What is the probability of 3 people sharing the same birthdays? How many different pairs of people are there when there are three humans? (Think nPr or nCr)

Answers

Answer 1

The probability of three people sharing the same birthdays is approximately [tex]0.0000075[/tex] or [tex]0.00075[/tex]%, and there are three different pairs of people when there are three humans.

The probability of three people sharing the same birthday depends on the assumptions made about the distribution of birthdays. Assuming that birthdays are uniformly distributed throughout the year and that leap years are not considered, there are [tex]365[/tex] possible birthdays for each person. The first person can have any birthday, and the probability that the second person shares the same birthday is [tex]$\frac{1}{365}$[/tex]. Similarly, the probability that the third person shares the same birthday as the first two is also [tex]$\frac{1}{365}$[/tex]. Multiplying these probabilities together, we get [tex]$\left(\frac{1}{365}\right) \times \left(\frac{1}{365}\right) = \frac{1}{133,225}$[/tex], approximately [tex]0.0000075[/tex] or [tex]0.00075\%[/tex].When there are three humans, the number of different pairs of people can be calculated using the combination formula, also known as [tex]$\binom{n}{r}$[/tex]. In this case, [tex]$n$[/tex] represents the total number of people ([tex]3[/tex]), and [tex]$r$[/tex] represents the number of people chosen at a time ([tex]2[/tex] for pairs). Applying the formula, we have [tex]$\binom{3}{2} = 3$[/tex]. Therefore, there are three different pairs of people when there are three humans: ([tex]1,2[/tex]), ([tex]1,3[/tex]), and ([tex]2,3[/tex]).

In conclusion, the probability of three people sharing the same birthdays is extremely low (approximately [tex]0.0000075 \ or \ 0.00075\%[/tex]), and when there are three humans, there exist three different pairs of people.

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Related Questions

Write the equation of the line if the slope is 6 and the y-intercept is -2.

Answers

Answer:

y=6x-2

Step-by-step explanation:

slope=6

y-intercept=-2

y=6x-2

the measure of the vertex angle of an isoceles triangle is 120 degrees and the length of a leg is 8 cm. find the length of the diameter circumcised about this triangle

Answers

The length of the diameter circumcised about this isosceles triangle is 32 cm.

To find the length of the circumcircle's diameter, we can use the properties of an isosceles triangle.

In an isosceles triangle, the vertex angle is the angle formed by the two congruent sides. In this case, the vertex angle is given as 120 degrees.

We know that the vertex angle of an isosceles triangle is located opposite the base. Let's denote the base as side a, and the congruent sides as side b.

In an isosceles triangle, the base angles are congruent. Since the sum of the angles in a triangle is 180 degrees, each base angle in this triangle measures (180 - 120) / 2 = 30 degrees.

Now, we can apply the Law of Sines to find the length of the base, side a. The Law of Sines states:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, since angle A is the vertex angle and side a is the base, we have:

a/sin(120) = b/sin(30)

Using the given length of the leg (side b) as 8 cm, we can solve for side a:

a/sin(120) = 8/sin(30)

a = (8 × sin(120)) / sin(30)

Using the values of sin(120) and sin(30) from a trigonometric table or calculator:

a ≈ (8 × √3) / (1/2) = 16√3 cm

Now, let's find the length of the diameter of the circumcircle. The circumcircle of a triangle passes through the vertices of the triangle and has its center at the intersection of the triangle's perpendicular bisectors.

Since the triangle is isosceles, the perpendicular bisector of the base will pass through the vertex angle and bisect it, resulting in two 60-degree angles.

In an equilateral triangle, the perpendicular bisector of a side passes through the triangle's center, which coincides with the center of the circumcircle. Since our isosceles triangle has two congruent sides, we can treat it as half of an equilateral triangle.

