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3 years ago

Solve for z. 12=15(z-1/5)

Mathematics

1 answer:

OLga [1]3 years ago

6 0

Answer:

z = 1 i hope this helps! :)

Step-by-step explanation:

given 12 = 15(z - 1/5)

distribute the 15 to both the z and the - 1/5

12 = 15z - 3

add 3 to both sides

15 = 15z

divide both sides by 15

1 = z

flip the equation around so the variable is on the left

z = 1

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The best answer gets brainliest

faltersainse [42]

Answer:

ok?

Step-by-step explanation:

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2 years ago

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Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

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

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0

3 years ago

To the nearest thousand the population of Texas was estimated to be 24,327,000 in 2008. Describe the actual population that Texa

azamat

To the nearest thousand, population is 24,327,000

that means the population could range between 24,326,500 and 24,327,499

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3 years ago

A square garden has 49 square feet. So the perimeter of the garden must be----feet.

lianna [129]

The side length of a square is the square root of the area:

Side length = √49 = 7 feet.

The perimeter of a square is 4s = 4*7 = 28 feet.

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2 years ago

Read 2 more answers

one month Miguel rented 5 movies and 3 video games for a total of $27. The next month he ordered 2 movies and 6 video games for

34kurt

Answer:

The price of each movie is $2.25

The price of each video games is $5.41

Step-by-step explanation:

Given as :

Miguel rented 5 movies and 3 video games for a total cost = $27

Next day Miguel rented 2 movies and 6 video games for a total cost = $36

Let The cost of each movie = $m

And The cost of each video game = $v

Now, According to question

5 m + 3 v = 27 .....1

2 m + 6 v = 36 ...........2

Now, solving the equation

2 × (5 m + 3 v) - (2 m + 6 v) = 2 × 27 - 36

Or, 10 m + 6 v - 2 m - 6 v = 54 - 36

Or, (10 m - 2 m) + (6 v - 6 v) = 18

Or, 8 m + 0 = 18

∴ m = $\dfrac{18}{8}$ = $\dfrac{9}{4}$

i.e m = $2.25

So, The price of each movie = m = $2.25

Again, put the value of m into eq 2

So, 2 × 2.25 + 6 v = 36

Or, 4.5 + 6 v = 36

Or, 6 v = 36 - 4.5

Or, 6 v = $32.5

∴ v = $\dfrac{32.5}{6}$

i.e v = $5.41

So, The price of each video games = v = $5.41

Hence, The price of each movie is $2.25 and

The price of each video games is $5.41 Answer

7 0

3 years ago