Help Please ~ 15 points

Rational vs Irrational

Alegbra 1

145.25 - rational irrational

^2√64 - rational irrational

-22 - rational irrational

0 - rational irrational

- rational irrational

√121 - rational irrational

0.6⁻ - rational irrational

The correct answer is all are rationals.

Step-by-step explanation:

Numbers that cannot be written as fraction of integers are irrationals.

145.25 is rational as it can be expressed as a fraction.

^2√64 is rational as this √64 is equal to 8.

-22 is a rational as integers are a subset of rationals only.

0 is a rational number.

√121 is rational as the value of √121 is 11 and 11 is rational.

0.6⁻ is rational as this can be expressed as fraction .

Answers:  36) 1 & 4      37) 16       38) 38     39) 16

Step-by-step explanation:

Notes:

U = {x | 3 ≤ x < 14, x ∈ N}

means that everything within the rectangular box (including the circles) contains the Natural Numbers of 3 through 14, including 3 but excluding 14.

R = {x | 5 ≤ x ≤ 8, x ∈ N}

means that everything within the circle of R (including the intersection with T) contains the Natural Numbers of 5 through 8, including 5 and 8.

T = {4, 7, 10, 13}

means that everything within the circle of T (including the intersection with R) contains 4, 7, 10, & 13.

Filling in the Venn Diagram:

R (only) contains 5, 6, 8

R∩T (the middle section of R and T) contains 7

T (only) contains 4, 10, 13

outside the circles but inside the rectangle (usually written on the lower left corner) is 3, 9, 11, 12

Statements:

1) R ∩ T = {7}

means the intersection of R and T (the middle circle) contains 7 and nothing else.  

Refer to your Venn Diagram. This statement is TRUE!

2) n(R ∪ T)' = 6

means the QUANTITY of numbers NOT in both R & T is 6.

The numbers that are not in either R or T are: 3, 9, 11, 12.  

That results in 4 numbers (not 6). This statement is False.

3) n(R' ∩ T) = 2

means the QUANTITY of numbers that are NOT in R but are in T is 2.

The numbers that are not in R but are in T are: 4, 10, 13.  

That results in 3 numbers (not 2). This statement is False.

4) n(R ∩ T') = 3

means the QUANTITY of numbers that are in R but NOT in T is 3.

The numbers that are in R but NOT in T are: 5, 6, 8.  

That results in 3 numbers. This statement is True!

Filling in the 2nd Venn Diagram:

A = 11; middle section = 13; B = 14, outside of circles = 2

37) (A') means NOT in A: 40 - 24 = 16

38) (A ∪ B) means all of the numbers in both A and B: 24 + 27 - 13 = 38

39) (A' ∪ B) means NOT in A and includes all in B: 40 - 24 = 16