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3 years ago

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? Explain?

Mathematics

1 answer:

sineoko [7]3 years ago

5 0

Answer:

none

Step-by-step explanation:

4+4.5=8.5 both of the smaller sides have to add up to a number greater than the largest side

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As part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each

Finger [1]

Answer:

Option d)$401,447.24

Step-by-step explanation:

We are given that as part of your retirement plan, you want to set up an annuity in which a regular payment of $35,000 is made at the end of each year at rate of 6% compounded annually for 20 years

So first of all we need to find the future value of annuity using the formula as shown below :

$FV= p\frac{[(1+\frac{r}{n})^{(n)(t)}-1)]}{\frac{r}{n}}$

Here, FV = future value of annuity

p = $35000 (annual deposit)

r is rate = 6% = 0.06

n = number of compounding = 1 ( as we are compounding annually )

t = number of years = 20

So plugging in all the values in the formula , we get

$FV= 35000\frac{[(1+\frac{0.06}{1})^{(1)(20)}-1)]}{\frac{0.06}{1}}$

Simplifying further , we get

$FV= 35000\frac{[(1+0.06)^{20}-1)]}{0.06}$

Plugging in the given values in the calculator , we get

FV = $ 1287495.69

So far we have got the Total amount for annuity , from here we need to use the concept of compound interest and find the principal amount to be deposited to get the required total amount of $ 1287495.69

The formula for compound interest when compounded annually is given by:

$A=P(1+r)^t$

Here A = 1287495.69 (Total amount required)

P = ( principal amount to be deposited to meet the required total amount )

r = 6% = 0.06

t = 20

So plugging in all the known values in the formula , we get

$1287495.69= P(1+0.06)^{20}$

simplifying further, we get

$\frac{1287495.69}{(1.06)^{20}}= P$

so required amount to be deposited is given by :

P = $401,447.24

Hope it was helpful !:)

6 0

3 years ago

2. Write an expression to represent f (20)

Furkat [3]

Answer:

I just learned this topic and have the same question, so I'm not sure if this right. However, I see a fellow student struggling and have to at least put in what I know. My equation was f(n) = 64(1/2)^n-1, then the question was write an expression to represent f(20).

Step-by-step explanation:

So, my answer was f(20) = 64(1/2)^19

f(20) is the number you plug into n. And because the exponent is n-1, I knew to subtract 1 from 20 to get 19.

Then I just wrote the equation out like the original expect with the numbers pluged in: f(20) = 64(1/2)^19

I hope this helps!

7 0

4 years ago

The common denominator of 3/4 and 1/6 is 24. True False

Viktor [21]

Actually, this is false. 6 and 4 both have 12 in common because 6*2=12 and 4*3 is 12. So the least common denominator is really 12.

6 0

4 years ago