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2 years ago

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Mathematics

1 answer:

vladimir1956 [14]2 years ago

5 0

Answer:

Inequality: 0.08x + 2300 ≥ 2800

Liz needs to sell products of $6250 at least.

Step-by-step explanation:

Given that:

Per month salary of Liz = $2300

Commission = 8% = $\frac{8}{100}}$ = 0.08

Amount Liz wants to earn = $2800

Let,

x be the amount of sales.

0.08x + 2300 ≥ 2800

0.08x ≥ 2800 - 2300

0.08x ≥ 500

Dividing both sides by 0.08

$\frac{0.08x}{0.08}\geq \frac{500}{0.08}\\x\geq 6250$

Hence,

Liz needs to sell products of $6250 at least.

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Answer:

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Raise n to the 6th power, then add 5 to the result

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3 years ago

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

Lesechka [4]

Answer:

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=54$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=21$ represent the sample standard deviation

n=16 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.90 or 90%, the value of $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that $z_{\alpha/2}=1.64$

Now we have everything in order to replace into formula (1):

$54-1.64\frac{21}{\sqrt{16}}=45.39$

$54 +1.64\frac{21}{\sqrt{16}}=62.61$

So on this case the 90% confidence interval would be given by (45.39;62.61)

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3 years ago

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2 years ago

The value of a car decreases about 7% percent each year after it is manufactured.The 2017 Honda Civic costs $19,540

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Answer: a) , where 'A' is the value of car after 't' years.

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Step-by-step explanation:

Given: A new car that sells for $21,000 depreciates (decreases in value) 16% each year.

Then a function that models the value of the car will be

, where 'P' is the selling price of car, 'r' is the rate of depreciation in decimal, 't' is the time in years and 'A' is the value of car after 't' years.

Thus after substituting given value, the function becomes

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Hence the value of car after 3 years=$12446.784

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3 years ago