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goldfiish [28.3K]
3 years ago
10

Jonathon saves $4,000 at the end of each quarter for 10 years. Assume 12% compounded quarterly and find the present value.

Mathematics
1 answer:
charle [14.2K]3 years ago
5 0

Answer:

Results are below.

Step-by-step explanation:

1. <u>First, we need to calculate the Future Value:</u>

FV= {A*[(1+i)^n-1]}/i

A= quarterly deposit

n= 10*4= 40

i= 0.12/4= 0.03

FV= {4,000*[(1.03^40) - 1]} / 0.03

FV= $301,605.04

Now, the present value:

PV= FV/(1+i)^N

PV= 301,605.04/(1.03^40)

PV= $92,459.09

2. <u>First, we need to calculate the value of the first year of college:</u>

FV= PV*(1+i)^n

FV= 24,000*(1.04^3)

FV= $26,996.74

Now, the quarterly payments:

FV= {A*[(1+i)^n-1]}/i

A= quarterly deposit

Isolating A:

A= (FV*i)/{[(1+i)^n]-1}

i= 0.08/4= 0.02

n= 3*4= 12

A= (26,996.74*0.02) / [(1.02^12) - 1]

A= $2,012.87

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salantis [7]

Answer:

a) Let X the random variable of interest, on this case we know that:

X \sim Binom(n=20, p=0.411)

This random variable represent that two people have the same birthday in just one classroom

b) We can find first the probability that one or more pairs of people share a birthday in ONE class. And we can do this:

P(X\geq 1 ) = 1-P(X

And we can find the individual probability:

P(X=0) = (20C0) (0.411)^0 (1-0.411)^{20-0}=0.0000253

And then:

P(X\geq 1 ) = 1-P(X

And since we want the probability in the 3 classes we can assume independence and we got:

P= 0.99997^3 = 0.9992

So then the probability that one or more pairs of people share a birthday in your three classes is approximately 0.9992

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:  

P(X)=(nCx)(p)^x (1-p)^{n-x}  

Where (nCx) means combinatory and it's given by this formula:  

nCx=\frac{n!}{(n-x)! x!}  

Solution to the problem

Part a

Let X the random variable of interest, on this case we know that:

X \sim Binom(n=20, p=0.411)

This random variable represent that two people have the same birthday in just one classroom

Part b

We can find first the probability that one or more pairs of people share a birthday in ONE class. And we can do this:

P(X\geq 1 ) = 1-P(X

And we can find the individual probability:

P(X=0) = (20C0) (0.411)^0 (1-0.411)^{20-0}=0.0000253

And then:

P(X\geq 1 ) = 1-P(X

And since we want the probability in the 3 classes we can assume independence and we got:

P= 0.99997^3 = 0.9992

So then the probability that one or more pairs of people share a birthday in your three classes is approximately 0.9992

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3 years ago
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Ivanshal [37]

Answer:

6

Step-by-step explanation:

Hello,

The two triangles are <u>similar</u> and x is <u>positive</u>, <u>different from 0</u>, so we can write.

\dfrac{x}{9}=\dfrac{12}{x}\\\\x^2=12\times 9\\\\ x = \sqrt{4\times 3 \times 9}=2\times 3 \times \sqrt{3}\\\\ \boxed{\sf \bf x=6\sqrt{3} }

Thanks

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3 years ago
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weqwewe [10]

Answer:

The probability that Chang gets dressed with a white shirt and tan pants is 25%.

Step-by-step explanation:

Given that Chang has 2 shirts, a white one and a black one, and he also has 2 pairs of pants, one blue and one tan, to determine what is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants the following calculation must be performed:

Each shirt = 50% chance

Each pants = 50% chance

0.50 x 0.50 = X

0.25 = X

Therefore, the probability that Chang gets dressed with a white shirt and tan pants is 25%.

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How many rays make a right angle? A) 0 B) 1 C) 2 D) not enough information
Nana76 [90]
Hello!

Two rays make any angle

The answer is C)2

Hope this helps!
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