Triangle ABC, with angles and lengths as marked, is shown below.

Mathematics

1 answer:

zalisa [80]3 years ago

3 0

B. BC

he determined the measure for BC as Tan belongs to the bigger side of the rriangle.

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An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th

anastassius [24]

Answer:

0.288

Step-by-step explanation:

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

Normal probability distribution

Problems of normally distributed samples are solved using 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.

In this question, we have that:

$\mu = 17.48, \sigma = 3.25, n = 10, s = \frac{3.25}{\sqrt{10}} = 1.027740$

Find the probability that the mean printing speed of the sample is greater than 18.06 ppm.

This is 1 subtracted by the pvalue of Z when X = 18.06. So

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

By the Central Limit Theorem

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

$Z = \frac{18.06 - 17.48}{1.027740}$

$Z = 0.56$

$Z = 0.56$ has a pvalue of 0.712

1 - 0.712 = 0.288

The answer is 0.288

7 0

3 years ago

If f and g are functions of time, and at time t = 3, f equals 8 and is rising at a rate of 2 units per second, and g equals 3 an

Sidana [21]

It gives you a few values. The values of f(t) and g(t) when time t=3, and
the values of the rates of change (first derivative) for both at the same time t=3.

f(3) = 8 unit
f ' (3) = 2 unit/s
g(3) = 3 unit
g ' (3) = 8 unit/s

--and also a value of the ratio of the two functions at t=3
$\frac{f(3)}{g(3)} = \frac{8}{3}$