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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Find the difference. Write your answer in simplest form.
9/10 - 5/10
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!
Simplify: 6a - 2(5a - 6)
Answer:
[tex]-4a + 12[/tex]
Step-by-step explanation:
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
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
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.
Answer:
B is the correct answer
Step-by-step explanation:
anyone know this or can help pls
Answer:
A pyramid
Step-by-step explanation:
10/y=2/9, find the solution of y. stat.
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
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
Answer:
D
Step-by-step explanation:
EXPLAIN THE DIFFERENCE OF THE CIRCUMFERENCE AND THE AREA OF THE CIRCLE.
PLS ANSWER IT.
circumference is around the circle the border of the circle the area of the circle is the space in the circle
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.
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.
determine the volume of the rectangular prism.
height:12ft
width:6ft
length:3ft
Answer:
216 ft³
Step-by-step explanation:
h*w*l=v
[tex]12 \times 6 \times 3 = 216[/tex]
Write the equation of the line if the slope is 6 and the y-intercept is -2.
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
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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convert from vertex form to standard form... y= -(x-3)^2-8
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
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
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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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:
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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what number adds up to three and multiples 22 to
Answer:
Factors of 22: 1, 2, 11, and 22.
Prime Factorization of 22: 22 = 2 × 11.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?
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?
I need help I don’t really get it
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
Solve the linear system X 1 X1 + 2x2 3.21 + 4.02 IL || -1 -1 = via Cramer's rule if possible.
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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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?
Answer:
I DO NOT KNOW
Step-by-step explanation:
I am here for the answers
I am hungry
Pizza
A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the box?
Thanks in advance!
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
ver imagen para la pregunta
Answer: C
Step-by-step explanation:
What is angle BXC and why?? Please help
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
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 =_____
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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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
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
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?
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
Pls helpppp and thank you
26.2 miles in 4 hours. Find the unit rate
Answer:
Step-by-step explanation:
Unit rate = 26.2 ÷ 4 = 6.55
(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?
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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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