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2 years ago

10

The circle graph shows how a family budgets its annual income. If the total annual income is 120,000, what amount is budgeted fo

r Clothing?

1 answer:

Bess [88]2 years ago

8 0

Answer:

$18000

Step-by-step explanation:

15% * 120000 = 18000, simply multiply the percentage and the total to get the answer.

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3 years ago

Complete the square for the expression, then factor the trinomial.

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Answer:

Completing the square we get: $(x-2)^2-(2)^2$

and factoring the term we get: $x(x-4)$

Step-by-step explanation:

We need to complete the square for the expression $x^2-4x$

For completing the square the expression would be of form $a^2+2ab+b^2=(a+b)^2$

For given expression we have to add (2)^2 and subtract to make it complete the square.

$x^2-2(x)(2)+(2)^2-(2)^2\\(x-2)^2-(2)^2$

Now, we have to factor the polynomial using formula $(a)^2-(b)^2=(a-b)(a+b)$

So, $(x-2)^2-(2)^2\\=(x-2-2)(x-2+2)\\=(x-4)(x-0)\\=x(x-4)$

Completing the square we get: $(x-2)^2-(2)^2$

and factoring the term we get: $x(x-4)$

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3 years ago

A 500 cm piece of wire with a radius of 0.2 cm has a resistance of 0.025 ohm. Find an equation that relates these variables.

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Step-by-step explanation:

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3 years ago

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth wh

nirvana33 [79]

Answer:

47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth

Step-by-step explanation:

For each individual, there are only two possible outcomes. Either they cover their mouth when sneezing, or they do not. The probability of an individual covering their mouth when sneezing is independent of other individuals. 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.

According to a study done by Otago University, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.

This means that $p = 0.267$

What is the probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth

10 individuals, so n = 10.

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

In which

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

$P(X = 0) = C_{10,0}.(0.267)^{0}.(0.733)^{10} = 0.0448$

$P(X = 1) = C_{10,1}.(0.267)^{1}.(0.733)^{9} = 0.1631$

$P(X = 2) = C_{10,2}.(0.267)^{2}.(0.733)^{8} = 0.2673$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0448 + 0.1631 + 0.2673 = 0.4752$

47.52% probability that among 10 randomly observed individuals fewer than 3 do not cover their mouth

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3 years ago