Share £180 in the ratio<br> 1:9

You plan to accumulate 100,000 at the end of 42 years by making the follow-

Mariana [72]

Answer:

Y = 479.17

Step-by-step explanation:

At the end of year 14, the balance from the deposits of X can be found using the annuity due formula:

A = P(1+r/n)((1 +r/n)^(nt) -1)/(r/n)

where P is the periodic payment, n is the number of payments and compoundings per year, t is the number of years, and r is the annual interest rate.

A = X(1.07)(1.07^14 -1)/0.07 ≈ 24.129022X

This accumulated amount continues to earn interest for the next 28 years, so will further be multiplied by 1.07^28. Then the final balance due to deposits of X will be ...

Ax = (24.129022X)(1.07^28) = 160.429967X

__

The same annuity due formula can be used for the deposits of Y for the last 10 years of the interval:

Ay = Y(1.07)(1.07^10 -1)/.07 = 14.783599Y

__

Now we can write the two equations in the two unknowns:

Ax +Ay = 100,000

X - Y = 100

From the latter, we have ...

X = Y +100

So the first equation becomes ...

160.429967(Y +100) +14.783599Y = 100000

175.213566Y +16,043.00 = 100,000

Y = (100,000 -16,043)/175.213566 ≈ 479.17

Y is 479.17

7 0

2 years ago

What’s the answer? Because am having a hard time with this math problem.

Studentka2010 [4]

9514 1404 393

Answer:

34.5 square meters

Step-by-step explanation:

We assume you want to find the area of the shaded region. (The actual question is not visible here.)

The area of the triangle (including the rectangle) is given by the formula ...

A = 1/2bh

The figure shows the base of the triangle is 11 m, and the height is 1+5+3 = 9 m. So, the triangle area is ...

A = (1/2)(11 m)(9 m) = 49.5 m^2

The rectangle area is the product of its length and width:

A = LW

The figure shows the rectangle is 5 m high and 3 m wide, so its area is ...

A = (5 m)(3 m) = 15 m^2

The shaded area is the difference between the triangle area and the rectangle area:

shaded area = 49.5 m^2 - 15 m^2 = 34.5 m^2

The shaded region has an area of 34.5 square meters.

7 0

1 year ago

Merrill Lynch Securities and Health Care Retirement Inc. are two large employers in downtown Toledo, Ohio. They are considering

ratelena [41]

Answer:

Step-by-step explanation:

We would determine the mean an standard deviation first

Mean = (107 + 92 + 97 + 95 + 105 + 101 + 91 + 99 + 95 + 104)/10 = 98.6

Standard deviation = √(summation(x - mean)/n

n = 10

Summation(x - mean) = (107 - 98.6)^2 + (92 - 98.6)^2 + (97 - 96.6)^2 + (95 - 98.6)^2 + (105 - 98.6)^2 + (101 - 98.6)^2 + (91 - 98.6)^2 + (99 - 98.6)^2 + (95 - 98.6)^2 + (104 - 98.6)^2 = 274

Standard deviation = √(274/10) = 5.23

The confidence interval is used to determine the range of values that could possibly contain a population parameter (population mean)

Confidence interval is written in the form,

(Point estimate - margin of error, Point estimate + margin of error)

The sample mean, x is the point estimate for the population mean.

We will use the t distribution because the sample size is small and the population standard deviation is not given.

Degree of freedom, df = 10 - 1 = 9

α = 1 - 0.99 = 0.01

z α/2 = 0.01/2 = 0.005

The area to the right of z 0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995. Using the t distribution table,

z = 3.25

Margin of error = z × s/√n

Where

s = sample standard Deviation = 5.23

Margin of error = 3.25 × 5.23/√10 = 5.38

Confidence interval = sample mean(point estimate) ± z × σ/√n

The lower boundary of the confidence interval is

98.6 - 5.38 = 93.22

The upper boundary of the confidence interval is

98.6 + 5.38 = 103.98

We estimate with 99% confidence that the mean weekly child care cost of their employees is between $93.22 and $103.98

Also,

99% of the confidence intervals constructed in this way would contain the true value for the population mean of mean weekly child care cost of their employees.

6 0

2 years ago

A Shampoo Problem: A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 of the bottle. How much shampoo is left? a. I

kotykmax [81]

Answer:

a) There is no a word problem for both expressions ( $m = 0.25\cdot 25.4$ and $m = 25.4-0.25$ ), b) A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.75 of the bottle. How much shampoo is left? A bottle contains 25.4 fluid ounces of shampoo. Katie uses 0.25 fluid ounces of the bottle. How much shampoo is left?