Question

1. the list below represents the number of text messages sent on a single day by a group of students. which statement is true? {35, 72, 16, 45, 60, 21, 60, 43} a. mean = median b. mean < median c. median > mode d. mean > median 2. the set of integers is a subset of which set of numbers? a. even numbers b. rational numbers c. natural numbers d. whole numbers 3. the difference of two - thirds of a number x and 6 is at least - 24. which inequality represents all possible values for x? a. x ≤ - 45 b. x ≥ - 45 c. x ≤ - 27 d. x ≥ - 27 4. what is the value of the expression below when a = - 13 and b = - 4? (a - 2b)^2 + b^3

Explanation:

Question 1

Step1: Calculate the mean

Sum of numbers: $35 + 72+16 + 45+60+21+60+43=352$. Mean = $\frac{352}{8}=44$.

Step2: Arrange in ascending order

$16,21,35,43,45,60,60,72$.

Step3: Calculate the median

Since $n = 8$ (even), median=$\frac{43 + 45}{2}=44$.

Step4: Find the mode

Mode is 60.

Integers include positive and negative whole - numbers and zero. Rational numbers are numbers that can be written as a fraction $\frac{p}{q}$ where $q
eq0$. Integers can be written as $\frac{n}{1}$, so integers are a subset of rational numbers. Even numbers are a subset of integers, natural numbers are positive integers, and whole numbers are non - negative integers.

Step1: Translate to an inequality

Two - thirds of a number $x$ is $\frac{2}{3}x$. The difference of $\frac{2}{3}x$ and 6 is $\frac{2}{3}x−6$. It is at least - 24, so $\frac{2}{3}x−6\geq - 24$.

Step2: Solve the inequality

Add 6 to both sides: $\frac{2}{3}x\geq-24 + 6=-18$. Multiply both sides by $\frac{3}{2}$: $x\geq-18\times\frac{3}{2}=-27$.

Answer:

A. mean = median

Question 2