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3 years ago

Can someone please explain?

Mathematics

1 answer:

geniusboy [140]3 years ago

6 0

This is an isosceles triangle. The angles at the base are congruent (they have the same measures).

Look at the picture.

We know: The sum of the measures of angles in a triangle is equal 180°.

Therefore we have the equation:

$2x-10+2x-10+3x+25=180$ <em>combine like terms</em>

$(2x+2x+3x)+(-10-10+25)=180$

$7x+5=180$ <em>subtract 5 from both sides</em>

$7x=175$ <em>divide both sides by 7</em>

$x=25$

$m\angle A=2x-10\to m\angle A=2(25)-10=50-10=40\\\\m\angle C=m\angle A=40\\\\m\angle B=3x+25\to m\angle B=3(25)+25=75+25=100^o$

<h3>Answer: D. m∠C = 40</h3>

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If we want to compute $f(2+h)$ , we have to substitute every occurrence of $x$ with $2+h$ in the definition of the function:

$f(x)=x^2-11x \implies f(2+h) = (2+h)^2-11(2+h) = 4+4h+h^2-22-11h = h^2-7h-18$

Similarly, computing $f(2)$ means to substitute the input with 2:

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So, we have

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3 years ago

The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed t

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Answer:

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

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So on this case the 90% confidence interval would be given by (10.013;10.147)

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 for the sample

$\mu$ population mean (variable of interest)

$\sigma =0.1$ represent the population standard deviation

n represent the sample size

Solution to the problem

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

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

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=10.08$

Since the Confidence is 0.90 or 90%, the value of $\alpha=0.1$ and $\alpha/2 =0.05$ , and we can use excel, a calculator or a tabel 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):

$10.08-1.64\frac{0.1}{\sqrt{6}}=10.013$

$10.08+1.64\frac{0.1}{\sqrt{6}}=10.147$

So on this case the 90% confidence interval would be given by (10.013;10.147)

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3 years ago

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Answer:

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Step-by-step explanation:

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We know:

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Then, the distance that he would have saved if he travels directly is:

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Answer:

he would have saved:

1.8 miles

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Answer:

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