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2 years ago

Find the exact length of the third side

Mathematics

1 answer:

Mumz [18]2 years ago

5 0

Answer:

Step-by-step explanation:

We know that 13 is the hypotenuse. With this we can use the Pythagorean Theorem to solve this problem.

Let the third side be x.

13^2=12^2+x^2

169=144+x^2

169-144=x^2

25=x^2

x=5

Solved.

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10. simplify the rational expression by rationalizing the denominator.( 1 point ) 4√150/√189x

ddd [48]

Rationalizing the denominator, simply means "getting rid of that pesky root at the bottom", and we do so by simply multiplying it by something to take it out, of course, we multiply the bottom, we have to also multiply the top,

$\bf \cfrac{4\sqrt{150}}{\sqrt{189x}}\cdot \cfrac{\sqrt{189x}}{\sqrt{189x}}\implies \cfrac{4\sqrt{150}\sqrt{189x}}{(\sqrt{189x})^2}\implies \cfrac{4\sqrt{(150)({189x})}}{189x}$

$\bf \cfrac{4\sqrt{28350x}}{189x}\qquad 
\begin{cases}
28350=2\cdot 3\cdot 3\cdot 3\cdot 3\cdot 5\cdot 5\cdot 7\\
\qquad 2\cdot 3^2\cdot 3^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2)^2\cdot 5^2\cdot 7\\
\qquad 2\cdot (3^2\cdot 5)^2\cdot 7\\
\qquad 2\cdot (45)^2\cdot 7\\
\qquad 14\cdot 45^2
\end{cases}\implies \cfrac{4\sqrt{14\cdot 45^2}}{189x}
\\\\\\
\cfrac{4\cdot 45\sqrt{14}}{189}\implies \cfrac{180\sqrt{14}}{189x}\implies \cfrac{20\sqrt{14}}{21x}$

4 0

3 years ago

What is the sum of 7x/(x^2-4) and 2/(x+2)

ioda

Answer:

The answer is 9x-4/(x+2)(x-2)

7 0

2 years ago

Read 2 more answers

What is the effect on the graph of the function f(x) = 2x when f(x) is replaced with f(0.5x)? A) vertical stretching B) vertical

PtichkaEL [24]

<h3><u>Answer:</u></h3>

Option: D

Horizontal stretching.

<h3><u>Step-by-step explanation:</u></h3>

We have to find the effect on the graph of the function f(x)=2x when it is replaced by f(0.5 x).

We know that when a parent function f(x) is replaced by f(kx) then either the graph is stretched horizontally or shrinked horizontally.

if k>1 then the graph is shrinked horizontally.

if k<1 then the graph is stretched horizontally.

Hence here k=0.5<1 so the graph of the function is stretched horizontally.

3 0

3 years ago

Read 2 more answers

The lengths of nails produced in a factory are normally distributed with a mean of 4.84 centimeters and a standard deviation of

Helga [31]

Answer:

Top 3%: 4.934 cm

Bottom 3%: 4.746 cm

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 4.84, \sigma = 0.05$

Top 3%

Value of Z when Z has a pvalue of 1 - 0.03 = 0.97. So X when Z = 1.88.

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

$1.88 = \frac{X - 4.84}{0.05}$

$X - 4.84 = 0.05*1.88$

$X = 4.934$

Bottom 3%

Value of Z when Z has a pvalue of 0.03. So X when Z = -1.88.

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

$-1.88 = \frac{X - 4.84}{0.05}$

$X - 4.84 = 0.05*(-1.88)$

$X = 4.746$

8 0

2 years ago

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made t

solniwko [45]

Answer:

B) Method 2 will increase the standard deviation of the students' scores.

Step-by-step explanation:

Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.

The average score for his students was 43 and the standard deviation of the scores was 5 points.

And now he is considering two different strategies for rescaling the exam results of which:

Method 1 = Add 17 points to everyone's score.

Method 2 = Multiply everyone's score by 1.7 .

And we have to check what will be the impact of these methods on the standard deviation of the students' scores.

For this let us consider a simple example to understand this:

Firstly, Formula for calculating Standard Deviation = $\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}$

Suppose,

X X - Xbar $(X - Xbar)^{2}$

3 3 - 6 = -3 -3 * -3 = 9

5 5 - 6 = -1 -1 * -1 = 1

10 10 - 6 = 4 4 * 4 = 16

<em>Mean of above data, Xbar</em> = $\frac{3+ 5+10}{3}$ = 6

<em>Standard Deviation of data </em>= $\sqrt{\frac{26}{3-1} }$ = 3.6055

Now let us suppose that we multiply each value of above data with 2 so the new data will be:

X X - Xbar $(X - Xbar)^{2}$

3*2 = 6 6 - 12 = -6 -6 * -6 = 36

5*2 = 10 10 - 12 = -2 -2 * -2 = 4

10*2 =20 20 - 12 = 8 8 * 8 = 64

<em>Mean of new data, Xbar </em>= $\frac{6+ 10+20}{3}$ = 12

<em>Standard Deviation of new data</em> = $\sqrt{\frac{104}{3-1} }$ = 7.2111

<em>Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as </em>

3.6055 * 2 = 7.2111

Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.

<em>And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.</em>

8 0

3 years ago