The length of the diameter of the circumcircle of an equilateral triangle is given by the formula:

Diameter = 2 × (side length) / √3

In our case, since we have half of an equilateral triangle, the diameter of the circumcircle will be:

Diameter = 2 × (16√3) / √3 = 32 cm

Therefore, the length of the diameter circumcised about this isosceles triangle is 32 cm.

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Ma Bernier has 52 cats and dogs in her house the number of cats is three times the number of dogs how many cats and dogs are in the house

Answers

Answer:

dogs - 13

cats - 39

Step-by-step explanation:

Let the number of dogs Ma Bernier have be represented with d

She has 3 times as many cats as dogs, the number of cats she has :

cats = 3d

The sum of the cats and dogs is 52

d + 3d = 52

4d = 52

divide both sides of the equation by 4

d = 13

She has 13 dogs

Cats = 3d

= 3 x 13 = 39

convert from vertex form to standard form... y= -(x-3)^2-8

Answers

Answer:

-x² + 6x - 17

Step-by-step explanation:

First, expand (x-3)² using FOIL

(x - 3)(x - 3)

= x² - 6x + 9

Distribute the negative sign to the expression:

-(x² - 6x + 9)

-x² + 6x - 9

Now, subtract 8 from this

-x² + 6x - 9

= -x² + 6x - 17

So, the equation in standard form is -x² + 6x - 17

The answer is.. x^2+6x-17

Find the difference. Write your answer in simplest form.

9/10 - 5/10

Answers

Answer:

2/5 is the simplest form.

Step-by-step explanation:

9/10 - 5/10 = 4/10 (9 - 5 = 4) 4/10 simplified is 2/5 (divide both 4 and 10 by 2 and you get 2/5).

Hope that helps!

For each of the days above, work out how much money would be made by each court if all seats were sold.

Seats:

Centre court has 14 979 seats for sale. No 1 court has 11 429 seats for sale. No 2 court has 4000 seats for sale. No 3 court has 2000 seats for sale.

Prices:

Centre Court: £56 No 1 Court: £45 No 2 Court: £41 No 3 Court: £41 Grounds Admission: £25

Answers

The total money made by each court would be as follows:

Centre Court: £838,824, No 1 Court: £514,305

No 2 Court: £164,000, No 3 Court: £82,000

To calculate the amount of money made by each court if all seats were sold, we need to multiply the number of seats by the corresponding ticket price for each court. Here are the calculations for each court:

Centre Court:

Number of seats: 14,979

Ticket price: £56

Total money made: 14,979 seats ×£56/seat = £838,824

No 1 Court:

Number of seats: 11,429

Ticket price: £45

Total money made: 11,429 seats ×£45/seat = £514,305

No 2 Court:

Number of seats: 4,000

Ticket price: £41

Total money made: 4,000 seats ×£41/seat = £164,000

No 3 Court:

Number of seats: 2,000

Ticket price: £41

Total money made: 2,000 seats × £41/seat = £82,000

Therefore, if all seats were sold, the total money made by each court would be as follows:

Centre Court: £838,824

No 1 Court: £514,305

No 2 Court: £164,000

No 3 Court: £82,000

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10/y=2/9, find the solution of y. stat.

Answers

Answer:

y=45

Step-by-step explanation:

Let's solve your equation step-by-step.

10 y = 2 /9

Step 1: Cross-multiply.

10 y = 2 /9

(10)*(9)=2*y

90=2y

Step 2: Flip the equation.

2y=90

Step 3: Divide both sides by 2.

2y /2 = 90 /2

y=45

brainliest please?

Answer:

y = 45

Step-by-step explanation:

10/y=2/9

10 = y * 2/9  

10 = 2/9y

10 * 9 = 2/9y * 9

90 = 2y

90/2 = 2y/2

y = 45

ps: * means multiply

Im new here :) but hey you got these qs try your best okie

I hope and im glad to help

what number adds up to three and multiples 22 to

Answers

Answer:

Factors of 22: 1, 2, 11, and 22.

