Question

SAVE ME. Please Answer my Questions Clevers.

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:
A. Prime numbers,
B. Composite numbers,
C. Divisible by three,
D. Square of 2.

Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

Q3. what is the solution set of
9x-4<13x-7 (domain, xez) ?

Q4. if three fourth of a number is one tenths, what is the number?

Q5. which one is the equation of the line passing through the origin and having a slope 4?

A. Y= -0.4x
B. Y= 4x
C. Y= -4x
D. Y= 0.4x

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Answer 1

See below

Explanation:

Q1. if a counting number is selected at random from a set of whole number less than or equal to 20 find the probability of getting:

Counting numbers are Natural numbers:
`\mathbb{N}`

Also, we have Whole numbers. Despite not having an official symbol, I usually denote the set as
`\mathbb{Z}_(\ge 0)`

Whole numbers less than or equal to 20:
`A\leq 20, A \subset \mathbb{Z}_(\ge 0) \\\implies A=\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20\}`

A. Prime numbers

From the set A, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19.

Once we have 21 numbers in total and 8 prime numbers, the probability is:

`$P=(8)/(21) \approx 40\%$`

B. Composite numbers

From the set A, the composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20.

Once we have 21 numbers in total and 11 composite numbers, the probability is:

`$P=(11)/(21) \approx 52\%$`

C. Divisible by three

From the set A, the numbers divisible by three are 3, 6, 9, 12, 15, 18.

Once we have 21 numbers in total and 6 numbers divisible by three, the probability is:

`$P=(6)/(21) \approx 30\%$`

D. Square of 2

From the set A, the numbers square of 2 are 0, 1, 4, 9, 16.

`√(0) =0`

`√(1) =1`

`√(4) =2`

`√(9) =3`

`√(16) =4`

Once we have 21 numbers in total and 5 numbers square of 2 , the probability is:

`$P=(5)/(21) \approx 24\%$`

Q2. The opposite angle of acyclic quadrilaterals is in the ratio of 2:3. Find the degree measure of each opposite angle?

Once they're opposite, they add up to 180º

`2x+3x=180 \implies 5x=180 \implies x=36`

The first angle is 72º

The second angle is 108º

Q3. what is the solution set of 9x-4<13x-7 (domain, x e z) ?

`x \in \mathbb{Z}\\`

`$x>(3)/(4) $`

`$x\in \left((3)/(4),\infty \right)$`

Q4. if three fourth of a number is one tenths, what is the number?

`$(3)/(4) x =(1)/(10) \implies 3x=(4)/(10) \implies \boxed{x = (2)/(15)} $`

Q5. which one is the equation of the line passing through the origin and having a slope 4?

`y=mx+b`

`m: \text{slope}`

`b: \text{y-intercept}`

B. Y= 4x