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4 days ago

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An equilateral triangle ΔLMQ (see picture to the right) is drawn in the interior of square LMNP so that side LM is common. Find

m∠LQP.

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Find a122 of the sequence 5, 8, 11

Svet_ta [12734]

To find a122 in the sequence beginning with 5, 8, 11, we recognize this series is arithmetic.

8 0

2 months ago

Albert Abbasi, VP of Operations at Ingleside International Bank, is evaluating the service level provided to walk-in customers.

babunello [11817]

Answer:

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

Step-by-step explanation:

Prior concepts

A normal distribution is characterized as a "probability distribution that is symmetric around the mean, indicating that data close to the mean are more frequent than those further away".

The Z-score refers to "a statistical measurement that reflects the relationship of a value to the mean of a group, measured in standard deviations".

Let X denote the random variable of interest, and we identify its distribution:

$X \sim N(\mu=15,\sigma=4)$

Also, let $\bar X$ signify the sample mean, whose distribution is:

$\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})$

In this case, $\bar X \sim N(15,\frac{4}{\sqrt{64}})$

Solution to the problem

We seek this probability

$P(13.5$

Applying the Z-score formula to the probability results in:

$P(13.5$

$=P(\frac{13.5-15}{\frac{4}{\sqrt{64}}}$

To determine these probabilities, we can refer to normal distribution tables, use Excel, or a calculator.

$P(-3$

The likelihood that Albert's sample of 64 will have a mean waiting time between 13.5 and 16.5 minutes is 0.9973.

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1 month ago

Which of the following represents the most accurate estimation of 388 - 212?

Zina [12379]

The correct response is 176

7 0

1 month ago

Uniforms are sold in packages of 8. The stores 127 employees will each be given 3 uniforms. How many packages will the store nee

Svet_ta [12734]

First, you would divide 127 by 8 and then multiply the result by three uniforms for each employee.

8 0

2 months ago

Use the geometric definition of the cross product and the properties of the cross product to make the following calculations. (a

tester [12383]

Answer:

Step-by-step explanation:

We understand that

$\vec{i}\times \vec{j}=\vec{k}$

$\vec{j}\times \vec{k}=\vec{i}$

$\vec{k}\times \vec{i}=\vec{j}$

(a) $\left [ \left ( \hat{i}+\hat{j}\right )\times \hat{i}\right ]\times \hat{j}$

$=\left [ \hat{i}\times \hat{i}+\hat{j}\times \hat{i}\right ]\times \hat{j}$

$=\left [ 0-\hat{k}\right ]\times \hat{j}$

$=\hat{i}$

(b) $\left ( \hat{j}+\hat{k}\right )\times \left ( \hat{j}\times \hat{k}\right )$

$=\left ( \hat{j}+\hat{k}\right )\times \left ( \hat{i}\right )$

$=\hat{k}+\hat{j}$

(c) $4\hat{i}\times \left ( \hat{i}+\hat{j}\right )$

$=4\hat{i}\times \hat{i}+4\hat{i}\times \hat{j}$

$=0+4\hat{k}$

(d) $\left ( \hat{k}+\hat{j}\right )\times \left ( \hat{k}-\hat{j}\right )$

$=\hat{k}\times \hat{k}-\hat{k}\times \hat{j}+\hat{j}\times \hat{k}-\hat{j}\times \hat{j}$

$=0+\hat{i}+\hat{i}-0$

$=2\hat{i}$

6 0

3 months ago