Prime Factorization of 22: 22 = 2 × 11.Step-by-step explanation:

Last season the girls' volleyball team had 5 seventh-grade students and 4 sixth-grade students. What is the ratio of sixth-grade students to seventh-grade students on the volleyball team? A 4:5 B 4:9 C 5:4 D5:9

Answers

Answer:

A) 4:5

Step-by-step explanation:

A) 4:5

B) 4:9

C) 5:4

D) 5:9

If there are 4 sixth grade students, you can already cross off D because there is no 4 as an option. There are 5 seventh grade students, you can cross off B because there's no 5. So now it's down to 4:5 or 5:4. Since it wants the ration of sixth to seventh, it's 4 to 5.

Hence, the ratio is 4:5, answer A

Hope this helps :)

Stay Cold,

Brook

26.2 miles in 4 hours. Find the unit rate

Answers

Answer:

Step-by-step explanation:

Unit rate = 26.2 ÷ 4 = 6.55

A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the​ box?

Thanks in advance!

Answers

Answer:

852 inches square

Step-by-step explanation:

2×(16×15 + 16×6 + 15×6)

Answer:

652 in²

Step-by-step explanation:

The formula is 2(wl+hl+hw)

h is height

w is width

l is length

Use PEMDAS/BIDMAS/BODMAS (do the parentheses then multiply it)

326*2 = 652

add your units

652 in^2

A roast beef sandwich costs $6.75. A customer buys multiple roast beef sandwiches. Write an equation that represents the situation. Use $x$ to represent the number of roast beef sandwiches. Then determine how many sandwiches the customer buys.

Amount Used for Payment $80
Change Received $19.25
An equation that represents this situation is
.

The customer buys
sandwiches.

Answers

Answer:

[tex]\frac{80-19.25}{6.75} = x[/tex]

Step-by-step explanation:

Subtract $19.25 from the Amount Used for Payment ($80) to get the amount spent, then divide the amount of each sandwich to get the amount of sandwiches bought.

Question 2 of 10
If f(x) = 3x - 1 and g(x) = x + 2, find (f+ g)(x).
A. 4x + 1
B. 2x - 3
с. 3х – 3
D. 2x - 1

Answers

Cnski kaoushe e bad djjd. R

ver imagen para la pregunta

Answers

Answer: C

Step-by-step explanation:

I need help I don’t really get it

Answers

Answer:

A. 72 cm

Step-by-step explanation:

72 x 2/3 = 48

Answer:

72 cm

Step-by-step explanation:

if the smaller figure is 48 cm and its a 2/3 ratio

lets just say 2x:3x

2x=48 so x would =24

then the larger perimeter would be 3*24 which is 72

Sophia invest $12,350 in a account that earns 4.5% annual simple interest. Assuming she makes no additional deposits or withdrawals, how much interest will Sophia earn after 36 months?

Answers

You would find out how many years is 36 months and then do 12,350 x4.5x
X being the number of years.

Answer:

I DO NOT KNOW

Step-by-step explanation:

I am here for the answers

I am hungry

Pizza

What is angle BXC and why?? Please help

Answers

Answer:

BXC=70 degrees

Step-by-step explanation:

XBC = 55

corresponding angles are equal

XCB=55

isosceles base angles are equal

BXC=70

angles in a triangle add up to 180 degrees

EXPLAIN THE DIFFERENCE OF THE CIRCUMFERENCE AND THE AREA OF THE CIRCLE.



PLS ANSWER IT.​

Answers

circumference is around the circle the border of the circle the area of the circle is the space in the circle

A gardener made a scale drawing of a lawn with a scale factor of 1:4 The dimensions of her drawing are 15 inches long by 10 inches wide. Her partner plans to make another scale drawing of the lawn, but with a scale factor of 1:20. What are the dimensions of her scale drawing? O A. The length is 50 inches and the width is 75 inches, OB. The length is 3 inches and the width is 2 inches. O Q. The length is 75 inches and the width is 50 inches. O D. The length is 2 inches and the width is 3 inches.​

Answers

Answer:

B is the correct answer

Step-by-step explanation:



Yesterday, the temperature change for a 5-hour period of time was – -degree per
hour. Which statement describes this change?
A
The temperature rose 5 degrees.
B
The temperature rose 4 1/4 degrees.
с
The temperature fell 4 degrees.
D
The temperature fell 5 4/5
degrees

Answers

Answer:

D

Step-by-step explanation:

Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.

