URGENT!! LAW OF SINES WORK

Mathematics

1 answer:

Lynna [10]2 years ago

6 0

Answer:

1. 7.1 cm

2. 10.9 cm

Step-by-step explanation:

1. You know the legs of a right triangle must be shorter than the hypotenuse. The only answer choice shorter than 8 cm is 7.1 cm.

2. By the Law of Sines, ...

AB/AC = sin(ACB)/sin(B)

AB = AC·sin(72°)/sin(38°) = 1.545·AC

The approximate value of AC from problem 1 is sufficient to get you close to the answer.

AB ≈ 7.1×1.545 ≈ 10.9 . . . cm

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eimsori [14]

Answer:

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3 years ago

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$7.50 admission; 20% off

kirill [66]

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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

Orlov [11]

Answer:

95.44% probability that the sample proportion will differ from the population proportion by less than 0.03.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean $\mu = p$ and standard deviation $s = \sqrt{\frac{p(1-p)}{n}}$