Assuming boys and girls are equally likely, find the probability of a couple having a baby boyboy when their sixthsixth child is born, given that the first fivefive children were all boysall boys.
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.
Use the expression below to complete the following tasks. (3a2 - 5ab + b2) - (-3a2 + 2b2 + 8ab) What is the additive inverse of the polynomial being subtracted?
Answer:
Option 3
Step-by-step explanation:
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Jack purchased a box of 1,000 candy guitar lollipops to sell in the bakery for $20.00. How much did he pay for each lollipop?
Noah makes ceramic pots for the market. On the weekends he makes 11 more pots than he does during the week. Noah represented the number of pots he makes on weekends using the expression p + 11. Which expression represents the total mumber of pots Noah made one weekend if he made 14 more than his usual number?
what are two functions, f(x) and g(x), that would result in a rational function?
Lexi's bulletin board is 40 centimeters wide. each of her ribbons is 4 centimeters wide, and her photos are 12 centimeters wide. what combination of ribbons and photos will fit side by side with no overlap on Lexi's bulletin
Where is the vertex of the quadratic y = (x -7)2 + 9
Final answer:
The vertex of the quadratic function y = (x -7)² + 9 is at the point (7, 9).
Explanation:
Vertex of a quadratic function is the highest or lowest point on the graph of the function. In this case, the quadratic function is in the form y = (x -7)² + 9.
To find the vertex, we notice that the function is in the form y = (x - h)² + k, where (h, k) represents the vertex. Therefore, the vertex of the given quadratic function is at (7, 9).
Brooke earns $7 an hour at her job now. She can represent the total she makes in a week using the expression 7r. Brooke has asked for a $1 an hour raise. Which expressing would represent the amount Brooke would make in a week after the raise?
find the difference of the least common multiple and the greatest common factor of 12 and 32 show your work please
Janet makes homemade dolls. Currently, she produces 23 dolls per month. If she increased her production by 18%, how many dolls would Janet produce each month?
The range of F(x) = 6 * 3x is all positive real numbers.
Workers in france average 5 fewer days of vacation a year than italians. americans average 24 fewer vacation days than the french. if the italians average 42 vacation days each year (the most in the world), how many does the average american worker have a year?
4x. (2x^3 — x^2–18x+15) Standard Form
Describe the test grades using the measures of center
An Native American tepee is a conical tent. Find the number of cubic feet of air in a teepee 10 ft. in diameter and 12 ft. high. 100 cu. ft. 300 cu. ft. 400 cu. ft.
Answer:
100 pi cubic feet
Step-by-step explanation:
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5. Marco wrote the equation below.
cos(-pi/2)=cos(3pi/2)
which statement best describes marcos equation?
a. it is true because the cosine function is odd
b. it is false because the cosine function is even
c. it is true because the cosine function has a period of 2pi
d. it is false because the cosine function has a period of pi.
The given equation is represented below:
cos(-pi/2)=cos(3pi/2)
The value of cos(-pi/2) is 0 and the value of cos(3pi/2) is also 0
Further a function is defined as an even function if f(x) = f(-x)
Cosine function is an even function.
Therefore it is true and the correct option is c
It is true because the cosine function has a period of 2pi
Hope it helps ..!!
Answer:
Option C - It is true because the cosine function has a period of [tex]2\pi[/tex].
Step-by-step explanation:
Given : Marco wrote the equation below.
[tex]\cos (-\frac{\pi}{2})=\cos (\frac{3\pi}{2})[/tex]
To find : Which statement best describes Macro equation?
Solution :
Since, the period of the given cos function is 360°
So, it holds the property of trigonometric :
[tex]\cos \theta=\cos (2\pi+\theta)[/tex] then the function is an even function.
Taking [tex]\theta =-\frac{\pi}{2}[/tex]
Then , [tex]2\pi+\theta = 2\pi-\frac{\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{4\pi-\pi}{2}[/tex]
[tex]2\pi+\theta = \frac{3\pi}{2}[/tex]
So, the given function is a even function in a period of [tex]2\pi[/tex].
Therefore, Option C is correct.
It is true because the cosine function has a period of [tex]2\pi[/tex].
Jeannie's restaurant served 58 customers on Monday. After the first day the amount of customers served decreases at a rate of 2.5% each day.
What is the explicit rule for this situation and approximately how many customers will be served on the 6th day?
Round to the nearest customer.
Drag and drop the answers into the boxes to match the situation.
Explicit rule
Number of customers on the 6th day.
A n = 58 x (0.975) n - 1, A n = 58 x (0.025) n - 1, A n = 58 (1.025) n - 1, 51, 49, 48, 46,
Answer:
51 customers
Step-by-step explanation:
Jeannie's restaurant served 58 customers on Monday.
Rate of decrement r =2.5 % = 0.025
Formula : [tex]y=a(1-r)^{n-1}[/tex]
A is the initial amount
r is the rate
n is the no. of days
So, Substitute the values
[tex]y=58(1-0.025)^{n-1}[/tex]
[tex]y=58(0.975)^{n-1}[/tex]
So, explicit rule : [tex]A_n=58(0.975)^{n-1][/tex]
Now to find the no. of customers will be served on the 6th day
Substitute n = 6
[tex]A_6=58(0.975)^{6-1}[/tex]
[tex]A_6=51.1035[/tex]
So, 51 customers will be served on the 6th day
John always wears a shirt, pants, socks, and shoes. He owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. How many different outfits can John make?
