explanation:

See image below:)

The factored form of the expression will be [tex]4cp^2 (4c^3+5p)[/tex]

Factorization:

Given the expression  16c^4p^2+20cp^3​

Get the factor for each term

[tex]16c^4p^2 = 4 * 4 * c^3 * c * p^2 \\20cp^3= 4 * 5 * c * p^2 * p[/tex]

From the factors, you can see that 4cp^2 is common to both terms. Hence the factored form of the expression will be:

[tex]4cp^2 (4c^3+5p)[/tex]

Learn more on factored form here: https://brainly.com/question/25948667


Write the number 2.4 in the form
A/B, using integers,

Answers

Answer:

[tex] \frac{12}{5} [/tex][tex]2 \frac{2}{5} [/tex]

Step-by-step explanation:

Convert to simplified fraction:

Convert to a mixed number by placing the numbers to the right of the decimal over 10. Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

Convert to Mixed fraction:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10[tex] ^{1} [/tex](10). Next, add the whole number to the left of the decimal.

[tex]2 \frac{4}{10} [/tex]

Reduce the fractional part of the mixed number.

[tex]2 \frac{2}{5} [/tex]

Hope it is helpful...

Determine the number of solutions for the system 2x+3y=5 and -9y=6x-15

Answers

9514 1404 393

Answer:

  infinite number of solutions

Step-by-step explanation:

The two equations describe the same line.

Adding 9y+15 to the second equation makes it be ...

  15 = 6x +9y

Dividing that by 3 gives you ...

  5 = 2x +3y . . . . . . identical to the first equation

The lines intersect at every point, so there are an infinite number of solutions.

If triangle ABC is reflected across the y-axis and then rotated 90 degrees clockwise about the origin, what would the coordinates of point A’ of the transformed triangle be?

Answers

Answer:

A' (2,-1) B' (4.-1) C' (1,-4)

Step-by-step explanation:

Answer:

(-2,-1)

Step-by-step explanation:

which numbers in the set (2, 3, 4, 5,) are solutions to the inequality 19- 4x>3

Answers

Answer:

2 and 3

Step-by-step explanation:

Given the set (2, 3, 4, 5,) and inequality 19- 4x>3

To obtain which number gives a solution, we test each value in the set ;

19- 4x>3

For x = 2

19- 4(2)>3

19 - 8 > 3

11 > 3 (true)

x = 3

19- 4(3)>3

19 - 12 > 3

7 > 3 (true)

For x = 4

19- 4(4)>3

19 - 16 > 3

3 > 3 (false )

For x = 5

19- 4(5)>3

19 - 20> 3

-1 > 3 (false)

100 students attended a revision lesson at the weekend.
Each student went to Maths or English or Science.
55 of these students attended on Saturday.
Over the weekend a total of 40 students went to Maths.
12 of the 27 students that went to Science went on Sunday.
10 students went to English on Saturday.
How many students went to the Maths revision lesson on Saturday?

Answers

Answer:

I am pretty sure its 30 students

A model train is built at a scale of 1 to 60. If the model train is 10 inches long, how many feet long is the actual train?

Answers

Answer:

60 feet

Step-by-step explanation:

You measure 30 dogs' weights, and find they have a mean weight of 31 ounces. Assume the population standard deviation is 6.1 ounces. Based on this, construct a 95% confidence interval for the true population mean dog weight. Give your answers as decimals, to two places

Answers

Answer:

The answer is "[tex](32.8318736, 29.1681264)[/tex]"

Step-by-step explanation:

When the [tex]95\%[/tex] of the confidence interval are true population means of the dog weight then:

[tex]=\bar{x} \pm \frac{\sigma }{\sqrt{n}} \times z_{0.05}\\\\=31 \pm \frac{6.1}{\sqrt{30}}\times 1.64485\\\\=31 \pm 1.83187361\\\\=(32.8318736, 29.1681264)[/tex]

Please help me with these questions

Answers

Answer:

okay the first questions answer is ,c,is true and rest of them are false

kathy runs a 26.2-mi;e marathon at an average pace of 6.2 minutes per mile how long will it take her to finish the marathon round your answer to the nearest minute

Answers

Answer:

162 minutes

Step-by-step explanation:

Since she takes 6.2 minutes a mile, you multiply it by 26.2 for every mile. 6.2x26.2= 162.44, then round it to 162

Choose the answer that represents the product below as a exponential
expression.
(-4).(-4).(-4).(-4).(-4).(-4)
A. (-4)^6
B. (-4)^4
C. 6•(-4)
D. (-6)^-4

Answers

Answer:

(-4) ^6

Step-by-step explanation:

(-4)*(-4)*(-4)*(-4)*(-4)*(-4)

There are six (-4)'s multiplied together

(-4) is the base and 6 is the exponent

(-4) ^6

Q1: Suppose that the numbers of persons per car arriving at the entrance to an amusement park has an average 2. What is the probability that a car arriving at the entrance contains a) No person b) Only one person c) More than one person d) Eight persons e) At least 3 person

Answers

B because it’s 8 people total

A scuba diver is swimming 28 feet below the water’s surface. The diver swims up slowly at a rate of 0.3 feet per second for 6 seconds. Then they swim back down for 4 seconds at a rate of 0.3 feet per second. What is the diver’s new depth?

