# Consider the figure shown below. Find the value of each variable mentioned in the figure below​

3 weeks ago

## Solution 1

Guest #7253155
3 weeks ago
• a = 26, b = 64, c = 42

-------------------

The measure of an inscribed angle is half the measure of the intercepted arc:

• a = 52/2 = 26,
• c = 84/2 = 42.

Angles a and b sum to a right angle since inscribed between the tangent and diameter.

Then we have:

• a + b = 90
• 26 + b = 90
• b = 90 - 26
• b = 64

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The required closest approximation of city A's population is 1.185 million.

### What is percent?

Percentages  are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, on the off chance that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.

### According to question:

We have, city A is 23.5% of city B

A/B = 235/1000 = 47/200 = (B)47/200-----------(1)

and, city B is 51% of city C.

B/C = 51/100

B = (51/100)×9.89 = 5.0439 million

As C = 9.89 million

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Thus, required population of city A is 1.185 million.

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Question
Derrick deposited $700 in a savings account that pays 2.5% simple interest on a quarterly basis. After the initial deposit, he did not make any deposits and withdrawals. How many years ago did he invest the money if his current balance on the account is$980?
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Solution 1

The required number of year at 2.5% simple interest on a quarterly basis is 4%.

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### According to question:

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To calculate number of years,

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If company JCN made a $1196.7 million profit last year, with$798.9 million of that profit brought in by the sales department, then approximately what percent of the total profit was not brought in by the sales department?
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The required percent of the total profit was not brought in by the sales department is 33%.

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Simple Interest (S.I.) is the strategy for working out the premium sum for a specific chief measure of cash at some pace of revenue. For instance, when an individual takes a credit of Rs. 5000, at a pace of 10 p.a. for a considerable length of time, the individual's advantage for quite some time will be S.I. on the acquired cash.

### According to question:

profit amount = $1196.7 Amount used in sales =$798.9

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### According to question:

We have,

Amount of four year = $1200 simple interest = 10% Let loaned amount is x Then, interest of four year =×4 x×10/100 = 4x/10 According, x + 4x/10 =$1200

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X = $857 (appox) Thus, the required loaned amount is$857.

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Question

Given g(x) = -5x + 1, find g(1).
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Step-by-step explanation:

Solution 2

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Step-by-step explanation:

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Question
Fred deposits $6,500 in a saving account that pays 0.5% interest, compounded quarterly. Round each answer to the nearest cent. a. Find the first quarter's interest. b. Find the first quarter's ending balance. c. Find the second quarter's interest. d. Find the second quarter's ending balance. e. Find the third quarter's interest. f. Find the third quarter's ending balance. g. Find the fourth quarter's interest. h. What is the balance at the end of one year? i. How much interest does the account earn in the first year? Solution 1 The amount of interest earned quarterly at 0.5% interest rate compounded quarterly are; a. Interest for the first quarter =$8.125

b. First quarter ending balance = $6,508.125 c. Interest for the second quarter =$8.13515625

d. Second quarter ending balance = $6,516.26015625 e. Interest for the third quarter =$8.1432520325

f. Third quarter closing balance = $6,524.40548145 g. Interest for the fourth quarter =$8.15550685975

h. The amount of interest earned in a year is about $32.56 ### What is an interest earned on an amount? An interest is the amount a borrower pays to a lenders as to make use of the lender's funds. The amount Fred deposited, P =$6,500

The interest paid by the account, r = 0.5% compounded quarterly

a. The first quarter interest can be found by the formula;

$$C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times \dfrac{1}{4} }- P$$

Therefore;

$$C.I. = 6500\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6500 = 8.125$$

The interest after the first period is $8.125 b. The first quarter ending balance is therefore; A = P + C.I. A =$6,500 + $8.125 =$6,508.125

c. The second quarter's interest can be found from the formula;

$$C.I. = P\cdot \left(1 + \dfrac{r}{4} \right)^{4\times t} - P$$

Here, P = The balance from the first quarter = $6,508.125 t = 1/4 for one quarter Therefore; $$C.I. = 6508.125\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6508.125 = 8.13515625$$ The second quarter's interest is$8.13515625

d. The second quarter ending balance is therefore;

A = $6,508.125 +$8.13515625 = $6,516.26015625 The second quarter ending balance is$6,516.26015625

e. The third quarters interest is therefore;

$$C.I. = 6516.26015625\times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6516.26015625 = 8.1432520325$$

The third quarter's interest is about $8.1433 f. The third quarter's ending balance is therefore; A ≈$6516.26015625 + $8.1432520325 =$6,524.40548145

The third quarter's ending balance is $6,524.40548145 g. The fourth quarter's interest can be found as follows; $$C.I. = 6,524.40548145 \times \left(1 + \dfrac{\frac{0.5}{100} }{4} \right)^{4\times \dfrac{1}{4} }- 6524.40548145 = 8.15550685975$$ The fourth quarter's interest is;$8.15550685975

h. The balance at the end of one year is therefore;

Balance = C.I. fourth quarter + Principal for the fourth quarter

Therefore;

Balance = $6,524.40548145 +$8.15550685975 = $6,532.56098831 i. The interest the account earns in a year is therefore;$6,532.56098831 - $6,500 =$32.5609883

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