Answer:
900
Step-by-step explanation:
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Box i contains 4 red and 8 blue marbles while box ii contains 5 red and 3 blue marbles. an unfair coin is tossed –whose probability of turning up heads is 40%. if the coin comes up heads box i is chosen and a random marble is chosen, otherwise if it is tails the marble is chosen from box ii.(a)find the probability a red marble is chosen.(b)if a red marble is chosen, what is the probability it came from box i? (c)if a blue marble is chosen, what is the probability it came from box i?
A guy-wire is attached from the ground to the top of a pole for support. If the angle of elevation to the pole is 67° and the wire is attached to the ground at a point 137 feet from the base of the pole, what is the height of the pole (round to 2 decimal places)?
Answer:
The height of the pole is 322.75 feet.
Step-by-step explanation:
Let the triangle Δ ABC with AC be the length of wire and AB be the Height of the pole
Length between the point of attachment of wire from base of the pole = BC = 137 feet
Angle of elevation to the pole = θ = 67°
We have to find the length of the pole that is AB Let the height of pole be h feet.
According to trigonometry :
[tex]\tan C=\frac{\text{perpendicular}}{\text{base}}[/tex]
Here, C = 67° , perpendicular = AB = h , base = BC = 137
Substitute the values,
[tex]\tan 67^{\circ}=\frac{AB}{BC}[/tex]
[tex]\tan 67^{\circ}=\frac{h}{137}[/tex]
[tex]h=\tan 67^{\circ} \times 137[/tex]
[tex]h=322.75[/tex]
Thus, the height of the pole is 322.75 feet.
Answer:60.1
Step-by-step explanation:
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Brent was looking at his cell phone bill and saw that the total number of texts he has sent is tracked, as shown below:
Month
Texts
1
120
2
237
3
354
4
471
The function representing Brent's texting per month is f(m) = 117m + 3. What does the 117 represent?
It should be the additional texts per month or D
Answer:
The number of texts he sends per month
Step-by-step explanation:
The function f(m) = 117m + 3 is a linear function, which is in the form f(x) = mx+b. In this form, m (the number beside our variable) is the slope, or rate of change, and b (the number added or subtracted) is the y-intercept.
In our function, 117 is the number beside the variable, which makes it the slope. This is the rate of change of this function; it describes how the dependent variable (number of texts) changes for every change in the independent variable (months).
In other words, it tells how many texts he sends per month.
Two rectangular prisms have the same volume. The area of the base of the blue prism is 216 square units. The area of the base of the red prism is one third that of the blue prism. Which statement is true?
a) The height of the red prism is one-third the height of the blue prism.
b) The height of the red prism is the same as the height of the blue prism.
c) The height of the red prism is six times the height of the blue prism.
d) The height of the red prism is three times the height of the blue prism.
Answer:
D
Step-by-step explanation:
Which of these is a point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7)
A. y+7=4(x-3)
B. y-7= -1/4(x+3)
C. y+7= -1/4(x-3)
D. y-7= -4x(x+3)
The point-slope equation of the line that is perpendicular to y-3=4(x-10) and passes through(-3,7) is:
B. [tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
The slope intercept form is y=mx+b where m is slope.
We have given perpendicular line as:
y-3=4(x-10)
y-3=4x-40
y=4x-37
The slope intercept form of the given line is
y=4x-37
Slope of this line is m=4
Now, as we know the two perpendicular lines have negative reciprocal slope.
Thus the other line have slope [tex]m=-\frac{1}{4}[/tex]
Now. the equation of line passing through point (-3,7) and having slope [tex]\frac{-1}{4}[/tex] is:
[tex]y-7=\frac{-1}{4} (x+3)\\[/tex]
Therefore the correct option is B.
Learn more: brainly.com/question/18595188
Kens turtle competed in a 0.50- meter race. His turtle had traveled 49/100 meter when the winning turtle crossed the finish line. What is 49/100 written as a decimal
Well, to make it simple it's 0.49. Hope it helps!
y = -16x2 + 32x - 10 This parabola has x-intercepts, representing the times when the dolphin's height above water is feet.
Answer:
2
0
two real solutions
Step-by-step explanation:
from edge!!
To find the x-intercepts of the quadratic equation representing the height of a dolphin's jump, we can use the quadratic formula by plugging in the coefficients from the equation y = -16x^2 + 32x - 10. The intercepts indicate the times when the dolphin's height above water is zero feet.
Explanation:The question involves finding the x-intercepts of a quadratic equation, which represent the points where a parabola crosses the x-axis. In this context, the x-intercepts correspond to the times when the dolphin's height above water is 0 feet. To find the x-intercepts, we can use the quadratic formula:
x = −b ± √(b² − 4ac) / (2a)
For the equation y = −16x² + 32x − 10, the coefficients are a = −16, b = 32, and c = −10. By substituting these values into the quadratic formula, we can calculate the times when the dolphin is at the water level (y=0). Since this is a mathematical problem involving a real-world scenario, it is essential to check that the resulting times make sense within the context. Negative values for time, for example, would not be physically meaningful.
Learn more about Quadratic Equation here:https://brainly.com/question/30098550
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Which of the following would NOT be a deduction from a paycheck?
Select the best answer from the choices provided.
taxes
FICA
hourly wages
health insurance
Cheryl paid $3.00 for a pair of socks and eight times as much for a pair of shoes. Her brother Kevin also bought socks and shoes but paid twice as much as Cheryl did for each. How much money did they spend together ?
Lines l and m are parallel and intersected by transversals t and s as shown in the figure below.
What is m
A) 180 degrees
B) 360 degrees
C) 540 degrees
D) 720 degrees
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