Question 1

Write as a real number or a product of a real number and i.
-$- \sqrt { - 16 }$
A) $i$
B) $- 4 i$
C) 4
D) $4 \mathrm { i }$

Accepted Answer

$- \sqrt { - 16 } = - 4i$ because the square root of $-16$ is $4i$, and the negative sign makes it $-4i$.

Question 2

Solve the problem.
-The appliance store where the Scott family shops offers a 6% discount for paying cash. The Scott family received a discount of $60. What was their total bill before the discount?
A)$4
B)$400
C)$10
D)$1000

Accepted Answer

The discount is 6% of the total bill. If the discount is $60, then $60 is 6% of the total bill. To find the total bill, divide $60 by 0.06, which equals $1000.

Question 3

Find the power of i.
-$\mathrm { i } ^8$
A) $- \mathrm { i }$
B) 1
C) $\mathrm { i }$
D) $- 1$

Accepted Answer

The power of $i$ can be determined by knowing that $i^2 = -1$. Therefore, $i^8 = (i^2)^4 = (-1)^4 = 1$.

Question 4

Solve the problem.
-Midtown Antiques collects 5% sales tax on all sales. If total sales including tax are $1248.70, find the portion that is the tax amount.
A)$62.44
B)$1189.24
C)$59.46
D)$49.46

Accepted Answer

The total amount including tax is $1248.70, and the tax rate is 5%. To find the portion that is the tax amount, divide the total by 1.05 (100% + 5% tax = 105%, or 1.05 in decimal form). This gives the pre-tax amount. Subtracting the pre-tax amount from the total gives the tax amount: $1248.70 / 1.05 = $1189.24 (pre-tax amount). $1248.70 - $1189.24 = $59.46, which is the tax amount.

Question 5

Write as a real number or a product of a real number and i.
-$\sqrt { - 5 } \cdot \sqrt { - 5 }$
A) $2 i \sqrt { - 5 }$
B) $- 5$
C) 5
D) $- 5 \mathrm { i }$

Accepted Answer

The product of two square roots of negative numbers, $\sqrt{-5} \cdot \sqrt{-5}$, simplifies to $\sqrt{(-5) \cdot (-5)} = \sqrt{25} = 5$. However, since both -5 are under square roots and are multiplied, the negative signs cancel out (because $i^2 = -1$), resulting in a positive real number, not 5. The correct simplification should be $(-i\sqrt{5}) \cdot (-i\sqrt{5}) = (-i)^2(\sqrt{5})^2 = 1 \cdot 5 = 5$, indicating an error in my initial explanation. The correct answer is actually -5, considering the properties of imaginary numbers correctly, where the multiplication of two identical square roots of negative numbers results in the positive value of the number under the square root.

Question 6

Solve the problem.
-Last season, a football team won 35 games and lost 72. Finding the winning percentage (ie the percentage of games which were won).
A)48.6%
B)67.3%
C)35.0%
D)32.7%

Accepted Answer

The winning percentage is calculated by dividing the number of games won by the total number of games played and then multiplying by 100. Here, the team won 35 games out of a total of 107 games (35 wins + 72 losses). So, the winning percentage is (35/107) * 100 = 32.7%.

Question 7

Write as a real number or a product of a real number and i.
-$5 + \sqrt { - 36 }$
A) $5 + 6 \mathrm { i }$
B) $- 1$
C) $5 + \mathrm { i }$
D) $5 - 6 \mathrm { i }$

Accepted Answer

The square root of -36 is $6i$, so the expression simplifies to $5 + 6i$.

Question 8

Solve the problem.
-The normal gasoline mileage of a car is 22 mpg. What is its mileage on a smooth road (12% increase)?
A)50 mpg
B)2.6 mpg
C)22 mpg
D)24.6 mpg

Accepted Answer

A 12% increase in the normal gasoline mileage of 22 mpg results in an increase of 2.64 mpg (0.12 * 22 = 2.64), making the mileage on a smooth road 24.64 mpg, which rounds or is approximately 24.6 mpg.

Question 9

Write as a real number or a product of a real number and i.
-$\sqrt { - 16 }$
A) 4
B) $- 4 i$
C) $\mathrm { i }$
D) $4 \mathrm { i }$

Accepted Answer

The square root of -16 is $4i$, because $\sqrt{-16} = \sqrt{16} \cdot \sqrt{-1} = 4i$, where $i$ is the imaginary unit.

Question 10

Find the power of i.
-$\mathrm { i } ^ { 9 }$
A) 1
B) $- \mathrm { i }$
C) $\mathrm { i }$
D) $- 1$

Accepted Answer

$\mathrm { i } ^ { 9 } = \mathrm { i } ^ { 8 } \cdot \mathrm { i } = ( \mathrm { i } ^ { 4 } ) ^ { 2 } \cdot \mathrm { i } = 1 ^ { 2 } \cdot \mathrm { i } = \mathrm { i }$.

Question 11

Write as a real number or a product of a real number and i.
-$\frac { \sqrt { - 10 } \cdot \sqrt { - 5 } } { \sqrt { 2 } }$
A) 5
B) $25 \mathrm { i }$
C) $5 \mathrm { i }$
D) $- 5$

Accepted Answer

The answer of Write as a real number or a...

Question 12

Write as a real number or a product of a real number and i.
-$\sqrt { - 17 }$
A) $4 \mathrm { i }$
B) $\mathrm { i }$
C) $\mathrm { i } \sqrt { - 17 }$
D) $i \sqrt { 17 }$

Accepted Answer

The square root of a negative number can be expressed as the square root of the positive part times $i$, hence $\sqrt{-17} = i\sqrt{17}$.

