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3 years ago

15

Matthew invested $5,800 in an account paying an interest rate of 4.9% compounded continuously. Assuming no deposits or withdrawa

ls are made, how much money, to the nearest cent, would be in the account after 7 years?

1 answer:

DIA [1.3K]3 years ago

4 0

Answer:

20,897

Step-by-step explanation:

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Which is the inverse of the function a(d)=5d-3? And use the definition of inverse functions to prove a(d) and a-1(d) are inverse

Drupady [299]

Answer:

$a'(d) = \frac{d}{5} + \frac{3}{5}$

$a(a'(d)) = a'(a(d)) = d$

Step-by-step explanation:

Given

$a(d) = 5d - 3$

Solving (a): Write as inverse function

$a(d) = 5d - 3$

Represent a(d) as y

$y = 5d - 3$

Swap positions of d and y

$d = 5y - 3$

Make y the subject

$5y = d + 3$

$y = \frac{d}{5} + \frac{3}{5}$

Replace y with a'(d)

$a'(d) = \frac{d}{5} + \frac{3}{5}$

Prove that a(d) and a'(d) are inverse functions

$a'(d) = \frac{d}{5} + \frac{3}{5}$ and $a(d) = 5d - 3$

To do this, we prove that:

$a(a'(d)) = a'(a(d)) = d$

Solving for $a(a'(d))$

$a(a'(d)) = a(\frac{d}{5} + \frac{3}{5})$

Substitute $\frac{d}{5} + \frac{3}{5}$ for d in $a(d) = 5d - 3$

$a(a'(d)) = 5(\frac{d}{5} + \frac{3}{5}) - 3$

$a(a'(d)) = \frac{5d}{5} + \frac{15}{5} - 3$

$a(a'(d)) = d + 3 - 3$

$a(a'(d)) = d$

Solving for: $a'(a(d))$

$a'(a(d)) = a'(5d - 3)$

Substitute 5d - 3 for d in $a'(d) = \frac{d}{5} + \frac{3}{5}$

$a'(a(d)) = \frac{5d - 3}{5} + \frac{3}{5}$

Add fractions

$a'(a(d)) = \frac{5d - 3+3}{5}$

$a'(a(d)) = \frac{5d}{5}$

$a'(a(d)) = d$

Hence:

$a(a'(d)) = a'(a(d)) = d$

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2 years ago

(PLS HELP NOW WILL GIVE BRINIEST!!!!!) A figure is formed by two pairs of parallel sides that are the same length. Which type of

Gekata [30.6K]

Answer: B. Square

Step-by-step explanation:

All sides of a square have the same length
All four angles of a square = 90°
A square has two parallel sides

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3 years ago

Read 2 more answers

You are analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur. As p

kvasek [131]

Answer:

0.784

Step-by-step explanation:

Given that you are analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur.

As part of your research, you collect the following data:

Total individuals: 1,000

Red fur individuals: 216

So black fur individuals = $1000-216\\=784$

p2 = proportion of black fur individuals to total individuals

= $\frac{784}{1000} \\=0.784$

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3 years ago

Help me with (d)(ii).<br><br> Thank you!

lord [1]

$q=\frac{h^{2}-k^{2}}{3m}$
Cross-multiplying and rearranging, we get:
$k^{2}=h^{2}-3mq$
or written without using latex:
k^2 = h^2 - 3mq
Can you finish now?

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3 years ago

Mario is missing half of his assignments (a). The expression is: a/2. True or false?

ipn [44]

Answer:

true

Step-by-step explanation:

because yo mama buttt stinks

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3 years ago