birthdays of 10 members of a club are assumed to be independently and uniformly distributed over the twelve months of the year. let z be the number of months in which at least one member has a birthday. find e(z).

Answers

Answer 1

E(z),the expected value of z in which at least one member has a birthday in 12 months is (11/12)^10

Define the random variable Zi’s as

[tex]Z_{i}[/tex]= 1 : if no member of the club has a birthday in the month

   = 0: otherwise   for, i =1,2, ......,12 .

Now, we have,

= P ([tex]Z_{i}[/tex] =1) .

=p( no member of the club has a birthday in month i).

= p, say.

Now, there are a total of 10 members in the club and their birthdays are assumed to be independently and uniformly distributed over the 12 months of the year. So, there are 12 possible choices of months for each of the 10 members for their birthday. Thus, the total no. of exhaustive mutually exclusive and equally likely no. of ways of birthdays 12^10.

Again, if no member of the club has a birthday in month 'i'; then, all of their birthdays should be on the remaining (12 - 1) = 11 months of the year. So, there are possible choices of birthday months for each of the 10 members of the club. So, the no. of cases for the event (Zi=1) is 11^10.

So, p([tex]Z_{i}[/tex]=1) = Favorable no. of cases for Zi=1) / Total no. of all possible cases

= 11^10 / 12^10

By the classical definition of probability.

= (11/12)^10

p([tex]Z_{i}[/tex] = 1) = (11/12)^10

E(Zi).= (11/12)^10

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Related Questions

Without doing any calculations, compare Expression A to Expression B.

A (34 + 25) ÷ 14

B 34 + 25

Answers

Answer:

A < B

Step-by-step explanation:

well lets see, they are both adding 34 and 25

But in a, they are dividing, and because dividing usually makes the number smaller, B is larger

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Expression A is less than expression B

Step-by-step explanation: Connexus  

Can someone help me with this. Will Mark brainliest. Need answer and explaination/work. Thank you.

Answers

Answer:

Yes, quadrilateral MATH is a rectangle.

Step-by-step explanation:

If you plot the coordinates onto a graph, you will get a rectangle. You can determine it is a rectangle because there are four right angles, and two adjacent sides that are equal in length.

M (-4,-1)

A (-3,2)

T (3,0)

H (2,-3)

Josea went out to dinner at an Indian restaurant. The
total bill was $38. She wanted to leave a 15% tip.
If you use the idea of scaling to find the tip amount,
what would she need to multiply by?

Answers

She will give 43.70




H

Danielle has to walk 2 miles to reach a hidden temple. She has walked 1 1/4 miles, how many more miles does Danielle need to walk to reach the hidden temple.

Answers

Answer:

[tex]\dfrac{3}{4}\ miles[/tex]

Step-by-step explanation:

Total distance to a temple = 2 miles

She has walked 1 1/4 miles or 5/4 miles

More miles to reach the hidden temple = total distance - walked distance

[tex]=2-\dfrac{5}{4}\\\\=\dfrac{8-5}{4}\\\\=\dfrac{3}{4}[/tex]

So, she has to travel [tex]\dfrac{3}{4}[/tex] miles to reach the hidden temple.

What best describes how many real number solutions the equation has?

Answers

Answer:

zero, because the discriminant is negative

Step-by-step explanation:

By writing the quadratic formula, we have the discriminant written in the root as;

b^2-4ac

Now, given the expression, we can see that the discriminant here is -19

What this mean is that we have a negative discriminant

Hence, we can conclude that the roots are complex and as such, none of the roots are real

Simplify the following equation

Answers

Answer:

3x - 2

Step-by-step explanation:

Answer:

3x−2

Heart if this helped!

A population of 120 beetles increases at an annual rate of 30%. How many beetles will there be in 16 years? Write an expression to represent the equivalent monthly population increase rate.

Answers

Answer:

Expression: [tex]120(1.3)^{16}[/tex]

Beetles after 16 years: 7984 beetles

Step-by-step explanation:

Since the population increases 30% annually every year on the population size of that year, then we need to use a compound interest formula which would be the following

A = P (1 + r/n) (nt)

A = the future amount

P = the initial amount

r = the annual increase rate (decimal)

n = the number of times that interest/increase is compounded per unit t

t = the number of years

Using the values in the question the expression for this scenario would be the following

120(1 + (0.30 / 1))^(1*16)

[tex]120(1.3)^{16}[/tex]

7984.99

The senior classes at Portland High School and Biddeford High School planned separate
trips to New York City. The senior class at Portland High School rented and filled 1 van
and 6 buses with 372 students. Biddeford High School rented and filled 4 vans and 12
buses with 780 students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry?

