Answer:
(a)The probability that a person 65 or over and has a loan is 0.052.
(b)The probability that a person 65 or over and has a loan is 0.476
(c) The probability that a person is 65 or over and has a loan independent is 0.0952
Step-by-step explanation:
Conditional probability:
Let A and B any two event is connected to a given random experiment E. The conditional probability of the event A on the hypothesis that the event B is occurred, denoted by P(A|B), is defined as,
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
So, P(A∩B) = P(B).P(A|B)
Given that,
The age of 20% of population are 65 years or over.
26% of those whose age 65 years or more have loans.
53% of those whose age under 65 years have loans.
E= the person is 65 or more.
F= the person has loan.
P(E)= 20%=0.2
P(F|E)=26%=0.26
P(F|E')=53%=0.53
So,
P(E')=1-0.2=0.8
P(F'|E)= 1-0.26=0.74
P(F'|E')= 1-0.53=0.47
(a)
The probability that a person 65 or over and has a loan is
=P(E∩F)
=P(F|E).P(E)
=0.26×0.2
=0.052
(b)
A person who has a loan either 65 or more , or under 65.
P(F)= P(F∩E)+P(F∩E')
=P(F∩E)+P(E').P(F|E')
= 0.052+ (0.8).(0.53)
=0.476
(c)
Independent event:
If A and B are two independent event,
Then,P(A∩B)=P(A).P(B)
The probability that a person is 65 or over and has a loan independent is
=P(E∩F)
=P(E).P(F)
=(0.2)×(0.476)
=0.0952
The probability that a person is 65 or over and has a loan is 0.052, the probability that a person has a loan is 0.476, and the probability that a person is 65 or over and that the person has a loan independent is 0.0952.
Given :
Suppose 20% of the population are 65 or over, 26% of those 65 or over have loans, and 53% of those under 65 have loans.
Let A represent the person who is 65 or more and B represents the person who has a loan.
If (P(A) = 20% = 0.2) then (P(A') = 1 - 0.2 = 0.8)
If (P(B|A) = 26% = 0.26) then (P(B'|A) = 1 - 0.26 = 0.74)
If (P(B|A') = 53% = 0.53) then (P(B'|A') = 1 - 0.53 = 0.47)
a) The probability that a person is 65 or over and has a loan is:
[tex]\rm = P(A\cap B)[/tex]
[tex]\rm = P(B|A)\times P(A)[/tex]
[tex]=0.26\times 0.2[/tex]
= 0.052
b) The probability that a person has a loan is:
[tex]\rm P(B) = P(A\cap B)+P(B\cap A')[/tex]
[tex]\rm = P(B \cap A)+P(A')\times P(B|A')[/tex]
[tex]=0.52+0.8\times 0.53[/tex]
= 0.476
c) The probability that a person is 65 or over and that the person has a loan independent is:
[tex]= \rm P(A\cap B)[/tex]
= P(A).P(B)
= (0.2)[tex]\times[/tex](0.476)
= 0.0952
For more information, refer to the link given below:
https://brainly.com/question/23044118
The area of the scale model of a garden is 15 square feet. The scale model is enlarged by a scale factor of 3 to create the actual garden. Which expression finds the area of the actual garden?
StartFraction 15 over 3 squared EndFraction
StartFraction 15 over 3 EndFraction
15 times 3
15 times 3 squared
Answer:
15 x 3^2
Step-by-step explanation:
The area of a square or rectangle is equal to the length x width.
If you want to scale the figure you multiply 3 to both the width and the length.
Because you are multiply 3 twice, you are essentially doing 3x3 = 9 or 3^2
15 ^ 3^2 is the answers.
You can also check on a calculator and it will also come as true
The expression finds the area of the actual garden is 15 ^ 3^2.
We have given that,
The area of the scale model of a garden is 15 square feet.
The scale model is enlarged by a scale factor of 3 to create the actual garden.
We have to determine which expression finds the area of the actual garden.
15 x 3^2
What is the area of rectangel?The area of a square or rectangle is equal to the length x width.
If you want to scale the figure you multiply 3 by both the width and the length.
