A meal at a restaurant cost $34.50, before tip. You decide to leave the server an 18% tip. What is your total bill?

At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t

grandymaker [24]

Answer:

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

(a2) The probability that temperature increase will be between 20°C and 22°C is 0.133.

(b) The probability that at any point of time the temperature increase is potentially dangerous is 0.467.

(c) The expected value of the temperature increase is 17.5°C.

Step-by-step explanation:

Let X = temperature increase.

The random variable X follows a continuous Uniform distribution, distributed over the range [10°C, 25°C].

The probability density function of X is:

$f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.$

(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 X 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.

7 0

3 years ago

Please help me with this

mrs_skeptik [129]

Answer:

the second one

Step-by-step explanation:

the second one is the right answer

6 0

2 years ago

Read 2 more answers

Small library contains 700 novels. how many ways can You check out three novels

schepotkina [342]

The first book you select can be any one of 700.

. . . For each of those ...

The second book can be any one of the other 699.

. . . For each of those ...

The third book can be any one of the remining 698.

The total number of ways to gather three books from the shelves into your hands is (700 · 699 · 698) = 341,531,400 ways .

BUT ...

When you bring three books to the check-out counter, Marian the Librarian doesn't know in which order you took them down off the shelves. You could have gathered the same three books in (3 · 2 · 1) = 6 different ways.

So, even though there are 341,531,400 ways to gather up three books, there are only (341,531,400 / 6) = 56,921,900 different GROUPS of three books that you can choose to take home.

8 0

3 years ago

Write the standard form of the equation of the line through the given point with the given slope. Through (-2,5), slope =-4

AleksandrR [38]

Answer:

$\huge\boxed{4x+y=-3}$