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3 weeks ago

**Answer:**

Explanation: The idea is to draw a Venn Diagram and find the intersection. We have one circle of 70 and another with 40. When we add the two circles plus the 10 students who joined neither, we should get 100 students.

**Step-by-step explanation:**

Question

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

Solution 1

- 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**

Question

You buy a stock for $100. In one year its price rises to $114, and it pays a $1 dividend. Your capital gains yield is _____

Solution 1

**Answer:**

**Step-by-step explanation:**

$13

Question

The population of city A is 23.5% of city B and the population of city B is 51% of city C. If city C has 9.89 million people, which of the following is the closest approximation of city A's population in millions?

0.95 million

1.2 million

1.25 million

1.3 million

1.42 million

0.95 million

1.2 million

1.25 million

1.3 million

1.42 million

Solution 1

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

**Percentages** are basically divisions where the denominator is 100. To show that a **numbe**r 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%.

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

Put the value of c in equation (1)

A = (5.0439)47/200 = 1.185 million

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?

1

2

4

8

16

1

2

4

8

16

Solution 1

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

if the** interest** rate is 8% each year, however the estimation being referred to requires a **quarterly financing cost**, then, at that point, the significant loan cost is 2% per quarter. The 2% per quarter is comparable to a straightforward loan fee of 8% each **year**

We have,

Interest in 3 months = 2.5%

So, interest in one year = 4(2.5%) = 10%

**Principle** amount = $700

Final amount = $980

To calculate number of years,

total interest = 980 - 700 = $280

Let number of years be t.

Then,

$280/t = 10% of $700

t = $280/$70 = 4 years

Thus, required years 4.

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Question

The coupon rate of a bond determines the percentage of interest earned on the bond each year. Samantha purchased a five-year municipal bond for $600. After the bond matured five years later, she had received a total of $720 in principal plus interest payments. What is the coupon rate of Samantha's bond?

4%

5%

10%

12%

20%

4%

5%

10%

12%

20%

Solution 1

The required coupon rate of **Samantha's bond** is 4%.

The **coupon rate** is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon **payments** by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c

We have,

principal amount = $600

Amount after** five year** = $720

Interest of five year = $(720 - 600) = $120

Then,

**Interest** of one year = $120/5 = $24

Now,

Coupon rate = ($24/600)×100 = 4%

Thus, required coupon rate is 4%.

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Question

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?

3.3%

6.6%

20%

33%

67%

3.3%

6.6%

20%

33%

67%

Solution 1

The required **percent **of the total profit was not brought in by the sales department is 33%.

**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.

profit amount = $1196.7

**Amount **used in sales = $798.9

**Amount** was not used in sales = $1196.7 - $798.9 = $397.8

Now, then approximately percent of the total profit was not brought in by the **sales department.**

($397.8/$1196.7) × 100 = 33%

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Question

Adrian took out a students' loan that charges 10% annual simple interest. If Adrian paid back a total of $1200 in interest alone during the first four years , how much was Adrian's original loan, in dollars?

$1,000

$3,000

$4,000

$ 6,000

$12,000

$1,000

$3,000

$4,000

$ 6,000

$12,000

Solution 1

The required **simple interest **of 10% of four year on principle amount is $857.

**Simple interest** depends on the chief measure of a credit or the first store in quite a while account. Straightforward interest doesn't build, and that implies a loan boss will just compensation interest on the chief sum and a borrower couldn't have ever to pay more interest on the recently gathered** interest.**

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

14x/10 = $1200

x = $12000/14

X = $857 (appox)

Thus, the required **loaned amount** is $857.

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Question

what is the recursive formula

Solution 1

**Answer: The recursive formula generate term at a time by relating the term to one or more previous terms**

**Step-by-step explanation: The formula for recursive is **

**f(1)=6,f(n)=f(1)+f(n-1),n>1**

Question

Given g(x) = -5x + 1, find g(1).

Solution 1

Answer:

-4

Step-by-step explanation:

Solution 2

**Answer:**

-4

**Step-by-step explanation:**

g(x) tells us what the variable is and what variable should be replaced with a value.

g(1) tells us the value that will replace x.

Plug in 1 to the equation:

-5(1) + 1 = g(1) (multiply)

-5 + 1 = g(1) (combine like terms)

-4 = g(1)

Therefore, g(1) is equal to -4

Question

Determine the value of x in the following triangle.

Solution 1

**Answer:**

the value of x is 9

**Step-by-step explanation:**

the sum of all angles of a triangle is 180

one side is 90 so,

90+7x+3x = 180

10x = 180-90

10x = 90

x=9

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