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3 years ago

11

A white-tailed deer is running from a black bear at 20 miles per hour. It is 1/3 miles in front of the bear. The bear is running

at 30 miles per hour. How many minutes will it take the bear to catch the deer? Assume both continue running at a constant pace.

1 answer:

Soloha48 [4]3 years ago

6 0

Answer:

Step-by-step explanation:

d=20t+1/3, b=30t

20t+1/3=30t

10t=1/3

t=1/30 hr

t=(1/30)60=2 min

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(a1) The probability that temperature increase will be less than 20°C is 0.667.

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Step-by-step explanation:

Let <em>X</em> = temperature increase.

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The probability density function of <em>X</em> is:

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(a1)

Compute the probability that temperature increase will be less than 20°C as follows:

$P(X$

Thus, the probability that temperature increase will be less than 20°C is 0.667.

(a2)

Compute the probability that temperature increase will be between 20°C and 22°C as follows:

$P(20$

Thus, the probability that temperature increase will be between 20°C and 22°C is 0.133.

(b)

Compute the probability that at any point of time the temperature increase is potentially dangerous as follows:

$P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467$

Thus, the probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c)

Compute the expected value of the uniform random variable <em>X</em> as follows:

$E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5$

Thus, the expected value of the temperature increase is 17.5°C.

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