Answer:
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
Step-by-step explanation:
For each child, there are only two possible outcomes. Either it is a boy, or it is a girl. The probability of a child being a boy or a girl is independent of the other children. So we use the binomial probability distribution to solve this question.
The conditional probability formula is also used.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Find the probability of a couple having a baby boyboy when their sixth child is born, given that the first five children were all boys.
Event A: First five children being boys.
Event B: Sixth children being a boy.
P(A):
First five children being boys.
P(X = 5) when n = 5.
Equally likely to be boy or girl, so p = 0.5.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A) = P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
Intersection:
Intersection between the first five children being boys and the sixth also being a boy, so [tex]P(X = 6)[/tex] when n = 6.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(A \cap B) = P(X = 6) = C_{6,6}.(0.5)^{6}.(0.5)^{0} = 0.015625[/tex]
Probability:
[tex]P(B|A) = \frac{0.015625}{0.03125} = 0.5[/tex]
50% probability of a couple having a baby boyboy when their sixth child is born, given that the first five were all boys.
Shoe store A is having a sale in which every pair of shoes is 40% off the regular price.
Shoe store B is having a sale in which $40 is deducted from the regular price.
Richard is comparing the price of the same pair of shoes in both shoes in both stores.In both stores, the shoes normally sell for $120. Which store has the better bargain?
Explain the rules for multiplication and division to convert units. How do you know when to multiply and when to divide to convert untis of measurement?
a rectangle that is 2 inches by 3 Inches has been scaled by factor of 7 suppose you want to scale the copy back to its original size what scale factor would you use?
This is about transformation of objects.
Scale factor back to original size = 1/7
We are told that the rectangle was scaled by a factor of 7.What this means is that if the length and width are x and y respectively, then the new scaled measurements will be;
7x and 7y.
Now,for us to scale back to the original size, all we need to do is to divide the new scale measurements by a factor of 7.This means the original size will be;
Length = 7x × 1/7
Width = 7y × 1/7
Thus,the scale factor will be 1/7 back to the original size.Read more at; https://brainly.com/question/17292295
Shondra found large candles on sale at her favorite store. She has a large family and many friends, so she bought as many of the candles she could fit in her trunk to give as gifts. Her trunk is 2 feet deep, 4 feet wide, and 3 feet long. If each candle comes in a cube box with 1 foot edges, how many candles will fit in her trunk? A) 9 candles B) 10 candles C) 14 candles D) 24 candles
If the original 24 m edge length x of a cube decreases at the rate 5m/min, when x=3 at what rate does the cube's surface area change
The change in the cube's surface area is -180 m^2/min when the edge length is 3 m. This is found by differentiating the surface area with respect to time and substituting the given values.
Explanation:The subject of the question is related to rates of change in the context of the geometry of a cube. To address this problem, we use the formula for a cube's surface area, which is given by A = 6x^2, where x represents the length of an edge. If x changes with respect to time, we denote this change as dx/dt, which is given as -5m/min. You want to find how quickly the surface area, A, changes when x = 3.
First, let us differentiate the surface area A with respect to time t. By the chain rule of differentiation, dA/dt = dA/dx * dx/dt. Given A = 6x^2, dA/dx = 12x. substituting x=3 and dx/dt=-5, we find that dA/dt = 12*3*-5, which equals -180m^2/min.
Therefore, the change in the cube's surface area is -180 m^2/min when the edge length is 3 m.
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9ax+9b-6=21
based on the equation above what is the value of ax+b
The value of equation ax + b is 3.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the value of ax + b, we need to isolate that expression on one side of the equation.
Starting with:
9ax + 9b - 6 = 21
We can add 6 to both sides:
9ax + 9b = 27
Then, we can factor out 9 from the left-hand side:
9(ax + b) = 27
Dividing both sides by 9, we get:
ax + b = 3
Therefore,
The value of equation ax + b is 3.
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a bike path is 6 3/4 miles long. what whole number is closest to 6 3/4
which relation defined by mapping diagram is a function
a triangle has an area of 54 m2 and a height of 9m how long is the base of the triangle entered your answer in the box
Enrique charges $5 for every 1/5 hour he spends walking dogs.in the morning he walks buttons for 2/5 hour bruno for 1/5 hour and pepper for 3/5 hour. Monday thru friday. On saturdays he takes mimi diva and coco to the dog park for 4/5 of an hour. On wendsday this week it rained and pepper wanted to stay out for only 1/5 hour. How many hours did enrique spend with the dogs this week. Explain your method
There are fewer than 8 gallons of gas in the tank how do I write an inequality for that
Find the equation of the plane through the point p=(5,5,4)p=(5,5,4) and parallel to the plane 5x+2y−z=−6.
A swimmer swam 49 kilometers in d days. what is the value of d if the swimmer swam an average of 3.2 kilometers daily?
Which is a correct way of evaluating the expression 25x + 40x for x = 4?
