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Step2247 [10]
3 years ago
11

What type of number can be written as a fraction a over b, where a and b are integers and b is not equal to zero?

Mathematics
2 answers:
vova2212 [387]3 years ago
7 0

Answer:

This is the definition of rational number.

These include: Integers, Terminating Decimals, Repeating Decimals, or Proper, Improper, and Mixed Fractions where each part is an integer.  

Step-by-step explanation:

This is the definition of rational number.

Here are some examples of rational number:

-3  (negative integers are included because they can be rewritten; here -3=-3/1)

5 (positive integers are included because they can be rewritten; here 5=5/1)

0 (neutral integers are included also because 0/4 or 0/1 are still 0)

5/3 (impropert fractions where top and bottom are integers; this is already written in the form required)

1   2/3  (mixed fractions because they can rewritten as improper fractions with top and bottom as integers; example here this 5/3)

2/5  (proper fractions where top and bottom are integers; this is already written in the form required)

.55555555555...=. \overline{5} (repeating decimals; example this one can be written as 5/9)

.23 (terminating decimals; example this can be written as 23/100 )

musickatia [10]3 years ago
4 0
It could be any fraction really. Some examples are 5/6, 7/9 or 12/24. It doesn’t really matter what the fraction ks
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4 years ago
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
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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 !:)




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