Answers

I believe it would be 47

A person paid by the hour works 22 hours a week and makes $459. How much would they make if they work 39 hours?

Answers

Answer:

813.681818182

(That's the exact number, but you can circle it to 813.7 )

Step-by-step explanation:

459%22=20.8636363636

20.8636363636 x 39= 813.681818182

I need help FAST pleaseeeee

Answers

Answer:

20 i think

Step-by-step explanation:

HELP!! 4 questions !!! easy points!! 25 points!! please answer quick!

Answers

Step-by-step explanation:

(i) From the graph value of x varies -3 to 3 i.e.

[tex]-3\leq x\leq 3[/tex]

and domain in the input values which function can take

So, option (d) is correct.

(ii) option (d) is correct as it represent the function [tex]y=x[/tex]. While all the other function does not satisfy the given conditions.

(iii) [tex](-14,-15), (-9,-10)[/tex] are the parts of solution pair.

(iv) Option (c) and (d) represents the function as each element of the first set has a unique image in the second set.

Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.15%. They
have 500 grams of substance B which decays at a rate of 0.37%. They are trying to determine how many years it will be before the substances
have an equal mass.
If Mrepresents the mass of the substance and trepresents the elapsed time in years, then which of the following systems of equations can be
used to determine how long it will be before the substances have an equal mass?

Answers

Answer:

231.59 years

Step-by-step explanation:

To model this situation we are going to use the exponential decay function:

f(t)= a (1-b)^t

where f(t) is the final amount remaining after t years of decay

a is the final amount

b is the decay rate in decimal form

t is the time in years

For Substance A:

Since  we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r = 0.15/100 = 0.0015. Replacing the values in our function:

f(t) = a (1-b)^t

f(t) = 300 (1-0.0015)^t

f(t) = 300 (0.9985)^t equation (1)

For Substance B:

Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:

r=0.37/100= 0.0037. Replacing the values in our function:

f(t) = a (1-b)^t

f(t)= 500 (1-0.0037)^t

f(t)=500(0.9963)^t equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:

M=300(0.9985)^t equation (1)

M=500(0.9963)^t equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :

{M=300(0.9985)^t

{M=500(0.9963)^t


Write the linear equation given slope and point.
(-4,-7); slope = 3

Answers

Answer:

Step-by-step explanation:

Use the "point-slope" formula for the equation of a straight line,

y - k = m(x - h)

Here the slope, m, is 3 and the line passes through (h, k):  (-4, -7), so the proper equation in this case is

y - (-7) = 3(x + 4), or:

y + 7 = 3(x + 4).

If you wish you may rewrite this equation in slope-intercept form, as follows:

y = 3x - 7 + 12, or y = 3x + 5

i need help btw i am in middle school

Answers

Answer: J

Step-by-step explanation: It is very cool you are in middle schopol

Kelly has $100 she received for her birthday She saves $10 each week from doing chores Which function can be used to find t the amount of money Kelly will have saved

Answers

Answer:

$620 every year

Step-by-step explanation:

Since the question didn't specify how long she would have to save for, let's just assume that it's one year. There are 52 weeks in a year which is $520, and on her birthday she would have an extra $100, so every year she saves $620 in total.

(Write the equation) Thank you if you answer it <3

Answers

Answer:

10 - 2 = (x + 6)

Explanation:

The Sum Of x And 6 Is Two Less Than Ten.

The Sum Of x And 6: x + 6

Two Less Than Ten: 10 - 2

Put The Two Terms Together10 - 2 = (x + 6)
answer is: 10-2=(x+6)

I will mark brainliest

Answers

Answer:

I think that it is positive 650.

Answer:

you got it

Step-by-step explanation:

that is itdescribe your answer to gt i wrie u are doing a test

The ratio of cyclists to pedestrians on a certain trail was 2 to 7. If there were 27 people on the trail, how many more pedestrians were there than cyclists?​

Answers

Answer:

15 more pedestrians than cyclists

Step-by-step explanation:

2:7 ratio tells us two cyclists for every seven pedestrians so out of every 9 people 2 are cyclists and 7 are pedestrians.

