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Neporo4naja [7]
3 years ago
7

Janet Fog's uncle, Pete Moore, promised her a gift of $30,000 upon her graduation from law school or $1500 every quarter for the

next four years. if the money could be invested at 12% compounded quarterly, which offer should Janet choose?
Mathematics
1 answer:
LenaWriter [7]3 years ago
5 0
First calculate the future value of the annuity
The formula to find the future value of an annuity ordinary is
Fv=pmt [((1+r/k)^(kn)-1)÷(r/k)]
Fv future value?
PMT quarterly payment 1500
R interest rate 0.12
K compounded quarterly 4
N time 4 years
Fv=1,500×(((1+0.12÷4)^(4×4)
−1)÷(0.12÷4))
=30,235.32

Now compare the amount of the annuity with amount of the gift
30,235.32−30,000=235.32
So as you can see the amount of the annuity is better than the amount of the gift by 235.32

Second offer is better

Hope it helps!
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What is the value of x
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Answer:Here is something to help you "The horizontal value in a pair of coordinates: how far along the point is. The X Coordinate is always written first in an ordered pair of coordinates (x,y), such as (12,5). In this example, the value "12" is the X Coordinate". Also called "Abscissa"

Step-by-step explanation:

4 0
3 years ago
Which expressions are equivalent to 2 ln a 2 ln b - ln a? Check all that apply. Ln ab2 - ln a ln a 2 ln b ln a2 ln b2 - ln a 2 l
marysya [2.9K]

Equivalent expressions are expressions with same simplified form. Equivalent expressions for the given expression are;

  • Expression 2:  \ln(a) + 2\ln(b) = \ln(a) + \ln(b^2)  = \ln(ab^2)
  • Expression 3:  \ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)
  • Expression 5:  \ln(ab^2)

<h3>What are equivalent expressions?</h3>

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

<h3>What is logarithm and some of its useful properties?</h3>

When you raise a number with an exponent, there comes a result.

Lets say you get

a^b = c

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

b = log_a(c)

Some properties of logarithm are:

log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b^c) = c \times log_a(b)\\\\log_b(b) = 1\\\\ log_a(b) + log_b(c) = log_a(c)

Log with base e = 2.71828.... is written as \ln(x) simply.

The expression given is 2\ln(a) + 2\ln(b) - \ln(a)

We get its simplified form as

2\ln(a) + 2\ln(b) - \ln(a) = \ln(a) + \ln(b^2) = \ln(ab^2)

Simplifying given expressions:

  • Expression 1:  \ln(ab^2) - \ln(a) = \ln(ab^2/a)  = \ln(b^2)

This isn't same as simplified form of original

. Thus , this expression is not equivalent to the given expression.

  • Expression 2:  \ln(a) + 2\ln(b) = \ln(a) + \ln(b^2)  = \ln(ab^2)

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

  • Expression 3:  \ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

  • Expression 4:  2\ln(ab) = \ln((ab)^2) = \ln(a^2b^2)

This isn't same as simplified form of original expression. Thus , this expression is not equivalent to the given expression.

  • Expression 5:  \ln(ab^2)

This is same as simplified form of original expression. Thus , this expression is equivalent to the given expression.

Thus, equivalent expressions for the given expression are;

  • Expression 2:  \ln(a) + 2\ln(b) = \ln(a) + \ln(b^2)  = \ln(ab^2)
  • Expression 3:  \ln(a^2) + \ln(b^2) - \ln(a) = \ln(a^2b^2/a) = \ln(ab^2)
  • Expression 5:  \ln(ab^2)

Learn more about equivalent expressions here:

brainly.com/question/10628562

4 0
2 years ago
Use the given information to find amount A in the account earning compound interest after six years when the principal is 3,500
stealth61 [152]
A=p(1+i/m)^mn
A=3,500×(1+0.0229÷12)^(12×6)
A=4,014.98
4 0
3 years ago
GEOMETRY HELP PLEASE :)
Fittoniya [83]

Answer:

never; they are supplementary

3 0
3 years ago
A suitcase measures 24 inches long and the dialogue is 30 inches long. How much material is needed to cover one side of the suit
borishaifa [10]

Answer:

432 in.^2

Step-by-step explanation:

The side of the suitcase is a rectangle. One length is 24 inches. The diagonal of the rectangle is 30 inches long. The diagonal is a hypotenuse of a right triangle. The length is a leg. We need to find the other leg.

We use the Pythagorean theorem,

a^2 + b^2 = c^2

(24 in.)^2 + b^2 = (30 in.)^2

576 in.^2 + b^2 = 900 in.^2

b^2 = 324 in.^2

b = sqrt(324 in^2)

b = 18 in

area of rectangle = length * width

A = 24 in. * 18 in.

A = 432 in.^2

6 0
3 years ago
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