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3 years ago

HELP ASAP PLEASE I NEED ANS N SOLUTION

Mathematics

1 answer:

Blababa [14]3 years ago

5 0

Given:

A bowl contains 25 chips numbered 1 to 25.

A chip is drawn randomly from the bowl.

To find:

The probability that it is

a. 9 or 10?

b. even or divisible by 3?

c. divisible by 5 and divisible by 10?

Solution:

a. We have,

Number of total chips = 25

Favorable out comes are either 9 or 10. So,

Number of favorable outcomes = 2

The probability that the selected chip is either 9 or 10 is:

$\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}$

$\text{Probability}=\dfrac{2}{25}$

Therefore, the probability that the selected chip is either 9 or 10 is $\dfrac{2}{25}$ .

b. The numbers that are even from 1 to 25 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

The numbers from 1 to 25 that are divisible by 3 are 3, 6, 9, 12, 15, 18, 21, 24.

The numbers that are either even or divisible by 3 are 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24.

Number of favorable outcomes = 16

The probability that the selected chip is either even or divisible by 3 is:

$\text{Probability}=\dfrac{16}{25}$

Therefore, the probability that the selected chip is either even or divisible by 3 is $\dfrac{16}{25}$ .

c. The numbers from 1 to 25 that are divisible by 5 are 5, 10, 15, 20, 25.

The numbers from 1 to 25 that are divisible by 10 are 10, 20.

The numbers that are divisible by both 5 and 10 are 10 and 20.

Number of favorable outcomes = 2

The probability that the selected chip is divisible by 5 and divisible by 10 is:

$\text{Probability}=\dfrac{2}{25}$

Therefore, the probability that the selected chip is divisible by 5 and divisible by 10 is $\dfrac{2}{25}$ .

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Answer:

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Step-by-step explanation:

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3 years ago

Find the area of each figure. Round to the nearest hundredth where necessary.

Papessa [141]

Answer:

The answer to your question is Triangle's area = 520 in², Square's area = 576 in²

Step-by-step explanation:

Process

1.- Calculate the area of the triangle

-Find the length of the base using the Pythagorean theorem

c² = a² + b²

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b² = c² - a²

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I'm having trouble with #2. I've got it down to the part where it would be the integral of 5cos^3(pheta)/sin(pheta). I'm not sur

Butoxors [25]

$\displaystyle\int\frac{\sqrt{25-x^2}}x\,\mathrm dx$

Setting $x=5\sin\theta$ , you have $\mathrm dx=5\cos\theta\,\mathrm d\theta$ . Then the integral becomes

$\displaystyle\int\frac{\sqrt{25-(5\sin\theta)^2}}{5\sin\theta}5\cos\theta\,\mathrm d\theta$
$\displaystyle\int\sqrt{25-25\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{1-\sin^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

Now, $\sqrt{x^2}=|x|$ in general. But since we want our substitution $x=5\sin\theta$ to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means $\theta=\sin^{-1}\dfrac x5$ , which implies that $\left|\dfrac x5\right|\le1$ , or equivalently that $|\theta|\le\dfrac\pi2$ . Over this domain, $\cos\theta\ge0$ , so $\sqrt{\cos^2\theta}=|\cos\theta|=\cos\theta$ .

Long story short, this allows us to go from

$\displaystyle5\int\sqrt{\cos^2\theta}\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$

to

$\displaystyle5\int\cos\theta\dfrac{\cos\theta}{\sin\theta}\,\mathrm d\theta$
$\displaystyle5\int\dfrac{\cos^2\theta}{\sin\theta}\,\mathrm d\theta$

Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

$\dfrac{\cos^2\theta}{\sin\theta}=\dfrac{1-\sin^2\theta}{\sin\theta}=\csc\theta-\sin\theta$

Then integrate term-by-term to get

$\displaystyle5\left(\int\csc\theta\,\mathrm d\theta-\int\sin\theta\,\mathrm d\theta\right)$
$=-5\ln|\csc\theta+\cot\theta|+\cos\theta+C$

Now undo the substitution to get the antiderivative back in terms of $x$ .

$=-5\ln\left|\csc\left(\sin^{-1}\dfrac x5\right)+\cot\left(\sin^{-1}\dfrac x5\right)\right|+\cos\left(\sin^{-1}\dfrac x5\right)+C$

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to

$=-5\ln\left|\dfrac{5+\sqrt{25-x^2}}x\right|+\sqrt{25-x^2}+C$

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3 years ago

Read 2 more answers

The total of a regular polygon's interior angles is 3420°.

DanielleElmas [232]

Step-by-step explanation:

(n-2)×180=3420

180n-360=3420

180n=3420+360

180n=3780

n=3780/180

n=21

that is, the number of sides is 21

to get the size of each exterior angle=

360/21

=17.14°

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