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3 years ago

Could someone explain this to me?

Mathematics

1 answer:

garik1379 [7]3 years ago

5 0

Answer:

B.97

Step-by-step explanation:

Heyy so angle ADC and DAB are supp to one another, thus

83 + DAB = 180 --> subtracting

DAB =97. B

Hope that made sense :)

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In 2 years, you want to have $5000 in your savings account. Find the amount you should deposit if the account pays 3% annual int

muminat

The amount you should deposit is $4709.18

Step-by-step explanation:

The formula for compound interest, including principal sum is

$A=P(1+\frac{r}{n})^{nt}$ , where:

A is the future value of the investment/loan, including interest
P is the principal investment amount
r is the annual interest rate in decimal
n is the number of times that interest is compounded per unit t
t is the time the money is invested or borrowed for

∵ You want to have $5000 in your savings account in 2 years

∴ A = 5000

∴ t = 2

∵ The account pays 3% annual interest, compounded monthly

∴ r = 3% = 3 ÷ 100 = 0.03

∴ n = 12 ⇒ compounded monthly

- Substitute these values in the formula above

∴ $5000=P(1+\frac{0.03}{12})^{(12)(2)}$

∴ $5000=P(1+0.0025)^{24}$

∴ $5000=P(1.0025)^{24}$

- Divide both sides by $(1.0025)^{24}$

∴ P = 4709.18

The amount you should deposit is $4709.18

Learn more:

You can learn more about the compounded interest in brainly.com/question/2514241

#LearnwithBrainly

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3 years ago

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3 years ago

Read 2 more answers

Question 2 of 5

AlekseyPX

Given:

The different recursive formulae.

To find:

The explicit formulae for the given recursive formulae.

Solution:

The recursive formula of an arithmetic sequence is $f(n)=f(n-1)+d, f(1)=a,n\geq 2$ and the explicit formula is $f(n)=a+(n-1)d$ , where a is the first term and d is the common difference.

The recursive formula of a geometric sequence is $f(n)=rf(n-1), f(1)=a,n\geq 2$ and the explicit formula is $f(n)=ar^{n-1}$ , where a is the first term and r is the common ratio.

The first recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+5$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 5. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(5)$

$f(n)=5+5(n-1)$

Therefore, the correct option is A, i.e., $f(n)=5+5(n-1)$ .

The second recursive formula is:

$f(1)=5$

$f(n)=3f(n-1)$ for $n\geq 2$ .

It is the recursive formula of a geometric sequence with first term 5 and common ratio 3. So, the explicit formula for this recursive formula is:

$f(n)=5(3)^{n-1}$

Therefore, the correct option is F, i.e., $f(n)=5(3)^{n-1}$ .

The third recursive formula is:

$f(1)=5$

$f(n)=f(n-1)+3$ for $n\geq 2$ .

It is the recursive formula of an arithmetic sequence with first term 5 and common difference 3. So, the explicit formula for this recursive formula is:

$f(n)=5+(n-1)(3)$