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4 years ago

15

Which one is a rule for the nth term of an arithmetic sequence with a8 = 56 and d = 5?

1 answer:

Mamont248 [21]4 years ago

7 0

An for arithmetic sequence, an = a + (n - 1)d
a8 = a + (8 - 1) x 5 = a + 7 x 5 = a + 35 = 56
a = 56 - 35 = 21

Therefore, an = 21 + (n - 1) x 5 = 21 + 5n - 5 = 16 + 5n
an = 16 + 5n

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an envelope from the post office is 3 inches wide with a total area of 30 square inches what is the height of the envelope

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3 years ago

Suppose you deposit $2500 in a savings account that pays you 5% interest per year. (Calculator)

BARSIC [14]

Answer:

14.20669 years

Roughly 14 years and 2.5 months.

Step-by-step explanation:

Assuming this is compound interest.

The formula is $A=P(1+\frac{r}{n})^{nt}$

$A=$ Final Amount

$P=$ Principal Amount

$r=$ Interest Rate

$n=$ # of times interest is compounded per year

$t=$ Time in years

We are looking for the times in years to double the money so

$2500*2=5000$

$A=5000$

$P=2500$

$r=0.05$

$n=1$

$t=?$

Lets solve for $t$ .

Step 1.

Plug in our numbers into the compound interest formula.

$5000=2500(1+\frac{0.05}{1}) ^{1*t}$

Step 2.

Simplify the equation.

Evaluate $1+\frac{0.05}{1}=1.05$

Evaluate $1*t=t$

$5000=2500(1.05) ^{t}$

Step 3.

Divide both sides of the equation by $2500$

$\frac{5000}{2500}=1.05 ^{t}$

Evaluate $\frac{5000}{2500}=2$

$2=1.05 ^{t}$

Step 4.

Take the natural log of both sides of the equation and rewrite the right side of the eqaution using properties of exponents/logarithms.

$ln(2)=t*ln(1.05)$

Step 5.

Divide both sides of the equation by $ln(1.05)$

$\frac{ln(2)}{ln(1.05)}=t$

Step 6.

Evaluate

$t=14.20669$

Roughly 14 years and 2.5 months.

4 0

2 years ago

Laura can finish payroll in 3 hours. it takes ben 5 hours to do the same job. If they work together, how long should it take the

rjkz [21]

Answer:

15/8 hours .................

Step-by-step explanation:

Let L be Laura, and B be Ben. Then:

3L=1

5B=1

Next:

15L=5

15B=3

15(L+B)=5+3=8

15/8 (L+B)=1

5 0

3 years ago

4/5 times 3/4 and 5/7 9/10

VikaD [51]

Answer:

(20) ( 12) (35), (90)= 756,000

Step-by-step explanation: because you multiply all of them which gives you 756,000.

5 0

3 years ago

7<br> The function g(r) = 25 - A. The value of g(5) is

miskamm [114]

Answer:

I believe it would be 20

Step-by-step explanation:

because if you plug 5 into the function like 25-5 you would get 20

hope this helps.

4 0

3 years ago

Read 2 more answers