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2 years ago

Can someone help me out with this?

Mathematics

1 answer:

dexar [7]2 years ago

4 0

Answer:

-7.5x -12.5, x < -1
7.5x +2.5, x ≥ -1

Step-by-step explanation:

The absolute value function changes slope at its vertex. Here, that vertex is translated to x = -1. To the left of that point, the function is equivalent to one that negates its argument:

|x| = -x . . . for x < 0

|x| = x . . . for x ≥ 0

y = -7.5(x +1) -5 = -7.5x -12.5

y = 7.5(x +1) -5 = 7.5x +2.5

This means we can write the piecewise function as ...

$y=\begin{cases}-7.5x-12.5,&\text{if }x$

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Need help

aleksandr82 [10.1K]

Using the normal distribution, the probabilities are given as follows:

a. 0.4602 = 46.02%.

b. 0.281 = 28.1%.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

The parameters are given as follows:

$\mu = 959, \sigma = 263, n = 37, s = \frac{263}{\sqrt{37}} = 43.24$

Item a:

The probability is <u>one subtracted by the p-value of Z when X = 984</u>, hence:

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

$Z = \frac{984 - 959}{263}$

Z = 0.1

Z = 0.1 has a p-value of 0.5398.

1 - 0.5398 = 0.4602.

Item b:

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

By the Central Limit Theorem:

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

$Z = \frac{984 - 959}{43.24}$

Z = 0.58

Z = 0.58 has a p-value of 0.7190.

1 - 0.719 = 0.281.

More can be learned about the normal distribution at brainly.com/question/4079902

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8 0

2 years ago

Juan y Andrés son adultos mayores y maratonistas. Hoy participaron en la maratón internacional de los Andes.El locutor que cubre

Ira Lisetskai [31]

Answer:

3 hours 8 seconds

Step-by-step explanation:

Juan and Andrés are older adults and marathoners. Today they participated in the international marathon of the Andes. The announcer who covers this sporting event reported that Juan had finished the race with a time of 3¾ hours. Tijuanito the route in ⅔ of hours more than Andrés, how long did Andrés finish the marathon ?.

It is given that,

Juan had finished the race with a time of 3¾ hours.

He takes ⅔ of hours more than Andrés.

We need to find how long did Andrés finish the marathon.

Time taken by Juan = $\dfrac{15}{4}$ hours