Five hummingbirds drink 7.5 ounces of sugar water a day. How much sugar water is needed for 14 hummingbirds?
what is the answer to m-1/6-4m+5/6
A chef uses 3 3/4 pounds of semolina flour and 1 5/8 pounds whole wheat flour for each batch of pasta she makes. One week she uses a total of 86 pounds of flour.
Write an equation to solve for b, the number of batches of pasta the chef makes during the week.
How many batches of pasta does she make? Show your work.
To find the number of batches of pasta, convert the amount of flour per batch to an improper fraction, create an equation based on the total flour used, and solve for the number of batches, which is 16.
To solve for b, the number of batches of pasta the chef makes during the week using a total of 86 pounds of flour:
First, convert the amounts of each flour from mixed numbers to improper fractions:
1 5/8 pounds = 13/8 pounds
Now add the two amounts together to get the total flour used per batch:
(15/4) + (13/8) = 30/8 + 13/8 = 43/8 pounds per batch
The equation to solve for b is:
(43/8) * b = 86
To find b:
b = 86 / (43/8)
Multiply both sides by the reciprocal of 43/8:
b = 86 * (8/43)
b = (86 * 8) / 43
Calculate the value of b:
b = 688 / 43
b = 16
Which of the following can only be used after you prove triangles are congruent? Alternate Interior Angles Reflexive Substitution CPCTC
Final answer:
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent and can only be used after proving triangles are congruent. It helps in confirming that corresponding parts of congruent triangles are congruent.
Explanation:
CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It can only be used after you prove triangles are congruent. When two triangles are proven congruent, CPCTC allows you to show that corresponding parts like angles and sides are congruent as well.
Suppose that the polynomial function A(x) = - 0.0082x2 + 0.06x approximates a person's blood-alcohol level x hours after drinking 5 ounces of 80-proof whiskey. What is the person's blood-alcohol level after 3 hours?
If changes are made to a signature while using version 5.x signature files, are they visible in the router running the configuration?
Which expression is equivalent to 10b - 25? 10(b - 15) 5(b - 5) 5(5b - 20) 5(2b - 5)
A school sold small and large boxes of fruit as a fundraiser. One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218. Let x represent the price of a small box and y represent the price of a large box. Solve the system to determine the price of each size box of fruit.
A The price of a small box of fruit is $10 and the price of a large box of fruit is $14.
B The price of a small box of fruit is $8 and the price of a large box of fruit is $14.
C The price of a small box of fruit is $10 and the price of a large box of fruit is $16.
D The price of a small box of fruit is $14 and the price of a large box of fruit is $16.
The answer is y=14 and x= 10
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: One student sold 5 small boxes and 13 large boxes for $232. Another student sold 12 small boxes and 7 large boxes for $218.
Then we have 5x+13y=232
12x+7y=218
Solving these two equations here we get y=14 and x= 10
Hence, The answer is y=14 and x= 10
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2 to the x power equals 512
A Broadway musical was attended by a total of 2,838 people, including men, women, and children. The number of women who attended the event was 5 more than 3 times the number of children, while the number of men was 3 less than 4 times the number of women. Write an equation to model this situation. Then, use the equation to find the number of men, women, and children who attended the musical.
which equation is the inverse of y=100-x2
Answer:
Inverse of y = [tex]f^{-1}(x)[/tex] = [tex]\sqrt{100 -x}[/tex].
Step-by-step explanation:
Given : f(x) = y = 100 - x²
To find : Find inverse.
Solution : We have given that :
f(x) = y = 100 - x²
Step1) : Replace every x with a y and replace every y with an x .
x = 100 - y².
Step 2): Solve for y
On subtracting 100 from both sides
x - 100 = -y²
On multiplying both side by -1
100 -x = y²
Taking square root both sides and switching sides
y = ± [tex]\sqrt{100-x}[/tex].
Step3 ) : Replace y with [tex]f^{-1}(x)[/tex].
[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Therefore, inverse of y = [tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{100-x}[/tex].
Answer:
A on edge
Step-by-step explanation:
i need help on this one :)
William runs 5 meters in 20 steps. How many kilometers will he run if he takes 1,000 steps ?
"how few colors can be used so that each room is painted a color so in which no two adjacent rooms are the same color?"
We can see here that to guarantee that no two adjacent rooms are the same color, a minimum of four colors is generally needed.
To determine the minimum number of colors needed to paint each room in a way that no two adjacent rooms have the same color, we can use a coloring algorithm known as the "Four Color Theorem." According to this theorem, it is possible to color any map on a plane using at most four colors, ensuring that no two adjacent regions have the same color.
Applying this concept to the rooms, we can conclude that a minimum of four colors is needed to satisfy the given condition. By using these four colors, we can ensure that no two adjacent rooms share the same color.
in 3/4 identify the role of 3. Then explain how to read tbis number
Answer:
The 3 is the numerator, To read the number is "three-fourths"
Step-by-step explanation:
I hope this helps!
A vegetable farmer fills 2/3 of a wooden crate with 5/7 pound of tomatoes. How many pounds of tomatoes can fit into one crate?