For a group of 70 people, assuming that each person is equally likely to have a birthday on each of 365 days in the year, compute (a) The expected number of days of the year that are birthdays of exactly 4 people:

Answers

Answer 1

Answer:

0.0157

Step-by-step explanation:

From the information given:

The sample size  = 70

The expected no. of days of year that are birthday of exactly 4 people is:[tex]P = \bigg [ \dfrac{1}{365} \bigg]^4[/tex]

The expected number of days with 4 birthdays = [tex]\sum \limits ^{365}_{i=1} E(x_i)[/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ ^{70}C_{4} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{70-4} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ \dfrac{70!}{4!(70-4)!} \times ( \dfrac{1}{365})^4 ( 1 - \dfrac{1}{365})^{66} \bigg][/tex]

[tex]\sum \limits ^{365}_{i=1} E(x_i) = 365 \times \bigg[ \ 916895 \times 5.6342 \times 10^{-11} \times 0.8343768898 \bigg][/tex]

= 0.0157

Therefore, the required probability = 0.0157


Related Questions

someone help me with this

Answers

Answer:

-30 is the right one if u need help tell me ;)-

Step-by-step explanation:

:)

Dalia used a balancing move to begin to solve the
equation below.
6x + 12 = 10x - 4
The result of Dalia's first step was 12 = 4x – 4.
Describe the first step Dalia made to solve the equation.

Answers

To combine like terms and single out one term to take it easier to solve, the 6x was moved to the other side to combine like terms.
Subtracting 6x from 10x which is 4x

.helppppppppppppppp!!!!!

Answers

answer: B

Step-by-step explanation: Its the only one that makes sense because as you see there are only four numbers to go off of, and b is the only one tht makes sense tbh

Use the figure to find the measure of the angle.Explain your reasoning.

Answers

angle2=180-152=28

angle3=28

angle4=152

angle5=152

angle6=28

angle7=28

angle8=152

The values of the marked angles: angle 2, angle 3,  angle 4,  angle 5,  angle 6,  angle 7,  angle 8 are 28°, 28°, 152°, 152°, 28°, 28°, 152°.

What is an angle?

When two lines or rays meet at a point, then the geometrical figure is formed, is called an angle.

Given, angle 1 = 152°

We know, angle 1 + angle 2 is 180°.     (supplementary angles)

Therefore, angle 2 = (180° - 152°) = 28°.

Again, angle 2 = angle 3.             (opposite angles)

Therefore, angle 3 = 28°.

Similarly, angle 1 = angle 4

Therefore, angle 4 = 152°.

Now, angle 1 = angle 5        (corresponding angle)

Therefore, angle 5 = 152°.

Now, angle 2 = angle 6        (corresponding angle)

Therefore, angle 6 = 28°.

Now, angle 3 = angle 7        (corresponding angle)

Therefore, angle 7 = 28°.

Now, angle 4 = angle 8        (corresponding angle)

Therefore, angle 8 = 152°.

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What is 9.52% expressed as a decimal?​

Answers

Answer:

0.0952

Step-by-step explanation:

Percent just divide by 100

9.52 ÷ 100 = 0.0952

Answer:

0.0952

Step-by-step explanation: In order to get a decimal out of a percentage you take the decimal and put it two places to the left. Hope this helps!

PLZ HELP IM WASTING MY POINTS FOR THIS Match each expression to its value.

1. -1 + 2
1
2. 1 + (-2)
-3
3. -1 - 2
3
4. 1 - (-2)
-1

Answers

Answer:

1. 1

2. -1

3. -3

4. 3

If you have any questions on the topic let me know. :)

Answer:

1. 1

2. -1

3. -3

4.3

Step-by-step explanation:

...

Help people help!!!!

Answers

Answer:

I think that it is

C

Please let me know if it is not correct!!!!

Answer:

A would most likly be the answer

Step-by-step explanation:

because in the equation sinse A =  -5 1/4 which is whe he was at the end hopefully you understand

Xander takes a quiz worth 150 points. Each question is worth 30 points. Sketch a graph to show his score if he misses 1,2,3,4 or 5 questions.

