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3 years ago

Can someone please check if this is correct?

Mathematics

1 answer:

Solnce55 [7]3 years ago

7 0

Answer:

Just two corrections! See attached image.

Step-by-step explanation:

The product of 8 and b taken <u>from</u> 10 means begin with 10 and subtract 8b from it.

8 times the difference of 10 and b means find 10 - b first, <u>then</u> multiply by 8.

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Increase the number 120 by 70%

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Answer:

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

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

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

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".

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

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

And for this case the 95% confidence interval is given by (2.13; 2.37)

We have a point of estimate for the sample mean with this formula:

$\bar X = \frac{Upper+ Lower}{2}= \frac{3.37+2.13}{2}= 2.75$

And for the margin of error we have the following estimation:

$ME= \frac{Upper -Lower}{2}= \frac{3.37-2.13}{2}= 0.62$

5 0

3 years ago

What is the factored form of y=x^3+3x^2-x-3 and what the zeros

PSYCHO15rus [73]

y = x³ + 3x² - x - 3
0 = x³ + 3x² - x - 3
0 = x²(x) + x²(3) - 1(x) - 1(3)
0 = x²(x + 3) - 1(x + 3)
0 = (x² - 1)(x + 3)
0 = (x² + x - x - 1)(x + 3)
0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
0 = (x(x + 1) - 1(x + 1))(x + 3)
0 = (x - 1)(x + 1)(x + 3)
0 = x - 1 or 0 = x + 1 or 0 = x + 3
+ 1 + 1 - 1 - 1 - 3 - 3
1 = x or -1 = x or -3 = x

Solution Set: {-3, -1, 1}

3 0

3 years ago