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3 years ago

I NEED HELP PLS I WILL MARK BRAINLIEST

Mathematics

1 answer:

ANEK [815]3 years ago

8 0

Answer:

$\approx 11.2\:\mathrm{in}$

Step-by-step explanation:

The swing of the tip of pendulum is creating an arc. The question is actually asking for the length of this arc. The length of an arc is given by $2r\pi\cdot \frac{\theta}{360}$ , where $r$ is the radius of the circle and $\theta$ is the angle of the arc.

In this problem, we're given:

$\theta = 40^{\circ},\\r=16$

Substituting given values, we get:

$2\cdot 16\cdot \pi \cdot \frac{40}{360}=32\pi\cdot \frac{1}{9}\approx \boxed{11.2\:\mathrm{in}}$

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For each of the following binomial random variables, specify n and p. (a) A fair die is rolled 50 times. X = number of times a 5

Keith_Richards [23]

Answer:

a) $n = 50, p = \frac{1}{6}$

b) $n = 16, p = \frac{1}{100}$

c) $n = 26, p = 0.25, \mu = 6.5$

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $p$ is the probability of X happening.

(a) A fair die is rolled 50 times. X = number of times a 5 is rolled

The die is rolled 50 times, so $n = 50$ .

Each roll can have 6 outcomes. So the probability that 5 is rolled is $p = \frac{1}{6}$

(b) A company puts a game card in each box of cereal and 1/100 of them are winners. You buy sixteen boxes of cereal, and X = number of times you win.

You buy 16 boxes of cereal, so $n = 16$ .