What is the probability that this year's graduation will fall on the birthday of exactly one of the 68 Seniors? What is the probability that there is more than one such Senior?
Answers
The probabilities are given as follows:
Birthday of one student: 0.1550 = 15.50%.Birthday of more than one student: 0.0152 = 1.52%.What is the binomial distribution formula?The mass probability formula, giving the probability of x successes, is of:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are given by:
n is the number of trials of the experiment.p is the probability of a success on a single trial of the experiment.The parameter values for this problem are given as follows:
n = 68, as the class is composed by 68 Seniors.p = 1/365, as the year has 365 days, hence the probability of a person having a given day as a birthday is of 1/365.Hence the probability of one senior having the birthday on the same day as the graduation is of:
P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.
The probability of more than one is given as follows:
P(X > 1) = 1 - P(X <= 1).
In which:
P(X <= 1) = P(X = 0) + P(X = 1)
Hence:
P(X = 0) = (364/365)^68 = 0.8298.P(X = 1) = 68 x 1/365 x (364/365)^67 = 0.1550.Finally:
P(X <= 1) = 0.8298 + 0.1550 = 0.9848.P(X > 1) = 1 - P(X <= 1) = 1 - 0.9848 = 0.0152.More can be learned about the binomial distribution at https://brainly.com/question/24756209
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Related Questions
I’m giving BRAIN LIST
Answers
Answer:
SKT is the triangle, by the SAS theorem
Step-by-step explanation:
2 sides are congruent, and the angle in the middle are congruent because of the vertical angles theorem.
does 3.2x - 5 = 3.2(x - 5) have infinitely many solution
Answers
Answer:no solution
Step-by-step explanation:3.2x-5=3.2(x-5) We need to distrube. 3.2 times x= 3.2x.
3.2 x-5= -16. Now our equation is 3.2x-5=3.2x-16. Cancel the numbers out. 5+-16= -11.
3.2x-3.2x= 0. We’re left with 0=-11
The equation does not have infinitely many solutions.
Given is an equation 3.2x - 5 = 3.2(x - 5) we need to see if it has infinitely many solution or not,
Let's solve the equation and see if it has infinitely many solutions.
3.2x - 5 = 3.2(x - 5)
Distribute the 3.2 first on the right side as follows:
3.2x - 5 = 3.2x - 16
3.2x should then be subtracted from both sides to get the constant term:
-5 = -16
This equation is false, though.
Right side is -16, while left side is -5.
There is no solution to the equation since -5 is not equal to -16.
The equation 3.2x - 5 = 3.2(x - 5) does not, therefore, have an endless number of solutions.
It cannot be resolved.
Hence the equation does not have infinitely many solutions.
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Assume thst y varies directly with x then solve if y=4 when x=12 find y when x=-24
Answers
Answer:
-8
Step-by-step explanation:
y=(1/3)x
4 = (1/3)12
y=(1/3)(-24)
y= -8
1. When two lines are parallel, which one of the following statements is not true?
(A) corresponding angles are congruent
(B) alternative interior angles are congruent
(C) consecutive interior angles are congruent (D) alternative exterior angles are congruent
Answers
Answer:
A
Step-by-step explanation:
the parrallel lines are not intersecting look up what congruent means and it will help you out
What is the slope of the line through ( 10, 1) and (0,4)?
khan Academy
Answers
Answer:
-1/2
Step-by-step explanation:
\(y^{2} = -4 \\y^{1} =-1\\x^{2} = 0\\x^{1} = -10\)
Using the formula \(\frac{y^{2}-y^{1} }{x^{2}-x^{1} }\)
\(\frac{-4-1}{0-(-10)}\)
Simplifly
\(\frac{-5}{10} = \frac{-1}{2}\)
In a bag of buttons, $80\%$ are brown, and the rest of the buttons are blue. The difference between the number of brown buttons and the number of blue buttons is 72 buttons. How many brown buttons are there?
Answers
There are 96 brown buttons in the bag out of 120 buttons.
80% of the buttons in the bag are brown, and the remaining buttons are blue.
The difference between the number of brown buttons and the number of blue buttons is 72.
Let the total number of buttons in the bag is x.
Since 80% of the buttons are brown, 80% of x is
= 0.8x.
The remaining buttons are blue, so the number of blue buttons is
= x - 0.8x
= 0.2x.
