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2 years ago

Manuel borrowed $1,500 from his bank and signed a

Mathematics

1 answer:

Mice21 [21]2 years ago

3 0

Answer:

The total interest to pay back on the loan is $122.40

Step-by-step explanation:

Here. we want to get the amount of interest on the loan

We are going to use the compound interest formula here

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

where A is the amount to be paid back

P is the amount borrowed called the principal which is $1,500

r is the interest rate which is 4% annually

This is same as 4/100 = 0.04

n is the number of times the interest will be compounded per year ; annually means yearly and so for this case, n = 1

t is the number of years = 2

So we have;

A = 1500(1 + 0.04/1)^(2)(1)

A = 1500(1.04)^(2)

A =$ 1,622.40

So the amount of interest is the difference between the amount borrowed and the value to pay back

That will be;

$1,622.40 - $1,500

= $122.40

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According to a study by de Anna students, the height for Asian adult males is normally distributed with an average of 66 inches

Maslowich

A. X ~ N(66, 6.25)

b. $z_{1} =\frac{65-66}{2.5}=-0.4$
$z_{2} =\frac{69-66}{2.5}=1.2$
Using a standard normal probability table to find probability values for the z-scores, we get:
P(65 < X < 69) = 0.1554 + 0.3849 = 0.5403

c. z= 0.524 and -0.524
$0.524=\frac{X-66}{2.5}$
1.31 = X - 66
X = 67.31
When z = -0.524, X = 64.69.
P(64.69 < X < 67.31) = 0.4

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3 years ago

A Martian couple has children until they have 2 males (sexes of children are independent). Compute the expected number of childr

Ne4ueva [31]

Answer:

a) 6

b) 4

c) 3

Step-by-step explanation:

Let p be the probability of having a female Martian, and of course, 1-p the probability of having a male Martian.

To compute the expected total number of trials before 2 males are born, imagine an experiment simulating the fact that 2 males are born is performed n times.

Let ak be the number of trials performed until 2 males are born in experiment k. That is,

a1= number of trials performed until 2 males are born in experiment 1

a2= number of trials performed until 2 males are born in experiment 2

and so on.

If a1 + a2 + … + an = N

we would expect Np females.

Since the experiment was performed n times, there 2n males (recall that the experiment stops when 2 males are born).

So we would expect 2n = N(1-p), or

N/n = 2/(1-p)

But N/n is the average number of trials per experiment, that is, the expectation.

We have then that the expected number of trials before 2 males are born is 2/(1-p) where p is the probability of having a female.

Here we have the probability of having a male is half as likely as females. So

1-p = p/2 hence p=2/3

The expected number of trials would be

2/(1-2/3) = 2/(1/3) =6

This means the couple would have 6 children: 4 females (the first 4 trials) and 2 males (the last 2 trials).

Here the probability of having a female = probability of having a male = 1/2

The expected number of trials would be

2/(1/2) = 4

This means the couple would have 4 children: 2 females (the first 2 trials) and 2 males (the last 2 trials).

Here, 1-p = 2p so p=1/3

The expected number of trials would be

2/(1-1/3) = 2/(2/3) = 6/2 =3

This means the couple would have 3 children: 1 female (the first trial) and 2 males (the last 2 trials).

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3 years ago

The point given is on the terminal side of an angle theta. Find the exact values of the six trig functions of theta.. (-3,2)

Dima020 [189]

We can use SOH, CAH and TOA, but first we must find the length of a hypotenuse:
h = $\sqrt{(-3) ^{2}+2^{2} } = \sqrt{9+4}= \sqrt{13}$
sin (theta)= 2/√13
cos ( theta) = -3/√13
tan (theta) = -2/3
cot (theta ) = -3/2
sec (theta) = 1/cos(theta ) = -√13/3
csc(theta ) = 1/ sin (theta) = √13/2

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3 years ago

For which mapped relation is the domain {1,2,3}?

Serga [27]

Answer:

Step-by-step explanation:

For any given function, all first input values (x-values/coordinates) in the relation are considered as the domain values. While the output values (y-values/coordinates) make up the range of the given function.

The mapped relation that has a domain of {1,2,3}, is the mapped relation that has 1, 2, and 3 on the input side on our left.

Therefore, the mapped relation in option C is the answer.

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3 years ago

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irakobra [83]

Answer:

Step-by-step explanation:

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2 years ago