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3 years ago

Given: ∆ABC, m∠C = 90° m∠BAC = 2m∠ABC BC = 24, AL −∠ bisector Find: AL

1 answer:

6 0

The answer is that AL is equal to 16.

Given that in triangle ABC, m∠C=90,
it means m∠A +∠B= m∠BAC + m∠ABC = 90
m∠ABC = 90 - m∠BAC
Also given that;m∠BAC = 2m∠ABC
So,
m∠BAC = 2(90 - m∠BAC) = 180 - 2m∠BAC
m∠BAC +2m∠BAC = 180
3m∠BAC = 180
m∠BAC=180/3 = 60
m∠ABC = 60/3 = 30
thus,ΔBAC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:BC=1:√3, AC=BC/√3BC=24, So,
AC=24/√3=8√3AL bisects angle A =>m∠LAC=30
ΔALC is a 30-60-90 right triangle, in which the ratio of the side lengths is 1:√3:2AC:AL=√3:2AL=2AC/√3=2x8√3/√3=16

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Suppose that the walking step lengths of adult males are normally distributed with a mean of 2.5 feet and a standard deviation o

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Answer:

0% probability that the mean of the sample taken is less than 2.2 feet.

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 normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes 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.

Mean of 2.5 feet and a standard deviation of 0.2 feet.

This means that $\mu = 2.5, \sigma = 0.2$

Sample of 41

This means that $n = 41, s = \frac{0.2}{\sqrt{41}}$

Find the probability that the mean of the sample taken is less than 2.2 feet.

This is the p-value of Z when X = 2.2 So

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

By the Central Limit Theorem

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

$Z = \frac{2.2 - 2.5}{\frac{0.2}{\sqrt{41}}}$

$Z = -9.6$

$Z = -9.6$ has a p-value of 0.

0% probability that the mean of the sample taken is less than 2.2 feet.

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3 years ago

PLEASE HELP ASAP!!! PLEASE ALSO GIVE EXPLANATION WITH EQUATION AND WORDS!!

tia_tia [17]

Using proportions, it is found that the two cities are 27.5 miles apart.

<h3>What is a proportion?</h3>

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the given scale, we have that <u>each inch of distance represents 10 miles</u>. Hence the distance in miles for a distance of 2 and 3/4 miles = 2.75 miles is given by:

D = 10 x 2.75 = 27.5 miles.

Hence, the two cities are 27.5 miles apart.

More can be learned about proportions at brainly.com/question/24372153

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1 year ago

A real estate sales agent receives a salary of $250 per week plus a commission of 2% of sales.Write an equation that gives the w

lisabon 2012 [21]

The equation y=0.02x+250 gives the weekly income y in terms of sales x.

Step-by-step explanation:

Given,

Weekly salary of real estate agent = $250