Answers

The linear system X₁ + 2X₂ = 3.21 and 4.02X₁ + IL || -1 = -1 using Cramer's rule, we need to find the values of X₁ and X₂.

To apply Cramer's rule, we first need to calculate the determinant of the coefficient matrix and the determinants of the matrices obtained by replacing each column of the coefficient matrix with the constant terms.

The coefficient matrix is:

| 1   2 |

| 4.02  IL || |

The determinant of the coefficient matrix, denoted as D, is given by:

D = (1 * IL ||) - (2 * 4.02)

  = IL || - 8.04

The matrix obtained by replacing the first column with the constant terms is:

| 3.21   2 |

| -1     IL || |

The determinant of this matrix, denoted as D₁, is given by:

D₁ = (3.21 * IL ||) - (-1 * 2)

   = 3.21IL || + 2

The matrix obtained by replacing the second column with the constant terms is:

| 1   3.21 |

| 4.02  -1 |

The determinant of this matrix, denoted as D₂, is given by:

D₂ = (1 * -1) - (4.02 * 3.21)

   = -1 - 12.9042

   = -13.9042

Now, we can find the values of X₁ and X₂ using the formulas:

X₁ = D₁ / D

X₂ = D₂ / D

Substituting the values we calculated earlier, we have:

X₁ = (3.21IL || + 2) / (IL || - 8.04)

X₂ = (-13.9042) / (IL || - 8.04)

This gives us the solution to the linear system.

Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.

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(a) Bob wants to open a new fastfood shop. He estimates he needs to spend at least $100,000 on renovation and buying commercial kitchen appliances. The average running cost per customer (for food, staff salary, etc.) is $7. Each customer spends $15 on average.

(i) If the number of customers is n, write down the cost function and revenue function as functions of n.

(ii) Determine the minimum number of customers for the business to breakeven.

(iii) Bob has to borrow $100,000 from a bank with interest rate of 3% p.a. with interest payable monthly. If Bob does not repay a single cent, how much does Bob owe the bank after 3 years?

Answers

i) The cost function is x = 100,000 + 7n while the revenue function is y = 15n.

ii) The minimum number of customers for the business to break even is 12,500.

iii) The amount that Bob owes the bank after 3 years at 3% p.a. interest payable monthly, but without any repayment, is $109,272.70.

What is a function?

A function is a mathematical equation showing the equality of two or more algebraic expressions.

a) Renovation and appliances costs = $100,000

Average running cost per customer = $7

Selling price per customer = $15

i) Let the number of customers = n

Cost function, x = 100,000 + 7n

Revenue function, y = 15n

ii) For the business to break even, y must be equal to x:

15n = 100,000 + 7n

8n = 100,000

n = 12,500

iii) Bank loan = $100,000

Interest rate = 3% p.a.

Interest payment = monthly

Amount after 3 years without any repayment = $100,000 x 1.03^3

= $109,272.70 ($100,000 x 1.092727)

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You eat 11 grams of cereal each day. If you eat the same amount of cereal each day, how many grams of cereal will you eat in 5 days?

