If x is a positive real number such that x^{2} = 16, then x^{3} + √x = ?

Solution
To find what x^{3} + x equals, you need to first solve x^{2} = 16 for x. The solution is the square root of 16, which is 4. Then substituting into the original expression, you get 4^{3} + √4. This expression simplifies to 64 + 2, or 66.
What percent of 5 is 7?

Solution
To find what percent of 5 the number 7 is, you can simply divide 7 by 5 and multiply by 100%, as follows:
7/5 = 1.4
(1.4)(100) = 140%
Because 7 is greater than 5, you could have eliminated answer choices A, B, and C.
If 7x + 5 = 2x + 9, then x = ?

Solution
To solve for x in the equation 7x + 5 = 2x + 9, you could subtract 2x and 5 from both sides of the equation. That results in the equation 5x = 4. Dividing both sides by 5, the result is x = ^{4}⁄_{5}.
If mn = k and k = x^{2}n, and nk ≠ 0, which of the following is equal to m?

Solution
You are given that mn = k and k = x^{2}n. To solve this problem, first combine the equations into mn = x^{2}n. Then, divide both sides by n to get m = x^{2}.
Mandy and Jordan each bought some of the same notebooks and the same threering binder. Mandy paid $5.85 for 3 notebooks and 1 binder. Jordan paid $4.65 for 2 notebooks and 1 binder. What is the price of one of the notebooks?

Solution
To solve this problem, write an equation for the price of all of the notebooks and then solve for the price of one notebook. Make N the price of notebooks and B the price of binders purchased by Mandy and Jordan. If Mandy paid $5.85 for 3 notebooks and 1 binder, the result is 3N + B = 5.85. Likewise for Jordan, $4.65 for 2 notebooks and 1 binder can be represented in the equation 2N + B = 4.65.
Use substitution to solve these equations. Solving Jordan’s equation for B yields B = 4.65 − 2N. If you substitute 4.6−2N as B into Mandy’s equation, the result is 3N + (4.65 − 2N) = 5.85. Combining like terms yields N + 4.65 = 5.85. If you subtract 4.65 from both sides of the equation, you find that N = 1.20. Therefore, the price of one notebook is $1.20.
Which of the following numbers has the digit 5 in the thousandths place?

Solution
To solve this problem, you must remember that if you start at the decimal point and count to the right, the place values are tenths, hundredths, thousandths, tenthousandths, and so on. Therefore, the decimal 0.005 has the digit 5 in the thousandths place.
When written in symbols, “the product of r and s, raised to the fourth power,” is represented as:

Solution
The product of two numbers is found by multiplying them (r × s in this case). Raising the product of r and s to the fourth power is represented by (r × s)^{4}, since you are raising the entire product to the fourth power.
Remember that r × s is equivalent to rs.
What is the fourth term in the arithmetic sequence 13, 10, 7, …?

Solution
To solve, determine the pattern in the arithmetic sequence 13, 10, 7, ... The second term, 10, is 3 less than the first term, 13. Likewise, the third term, 7, is three less than the second term, 10. Therefore, the fourth term will be three less than the third term, 7, making it 7−3 = 4.
5x^{3} × 2xy × 3xy^{2} is equivalent to:

Solution
To find the equivalent expression, multiply the constants (5×2×3), combine the x terms (x^{3})(x)(x) = x^{3+1+1} = x^{5} (because when you have a common base you keep the base and add the exponents), and combine the y terms (y^{1})(y^{2}) = y^{1+2}, or y^{3}. The result is 30x^{5}y^{3}.
The minimum fine for driving in excess of the speed limit is $25. An additional $6 is added to the minimum fine for each mile per hour (mph) in excess of the speed limit. Rachel was issued a $103 fine for speeding in a 55mph speed limit zone. For driving at what speed, in mph, was Rachel fined?

Solution
You are given that Rachel paid a total of $103 for her speeding ticket, and that the basic fine for speeding is $25. This means that Rachel was charged an additional $78 (103 – 25). If the charge for each mile per hour over the speed limit is $6, then Rachel was driving 13 mph over the 55mph speed limit (78/6 = 13), or 68 mph.