Answers

Answer:

27.4 feet down deep

Step-by-step explanation:

28 feet down, swins up for 0.3 feet times 6 or 1.8 feet up

leaving a total of 26.2 under the sea and he swims back down at 0.3 feet times 4 or 1.2 feet down. and the new total is 26.2 + 1.2 which equals 27.4 feet down in the deep sea

Answer:

27.4 feet

Step-by-step explanation:

.3 ft per sec for 6 sec = 1.8 feet

.3 ft per sec for 4 sec = 1.2 feet

28 - 1.8 + 1.2 = 27.4

Find a polar equation of the conic in terms of r with its focus at the pole. Conic Eccentricity Directrix Parabola e = 1 x = −1

Answers

Answer:

Step-by-step explanation:

From the given information:

The Directrix  x = - 1

The eccentricity  e = 1

Since the Directrix x = - 1, it implies that the directrix appears on the left negative side of the pole and is vertical.

Hence, the conic equation in terms of r is:

[tex]\mathsf{r =\dfrac{ep}{1-e \ cos \ \theta}}[/tex]

From the directrix to the pole, the distance p = 1

So;

[tex]\mathsf{r =\dfrac{1*1}{1-1 \ cos \ \theta}}[/tex]

[tex]\mathbf{r =\dfrac{1}{1- \ cos \ \theta}}[/tex]

7 = -10s - 3 for iready

Answers

Answer:

-1 =s

Step-by-step explanation:

7 = -10s - 3

Add 3 to each side

7+3 = -10s - 3+3

10 = -10s

Divide by -10

10/-10 = -10s/-10

-1 =s

What is h(−8) for h(x)=1/4x^2+7x?

Answers

Answer:

h(-8) = -40

Step-by-step explanation:

Find h(-8) by plugging in -8 as x:

h(x) = 1/4x² + 7x

h(-8) = 1/4(-8)² + 7(-8)

Simplify:

h(-8) = 1/4(64) - 56

h(-8) = 16 - 56

h(-8) = -40

So, the answer is h(-8) = -40

The value of h(-8) is -40.

What is quadratic equation?

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given:

h(x)=1/4x²+7x

h(-8)= 1/4* 64+7*(-8)

      = 16-56

      = -40

Hence, h(-8)=-40.

Learn more about quadratic equation here:

https://brainly.com/question/2263981

#SPJ2

find the measure of one interior angle in a regular 23-gon

Answers

Answer: A polygon with 23 sides has a total of 3780 degrees. total interior angles = (n - 2)180°, where n is the number of sides.

The measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees

How to calculate the sum of the interior angle of a regular polygon?

The formula which is used to calculate the sum of the angle of regular polygon is given by

sum of the interior angles = ( n - 2 ) × 180 degrees

Where,

n is the number of sides

According to the given question.

We have a regular polygon with 23 sides.

⇒ n = 23

Therefore,

The sum of the interior angles of the given regular polygon

= (23-2) × 180

= 3,780 degrees

So, the measure of one interior angle = [tex]\frac{3780}{23} = 164.3 degrees[/tex]

Hence, the measure of one interior angle of the given regular polygon with 23 sides is 164.3 degrees.

Find out more information about interior angle of a regular polygon here:

https://brainly.com/question/22408868

#SPJ3

Solve 4(m-3)=24
Gggg

Answers

solution//

= 4(m-3) = 24

= 4m-12 = 24

= 4-12+12 = 24+12

= 4m = 36

= 4m = 36

4 4

= m = 9

Step-by-step explanation:

Thank you

[tex]\sf\purple{The\:value\:of\:m\:is\:9.}[/tex] ✅

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]4 \: (m - 3) = 24 \\ ⇝4 \: m - 12 = 24 \\ ⇝4 \: m = 24 + 12 \\ ⇝4 \: m = 36 \\ ⇝m = \frac{36}{4} \\ ⇝m = 9[/tex]

To verify:-

[tex]4(m - 3) = 24 \\ ⇝4(9 - 3) = 24 \\ ⇝4 \times 6 = 24 \\ ⇝24 = 24 \\ ⇝L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique }}{\orange{♡}}}}}[/tex]

BEDMASS or PADMASS solve this pls

Answers

Answer:

Step-by-step explanation:

376389546535150-540111-107525

Complete the factored form of the linear expression.
15x + 12y = ( )( + )

Answers

Answer:

3(5x + 4y)

Step-by-step explanation:

Given

15x + 12y ← factor out 3 from each term

= 3(5x + 4y) ← in factored form

3(5x+4y) both 15 and 12 have the common dividend of 3 therefore you take it out of the equation :)

HELPPP HOW MANU SURFACE AREAS DOES THIS HAVE DONT SEND A FILE!!

Answers

This has 6 surface areas ok zzmznznznznzjjznznsnjsowowokwkwnendmdmdmdm
the answer would be 6 i don’t know though

Find the volume of the composite figure.

Answers

96 cubic feet

Explanation:
Divide figure into 2 rectangular prism, one on top and one at the bottom.

Volume of top prism (length x width x height):
3 • 4 • 2 = 24 cubic feet

Volume of bottom rectangular prism:
9 • 4 • 2 = 72 cubic feet

Add the volume of both figure together:
24 + 72 = 96 cubic feet

Hope this helps!
-SpaceMarsh
24+72 24+72=96ft2 I think that’s the correct answer

Finding the volume of the solid.Use unit cubes to help.

Answers

Answer:

the answer is 125. if you cut them slice to slice you'll get 25 because of there five slices of 25 all you got to do is 25 x 5 and you'll get 125.

Hope this help

Have a nice day :)

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