Therefore,
⇒ 0.8x - 0.2x = 72.
Simplifying this equation, we get
⇒ 0.6x = 72.
⇒ x = 72 / 0.6.
⇒ x = 120.
Hence finding 0.8x
= 0.8 * 120
= 96
Therefore, the number of brown buttons is 96.
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Which is an irrational number? A)pi- 42.25 B)5.2 C)0/3 D)4.37124
pls help❤
Answers
Answer:
A
Step-by-step explanation:
An irrational number is one in which it cannot be represented as a fraction.
A) pi - 42.25 cannot be expressed as a fraction
B) 5.2 can be expressed as 26/5
C) 0/3 is already expressed as a fraction
D) 4.37124 can be expressed as 437124/100000
to find the height of an apple tree in her yard, susan held a clipboard near her eye so that the top of the tree was viewed along one edge of the book and base of th etree was viewed along the adjacent edge.. if her height of eye is 4.5 feet and she is standing 15 feet fromt he tree, how tall is the tree?
Answers
The height of the apple tree in Susan's yard is 9 feet.
To find the height of the apple tree in Susan's yard, we can use similar triangles.
Step 1: Identify the two similar triangles.
Triangle 1 is formed by Susan's eye height (4.5 feet), the ground, and her distance from the tree (15 feet). Triangle 2 is formed by the tree's height, the ground, and the same 15 feet distance.
Step 2: Set up the proportion.
Let 'h' be the height of the tree. The proportion can be written as:
(height of eye) / (distance from tree) = (tree height) / (distance from tree)
4.5 / 15 = h / 15
Step 3: Solve for 'h'.
Cross-multiply the proportion to solve for 'h':
4.5 × 15 = h × 15
67.5 = h × 15
Divide both sides by 15:
h = 67.5 / 15
h = 4.5
Step 4: Add Susan's eye height to find the total height of the tree.
Total tree height = height of eye + height of tree above eye level
Total tree height = 4.5 + 4.5
Total tree height = 9 feet
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A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3. 1g and a standard deviation of 0. 14g
Answers
a) 81.86 percent of the pennies will weigh between 2.7 and 3.3g. b) 100 percent of the pennies will weigh between 2.5 and 3.7g. c) 2.28 percent of the pennies will weigh less than 2.7g. d) 15.87 percent of the pennies will weigh more than 3.3g.
To solve these questions, we will use the properties of the normal distribution and z-scores.
a) To find the percentage of pennies that weigh between 2.7 and 3.3g, we need to calculate the area under the normal curve between these two values.
First, we need to standardize the values using z-scores:
z1 = (2.7 - 3.1) / 0.2 = -2
z2 = (3.3 - 3.1) / 0.2 = 1
Next, we can use a standard normal distribution table or a calculator to find the area between these two z-scores. The area between -2 and 1 is approximately 0.8186 or 81.86%.
Therefore, approximately 81.86% of the pennies will weigh between 2.7 and 3.3g.
b) Similarly, to find the percentage of pennies that weigh between 2.5 and 3.7g, we need to standardize the values and calculate the area between the corresponding z-scores.
z1 = (2.5 - 3.1) / 0.2 = -3
z2 = (3.7 - 3.1) / 0.2 = 3
The area between -3 and 3 encompasses the entire distribution and is equal to 1 or 100%.
Therefore, 100% of the pennies will weigh between 2.5 and 3.7g.
c) To find the percentage of pennies that weigh less than 2.7g, we need to calculate the area to the left of the corresponding z-score.
z = (2.7 - 3.1) / 0.2 = -2
Using a standard normal distribution table or a calculator, we find that the area to the left of -2 is approximately 0.0228 or 2.28%.
Therefore, approximately 2.28% of the pennies will weigh less than 2.7g.
d) To find the percentage of pennies that weigh more than 3.3g, we need to calculate the area to the right of the corresponding z-score.
z = (3.3 - 3.1) / 0.2 = 1
Using a standard normal distribution table or a calculator, we find that the area to the right of 1 is approximately 0.1587 or 15.87%.
Therefore, approximately 15.87% of the pennies will weigh more than 3.3g.
