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Mashutka [201]
3 years ago
12

Which ordered pair in the form (a, b) is a solution of this equation?

Mathematics
1 answer:
Evgen [1.6K]3 years ago
5 0

3a - 4b = 21


check (-2 , -3)


3(-2) -4(-3) =21


-6 +12  = 21


6 does not = 21  so NO


check (0 , 7)


3(0) -4(7) =21


0-28=21


-28 does not equal 21  so NO


check (-3 , -2)


3(-3) -4(-2) =21


-9 +8  = 21


1 does not = 21  so NO


check (7 , 0)


3(7) -4(0) =21


21  = 21

Choice D

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Suppose the number of children in a household has a binomial distribution with parameters n=12n=12 and p=50p=50%. Find the proba
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Answer:

a) 20.95% probability of a household having 2 or 5 children.

b) 7.29% probability of a household having 3 or fewer children.

c) 19.37% probability of a household having 8 or more children.

d) 19.37% probability of a household having fewer than 5 children.

e) 92.71% probability of a household having more than 3 children.

Step-by-step explanation:

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.

In this problem, we have that:

n = 12, p = 0.5

(a) 2 or 5 children

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

P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161

P(X = 5) = C_{12,5}.(0.5)^{5}.(0.5)^{7} = 0.1934

p = P(X = 2) + P(X = 5) = 0.0161 + 0.1934 = 0.2095

20.95% probability of a household having 2 or 5 children.

(b) 3 or fewer children

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

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

P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002

P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029

P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161

P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537

P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0002 + 0.0029 + 0.0161 + 0.0537 = 0.0729

7.29% probability of a household having 3 or fewer children.

(c) 8 or more children

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)

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

P(X = 8) = C_{12,8}.(0.5)^{8}.(0.5)^{4} = 0.1208

P(X = 9) = C_{12,9}.(0.5)^{9}.(0.5)^{3} = 0.0537

P(X = 10) = C_{12,10}.(0.5)^{10}.(0.5)^{2} = 0.0161

P(X = 11) = C_{12,11}.(0.5)^{11}.(0.5)^{1} = 0.0029

P(X = 12) = C_{12,12}.(0.5)^{12}.(0.5)^{0} = 0.0002

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.1208 + 0.0537 + 0.0161 + 0.0029 + 0.0002 = 0.1937

19.37% probability of a household having 8 or more children.

(d) fewer than 5 children

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

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

P(X = 0) = C_{12,0}.(0.5)^{0}.(0.5)^{12} = 0.0002

P(X = 1) = C_{12,1}.(0.5)^{1}.(0.5)^{11} = 0.0029

P(X = 2) = C_{12,2}.(0.5)^{2}.(0.5)^{10} = 0.0161

P(X = 3) = C_{12,3}.(0.5)^{3}.(0.5)^{9} = 0.0537

P(X = 4) = C_{12,4}.(0.5)^{4}.(0.5)^{8} = 0.1208

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0002 + 0.0029 + 0.0161 + 0.0537 + 0.1208 = 0.1937

19.37% probability of a household having fewer than 5 children.

(e) more than 3 children

Either a household has 3 or fewer children, or it has more than 3. The sum of these probabilities is 100%.

From b)

7.29% probability of a household having 3 or fewer children.

p + 7.29 = 100

p = 92.71

92.71% probability of a household having more than 3 children.

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Answer:

5 1/3

Step-by-step explanation:

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