Question 13

Solve the problem.
-The Perrones have saved $8600 for a down payment. If a 34% down payment is required, what price house can they buy?
A)$253
B)$292,400
C)$25,294
D)$2924

Accepted Answer

To find the price of the house they can buy, divide the down payment by the percentage required: $8600 / 0.34 = $25,294.

Question 14

Solve the problem.
-At a university, 80% of the students who apply are accepted. Of those who are accepted, 70% actually enroll. If 30,000 students apply, how many actually enroll?
A)16,800 students
B)28,500 students
C)29,850 students
D)13,200 students

Accepted Answer

First, 80% of 30,000 students are accepted, which is 24,000 students. Then, 70% of these 24,000 students actually enroll, which equals 16,800 students.

Question 15

Write as a real number or a product of a real number and i.
-$\frac { \sqrt { - 200 } } { \sqrt { - 8 } }$
A) 5
B) $5 \mathrm { i }$
C) $25 \mathrm { i }$
D) $- 5 \mathrm { i }$

Accepted Answer

The expression simplifies to $\frac{\sqrt{200}}{\sqrt{8}}$ after factoring out the negative signs under the square roots, which simplifies further to $\frac{10\sqrt{2}}{2\sqrt{2}} = 5$, making it a real number.

Question 16

Solve the problem.
-What percent of the figure is shaded? 
A)6.4%
B)0.64%
C)64%
D)60%

Accepted Answer

The answer of Solve the problem.
-What percent of the figure...

Question 17

Solve the problem.
-Brand X copier advertises that its copiers run 24% longer between service calls than its competitor. If Brand X copiers run 48,800 copies between services, how many copies would the competitor run?
A)27,727 copies
B)37,088 copies
C)39,355 copies
D)60,512 copies

Accepted Answer

Brand X runs 24% longer than its competitor, meaning it runs 124% (100% + 24%) of what the competitor runs. Let the number of copies the competitor runs be x. So, 1.24x = 48,800. Solving for x gives x = 48,800 / 1.24 = 39,354.8387, which rounds to 39,355 copies.

Question 18

Find the power of i.
-$\mathrm { i } ^{19}$
A) $i$
B) $- \mathrm { i }$
C) 1
D) $- 1$

Accepted Answer

The answer of Find the power of i.
-\(\mathrm { i...

Question 19

Solve the problem.
-A share of stock gains 8% in value and then loses 8% . How does its ending value compare with its initial value?
A)Less
B)The same
C)More

Accepted Answer

When a stock gains 8% in value and then loses 8%, its ending value is less than its initial value due to the way percentages work on different bases.

Question 20

Write as a real number or a product of a real number and i.
--176
A)i
B)13i
C)4i 11
D)-4i 11

Accepted Answer

The answer of Write as a real number or a...

Quiz 6: The Real Numbers and Their Representations

Write as a real number or a product of a real number and i. - $- \sqrt { - 16 }$

Solve the problem. -The appliance store where the Scott family shops offers a 6% discount for paying cash. The Scott family received a discount of $60. What was their total bill before the discount?

Find the power of i. - $\mathrm { i } ^8$

Solve the problem. -Midtown Antiques collects 5% sales tax on all sales. If total sales including tax are $1248.70, find the portion that is the tax amount.

Write as a real number or a product of a real number and i. - $\sqrt { - 5 } \cdot \sqrt { - 5 }$

Solve the problem. -Last season, a football team won 35 games and lost 72. Finding the winning percentage (ie the percentage of games which were won) .

Write as a real number or a product of a real number and i. - $5 + \sqrt { - 36 }$

Solve the problem. -The normal gasoline mileage of a car is 22 mpg. What is its mileage on a smooth road (12% increase) ?

Write as a real number or a product of a real number and i. - $\sqrt { - 16 }$

Find the power of i. - $\mathrm { i } ^ { 9 }$

Write as a real number or a product of a real number and i. - $\frac { \sqrt { - 10 } \cdot \sqrt { - 5 } } { \sqrt { 2 } }$

Write as a real number or a product of a real number and i. - $\sqrt { - 17 }$

Solve the problem. -The Perrones have saved $8600 for a down payment. If a 34% down payment is required, what price house can they buy?

Solve the problem. -At a university, 80% of the students who apply are accepted. Of those who are accepted, 70% actually enroll. If 30,000 students apply, how many actually enroll?

Write as a real number or a product of a real number and i. - $\frac { \sqrt { - 200 } } { \sqrt { - 8 } }$

Solve the problem. -What percent of the figure is shaded?

Solve the problem. -Brand X copier advertises that its copiers run 24% longer between service calls than its competitor. If Brand X copiers run 48,800 copies between services, how many copies would the competitor run?

Find the power of i. - $\mathrm { i } ^{19}$

Solve the problem. -A share of stock gains 8% in value and then loses 8% . How does its ending value compare with its initial value?

Write as a real number or a product of a real number and i. --176

Quiz 6: The Real Numbers and Their Representations

Write as a real number or a product of a real number and i. - −−16- \sqrt { - 16 }−−16​

Solve the problem. -The appliance store where the Scott family shops offers a 6% discount for paying cash. The Scott family received a discount of $60. What was their total bill before the discount?

Find the power of i. - i8\mathrm { i } ^8i8