Because you are multiplying 3 twice,
3x3 = 9 or 3^2
The expression finds the area of the actual garden is 15 ^ 3^2.
To learn more about the area of the rectangle visit:
https://brainly.com/question/1549055
#SPJ5
PLEASE HELP MEE
The radius of a mini-basketball is 4 inches. A pump can inflate the ball at a rate of 6 cubic inches per second. How long will it take to inflate the ball? Round to the nearest tenth.
Answer:
44.7 seconds
Step-by-step explanation:
The volume of a sphere is given by the formula ...
V = (4/3)πr³
For the given radius, the volume of the ball is ...
V = (4/3)π(4 in)³ ≈ 268.08 in³
At an inflation rate of 6 in³/s, the time required to deliver that volume is ...
(268.08 in³)/(6 in³/s) ≈ 44.68 s
It will take 44.7 seconds to inflate the ball.
To inflate a mini-basketball with a 4-inch radius, it takes approximately 44.7 seconds. This is found by calculating the volume of the basketball and dividing it by the pump's inflation rate of 6 cubic inches per second.
Inflating a Mini-Basketball
To determine how long it will take to inflate a mini-basketball with a radius of 4 inches, we need to find the volume of the basketball and divide it by the inflation rate of the pump.
→ The volume V of a sphere is calculated using the formula:
V = (4/3)πr³
→ For a radius (r) of 4 inches:
V = (4/3)π(4³)
= (4/3)π(64)
≈ 268.1 cubic inches
→ The pump inflates at a rate of 6 cubic inches per second. To find the time (t) it takes to inflate the ball, we use:
t = Volume / Rate
= 268.1 cubic inches / 6 cubic inches per second
≈ 44.7 seconds
So, it will take approximately 44.7 seconds to inflate the mini-basketball.
Which features describe the graph of
oth =1? Select two options.
a focus at (1040)
a focus at (0.-96)
a vertex at (-40,0)
a vertex at (0, 96)
the center at (0,0)
Answer:
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT
From the given equation,
a = 40
b = 96
(h,k) = (0,0), the center
The vertices are at (0,96) and at (0, -96).
The curves open upward and downward.
c² = a² + b² = 40² + 96² = 10816
c = 104
Therefore the foci are at (0, -104) and (0, 104).
Check the given answers:
1. a focus at (104, 0) is INCORRECT
2. a focus at (0, -96) is INCORRECT
3. a vertex at (-40, 0) is INCORRECT
4. a vertex at (0, 96) is CORRECT
5. the center at (0, 0) is CORRECT
Read more on Brainly.com - https://brainly.com/question/4411338#readmore
Answer:
a vertex at (0,96)
the center at (0,0)
Step-by-step explanation:
edge
ASAP ANSWER PLZ!!!!!!!!!!!!!!!!!!!!!
Answer:255 ft of fabric
Step-by-step explanation:
Just trust me
-hope this helped!
URGENT! The system of equations is shown in the graph. 2x + y = 4, x – y = 2 What is the solution of the system?
Answer:
It's already shown on the graph
Step-by-step explanation:
2(y+2)+ y = 4
x=y+2
2y+4+y=4 =) y=0
x=0+2 =) x= 2
{2,0}
Answer:
(2,0)
Step-by-step explanation:
Can random samples and proportional reasoning be used to determine precise information about a population? Explain.
Answer:
yes
Step-by-step explanation:
A population can be determined proportionally and can be used as random samples by explaining for example how much people speak a different language other than english or sampling peoples hair color,some predictions made can be true whether its asking 5,10,20,30,40,100 people.
what is 8×8 ? Correct answers only !!
Answer:
64
brainliest is appreciated :))))))
Step-by-step explanation:
4x^2 /9xy^3 divided by 12x^5y^4 / 18x^5y2
Answer:
[tex]\frac{2x}{3y^5}[/tex]
Step-by-step explanation:
See photo for steps.
Yelena has 24 apples. She packs an equal number of apples in each of b boxes. How many apples are in each box?
