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Ymorist [56]
3 years ago
10

For a group of 100 people, compute(a) the expected number of days of the year that are birthdays of exactly 3 people.(b) the exp

ected number of distinct birthdays.
Mathematics
1 answer:
Scilla [17]3 years ago
4 0

Answer:

Step-by-step explanation:

Leaving leap years, a year contains 365 days.

For a group of 100 people, each person is independent of the other and probability of any day being his birthday has a chance of

\frac{1}{365}

a) Probability that  exactly 3 people have same birthday = \frac{1}{365^3}

Each day is independent of the other

And hence no of days having exactly 3 persons birthday out of 100 persons is binomial with n = 365 and p = \frac{1}{365^3}

Expected value of days = np = \frac{1}{365^2}

b) Distinct birthdays is binomail with p =1/365 and n = 365

Hence

expected value = np =1

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Persons taking a​ 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a
mihalych1998 [28]

Answer:

y = 4.125x + 496.25

Step-by-step explanation:

Set the data up as points. Then deal with the points.

Givens

(30,620)

(70,785)

y2 = 785

y1 = 620

x2 = 70

x1 = 30

Formula

Slope = (y2 - y1) / (x2 - x1)

Solution

Slope = (785 - 620)/(70 - 30)

Slope = 165 / 40

Slope = 4.125

===================

Now you need the y intercept. Either one of the two given points will give you that.

y = 620

x = 30

m = 4.125

y = mx + b

620 = 4.125*30 + b

620 = 123.75 + b

620 - 123.75 + b

b = 496.25

5 0
3 years ago
Write a expression for j less than 113
kiruha [24]
So you just need to use the crocodile signs < or >
As j is less than 113 we put j on the smaller side and 113 on the bigger side to make:
j<113
4 0
3 years ago
Solve equation for 5x-14=8x+4
creativ13 [48]
My answer-

Simplifying 5x + -14 = 8x + 4
 
Reorder the terms: -14 + 5x = 8x + 4 Reorder the terms: -14 + 5x = 4 + 8x
 
Solving -14 + 5x = 4 + 8x Solving for variable 'x'.


Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. -14 + 5x + -8x = 4 + 8x + -8x

Combine like terms: 5x + -8x = -3x -14 + -3x = 4 + 8x + -8x

Combine like terms: 8x + -8x = 0 -14 + -3x = 4 + 0 -14 + -3x = 4 Add '14' to

 each side of the equation. -14 + 14 + -3x = 4 + 14

Combine like terms: -14 + 14 = 0 0 + -3x = 4 + 14 -3x = 4 + 14

 Combine like terms: 4 + 14 = 18 -3x = 18 <span>

Divide each side by '-3'. x = -6

Simplifying x = -6


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6 0
3 years ago
Read 2 more answers
Solve 3x-4=√(2x^2-2x+2)
DiKsa [7]

Answer:

Step-by-step explanation:

Begin the solution by squaring both sides of the given equation.  We get:

(3x - 4)^2 = 2x^2 - 2x + 2, or:

9x^2 - 24x + 16 = 2x ^2 - 2x + 2

Combining like terms results in:

7x^2 - 22x + 14 = 0

and the coefficients are a = 7, b = -22, c = 14, so that the discriminant of the quadratic formula, b^2 - 4ac becomes (-22)^2 - 4(7)(14) = 92

According to the quadratic formula, the solutions are

       -b ± √discriminant           -(-22) ± √92             22 ± √92

x = ------------------------------- = ----------------------- = ------------------------

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8 0
3 years ago
The product of twice a and b
Harman [31]
The product to your question is 2a+b
7 0
3 years ago
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