Question 1

Solve the problem.
-Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total
Interest for that year was $140, how much did Kevin invest in the mutual fund?

Accepted Answer

Let the amount invested in the certificate of deposit be $x. Therefore, the amount invested in the mutual fund is $5000 - x. The interest from the certificate of deposit is 0.02x, and the interest from the mutual fund is 0.04(5000 - x). The total interest is $140, so the equation is 0.02x + 0.04(5000 - x) = 140. Solving this equation gives x = $3000 for the certificate of deposit, meaning $2000 was invested in the mutual fund.

Question 2

Indicate whether the statement is true always, sometimes, or never.
-When i is raised to an odd power, the result is -1.

Accepted Answer

The answer of Indicate whether the statement is true always,...

Question 3

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$- 14 + \mathrm { i }$

Accepted Answer

The number $-14 + \mathrm{i}$ is a complex number because it has both a real part (-14) and an imaginary part ($\mathrm{i}$). Since it has a non-zero imaginary part, it is also a nonreal complex number.

Question 4

Indicate whether the statement is true always, sometimes, or never.
-When i is raised to an even power, the result is -1.

Accepted Answer

When $i$ is raised to an even power, the result alternates between $+1$ and $-1$. For example, $i^2 = -1$, but $i^4 = 1$. Therefore, the statement is true only sometimes.

Question 5

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-0

Accepted Answer

0 is both a real number and a complex number (with an imaginary part of 0).

Question 6

Solve the problem.
-A bank loaned out $69,000, part of it at the rate of 2.25% per year and the rest at a rate of 3.5% per year. If the interest received was $2065.00, how much was loaned at 2.25%?

Accepted Answer

The answer of Solve the problem.
-A bank loaned out $69,000,...

Question 7

Solve the problem.
-A person's emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 13 yr old person has an EQ of 97 what is that
Person's emotional age?

Accepted Answer

The formula for EQ is given as EQ = (Emotional Age / Chronological Age) * 100. Rearranging this formula to solve for Emotional Age gives Emotional Age = (EQ * Chronological Age) / 100. Substituting the given values (EQ = 97, Chronological Age = 13) yields Emotional Age = (97 * 13) / 100 = 1261 / 100 = 12.61 years old.

Question 8

Indicate whether the statement is true always, sometimes, or never.
-A real number is a complex number.

Accepted Answer

Every real number can be considered a complex number with an imaginary part of 0, thus making it always true that a real number is a complex number.

Question 9

Solve the problem.
-Your home state uses a linear model $y = 34 ( x - 70 ) + 4182$ to predict the number of vacationers $( y )$ as compared to the average temperature for that week $( x )$. Find the number of vacationers predicted for a week with an average temperature of 72 degrees.

Accepted Answer

The answer of Solve the problem.
-Your home state uses a...

Question 10

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
--1

Accepted Answer

-1 is a real number because it can be found on the number line. All real numbers are also complex numbers, so -1 is both real and complex.

Question 11

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$\pi$

Accepted Answer

$\pi$ is a real number, and all real numbers are also considered complex numbers with an imaginary part of 0.

Question 12

Indicate whether the statement is true always, sometimes, or never.
-The product of a pair of complex conjugates is a real number.

Accepted Answer

The product of a pair of complex conjugates is always a real number because the imaginary parts cancel out, leaving a real number.

Question 13

Indicate whether the statement is true always, sometimes, or never.
-The difference between two real numbers is a real number.

Accepted Answer

The difference between any two real numbers is always a real number due to the closure property of real numbers under subtraction.

Question 14

Solve the problem.
-A toy company uses the linear model $y = - 5 x + 560$ to predict the decline in sales of a toy after it has been on the market more than one year. If $\mathrm { x }$ is the number of months after the first year and $\mathrm { y }$ is the number of toys sold in hundreds during that month, how many toys will be sold 7 months after the first year?

Accepted Answer

Plugging $x = 7$ into the equation $y = -5x + 560$ gives $y = -5(7) + 560 = -35 + 560 = 525$. Since $y$ represents hundreds of toys, this means 525 hundred toys, or 52,500 toys.

Question 15

Indicate whether the statement is true always, sometimes, or never.
-The sum of two imaginary numbers is an imaginary number.

Accepted Answer

The sum of two imaginary numbers is sometimes an imaginary number. This is because if the imaginary parts cancel each other out, the result can be a real number. However, if they do not cancel out, the sum remains an imaginary number.

