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4 years ago

The legs of a right triangle are 12 cm and 16 cm. What is the length of the hypotenuse? 15 cm 17 cm 20 cm 28 cm

2 answers:

7 0

Answer: 20 cm

To solve this, use the Pythagorean Theorem, a² + b² = c², where a and b are the legs of the right triangle, and c is the hypotenuse of the right triangle.
**The Pythagorean Theorem only works for right triangles.**

Substitute in the values.
a² + b² = c²
12² + 16² = c²

Solve for c, the hypotenuse.
12² + 16² = c²
144 + 256 = c²
400 = c²
c = √400
c = 20

crimeas [40]4 years ago

3 0

Answer:

20cm

Step-by-step explanation:

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The shorter leg is??????????

Leto [7]

The shorter leg is

10·SIN(30°) = 5

3 0

3 years ago

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30 What score is necessary to reach

nlexa [21]

Answer:

A score of 150.25 is necessary to reach the 75th percentile.

Step-by-step explanation:

Problems of normal distributions can be 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.

A set of test scores is normally distributed with a mean of 130 and a standard deviation of 30.

This means that $\mu = 130, \sigma = 30$

What score is necessary to reach the 75th percentile?

This is X when Z has a pvalue of 0.75, so X when Z = 0.675.

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

$0.675 = \frac{X - 130}{30}$

$X - 130 = 0.675*30$

$X = 150.25$

A score of 150.25 is necessary to reach the 75th percentile.

7 0

3 years ago

Solve dis attachment and show all work ( I got it all wrong and I want to know how to solve it )

DedPeter [7]

(a) First find the intersections of $y=e^{2x-x^2}$ and $y=2$ :

$2=e^{2x-x^2}\implies \ln2=2x-x^2\implies x=1\pm\sqrt{1-\ln2}$

So the area of $R$ is given by

$\displaystyle\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\left(e^{2x-x^2}-2\right)\,\mathrm dx$

If you're not familiar with the error function $\mathrm{erf}(x)$ , then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.

(b) Find the intersections of the line $y=1$ with $y=e^{2x-x^2}$ .

$1=e^{2x-x^2}\implies 0=2x-x^2\implies x=0,x=2$

So the area of $S$ is given by

$\displaystyle\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}(2-1)\,\mathrm dx+\int_{1+\sqrt{1-\ln2}}^2\left(e^{2x-x^2}-1\right)\,\mathrm dx$
$\displaystyle=2\int_0^{1-\sqrt{1-\ln2}}\left(e^{2x-x^2}-1\right)\,\mathrm dx+\int_{1-\sqrt{1-\ln2}}^{1+\sqrt{1-\ln2}}\mathrm dx$

which is approximately 1.546.

(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve $y=e^{2x-x^2}$ and the line $y=1$ , or $e^{2x-x^2}-1$ . The area of any such circle is $\pi$ times the square of its radius. Since the curve intersects the axis of revolution at $x=0$ and $x=2$ , the volume would be given by

$\displaystyle\pi\int_0^2\left(e^{2x-x^2}-1\right)^2\,\mathrm dx$

5 0

3 years ago

A baker buys 10 pounds of peaches. She buys a total of 25 peaches. Given that 1 lb = 16 oz, what is the average weight, in ounce

creativ13 [48]

Answer:

the average weight of one peach is 6.4 ounces

Step-by-step explanation:

10lb of peaches

16 ounces in a pound

10 x 16 = 160 ounces

divide 160 (ounces) by 25 (Peaches)

= 6.4 ounces per peach

8 0

3 years ago

Select the correct answer. Fredrick manages a band and sings lead vocals. The band charges $700 per concert. Fredrick receives $

Kisachek [45]

Answer:

A. $105

Step-by-step explanation:

Given

total charge= $700 per concert

<u>solution</u>

If Fredrick receives $175 of that money, the balance will be

$700-$175= $525

The balance will be shared by the 5 members

<em>Hence each of them will take</em>

525/5=$105

7 0

3 years ago