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3 years ago

A carousel turns counterclockwise in one degree sections, a total of 280 times , The carousel has turned a total of degrees?

Mathematics

1 answer:

evablogger [386]3 years ago

5 0

Answer:

100800°

Step-by-step explanation:

One degree section is 360°

Turning 280 times will give 280 x 360 = 100800°

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(a) A parachutist lands at a point on the line between the points A and B, and the target is an operation at A. The operation fa

mr Goodwill [35]

Answer:

a) $\frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}$

b) $P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736$

Step-by-step explanation:

Part a

We assume that the parachutist lands at random point in the interval (x=A,y=B) we have a continuous random variable X. And the distribution of X would be uniform $Y\sim Unif(A,B)$ . And the density function would be given by:

$f(x) =\frac{1}{B-A} , A$

And 0 for other case.

The operation fails, if parachutist's distance to A is more than five times as much as her distance to B.

So the point P in the interval (A,B) at which the distance to A is exactly 5 times the distance to B is given by:

$P= A + \frac{5}{6} (B-A)= \frac{6A +5B -5A}{6}=\frac{A+5B}{6}$

And we can find the probability desired like this:

$P(d(P,A) \geq 5 d(P,B))= P(\frac{A+5B}{6} < X< B)$

And from the cumulative distribution function of X ficen by $F(X)\frac{X-A}{B-A}$ we got:

$\frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}$

Part b

For this case we assume that $X\sim Gamma (2,1)$

On this case we assume that $\alpha=2, \beta= 1$

The density function for the Gamma distribution is given by:

$P(X)= \frac{\beta^{\alpha} x^{\alpha-1} e^{-\beta x}}{\gamma(\alpha)}$

And on this case we can find the probability using the complement rule like this:

$P(X>1) = 1-P(X\leq 1)=0.736$

We can solve this problem with the following excel code:

"=1-GAMMA.DIST(1;2;1;TRUE)"

And if we do it by hand we need to do this:

$P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736$

6 0

2 years ago

Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are

Alla [95]

sample 1=1 rock=1,200songs

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3 years ago

The sum of two numbers is 24. One number is four less than the other. Find the numbers.

Alika [10]

Answer:

The correct answer is 10 and 14

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2 years ago

A receipe calls for 3/8 cup of chocolate chips and 1 1/2 cups of walnuts. Tameka wants to double the recipe. How many cups of wa

kirill115 [55]

Answer:

3 cups

Step-by-step explanation:

1 1/2 + 1 1/2 = 3

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2 years ago

Connie is packing for a trip. She has 17 pairs of jeans. If she has room to pack 6 pairs how many ways can she choose which jean

Evgesh-ka [11]

Answer:12,376

Step-by-step explanation:

Given

Connie has 17 Pairs of jeans

She has to choose 6 pairs out of 17

We know, no of ways to pick r items out of n items is $^nC_r$

$\therefore \text{No of ways is =}^{17}C_6\\\\\Rightarrow \dfrac{17!}{(17-6)!6!}=12,376\ \text{ways}$

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2 years ago