Answers

Answer:

If he missed five questions he can get a zero

Step-by-step explanation:

Given the expression, 3(y + 1) + 2y, which of the following expressions is equivalent?
A
3y + 3

B
5y + 1

C
5y + 3

D
9y + 3

Answers

Answer:

C

5y + 3

Step-by-step explanation:

Find how many solutions there are to the given equation that satisfy the given condition.
y1 +y2+y3+y4=27, each yi is a nonnegative integer.

Answers

Answer:

17550 solutions

Step-by-step explanation:

Given that:

y1 +y2+y3+y4=27

where;

(yi  ≥ 0 and yi [tex]\epsilon[/tex] [tex]{\displaystyle \mathbb {Z} }[/tex]  )

The no. of a nonnegative integer determines the number of ways to choose 27 objects from (4) distinct objects with repetition regardless of the order.

i.e

[tex]\bigg(^{27}_{4} \bigg)[/tex]

The number of nonnegative integer solution is [tex]\bigg(^{27}_{4} \bigg)[/tex]

[tex]= \dfrac{27!}{4!(27-4)!}[/tex]

[tex]= \dfrac{27!}{4!(23)!}[/tex]

[tex]= \dfrac{27\times 26\times 25\times 24 \times 23 !}{4\times 3\times 2\times 1(23)!}[/tex]

[tex]= \dfrac{27\times 26\times 25\times 24 }{4\times 3\times 2\times 1}[/tex]

[tex]= \dfrac{421200}{24}[/tex]

= 17550 solutions

A retail store makes k% profit on the selling price. What is the least integer value of k that will enable the store to make a profit of at least 30% of the cost of the item?

Answers

Answer:

k = 23% profit on sale price is needed to ensure 30% profit on cost price

Step-by-step explanation:

Let sale price be = s , Profit = k% of s

Let cost price be = 100 , Profit = 30% of c

Cost price (c) + profit (p)  = Sale price (s)

c + 0.3c = s

1.3c = s

Profit as a percentage of sale = (Profit / Sale) x 100

= (0.3c / 1.3c) x 100

= 23%

Can someone please help me with this question i have 3 minutes left

Answers

Answer:

It will cost 11 cents a day.

Step-by-step explanation:

1.98/18=11

plzz have brainiest

Use place value multiplication with powers of 10 or equivalent fractions to explain what is happening mathematically to the decimal points in the divisor and the dividend before dividing

Answers

Answer:

436.8 x 100 / 62.08 x 100 = 43680/6208

Step-by-step explanation:

When you write the problem as a fraction, multiply the numerator and denominator by 100.  Multiplying each by 100 resulted in both numbers being whole numbers. 436.8/62.08 is the same as 43,680/6,208.

what is 494 divided by 6.5

Answers

Answer:

76

Step-by-step explanation:

Answer:

494 divided by 6.5 =76

Step-by-step explanation:

Write the number below in expanded notation 75,966

Answers

7.596 to the 4th power

What is the special rule with multiplying or dividing an equality by a negative number?

Answers

Multiplying or dividing both sides by a negative number reverses the inequality.

Can someone please help me if you know! Thank you

Answers

Answer:

D

Step-by-step explanation:

the equation for Josh is 500 + 40x while the equation for Vanessa is only 60x

if josh's account balance is greater than it would be josh > vanessa or vanessa < josh

WHENS MY BDAY I SAID THIS

Answers

Answer:

reeee whenever it was happy bday ily by :)

Determine if the number is a negative or positive integer. Gain 4 yards in the last down.

Answers

Answer:

Positive

Step-by-step explanation:

It's positive because the person is gaining 4 yards, not losing it.

Explain what needs to be fixed.
2n + 10 = -2
2n = 12 Step one
n = 6 Step two

Answers

Answer:

step one needs to be fixed... you are supposed to subtract 10 from both sides of the equation.

Step-by-step explanation:

STEP 1: Move all terms not containing n to the right side of the equation.

[tex]2n=-12[/tex]

STEP 2: Divide each term by 2 and simplify.

[tex]n=-6[/tex]

What is a fraction equivalent to 4/4? Explain how you know.

Answers

Answer:  Any number over itself is equivlent to 4/4.

Examples: 3/3, 18/18, 5/5, 90/90

Step-by-step explanation:

Because 4/4 is equivalent to 1 whole.

A fraction that is equivalent to 4/4 would be, 5/5 as, After simplifying the fraction 5/5 is equal to 1.

