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2 years ago

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Find the accumulated value of an investment of $20,000 for 7 years at an interest rate of 5.5% if the money is:

2 answers:

Amiraneli [1.4K]2 years ago

5 0

Answer:

See below

Step-by-step explanation:

<u>Given:</u>

Investment P = $20000
Time t = 7 years
Interest rate r = 5.5% = 0.055

a. <u>compounded semiannually, n = 2</u>

$A = P*(1 + r/n)^{nt} = 20000(1+0.055/2)^{2*7} = 29239.88$

b. <u>compounded quarterly, n = 4</u>

$A = P*(1 + r/n)^{nt} = 20000(1+0.055/4)^{4*7} = 29315.30$

c. <u>compounded monthly, n = 12</u>

$A = P*(1 + r/n)^{nt} = 20000(1+0.055/12)^{12*7} = 29366.44$

d. <u>compounded continuously</u>

$A = Pe^{rt}=20000*e^{0.055*7}=29392.29$

olya-2409 [2.1K]2 years ago

4 0

Answer:

147,700 and A

Step-by-step explanation:

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The average of four different positive integers is 9. What is the greatest value for one of the integers?

saul85 [17]

From the given information; Let the unknown different positive integers be (a, b, c and d).

An integer is a set of element that are infinite and numeric in nature, these numbers do not contain fractions.

Suppose we make an assumption that (a) should be the greatest value of this integer.

Then, the other three positive integers (b, c and d) can be 1, 2 and 3 respectively in order to make (a) the greatest value of the integer.

Therefore, the average of this integers = 9

Mathematically;

$\mathbf{\dfrac{(a+b+c+d)}{4} =9}$

$\mathbf{\dfrac{(a+1+2+3)}{4} =9}$

$\mathbf{\dfrac{(6+a)}{4} =9}$

By cross multiplying;

6+a = 9 × 4

6+a = 36

a = 36 - 6

a = 30

Therefore, we can conclude that from the average of four positive integers which is equal to 9, the greatest value for one of the selected integers is equal to 30.

Learn more about integers here:

brainly.com/question/15276410?referrer=searchResults

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2 years ago

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The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

1a

$P(39 < X < 48 ) = 0.8767$

1b

95% of all sample means will fall between $40.1 < \mu < 49.9$

1c

$\= x = 41. 795$

2

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

So

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

$s = \frac{\sigma }{ \sqrt{n} }$

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

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2 years ago

Which of the following is the best definition of a circle?

Leona [35]

Answer:

The set of all points on a plane equidistant to a given point

Step-by-step explanation:

"following"?

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2 years ago

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Which function in vertex form is equivalent to f(x) = x² + x +1?

mylen [45]

Answer:

$\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$

Step-by-step explanation:

NOTE :

$x^2+ax=\left( x+\frac{a}{2} \right)^{2} -\left( \frac{a}{2} \right)^{2}$

………………………………………

f(x) = x² + x +1

$=x^{2}+2\times \frac{x}{2} +1$

$=\left( x+\frac{1}{2} \right)^{2} -\left( \frac{1}{2} \right)^{2} +1$

$=\left( x+\frac{1}{2} \right)^{2} - \frac{1}{4}+1$

$=\left( x+\frac{1}{2} \right)^{2} + \frac{3}{4}$

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1 year ago

You are planning to plant a triangular garden in your backyard, as shown. You plan to put up a fence around the garden to keep o

drek231 [11]

Answer:

See Explanation

Step-by-step explanation:

<em>The question is incomplete has the figure of the triangle is not given.</em>

<em>However, the following steps will guide you.</em>

To solve this question;

you need the lengths of the threes sides of the triangular fields

Represent these lengths with a, b and c

Next;

Sum these lengths together;

This gives the required length of fencing

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Take for instance;

<em /> $a =4;\ b = 3;\ c = 5$ <em />

<em>The required length of fence would be</em>

$Length = 4 + 3 + 5$

$Length = 12\ units$

<em>Apply these steps and you'll get your answer</em>

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3 years ago