Correct Question :
A group of students weighs 500 US pennies. They find that the pennies have normally distributed weights with a mean of 3.1g and a standard deviation of 0.2g
a) What percentage of pennies will weigh between 2.7 and 3.3g?
b) What percentage of pennies will weigh between 2.5 and 3.7g
c.) What percentage of pennies will weigh less than 2.7g?
d.) What percentage of pennies will weigh more than 3.3g?
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5/15 in simplest form please someone
Answers
Answer:
1/3
Step-by-step explanation:
5/15
= (5÷5)/(15÷5)
= 1/3
So, 1/3 is the simplest form.
Answer:
1/3
Step-by-step explanation:
You are required to: a.Rewrite the formulation above in the standard form by adding the required variables to replace the inequalities. b.Find a solution for the above formulation utilizing the linear programming simplex method.
Answers
Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.
a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:
Maximize P = 3x + 2y + 4z
Subject to:2x + y + z + s1 = 8
x + 2y + 3z + s2 = 10
x, y, z ≥ 0
b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.
To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.
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Please answer this (who ever answers correctly gets brainlest)
Answers
Answer:
0.171 m
Step-by-step explanation:
First, let's determine how many mm of track he has in total...
74mm+97mm=171 mm
Now, we can set up a unit converter to convert mm to m (note that 1 mm is \(10^{-3{\) m)...
\(171mm(\frac{10^{-3}m}{1mm})\)
The "mm" cancels out...
\(171*10^{-3}m=0.171m\)
Answer:
Step-by-step explanation:
74 + 97 = 171 mm
Length of the train track = 171 mm = 171÷ 1000 = 0.171 m
Doug is a zookeeper in charge of monitoring the "aquatic" section at the North End Zoo. A baby dolphin was born on Wednesday and weighed 31 pounds. The dolphin is growing at an average rate of 2.3lbs per day. Write a function that can be used to find the weight, w(x), of the dolphin after x, days.
Answers
Answer:
w(x)=2.3x+31
Step-by-step explanation:
From the information given, the function would indicate that the weight of the dolphin after x days would be equal to the 31 pounds the baby weighed when it was born plus 2.3 lbs that is the average rate it is growing for the number of days:
w(x)= 2.3x+31, where:
w(x)= weight of the dolphin
x=number of days
show that if x and y are independent, var[x y] = var[x] var[y]
Answers
First, we know that var[x] = E[(x - E[x])^2] and var[y] = E[(y - E[y])^2], where E denotes the expected value.
Next, let's calculate var[x y] = E[(xy - E[xy])^2]. Since x and y are independent, we have E[xy] = E[x] E[y]. Therefore, var[x y] = E[(xy - E[x] E[y])^2].
Expanding this expression further, we get var[x y] = E[(x-E[x])^2(y-E[y])^2].
Finally, we can use the independence of x and y to simplify this expression to get var[x y] = E[(x-E[x])^2] E[(y-E[y])^2] = var[x] var[y].
Therefore, we have shown that if x and y are independent, var[x y] = var[x] var[y].
If x and y are independent variables, it means that their occurrence or value does not depend on each other. To show that var[x y] = var[x] var[y] when x and y are independent, we can use the definition of variance and covariance.
Since x and y are independent, their covariance, cov[x, y] = 0. The variance of a product of two independent variables can be expressed as:
var[x y] = E[(x y)^2] - (E[x y])^2
Now, we use the property that the expected value of a product of independent variables is equal to the product of their expected values:
E[x y] = E[x] E[y]
So, we can rewrite the variance as:
var[x y] = E[(x y)^2] - (E[x] E[y])^2
Since x and y are independent, we can use the property E[XY] = E[X]E[Y] for the first term as well:
E[(x y)^2] = E[x^2] E[y^2]
Now we have:
var[x y] = E[x^2] E[y^2] - (E[x] E[y])^2
Recall the definitions of variance for x and y:
var[x] = E[x^2] - (E[x])^2
var[y] = E[y^2] - (E[y])^2
Multiplying var[x] and var[y]:
var[x] var[y] = (E[x^2] - (E[x])^2) (E[y^2] - (E[y])^2)
Expanding this, we get:
var[x] var[y] = E[x^2] E[y^2] - (E[x])^2 E[y^2] - E[x^2] (E[y])^2 + (E[x])^2 (E[y])^2
Notice that the last three terms in var[x] var[y] cancel out with the last three terms in var[x y]. Thus, we can conclude that:
var[x y] = var[x] var[y]
This shows that the variance of the product of two independent variables x and y is equal to the product of their individual variances.
