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3 years ago

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A road construction crew is resurfacing the highway between point d and e. The distance between point d and e is 93 miles of roa

d .The crew has completed
35 miles. If they work at a pace of 2.9 miles per day, how many more days will it take to finish?

1 answer:

Ulleksa [173]3 years ago

3 0

93 - 35 = 58
58/2.9 = 20
it will take them 20 more days.

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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

Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey?

Margarita [4]

Let x is Casey's sister age.
<span>3 years ago:
</span><span>Casey was twice as old as his sister: 2a - 3
Now:
</span><span>he is 5 years older than his sister: a + 5

2a - 3 = a + 5
subtract a to both sides
2a - 3 -a = a + 5 - a
simplify
a - 3 = 5
add 3 to both sides
a - 3 + 3 = 5 + 3
simplify
a = 8

His sister age is 8 years old now.
</span>Now:
he is 5 years older than his sister: a + 5 = 8 + 5 = 13
<span>
proof:
so 3 years ago,
his sister age: 8 - 3 = 5
Casey age 3 years ago:
13 - 3 = 10 (</span>C<span>asey was twice as old as his sister 3 years ago</span>)
<span>
Answer:
Casey is 13 years old now.

</span>

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dimaraw [331]

Answer:

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Step-by-step explanation:

The mean is the terms added together, then divided by the number of terms (in this case, 8):

$93+81+94+78+89+92+94+99=720\\\\\frac{720}{8} =90$

Done.

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Answer:

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Step-by-step explanation:

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TEA [102]

Answer:

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Step-by-step explanation:

One number is 2 times another number plus 3. Their sum is 21.

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x = smaller number = another number

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Combine like terms:

3x+3 = 21

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