Answers

Answer:

55 grams

Step-by-step explanation:

11×5=55 grams

if its the same amount everyday then 55

(it made me type more)

Answer:55

Step-by-step explanation: 11x5

Suppose that an urn contains 3 different types of balls: red, green and blue. Let pi denote the proportion of red balls, p2 denote the proportion of green balls and p3 denote the proportion of blue balls. Here ₁-1 Pi = 1. Suppose also that 100 balls are selected with replacement, and there are exactly 38 red, 29 green and 33 blue. Find the M.L.E. p; of p₁, i = 1, 2, 3. Warning: No credit for answers only! P₁=__ S=____ P3 =_____

Answers

Let's start solving the given problem. Suppose that an urn contains 3 different types of balls: red, green, and blue. Let pi denote the proportion of red balls, p2 denote the proportion of green balls, and p3 denote the proportion of blue balls.

Here Pi = 1.

Suppose also that 100 balls are selected with replacement, and there are exactly 38 red, 29 green and 33 blue.

We need to find the M.L.E. p; of p1, i = 1, 2, 3.

The probability of obtaining red ball from the urn = pi. The probability of obtaining green ball from the urn = p2. The probability of obtaining blue ball from the urn = p3

Given that, 100 balls are selected with replacement.

Let's calculate the probability of getting 38 red, 29 green, and 33 blue balls from the urn,

P(38 Red and 29 Green and 33 Blue) = P(Red)38 x P(Green)29 x P(Blue)33 = p₁³⁸ x p₂²⁹ x p₃³³

Therefore, the likelihood of obtaining the 38 red, 29 green, and 33 blue balls is L(p1,p2,p3) = p₁³⁸ x p₂²⁹ x p₃³³

Since, L(p1,p2,p3) is a continuous function, so we have to find the critical points of the function to obtain the minimum value of p₁. Let's take natural logarithm on both sides of the function, we get ln

L(p1,p2,p3) = 38 ln p₁ + 29 ln p₂ + 33 ln p₃.

So, taking partial differentiation with respect to p1, p2 and p3 and equating them to 0. We get the following equations,∂ ln L / ∂p1 = 38/p1 = 0∂ ln L / ∂p2 = 29/p2 = 0∂ ln L / ∂p3 = 33/p3 = 0On

solving the above three equations, we get p1 = 38/100 = 0.38p2 = 29/100 = 0.29p3 = 33/100 = 0.33

Therefore, P₁= 0.38, S= 0.29, P3 = 0.33. Hence, the required solution is P₁= 0.38, S= 0.29, P3 = 0.33.

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determine the volume of the rectangular prism.
height:12ft
width:6ft
length:3ft

Answers

Answer:

216 ft³

Step-by-step explanation:

h*w*l=v

[tex]12 \times 6 \times 3 = 216[/tex]

Five students took a quiz. The lowest score was 4, the highest score was 6, the average (mean) was 5.2, and the mode was 6. A possible set of scores for the students is:

Answers

A possible set of scores for the students is: 4, 4, 6, 6, 6

How to solve the measures of Central Tendencies?

We are given that five students took the quiz. If the lowest score is 4 and the highest score is 6, we can say that the set of values ​​can be expressed as:

4, x, y, z, 6

Here we can see that the mode is 6 and the mean is 5.2. Therefore, at least one other student of hers has scored her 6, which could result in:

4, x, y, 6, 6

Therefore:

(4 + x + y + 6 + 6)/5 = 5.2

16+x+y=26

x + y = 10

So the other two numbers are probably 6 and 4, because 6 is the mode, so they can't both be 5.

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Pls helpppp and thank you

Answers

If the question is y = blank(x) + blank (I can’t see the left of the equation
Then the answer is y = 2x + -4

Simplify: 6a - 2(5a - 6)

Answers

Answer:

[tex]-4a + 12[/tex]

Step-by-step explanation:

anyone know this or can help pls

Answers

Answer:

A pyramid

Step-by-step explanation:

using cramer’s rule, what are the values of x and y in the solution to the system of linear equations below?

Answers

The value of x =-3 and y=1 in the system of linear equation.

