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A worker at a factory earns $12 per hour plus 2.50 for each unit produced that hour. The worker earns a total of $27 in one hour

nevsk [136]

Answer:

The total number of units produced is 6 .

Step-by-step explanation:

Given as :

The earning of worker at the factory = $ 12 per hour + $ 2.50 each unit per hour

The total earning of worker per hour = $ 27

Let The total number of unit produced = x

According to question

The wage worker earn per hour + earning × per unit produced that hour = Total earning of worker per hour

Or, $ 12 per hour + $ 2.50 each unit per hour × x = $ 27

Or, $ 2.50 each unit per hour × x = $ 27 - $ 12

Or, $ 2.50 each unit per hour × x = $ 15

∴ x = $\frac{15}{2.50}$

Or, x = 6

Hence The total number of units produced is 6 . Answer

4 0

3 years ago

Jasmine bought a pennant (triangle) of the favorite baseball team. If the base is 16 inches and height is 24 inches, how much ar

KATRIN_1 [288]

D. 192in^2

This would be a simple area problem with a triangle. REMEMBER THIS EQUATION: a=bh*1/2 (b for base and h for height, these are multiplied together then that answer is halved out.)

So we just need to plug in our values into the equation, so the equation would look like a= (16)*(24)*1/2. 16 times 24 would then give you 384, you could either divide by 2 or multiply by 0.5 to get the next answer, as long as your HALVING the answer.

So we have our bh value so now we can multiply by 1/2 which will give us 384*1/2 which leaves us with 192.

I have also attached a photo of doing a longer(ish) way than this, that also proves that this equation works. Either one will provide you an answer.

6 0

3 years ago

I know the answers but I don't know how to solve it

lutik1710 [3]

You did it right. 1.35 + 7.00 and you have the right answer. is that what you mean?

4 0

3 years ago

I don’t get it. Please help thanks

Likurg_2 [28]

Answer:

$2,410.69

Step-by-step explanation:

$1,950 x 1.15 = $2,242.50 after 15% markup

$2,242.50 x 1.075 = $2,410.68 after the 7.5% sales tax.

or you can do:

$1,950 x 0.15 = $292.5 markup

$1,950 + $292.5 = $2,242.50

$2,242.50 x 0.075 = $168.19 for sales tax

$2,242.50 + $168.19 = $2,410.69 total

5 0

3 years ago

Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob

Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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 of 36 hours and a standard deviation of 5.5 hours.

This means that $\mu = 36, \sigma = 5.5$

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that $n = 9$ . So

$s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333$

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

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

$Z = \frac{38 - 36}{1.8333}$

$Z = 1.09$

$Z = 1.09$ has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

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

$Z = \frac{34.5 - 36}{1.8333}$

$Z = -0.82$

$Z = -0.82$ has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

4 0

3 years ago