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4 years ago

HELP ME! NEW AND WILL MARK BRAINLIEST!!!

Mathematics

1 answer:

vredina [299]4 years ago

6 0

The present age of the mother is 30 years.

<u>Step-by-step explanation</u>:

Step 1 :

At present,

Age of Jane = x
Age of Billy = 5x
Age of mother = 3(5x) = 15x

Step 3 :

After 2 years,

Age of Jane = x+2
Age of mother = 8 times as Jane = 8(x+2)

Step 3 :

Age of mother at present + 2 years = Age of mother after 2 years

⇒ 15x + 2 = 8(x+2)

⇒ 15x + 2 = 8x + 16

⇒ 7x = 14

⇒ x = 2

Step 4 :

Substitute x=2,

Age of mother at present = 15x = 30 years.

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Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 12 young adul

ddd [48]

Answer:

a) 0.194 = 19.4% probability that more than 7 preferred McDonald's

b) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

c) 0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

Step-by-step explanation:

For each young adult, there are only two possible outcomes. Either they prefer McDonalds, or they prefer burger king. The probability of an adult prefering McDonalds is independent from other adults. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

50% of all young adults prefer McDonald's to Burger King when asked to state a preference.

This means that $p = 0.5$

12 young adults were randomly selected

This means that $n = 12$

(a) What is the probability that more than 7 preferred McDonald's?

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.121$

$P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.054$

$P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.016$

$P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.003$

$P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.000$

$P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.121 + 0.054 + 0.016 + 0.003 + 0.000 = 0.194$

0.194 = 19.4% probability that more than 7 preferred McDonald's

(b) What is the probability that between 3 and 7 (inclusive) preferred McDonald's?

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.054$

$P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.121$

$P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.193$

$P(X = 6) = C_{12,6}.(0.5)^{6}.(0.5)^{6} = 0.226$

$P(X = 7) = C_{12,7}.(0.5)^{7}.(0.5)^{5} = 0.193$

$P(3 \leq X \leq 7) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) = 0.054 + 0.121 + 0.193 + 0.226 + 0.193 = 0.787$

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred McDonald's

(c) What is the probability that between 3 and 7 (inclusive) preferred Burger King?

Since $p = 1-p = 0.5$ , this is the same as b) above.

0.787 = 78.7% probability that between 3 and 7 (inclusive) preferred Burger King

7 0

3 years ago

The area of a rectangle in 24 square units. A diagonal drawn from one corner to another divides the rectangle into two right tri

Natasha2012 [34]

Hello from MrBillDoesMath!

Answer:

Discussion:

The two triangles shown are congruent by the SAS postulate so the area of a single triangle is one-half that of the rectangle. That is,

Area = (1/2) * 24 = 12

Thank you,

MrB

8 0

4 years ago

Read 2 more answers

A rectangular prism has a length of 9 inches and a width of 8 inches. The lateral area is 170 square inches. What is the height

evablogger [386]

Answer:

The height of the prism is 5 inches

Step-by-step explanation:

The rule of the lateral area of the rectangular prism is

L.A = 2(L + W) × H, where

L is the length of the base of the prism

W is the width of the base of the prism

H is the height of the prism

∵ A rectangular prism has a length of 9 inches and a width of 8 inches

∴ L = 9 inches

∴ W = 8 inches

∵ The lateral area of it is 170 square inches

∴ L.A = 170 square inches

→ Substitute them in the rule above to find the height of the prism

∵ 170 = 2(9 + 8) × H

∴ 170 = 2(17) × 5

∴ 170 = 34 × H

→ Divide both sides by 34 to find H

∴ 5 = H

∴ The height of the prism is 5 inches.

3 0

3 years ago

Order each model from greatest to least 5/6 7/8 2/3

Jlenok [28]

2,3,5,6,7,8 IM sorry if its not the answer u were asking for

8 0

4 years ago

Please help me it's urgent!

Crank

Answer:

y = 2x-5

y=-x+4

Step-by-step explanation:

Just need to solve the:

x+y=4

y-2x=-5

And we have:

x=3

y=1

Then replace x and y into the answer to find the correct one

7 0

3 years ago