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.

Given that,

The fraction is,

⇒ 4/4

Now, after simplifying the fraction we get;

⇒ 4/4

⇒ 1

So, Let a fraction that is equivalent to 4/4 would be;

⇒ 5/5

After simplifying we get;

⇒ 5/5 = 1

Therefore, A fraction that is equivalent to 4/4 would be, 5/5

To learn more about the fraction visit:

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Can someone please help me with this math problem I don’t understand it

Answers

Answer:

i  need points

Step-by-step explanation:

i need points ,, hope you find your answer

Enter a range of values for x.
+
42°
3x+156
23
21
[ ? ] 

Answers

Answer:

-5<x<9

Step-by-step explanation:

It took me a while to find figure it out.

Question 1) In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row. A) Write an iterative rule to model the sequence formed by the number of seats in each row. Show your work. (B) Use the rule to determine which row has 100 seats. Show your work. ( No Plagiarism and only answer if you know how to work this problem out. Will Mark Brainliest).​

Answers

Answer: Row 14

Step-by-step explanation:

Row 1= 22

Row 2= 28

Row 3= 34

Row 4= 40

Row 5= 46

Row 6= 52

Row 7= 58

Row 8= 64

Row 9= 70

Row 10= 76

Row 11= 82

Row 12= 88

Row 13= 94

Row 14= 100

This question is based on the sequence. Thus, the  row 14 has 100 seats.

Given:

In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row.

Now calculated the A part of the question.

According to the question,

By using iterative rule to model the sequence formed by the number of seats in each row.

Row 1= 22 Row 2= 28 Row 3= 34 Row 4= 40 Row 5= 46 Row 6= 52 Row 7= 58 Row 8= 64 Row 9= 70  Row 10= 76 Row 11= 82 Row 12= 88 Row 13= 94 Row 14= 100

(B) By using rule , we observe that row 14 has 100 seats.

For more details, prefer this link:

https://brainly.com/question/7854718

Solve for X: 6x+25=1

Answers

6x+25=1

move +25 to the other side

sign changes from +25 to -25

6x+25-25=1-25

6x=1-25

6x=-24

divide both sides by 6 to get x by itself

6x/6=-24/6

x=-4

answer: x=-4

X=-4
Subtract 25 form both sides which would end up as
6x=-24
Then divide 6for both side later which ends ups as
X=-4

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 11ft^3

Answers above on the picture^ thank you:)

Answers

Answer:

#3

Step-by-step explanation:

PLEASE HELP QUICKK
Which slopes could be the slopes of perpendicular lines?

Question 1 options:

1/2 and 2


8 and -1/8


2 and 2


1 and -1


0 and undefined

Answers

The answer would be:

8 and -1/8

1 and -1

And could be 0 and undefined, but I'm not 100% sure

what is the maximum number of cubes with side lengths of 1/2 cm that can fit into a right rectangular prism with base dimensions of 12 1/2 cm by 8 1/2cm and a height of 9 1/2cm?

Answers

Answer:

8075.

Step-by-step explanation:

Volume of the prism

= 12 1/2 * 8 1/2 * 9  1/2

= 25/2 * 17 / 2 * 19/2

= 8075/8 cm^3

The volume of the small cubes = (1/2)^3 = 1/8 cm^3

So the number required = 8075 / 8   /  1/8

= 8075*8 / 8

= 8075.

which of the following are exterior angles? help!

Answers

Answer:

2, 4, 6

Step-by-step explanation:

3x + 1 = 3(x - 1) + 4​

Answers

Simplifying

3x + 1 = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[-1 + x] + 4

1 + 3x = [-1 * 3 + x * 3] + 4

1 + 3x = [-3 + 3x] + 4

Reorder the terms:

1 + 3x = -3 + 4 + 3x

Combine like terms: -3 + 4 = 1

1 + 3x = 1 + 3x

Add '-1' to each side of the equation.

1 + -1 + 3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

0 + 3x = 1 + -1 + 3x

3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

3x = 0 + 3x

3x = 3x

Add '-3x' to each side of the equation.

3x + -3x = 3x + -3x

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

0 = 3x + -3x

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

0 = 0

This equation is an identity, all real numbers are solutions.

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