Camry is a popular car manufactured by Japanese Car manufacturer, Toyota. Being one of the best selling cars in USA, all of the

Answer:

(a1) The chance that the temperature rises by less than 20°C is 0.667.

(a2) The probability of the temperature increase falling between 20°C and 22°C is 0.133.

(b) The likelihood that the temperature increase could be hazardous at any moment is 0.467.

(c) The anticipated value of the temperature rise is 17.5°C.

Step-by-step explanation:

Let X denote the temperature increase.

The random variable X is distributed uniformly over the interval [10°C, 25°C].

The probability density function for X is shown here:

(a1)

The probability of the temperature increase being under 20°C can be calculated as follows:

Consequently, the chance that the temperature increase will be below 20°C is 0.667.

(a2)

The probability of the temperature rise being in the range from 20°C to 22°C is computed as follows:

This leads to the probability of the temperature increase being between 20°C and 22°C being 0.133.

(b)

To find the probability that the increase in temperature could be dangerous, we calculate:

This results in a probability of 0.467 that the temperature rise is potentially dangerous at any time.

(c)

The expected value of the uniform random variable X is determined as follows:

The expected value for the temperature increase computes to 17.5°C.

Answer: the boy won 10 games

Step-by-step explanation:

Let's denote B for the games won by the boy, and F for the games the father won.

We know that there are a total of 26 games:

B + F = 26.

For each game the boy wins, he gains 8 cents, while for each game lost to his father, he loses 5 cents. Since at the conclusion of the 26 games his total earnings net to zero, we have:

B*8 + F*(-5) = 0.

Now we form a system of equations:

B + F = 26

8*B - 5*F = 0.

Our first move is to isolate one variable. We'll start by expressing F in terms of B using the first equation:

B + F = 26

F = 26 - B.

Now substituting this into the second equation gives us:

8*B - 5*F = 0

8*B - 5*(26 - B) = 0

8*B + 5*B - 5*26 = 0

13*B = 5*26

B = 5*26/13 = 5*2 = 10

Thus, the boy emerged victorious in 10 games (the father won the remaining 16 games).