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2 years ago

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Assume a bank loan requires an interest payment of $85 per year and a principal payment of $1,000 at the end of the loan's eight

-year life. What would be the present value of this loan if it carried a 10% interest rate?

1 answer:

lapo4ka [179]2 years ago

3 0

Answer:

The present value is $PV = \$ 396,987$

Step-by-step explanation:

From the question we are told that

The interest payment per year is $C = \$ 85$

The principal payment is $P = \$ 1000$

The duration is n = 8 years

The interest rate is $r = 10\% = 0.10$

The present value is mathematically represented as

$PV = [ \frac{C}{r} * [1 - \frac{1 }{ (1 +r)^n} ] + \frac{P}{(1 + r)^n} ]$

substituting values

$PV = [ \frac{85}{0.10} * [1 - \frac{1 }{ (1 +0.10)^8} ] + \frac{1000}{(1 + 0.10)^ 8} ]$

$PV = \$ 396,987$

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The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minu

pochemuha

Answer:

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 265, \sigma = 50$

a) What is the probability that a battery lasts more than four hours?

4 hours = 4*60 = 240 minutes

This is 1 subtracted by the pvalue of Z when X = 240. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{240 - 265}{50}$

$Z = -0.5$

$Z = -0.5$ has a pvalue of 0.309

1 - 0.309 = 0.691

0.691 = 69.1% probability that a battery lasts more than four hours

b) What are the quartiles (the 25% and 75% values) of battery life?

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 265}{50}$

$X - 265 = -0.675*50$

$X = 231$

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

$Z = \frac{X - \mu}{\sigma}$

$0.675 = \frac{X - 265}{50}$

$X - 265 = 0.675*50$

$X = 299$

25% value = 231

75% value = 299

c) What value of life in minutes is exceeded with 95% probability?

The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

$Z = \frac{X - \mu}{\sigma}$

$-1.645 = \frac{X - 265}{50}$

$X - 265 = -1.645*50$

$X = 183$

8 0

2 years ago

A water mill grinds corn to make cornmeal. The water wheel has a radius of 18 feet. The wheel is rotating at 8 revolutions per m

Genrish500 [490]

Answer:

904.9 feet per minute

Step-by-step explanation:

The Angular distance can be calculated using below expression

S= r θ ..............eqn(1)

Where

θ = angular distance travelled

r= Radius= radius of 18 feet

But angular distance can also be expressed as

θ = wt...................eqn(2)

w= angular speed= 8 rev per minute= (8 × 2π)

t= time

Velocity can also be expressed as

V= s/t............eqn(3)

Where

V= velocity

s= distance

t= time

Substitute eqn(2) into eqn(3)

V=( r θ)/ t................eqn(4)

Substitute eqn(2) into eqn(4)

V=( r w t)/ t

V= r w ..............eqn(5)

V= 18×(8 ×2π)

=288π

= 904.9 feet per minute

Hence, the linear speed, in feet per minute, of the water. is 904.9 feet per minute

6 0

1 year ago

Alaina’s sugar cookie recipe calls for 21 4 cups of flour per batch. If she wants to make 2 3 a batch of cookies, how much flour

Over [174]

"Alaina’s sugar cookie recipe calls for 2 1/4

cups of flour per batch. If she wants to make 2/3

a batch of cookies, how much flour should she use?"

1 1/2 Cups, if she wants to make less than the original recipe, she would need less flour, you have to divide.

8 0

1 year ago

Read 2 more answers

ABCDEFGHIJ is a regular decagon. It rotates clockwise about its center to form the polygon A′B′C′D′E′F′G′H′I′J′. Match each angl

Lostsunrise [7]

A decagon has 10 sides.

It it is regular you can build 10 isosceles triangles from the center of the decagon to the 10 sides.

Each triangle has a common vertex where the angle of each triangle is 360° / 10 = 36°.

So each time that you rotate the decagon a multiple of 36° around the center you get an image that coincides with the original decagon.

If the letters are given clockwise:

- when you rotate 36° counter clockwise, the point A' (the image of A) will coincide with the point J.

- when you rotate 72° (2 times 36°) counter clockwise, the point A' will land on I.

- when you rotate 108° (3 times 36°) counter clockwise, the point A' will land on H.

- when you rotate 144° (4 times 36°) counter clockwise, the point A' will land on G.

- when you rotate 180° (5 times 36°) counter clockwise, the point A' will land on I.

- when you rotate 216° (6 times 36°) counter clockwise, the point A' will land on E.

- whn you rotate 252° (7 times 36°) counterclockwise, the point A' will coincide with D.

Add other 36° each time and A' will coincide successively with C, B and the same A.

8 0

1 year ago

Read 2 more answers

Martin chose two of the cards below. When he found the quotient of the numbers, his answer was -16/9. Write the division problem

Sveta_85 [38]

Answer:

The required division problem he must solve is:

$\frac{2}{3} \div \frac{-3}{8} =\frac{2}{3}\times\frac{-8}{3}=\frac{-16}{9}$

Step-by-step explanation:

Consider the provided information.

Martin chose two of the cards below. When he found the quotient of the numbers, his answer was -16/9.

As we know that the quotient of the number is a negative number.

Therefore, the sign of both numbers must be different,

Thus we can concluded he must select $\frac{2}{3}$ as one of the card, so that product is a negative number.

Let the selected card be x.

$\frac{2}{3} \div x =\frac{-16}{9}\\\\x=\frac{2}{3}\div\frac{-16}{9}\\\\x=\frac{2}{3}\times\frac{-9}{16}\\\\x=\frac{-3}{8}$

Hence, the two cards should be $\frac{2}{3}$ and $\frac{-3}{8}$

The required division problem he must solve is:

$\frac{2}{3} \div \frac{-3}{8} =\frac{2}{3}\times\frac{-8}{3}=\frac{-16}{9}$

3 0

1 year ago