if you’re good with set theory for math 30 please help with questions 34, 35, and 36!! real answers only !

34) 15   35) 4, 4, 3   36) 1, 4

Step-by-step explanation:

34)

Let Triangle = T, Circle = C, and Square = S, and Pentagon = P

Top Row:       4T = 8     -->  T = 2

2nd column:  2T + 2C = 10    --> C = 3

2nd row:        S + T + 2C = 12     --> S = 4

1st column:    T + 2S + P = 15       --> P = 5

3rd column:  x = T + C + 2P

                        = 2 + 3 + 2(5)

                        = 15

35)

 Fill in the puzzle as follows:

A = 4, B = 4, C = 3

36)

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 (from left to right):

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!

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

this is the formula: v = the value of investment at the end of the time period

p = the principal amount (the initial amount invested)

r = the annual interest rate

n = the annual frequency of compounding (how many times a year interest is added)

t = the number of years the money is invested

^ means raise to the power of