Finally, we can use the independence of x and y to simplify this expression to get var[x y] = E[(x-E[x])^2] E[(y-E[y])^2] = var[x] var[y].
Therefore, we have shown that if x and y are independent, var[x y] = var[x] var[y].
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What is C L in Roman numerals?
Answers
Answer:
150
Step-by-step explanation:
It's very simple
C=100
L=50
CL=150
Answer:
150
Step-by-step explanation:
There are seven symbols that are used in the Roman Numeral system.
What is the equation of a line that passes through the point (8, 1) and is perpendicular to the line whose equation is y=−23x 5? enter your answer in the box.
Answers
The equation of the line perpendicular to our supplied line is represented by the equation y = 3/2x - 11.
What is the Equation of the line?A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.
On the y-axis, this value c is referred to as the intercept.
So, we have the points (8, 1).
The given equation is y = 2/3x + 5.
We are aware that a perpendicular line's slope is the negative reciprocal of the provided line's slope.
As a result, the slope of the line perpendicular to line y = 2/3x + 5 will be equal to the reciprocal of -2/3.
Negative reciprocal of -2/3 = -(-3/2)
Negative reciprocal of -2/3 =3/2
When we enter the coordinates of the location (8, 1) and m = 3/2 into the slope-intercept form of the equation, we get:
1 = 3/2 * 8 + b
1 = 3 * 4 + b
1 = 12 + b
1 - 12 = 12 - 12 + b
- 11 = b
Therefore, the equation of the line perpendicular to our supplied line is represented by the equation y = 3/2x - 11.
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ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!
Answers
Answer:
C. $140
Step-by-step explanation:
Company C; $60 + ($20×4)
= 140
Answer:
Company C
Step-by-step explanation:
If f (x ) =
1/3-x - 1, what is f (-12) and f (9)?
Answers
Answer:
F(-12)=34/3 F(9)=-29/3
Step-by-step explanation:
PLSSS HELP I WILL MARK BRAINLIST
Answers
At age 45 when the deferred payments from his current contract ends, all-star shortstop Alex Rodriguez plans to have $230 million in savings from his baseball playing days. He wants two things from his savings: a 40-year ordinary annuity and $500 million at age 60 in order to purchase majority ownership in his native Miami's Florida Marlins. How large can his annual annuity payment be based on this information and assuming his savings can earn 8% annually after age 45 ? $6,069,727 $5,620,118 $6,906,832 $6,395,215
Answers
Therefore, the annual annuity payment can be approximately $6,069,727.
To calculate the size of the annual annuity payment, we can use the present value formula for an ordinary annuity. The formula is given by:
PMT = PV / [(1 - (1 + r)⁻ⁿ) / r]
Where:
PMT = Annual annuity payment
PV = Present value of the annuity
r = Annual interest rate
n = Number of periods
Given:
PV = $230 million
r = 8% = 0.08
n = 40 years
Using the formula, we can calculate the annual annuity payment:
PMT = 230,000,000 / [(1 - (1 + 0.08)⁻⁴⁰) / 0.08]
PMT ≈ $6,069,727
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MARK YOU THE BRAINLIEST !
Answers
Answer:
Angle C also measures 64°.
find the missing value in the ratio table
Answers
If 8/2x-3 = 4, what is the value of x?
Answers
Answer:
extract-7/4
decimal-1.75
mixed number-1 3/4
Step-by-step explanation:
Consider the following function. f(x) = (5 − x)(x + 1)2 (a) Find the critical numbers of f. (Enter your answers as a comma-separated list.) x = (−1,3) (b) Find the open intervals on which the function is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing (−1,3) decreasing (−[infinity],−1),(3,[infinity]) (c) Apply the First Derivative Test to identify the relative extremum. (If an answer does not exist, enter DNE.) relative maximum (x, y) = 3,75 relative minimum (x, y) = −1,0
Answers
The following parts can be answered by the concept of critical numbers.
a. The critical numbers: x = (-1, 3)
b. The intervals between critical numbers.
- f'(x) > 0 for (-∞, -1) and (3, ∞), so the function is decreasing on those intervals: (-∞, -1), (3, ∞).
