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Yakvenalex [24]
3 years ago
13

The diagram shows , , and . Which statement can be proven true from the diagram?

Mathematics
1 answer:
tresset_1 [31]3 years ago
3 0
What can be proven true in the diagram is the statement in letter C. angle CGB is complementary to angle AGD. It is because they both had the same vertex which is point G. Complementary angles are angles which are equal to 90 degrees wherein when you add both angles which are obviously 45 degrees, the sum is 90 degrees.
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Fifteen years ago, you deposited $12,500 into an investment fund. Five years ago, you added an
True [87]

Answer:

a) 8.16%

b) $65,762.50

c) $39,701.07

Step-by-step explanation:

Given:

15 years ago, Initial investment = $12500

5 years ago, Investment = $20000

Nominal interest = 8% semi annually for first 10 years

Interest2= 6.5% compunded annually for last five years

a) for the effective annual interest rate (EAR) in the first 10 years, let's use the formula:

[1+(nominal interest rate/number of compounding periods)]^ number of compounding periods-1

EAR = [1 + (\frac{0.08}{2})]^2 - 1

= (1 + 0.04)^2 - 1

= (1.04)^2 - 1

= 1.0816 - 1

= 0.0816

= 8.16%

The effective annual interesting rate, EAR = 8.16 %

b) To find the amount in my account today.

Let's first find the amount for $12500 for 10 years compounded semi annually

= 12,500 +( 12,500 * 8.160% * 10)

= $ 22,700

Let's also find the amount for $32,500($12,500+$20,000) for 5 Years compoundeed annually

$32,500 + ($32,500 * 6.5% *5)

= $ 43,062.50

Money in account today will be:

$22,700 + $43,062.50

= $65,762.50

c) Let's the amount I should have invested to be X

For first 10 years at 8.160%, we have:

Interest Amount = ( X * 8.160% * 10 ) = 0.8160 X

For next 5 years at 6.5%, we have:

Interest Amount = (X * 6.5% * 5) = 0.325 X

Therefore the total money at the end of 15 Years = 85000

0.8160X + 0.3250X + X = $85,000

= 2.141X = $85,000

X = 85,000/2.141

X = 39,701.074 ≈ $39,700

If I wish to have $85,000 now, I should have invested $39,700 15 years ago

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Eva8 [605]
Yintercepts are where x=0
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12 less than a number is the same as 5 times the same number increased by 4
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