Question

1. use the venn diagram. (lesson 3)

real numbers
rational numbers
whole numbers
integers
natural numbers
irrational numbers
a. determine whether the statement is true or false.
all integers are natural numbers.
b. if the statement is true, explain your reasoning. if the statement is false, provide a counter - example.

1. indicate the integer to which each square root is closest on a number line. (lesson 4)

7 8 9
√70
√79
√88
√52
√60
√47
√65

1. a shipping box, in the shape of a cube, has a volume of 2,300 cubic inches. estimate the length of the side of the shipping box to the nearest integer. (lesson 4)
2. consider the real numbers - 2 1/5 and - √7 (lesson 5)

a. compare the numbers. use <, >, or =

• 2 1/5 ___ - √7

b. graph - √7 and - 2 1/5 on the number line.

• 2.8 - 2.7 - 2.6 - 2.5 - 2.4 - 2.3 - 2.2 - 2.1 - 2.0

1. the table shows the number of aces per serving attempts for three players at a recent volleyball tournament. order the players from least aces per serving attempt to greatest aces per serving attempt. (lesson 5)

player number of aces
angela 9 out of 22
jaylin 22 2/3%
mya 3/10

Explanation:

16.

Step1: Recall number - set definitions

Natural numbers are positive integers starting from 1 ($1, 2, 3,\cdots$), and integers include positive and negative whole numbers and 0 ($\cdots,- 2,-1,0,1,2,\cdots$).

Step2: Determine truth - value

Since integers include negative numbers and 0 which are not natural numbers, the statement "All integers are natural numbers" is false.

Step3: Provide counter - example

The number 0 is an integer but not a natural number, and - 1 is an integer but not a natural number.

Step1: Find perfect squares around the given numbers

For $\sqrt{70}$, $8^2=64$ and $9^2 = 81$, and $70$ is closer to $64$ so $\sqrt{70}$ is closer to 8.
For $\sqrt{79}$, $8^2=64$ and $9^2 = 81$, and $79$ is closer to 81 so $\sqrt{79}$ is closer to 9.
For $\sqrt{88}$, $9^2=81$ and $10^2 = 100$, and $88$ is closer to 81 so $\sqrt{88}$ is closer to 9.
For $\sqrt{52}$, $7^2=49$ and $8^2 = 64$, and $52$ is closer to 49 so $\sqrt{52}$ is closer to 7.
For $\sqrt{60}$, $7^2=49$ and $8^2 = 64$, and $60$ is closer to 64 so $\sqrt{60}$ is closer to 8.
For $\sqrt{47}$, $6^2=36$ and $7^2 = 49$, and $47$ is closer to 49 so $\sqrt{47}$ is closer to 7.
For $\sqrt{65}$, $8^2=64$ and $9^2 = 81$, and $65$ is closer to 64 so $\sqrt{65}$ is closer to 8.

Step1: Recall the volume formula for a cube

The volume $V$ of a cube is $V = s^3$, where $s$ is the side - length of the cube. Given $V = 2300$, then $s=\sqrt[3]{2300}$.

Step2: Estimate the cube - root

$13^3=13\times13\times13 = 2197$ and $14^3=14\times14\times14=2744$. Since $2300$ is closer to $2197$, $\sqrt[3]{2300}\approx13$.

Answer:

A. False
B. Counter - example: 0 or - 1 (any non - positive integer)

17.