- f'(x) < 0 for (-1, 3), so the function is increasing on that interval: (-1, 3)
c. - f'(-1) changes from negative to positive, so there is a relative minimum at x = -1, f(-1) = 0. Hence, relative minimum (x, , y) = (-1, 0).
- f'(3) changes from positive to negative, so there is a relative maximum at x = 3, f(3) = 75. Hence, relative maximum (x, y ) = (3, 75).
Given the function f(x) = (5 - x)(x + 1)², we will find the critical numbers, intervals of increasing or decreasing, and apply the First Derivative Test to identify the relative extremum.
(a) The critical numbers are found by setting the first derivative equal to zero.
f'(x) = (-1)(x + 1)² + 2(x + 1)(5 - x) = 0
Solving for x, we find the critical numbers: x = (-1, 3)
(b) To determine intervals of increase or decrease, we examine the sign of f'(x) in the intervals between critical numbers.
- f'(x) > 0 for (-∞, -1) and (3, ∞), so the function is decreasing on those intervals: (-∞, -1), (3, ∞).
- f'(x) < 0 for (-1, 3), so the function is increasing on that interval: (-1, 3)
(c) Applying the First Derivative Test:
- f'(-1) changes from negative to positive, so there is a relative minimum at x = -1, f(-1) = 0. Hence, relative minimum (x, y) = (-1, 0).
- f'(3) changes from positive to negative, so there is a relative maximum at x = 3, f(3) = 75. Hence, relative maximum (x, y) = (3, 75).
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At Giant you can get 3 cases of water for $12.99. At Shoprite you can get 4 cases of water for $12.00. Which store is the best place to shop for water?
Answers
Answer:
Shoprite
Step-by-step explanation:
At giant each case of water is 4.33 You can figure this out by dividing the overall cost of 12.99 by 3 and that gives you the cost of one case of water. At Shoprite you get 4 cases for 12.00 again you divide the overall cost of 12.00 by 4 and that gives you 3.00 so you get a better deal at shoprite there fore shoprite is the better place to shop for water
determine if the argument is valid or a fallacy. give a reason to justify answer. if i'm hungry, then i will eat. i'm not hungry. i will not eat.
Answers
The argument is valid. According to modus tollens, the conclusion "I will not eat" logically follows
The argument follows a valid logical form known as modus tollens, which is a valid deductive argument form. Modus tollens states that if a conditional statement (e.g., "if A, then B") is true and the consequent (B) is false, then the antecedent (A) must also be false.
In this argument, the conditional statement is "If I'm hungry, then I will eat" (A = I'm hungry, B = I will eat), and the premise "I'm not hungry" establishes that the consequent (B) is false.
Therefore, according to modus tollens, the conclusion "I will not eat" logically follows
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Hesperia Community Center is buying new seating for their building. They want to purchase a combination of stools and chairs. Stools cost $15 and chairs cost $25. The center cannot spend more than $1500.
Which inequality represents all possible combinations of s stools and c chairs?
15s+25c<1500
15c+25s≥1500
15c+25s≤1500
15s+25c≤1500
Answers
Answer:
15s + 25c is less than or equal to (the sign that’s pointing left with the aural sign under it) 1500
also d lol
Step-by-step explanation:
the stools are s and each stool cost 15$ same thing with chairs. the chairs are c and they cost 25$, they have to equal or be less than 1500$
i need help with adding ratinal numbers
Answers
Addition of rational numbers
how many man are in 3.5×10
−2
krn? a) 3.5×10
−1
mm c) 3.5×10
−2
mm b) 3.5×10
−7
mm d) 3.5×10
5
mm e) 3.5×10
4
mm
Answers
There are 35,000 millimeters in 3.5×10^(-2) kilometers.
To convert from kilometers (km) to millimeters (mm), we need to multiply the given value by a conversion factor. There are 1,000,000 (1 million) millimeters in one kilometer.
We know: 3.5×10^(-2) km
To convert this to millimeters, we can use the conversion factor:
1 km = 1,000,000 mm
Therefore, the calculation becomes:
3.5×10^(-2) km × 1,000,000 mm/km = 3.5×10^(-2) × 1,000,000 mm
Simplifying the calculation:
3.5×10^(-2) × 1,000,000 = 35,000 mm
So, there are 35,000 millimeters in 3.5×10^(-2) km.
None of the provided options (a, b, c, d, e) represent the correct answer of 35,000 mm.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
Answers
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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