Question 16

Indicate whether the statement is true always, sometimes, or never.
-A complex number is an imaginary number.

Accepted Answer

A complex number is sometimes an imaginary number. Complex numbers include all the numbers of the form a + bi, where a and b are real numbers and i is the square root of -1. If a is 0, the complex number is purely imaginary; otherwise, it is not.

Question 17

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may
apply.
-$3 - 9 \mathrm { i }$

Accepted Answer

The answer of Identify the number as real, complex, pure...

Question 18

Indicate whether the statement is true always, sometimes, or never.
-The product of two imaginary numbers is a real number.

Accepted Answer

The product of two imaginary numbers is real sometimes because when you multiply two imaginary numbers (e.g., $i \times i = -1$), their product can be a real number. Imaginary numbers are of the form $bi$ where $b$ is a real number and $i$ is the square root of $-1$. Multiplying two such numbers, say $ai$ and $bi$, gives $-ab$, which is real.

Question 19

Solve the problem.
-A computer company uses the linear model $y = - 45 x + 34,030$ to predict the decline in sales of a computer after it has been on the market more than one year. If $\mathrm { x }$ is the number of months after the first year and $y$ is the number of computers sold during that month, how many computers will be sold 2 months after the first year?

Accepted Answer

To find the number of computers sold 2 months after the first year, substitute $x = 2$ into the equation $y = -45x + 34,030$. This gives $y = -45(2) + 34,030 = -90 + 34,030 = 33,940$.

Question 20

Indicate whether the statement is true always, sometimes, or never.
-$$\text { To find the quotient } \frac { 10 + 3 \mathrm { i } } { 10 - 3 \mathrm { i } } \text {, multiply numerator and denominator by } 10 + 3 \mathrm { i } \text {. }$$

Accepted Answer

To find the quotient of complex numbers in the form $\frac{a+bi}{c+di}$, one common method is to multiply both the numerator and denominator by the conjugate of the denominator to eliminate the imaginary part in the denominator. In this case, multiplying by $10 + 3i$, the conjugate of $10 - 3i$, is a correct approach to simplify the expression, making the statement always true.

Quiz 2: Equations and Inequalities

Solve the problem. -Kevin invested part of his $5000 bonus in a certificate of deposit that paid 2% annual simple interest, and the remainder in a mutual fund that paid 4% annual simple interest. If his total Interest for that year was $140, how much did Kevin invest in the mutual fund?

Indicate whether the statement is true always, sometimes, or never. -When i is raised to an odd power, the result is -1.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $- 14 + \mathrm { i }$

Indicate whether the statement is true always, sometimes, or never. -When i is raised to an even power, the result is -1.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. -0

Solve the problem. -A bank loaned out $69,000, part of it at the rate of 2.25% per year and the rest at a rate of 3.5% per year. If the interest received was $2065.00, how much was loaned at 2.25%?

Solve the problem. -A person's emotional quotient (EQ) is found by multiplying emotional age by 100 and dividing by chronological age. Using this information, if a 13 yr old person has an EQ of 97 what is that Person's emotional age?

Indicate whether the statement is true always, sometimes, or never. -A real number is a complex number.

Solve the problem. -Your home state uses a linear model $y = 34 ( x - 70 ) + 4182$ to predict the number of vacationers $( y )$ as compared to the average temperature for that week $( x )$ . Find the number of vacationers predicted for a week with an average temperature of 72 degrees.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. --1

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $\pi$

Indicate whether the statement is true always, sometimes, or never. -The product of a pair of complex conjugates is a real number.

Indicate whether the statement is true always, sometimes, or never. -The difference between two real numbers is a real number.

Indicate whether the statement is true always, sometimes, or never. -The sum of two imaginary numbers is an imaginary number.

Indicate whether the statement is true always, sometimes, or never. -A complex number is an imaginary number.

Identify the number as real, complex, pure imaginary, or nonreal complex. More than one of these descriptions may apply. - $3 - 9 \mathrm { i }$

Indicate whether the statement is true always, sometimes, or never. -The product of two imaginary numbers is a real number.

Indicate whether the statement is true always, sometimes, or never. - $\text { To find the quotient } \frac { 10 + 3 \mathrm { i } } { 10 - 3 \mathrm { i } } \text {, multiply numerator and denominator by } 10 + 3 \mathrm { i } \text {. }$