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vfiekz [6]
3 years ago
7

A driver and a passenger are in a car accident. Each of them independently has probability 0.3 of being hospitalized. When a hos

pitalization occurs, the loss is uniformly distributed on [0, 1]. When two hospitalizations occur, the losses are independent. Calculate the expected number of people in the car who are hospitalized, given that the total loss due to hospitalizations from the accident is less than 1.
Mathematics
1 answer:
kompoz [17]3 years ago
5 0

Answer:

0.534

Step-by-step explanation:

p(0 losses) = 0.7² = 0.49

p(1 loss) = 2 x 0.3 x 0.7 = 0.42

p(2 losses) = 0.09

This is a conditional probability problem. If the number of people hospitalized is 0 or 1, then the  total loss will be less than 1. However, if two people are hospitalized, the probability that the  total loss will be less than 1 is 0.5. we need to exclude the 50% x 0.09 chance of a double loss costing more than 1. So

P(Cost < 1)

= 0.49 + 0.42 +0.045

= 0.955

P(0 losses | Cost < 1)

= P(0 losses and Cost < 1) / P(Cost < 1)

= 0.49 / 0.955 = 0.513

P(1 loss | Cost < 1)

= 0.42 / 0.955 = 0.440

P(2 losses | Cost < 1) = 0.045 / 0.955 = 0.047

Now take the expectation:

E[X] = (0)(0.513) + (1)(0.440) + (2)(0.047)

= 0.440 + 0.094

= 0.534

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What is 575% written as a mixed number?
pav-90 [236]

<u><em>Answer:</em></u>

575% as a mixed number is 5\frac{3}{4}

<u><em>Explanation:</em></u>

575% is equivalent to \frac{575}{100} which is equal to 5.75

5.75 = 5 + 0.75

0.75 can be written as \frac{75}{100}. This value can be simplified by dividing both the numerator and the denominator by 25. This would give us \frac{3}{4}

<u>Back to our number:</u>

5.75 = 5 + 0.75 = 5 + \frac{75}{100} = 5 + \frac{3}{4} = 5\frac{3}{4}

Hope this helps :)

4 0
3 years ago
Read 2 more answers
The cost of a pizza with the works" is represented as a function of its
Nina [5.8K]

Answer:

diameter of the pizza = 21.88 centimeters

Step-by-step explanation:

Given:

C = d^2 – 2d + 447

where

C = cost of the pizza

d = diameter of the pizza

If the pizza costs $12.00, then what is a reasonable estimate for the diameter of the pizza?

12 = d^2 – 2d + 447

d^2 - 2d = 447 - 12

d^2 - 2d = 435

d^2 - 2d - 435 = 0

Solve the quadratic equation using formula

a = 1

b = -2

c = -435

d = -b +or- √b^2 - 4ac / 2a

= -(-2) +or- √(-2)^2 - (4)(1)(-435) / 2(1)

= 2 +or- √4 - (-1740) / 2

= 2 +or- √4 + 1740 / 2

= 2 +or- √1744 / 2

= 2 +or- 4√109 / 2

= 2/2 +or- 4√109/2

= 1 +or- 2√109

d = 1 + 2√109 or d = 1 - 2√109

= 1 + 2(10.44) or d = 1 - 2(10.44)

= 1 + 20.88 or d = 1 - 20.88

d = 21.88 or -19.88

diameter of the pizza = 21.88 centimeters

Therefore, the estimated diameter of the pizza can not be negative. So, diameter of the pizza = 21.88 cm

7 0
3 years ago
It takes Dan 32 minutes to complete 2 pages of math homework. At this rate, how many pages does he complete in 200 minutes?
Anna [14]
He can complete about 6 pages of math homework.
you first do 200 divided by 32 and you get 6.25. So therefore Dan can complete 6 pages in 200 minutes.
7 0
3 years ago
Read 2 more answers
Please help ASAP!
g100num [7]
So all you have to do to solve these problems is substitute the y coordinate and the x coordinate into the equation.

So question 1 would be true because when you substitute the numbers in it equals the y value.

Question 2 is (4, -7)

Question 3 is False

Question 4 is true

Question 5 is true

See if you can do the rest!
8 0
3 years ago
5. Given (x + 1) and (x-3) are factors of P(x) = x4-5x³-7x² + cx + d. Determine the values
Iteru [2.4K]

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

<h3>How to determine the missing coefficients of a quartic equation</h3>

A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:

(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0    

- c + d = 1      (1)

3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0    

3 · c + d = 117       (2)

The solution of this system is c = 29 and d = 30.

By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.

To learn more on polynomials: brainly.com/question/11536910

#SPJ1

4 0
2 years ago
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