Given equations

-2x+3y+z=7

-4x-y-2z=15

x+2y+3z=-7

Using cramer's rule to find x and y

First we make matrix of coefficient of x,y and z and then find the determinant

[tex]A = \left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Now we find determinant of A

|A|=-2(-3+4)-3(-12+2)+1(-8+1)

|A|=21

[tex]A_x=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Determinant of Ax

|Ax|=7(-3+4)-3(45-14)+1(30-7)

|Ax|=-63

[tex]A_y=\left[\begin{array}{ccc}7&15&-7\\-4&-1&-2\\1&2&3\end{array}\right][/tex]

Determinant of Ay

|Ay|=-2(45-14)-7(-12+2)+1(28-15)

|Ay|=21

[tex]A_z=\left[\begin{array}{ccc}-2&3&1\\-4&-1&-2\\7&15&-7\end{array}\right][/tex]

Determinant of Az

|Az|=-2(7-30)-3(28-15)+7(-8+1)

|Az|=-42

Now we find for x, y and z

[tex]x=\frac{|A_x|}{|A|}[/tex]

= -63/21 = -3

[tex]y = \frac{|A_y|}{|A|}[/tex]

= 21/21 = 1

[tex]z = \frac{|A_z|}{|A|}[/tex]

= -42/21

= 2

Thus, the value of x =-3 and y=1 in the system of linear equation.

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Given question is incomplete, the complete question is below

using cramer’s rule, what are the values of x and y in the solution to the system of linear equations below?

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Who doesn't have power in a monarchy I would appreciate if someone could help me with this problem and answer it I will give you a brainlist :) Order form least to greatest 0.777, 9/11, 5/9, 65%, 0.714, 83.3%, 0.583, 0.5, 0.75, 4/9 The cartesian product of two sets P and Q can be written as The parent of a preschool-aged child asks the nurse for ideas on preparing the child for abdominal surgery requiring general anesthesia. What would the nurse recommend for this parent? a. Encourage the child to ask questions and talk about fearsb. Help the child select a couple of toys appropriate to take to the hospitalc. Use play to demonstrate procedures on the child's toy dollsd. Schedule a tour, specific for children, of the hospital and surgical area Ms. Contento buys a BMW with an initial value of $45,000. Yearly, the car'svalue depreciates by 5%. How much will the car be worth after 8 yours? Explain how conduction, convection, and radiation occur involving a campfire Calculate the NPV for the following projects with a discount rate of 12%:a.Project 1 costs $100,000 and earns $50,000 each year for three years.b.Project 2 costs $200,000 and earns $150,000 in the first year, and then $75,000 for each of the next two years.c.Project 3 costs $25,000 and earns $20,000 each year for three years.d. If the projects are mutually exclusive, which should we accept?e. If the projects are independent, which should we accept? Crystal reads 25 pages in 1 hour. Write an equation to represent the 2relationship between the number of pages Crystal reads and how much time she spends reading. Let p = number of pages and t = number of hours. Given 9x2 + 4y2 18x + 16y 29 0, which graph represents the inequality?edge2021 Please select the word from the list that best fits the definitionStates that buoyant force = weight of the fluid displaced An amphoteric species is neither an acid nor a base. True or False what are angular shapes that uniform measurement 28)What is a molecule made from joining together small molecules called monomers?A)amino acidB)glucose moleculeC)nucleotideneD)polymer20 Which was an argument to justify imperialism at the turn of the century? Numbers 15-21 HELP PLEASE!! Solved ExaExample 1. An iron ball of mass 3 kg isreleased from a height of 125 m and fallsfreely to the ground. Assuming that thevalue of g is 10 m/s2, calculate(i) time taken by the ball to reach theground(ii) velocity of the ball on reaching theground(iii) the height of the ball at half the time ittakes to reach the ground. Below, you are provided with a consumer's income and the prices of two different goods. You will identify different combinations of the two goods that the consumer can afford and construct the consume What is the radius and diameter of the following circle?16 cm divide 3x2 11x 4 by x 4. (2 points) x 1 x 23 3x 1 3x 23