27/9=3

So we have 3 groups of 9...

3×2=6

&

3×7=21

so

6 cyclists and 21 pedestrians

subtract cyclists from pedestrians to find difference...

21-6=15

[tex]\sqrt[3]{11}[/tex]

Answers

Answer:

2.22

Step-by-step explanation:

[tex]\sqrt[3]{11} =2.223980091[/tex]

Rounded to hundredths: 2.22

What is 1/3÷9? hurry!

Answers

Exact Form:

1/27

Decimal Form:

0.037 (with a line over 037)

Please help me with this question!!

Answers

Answer:

Step-by-step explanation:

Mabye 7?

Challenge How many flowers, spaced every 6 in., are needed to surround a circular garden with a
200-ft radius? Use 3.14 for it.
Williams, Aaily
flowers are needed to surround the circular garden.

Answers

Answer:

1,256 flower

Step-by-step explanation:

First, we need to calculate the circumference of the circle. The formula for the circumference of the circle is:

C

=

2

π

r

If we substitute

100

ft

for

r

and use

3.14

to approximate

π

we get a circumference of:

C

=

2

3.14

100

ft

C

=

6.28

100

ft

C

=

628

ft

We can now convert the circumference in feet to inches;

628

ft

×

12

in

1

ft

628

ft

×

12

in

1

ft

628

×

12

in

7536

in

To find how many flowers we need we can divide the circumference in inches by the 6 inches between flowers giving:

7536

in

×

1

flower

6

in

7536

in

×

1

flower

6

in

7536

×

1

flower

6

7536

flower

6

1256

flower

You would require 1,256 flowers

Somebody please help me plsssss

Answers

Given:

The radius of the cylinder = 2 cm

Height of the cylinder = 5 cm

To find:

The volume of the cylinder.

Solution:

We know that, the volume of a cylinder is:

[tex]V=\pi r^2h[/tex]

Where, r is the radius and h is the height of the cylinder.

Putting [tex]r=2,h=5[/tex] in the above formula, we get

[tex]V=\pi (2)^2(5)[/tex]

[tex]V=\pi (4)(5)[/tex]

[tex]V=20\pi [/tex]

Therefore, the volume of the cylinder is [tex]20\pi [/tex] cubic cm and its approximate value is 62.832 cubic cm.

0.25% of 42 is what number

Answers

Answer:

0.105

Step-by-step explanation:

0.25/100 x 42 = 0.105

Answer: The answer is 0.105

A computer randomly selects a number from the given set. {1.2 5 10 25 30 36} What is the probability that an even number is selected? Enter your answer as a fraction, in simplest form, in the box. Pleven) =​

Answers

Answer:

4/7 (I may be wrong)

Step-by-step explanation:

There are 7 numbers, of which 4 are even. This could be %100 wrong/right.

Giving brainlist to whoever answers

Answers

Answer:

10 I believe I really hope it helped!

Step-by-step explanation:

Answer:

That's easy! 10 times

Step-by-step explanation:

60 divided by 6 is 10

Is u = 105 a solution to this equation

Answers

Answer:

im sorry what?

Step-by-step explanation:

A house that costs $125,400 appreciates at a rate of 3% each year. What is the value of the
home after 3 years.
a.$137027.97
b.$275503.80
c.$114449.19
d.$3385800

Answers

Answer:

The value after three years is $137,027.97

Step-by-step explanation:

Here, we want to get the value of the home after 3 years

Generally, we have the exponential formula as follows;

y = P(1 + r)^t

where P is the original cost which is $124,400

r is the rate of increase which is 3% = 3/100 = 0.03

t is the time which is 3 years

Substituting these values;

y = 125400(1 + 0.03)^3 = $137,027.97

What is the surface area of a rectangular prism that has a length of 4 cm, a height of 14 cm, and a width of 15 cm?
A. 660 cm2
B. 652 cm2
C. 326 cm2
D. 432 cm2

Answers

D or A I guess I am not 100% sure I am 20% sure I don’t really know I guess is D If is wrong maybe is A

Answer:

The answer is b I searched it on goggle and did the math.

Step-by-step explanation:

15 is 9 than j what is j in this question

Answers

Answer:

6

Step-by-step explanation:

15 is 9 more hence you subtract 9 from15

Hope this helps

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