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2 years ago

Find the difference. Enter your answer in lowest terms in the box below as a

Mathematics

1 answer:

lara [203]2 years ago

7 0

Answer:

76/165

Step-by-step explanation:

The difference of fractions can be found using the formula ...

a/b -c/d = (ad -bc)/(bd)

<h3>Difference</h3>

Using the given values in the formula, we have ...

$\dfrac{8}{11}-\dfrac{4}{15}=\dfrac{8(15)-11(4)}{11\cdot15}=\dfrac{120-44}{165}=\boxed{\dfrac{76}{165}}$

Here, the difference fraction does not need to be reduced. Many calculators and spreadsheets can do this arithmetic for you.

The above formula can also be used for sums of fractions. In that case, the sign changes from minus to plus.

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Answer:

0.9138 = 91.38%

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is defective, or it is not. The probability of an item being defective is independent of other items. 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.

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And p is the probability of X happening.

10 items

This means that $n = 10$

5 percent of the items shipped can be defective.

This means that $p = 0.05$

Probability that a batch that meets the contract requirements will be shipped without further inspection

Probability of 1 or fewer defects.

$P(X \leq 1) = P(X = 0) + P(X = 1)$

In which

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$P(X = 1) = C_{10,1}.(0.05)^{1}.(0.95)^{9} = 0.3151$

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So the answer is:

0.9138 = 91.38%

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Answer:

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