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3 years ago

8

pete's pools installs rectangular pools that are all 10 feet wide. the length can vary from 10 feet to 30 feet. the company inst

alled a pool with a perimeter of 76 feet. what was the length of the pool ?

1 answer:

Wittaler [7]3 years ago

3 0

The length is 28 because 76 -10x2 is 56 divided by 2 is 28

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Assume that a policyholder is four times more likely to file exactly two claims as to file exactly three claims. Assume also tha

kykrilka [37]

Answer:

1.3125

Step-by-step explanation:

Given that our random variable $X$ follows a Poisson distribution $P(X=k)=\frac{\lambda^k e^-^p}{k!} \ \ \ \ \ \ \ \ p=\lambda$

Evaluate the formula at $k=2,3:$

$P(X=2)=0.5\lambda^2e^{-\lambda}\\\\P(X=3)=\frac{1}{6}\lambda^2e^{-\lambda}$

#since

$4P(X=2)=P(X=3);\\\\0.5\lambda^2e^{-\lambda}=4\times\frac{1}{6}\lambda^3e^{-\lambda}\\\\0.5\lambda^2=\frac{2}{3}\lambda^3\\\\0.75=\lambda$

The mean and variance of the Poisson distributed random variable is equal to $\lambda$ :

$\mu=\lambda=0.75\\\sigma ^2=\lambda=0.75$

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$\sigma ^2=V(X)=E(X^2)-(E(X))^2=E(X^2)\\\\E(X^2)=\sigma^2+\mu^2=0.75+0.75^2=1.3125$

The expectation is 1.3125

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4 years ago

The angle between the top of a building and a point 80 feet away from the base (on level ground) is 70° . To the nearest foot, h

alekssr [168]

Answer: 220 feet tall

Step-by-step explanation:

1. Draw!

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3 years ago

Read 2 more answers

Find the exact value of cos(sin^-1(-5/13))

son4ous [18]

bearing in mind that the hypotenuse is never negative, since it's just a distance unit, so if an angle has a sine ratio of -(5/13) the negative must be the numerator, namely -5/13.

$\bf cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right] \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{then we can say that}~\hfill }{sin^{-1}\left( -\cfrac{5}{13} \right)\implies \theta }\qquad \qquad \stackrel{\textit{therefore then}~\hfill }{sin(\theta )=\cfrac{\stackrel{opposite}{-5}}{\stackrel{hypotenuse}{13}}}\impliedby \textit{let's find the \underline{adjacent}}$

$\bf \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{13^2-(-5)^2}=a\implies \pm\sqrt{144}=a\implies \pm 12=a \\\\[-0.35em] ~\dotfill\\\\ cos\left[ sin^{-1}\left( -\cfrac{5}{13} \right) \right]\implies cos(\theta )=\cfrac{\stackrel{adjacent}{\pm 12}}{13}$

le's bear in mind that the sine is negative on both the III and IV Quadrants, so both angles are feasible for this sine and therefore, for the III Quadrant we'd have a negative cosine, and for the IV Quadrant we'd have a positive cosine.

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3 years ago

Jason observed a large art sculpture in a local park and wanted to know its height, but the sculpture was much taller than he co

ZanzabumX [31]

The art sculpture was 70 inches aka 5.9feet tall and if we round it well it would be 6feet so that would be its highest piont

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3 years ago

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36 red beads, 49 green and 76 blue beads are to be packed into packets, each containing 3 red, 5 green and 7 blue beads respecti

lakkis [162]

9 packets.

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49 divided by 5 = 9.8
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Maximum packets that can be obtained is 9 packets because only 9 packets with 5 green beads each can be packaged.

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3 years ago