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IceJOKER [234]
3 years ago
13

8x + 6 + 2x = 12 + 4x​

Mathematics
1 answer:
weeeeeb [17]3 years ago
4 0

Answer:

x=1

Step-by-step explanation:

8x+6+2x=12+4x

10x+6=12+4x

     -6   -6

10x=6+4x

-4x      -4x

6x=6

x=1

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Inga can earn $375 per week in a plant store, or she can earn 3% of total sales. How much would Inga have to sell to earn more i
qwelly [4]

Answer:

Inga will have to sell $12,533 to earn more in commission than in salary.

Step-by-step explanation:

As the commission is the percentage of sales amount so, need to calculate the minimum sales value required.

Igna's salary = $375

Commission rate = 3%

Sale to earn more than salary = $376 / 3% = $12,533.33

Igna has to make a minimum sale of $12,533 per week in order to earn more commission than her salary.

8 0
3 years ago
A company makes car batteries and claims 80% of its ABC batteries are good for 70 months or longer. Assume that this claim is tr
vesna_86 [32]

Answer:

78.88% probability that this sample proportion is within 0.05 of the population proportion

Step-by-step explanation:

We need to understand the normal probability distribution and the central limit theorem to solve this question.

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 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.

For proportion p in a sample of size n, we have that \mu = p, s = \sqrt{\frac{\pi(1-\pi)}{n}}

In this question:

p = 0.8, n = 100

So

\mu = 0.8, s = \sqrt{\frac{0.8*0.2}{100}} = 0.04

What is the probability that this sample proportion is within 0.05 of the population proportion.

This is the pvalue of Z when X = 0.8 + 0.05 = 0.85 subtracted by the pvalue of Z when X = 0.8 - 0.05 = 0.75.

X = 0.85

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

By the Central Limit Theorem

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

Z = \frac{0.85 - 0.8}{0.04}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944.

X = 0.75

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

Z = \frac{0.75 - 0.8}{0.04}

Z = -1.25

Z = -1.25 has a pvalue of 0.1056.

0.8944 - 0.1056 = 0.7888

78.88% probability that this sample proportion is within 0.05 of the population proportion

6 0
3 years ago
There are 120 children at a school assembly. 15 are 3rd graders; 45 are 4th graders; and 60 are 5th graders. Each student has en
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Answer:

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Step-by-step explanation:

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