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Vlada [557]
3 years ago
6

You deposit $2000 into a savings account to pay 5% interest compounded annually if you make no more deposit or any withdrawal is

right in equation that shows how much money will be in the account after five years.
Mathematics
1 answer:
Bond [772]3 years ago
5 0

Answer: A = 2000(1.05)^5

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

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

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = $2000

r = 5% = 5/100 = 0.05

n = 1 because it was compounded once in a year.

t = 5 years

Therefore, the equation that shows how much money will be in the account after five years is

A = 2000(1 + 0.05/1)^1 × 5

A = 2000(1.05)^5

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alexdok [17]

Answer:

1.2%

Step-by-step explanation:

We are given that the students receive different versions of the math namely A, B, C and D.

So, the probability that a student receives version A = \frac{1}{4}.

Thus, the probability that the student does not receive version A = 1-\frac{1}{4} = \frac{3}{4}.

So, the possibilities that at-least 3 out of 5 students receive version A are,

1) 3 receives version A and 2 does not receive version A

2) 4 receives version A and 1 does not receive version A

3) All 5 students receive version A

Then the probability that at-least 3 out of 5 students receive version A is given by,

\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}\times \frac{3}{4}+\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{3}{4}+\frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}\times \frac{1}{4}

= (\frac{1}{4})^3\times (\frac{3}{4})^2+(\frac{1}{4})^4\times (\frac{3}{4})+(\frac{1}{4})^5

= (\frac{1}{4})^3\times (\frac{3}{4})[\frac{3}{4}+\frac{1}{4}+(\frac{1}{4})^2]

= (\frac{3}{4^4})[1+\frac{1}{16}]

= (\frac{3}{256})[\frac{17}{16}]

= 0.01171875 × 1.0625

= 0.01245

Thus, the probability that at least 3 out of 5 students receive version A is 0.0124

So, in percent the probability is 0.0124 × 100 = 1.24%

To the nearest tenth, the required probability is 1.2%.

4 0
3 years ago
If u-ai + bj and v-ci + dj are vectors, then which of the following statements is not true?
alukav5142 [94]

Answer:

Option C

Step-by-step explanation:

Given that u-ai + bj and v-ci + dj are vectors

We have dot product

u.v = (ai+bj).(ci+dj) hence inner product of u and v.  So option a is true

The dot product of u and v is a scalar is true because dot product is always a scalar

The dot product of u and v is a vector. is false because dot product is only a scalar and has no direction and hence cannot be a vector

The dot product of u and v is given by the expression ac+bd

True because we multiply corresponding i components and j components and add.

So only C is not true.

7 0
3 years ago
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Alik [6]

Answer:

See Below.

Step-by-step explanation:

We want to show that the function:

f(x) = e^x - e^{-x}

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A function is increasing whenever its derivative is positive.

So, find the derivative of our function:

\displaystyle f'(x) = \frac{d}{dx}\left[e^x - e^{-x}\right]

Differentiate:

\displaystyle f'(x) = e^x - (-e^{-x})

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Answer:

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