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2 years ago

Solve the equation. 3x + 2(4x − 6) = 8x + 1 What is the value for x?

Mathematics

2 answers:

Alja [10]2 years ago

5 0

Answer:

$x = \frac{13}{3}$

I hope this helps!

jenyasd209 [6]2 years ago

5 0

Answer:

$x=4\frac{1}{3}$

Step-by-step explanation:

The first thing I would do here is distribute.

If we distribute, our equation is now

$3x+8x-12=8x+1$

Then I want to isolate the variable, combining like terms as I go.

$11x-12=8x+1\\3x=13\\x=\frac{13}{3}$

$\frac{13}{3}$ can then be simplified to $4\frac{1}{3}$ . So,

$x=4\frac{1}{3}$

Hope this helps!

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A pharmacist needs 500 milliliters of a 20% phenobarbital solution but has only 5% and 25% phenobarbital solutions available. Fi

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Let x be ml of 5% soln.

let 500-x be ml of 25% soln.

x*.05=.05x

(500-x)*.25=125-.25x

500*.20=100

.05x+125-.25x=100

-.2x=-25

x=-25/-.2

x=125 ml of 5% soln.

500-x=375 ml of 25% soln.

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2 years ago

Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa

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Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

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 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.

Mean 8.7% and standard deviation 20.2%.

This means that $\mu = 8.7, \sigma = 20.2$

40 years:

This means that $n = 40, s = \frac{20.2}{\sqrt{40}}$

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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