Answer:
Multiple possible without box count: 1,2,3,4,6,12,24
Step-by-step explanation:
Without knowing how many boxes there are you can get multiple answers
if there are 24 boxes then 1 apple goes into each box
if there are 12 boxes then 2 apples can go into each box
if there are 8 boxes then 3 apples can go into each box
if there are 6 boxes then 4 apples can go into each box
if there are 4 boxes then 6 apples can go into each box
if there are 2 boxes then 12 apples can go into each box
if there is 1 boxes then 24 apples can go into that box
with added information i can edit my answer
A book store earned $235 in sales for 4 copies of a new cookbook and 5 copies of a new science fiction novel. The next day it earned $180 in sales for 3 copies of the cookbook and 4 copies of the science fiction novel. What was the price of each book?
The price of the cookbook is $40, and the price of the science fiction novel is $15. This was determined by setting up and solving a system of equations based on the sales data provided for two different days.
The student has asked to determine the price of each book based on the sales data for two days. This is a system of equations problem in which we have two equations with two unknowns, representing the prices of two different books. Let's denote C as the price of the cookbook and S as the price of the science fiction novel. From the information given:
4C + 5S = 235 (sales on the first day).
3C + 4S = 180 (sales on the second day).
By solving these two equations simultaneously, we can find the exact prices for both books.
Step 1: Multiply the second equation by 4/3 to align the coefficient of C with the first equation:
([tex]\frac{4}{3}[/tex])(3C + 4S = 180)
4C + ([tex]\frac{16}{3}[/tex])S = 240
Step 2: Subtract the first equation from this new equation:
[([tex]\frac{16}{3}[/tex])S - 5S] = [240 - 235]
[tex]S = \frac{5 }{ \frac{16}{3} - \frac{15}{3}}[/tex]
[tex]S = \frac{5 }{ \frac{1}{3}}[/tex]
S = $15 (price of the science fiction novel)
Step 3: Substitute the value of S in one of the original equations to find C:
3C + 4(15) = 180
3C + 60 = 180
3C = 120
C = $40 (price of the cookbook)
Travelling in Mexico is much cheaper now than it was ten years ago," says a friend. "ten years ago, a dollar bought 10 pesos; this year, a dollar buys 15 pesos." Is your friend right or wrong? Given that total inflation over this period was 25 percent in the United States and 100 percent in Mexico, has it become more or less expensive to travel in Mexico? Write your answer using a concrete example – such as an American hot dog versus a Mexican taco-that will convince your friend.
Answer:
The friend is wrong as the actual prices have increases over the past ten years
Step-by-step explanation:
Here we have
The cost of travelling in Mexico 10 years ago = X pesos
The cost of 10 pesos 10 years ago = $1.00
The cost of 15 pesos now = $1.00
Inflation in Mexico in 10 years = 100% in US = 25%
Therefore, before the inflation if
Price of one variety of American hot dog = $1.00 and
Price of one taco brand = 10 Pesos
After the inflation we have
25% Increase, price of the same hot dog = $1.25 while
100% increase, price for the taco = 20 pesos
However, 15 pesos is now $1.00, therefore;
20 pesos = $1.00 × 20/15 = $1.33
That is current selling price for taco is $1.33 which is more higher than previous $1.00
Where the cost of travelling in Mexico is directly related to the above example, then, travelling in Mexico is much expensive than it was ten years ago.
Despite the increase in the exchange rate, it has become more expensive to travel in Mexico due to higher inflation.
Explanation:Your friend is wrong. Despite the increase in the exchange rate, it has actually become more expensive to travel in Mexico over the past ten years due to higher inflation in Mexico compared to the United States.
Let's use the example of an American hot dog and a Mexican taco. Ten years ago, the hot dog cost $3 in the US and 30 pesos in Mexico.
Assuming the exchange rate was 10 pesos per dollar, the cost of the taco in dollars would be 30/10 = $3.
This year, with the exchange rate of 15 pesos per dollar, the cost of the taco in dollars would be 30/15 = $2.
Therefore, the taco is cheaper this year in dollars, but the hot dog in the US has only increased in price by 25% due to inflation.
This example clearly shows that despite the increase in the exchange rate, the higher inflation in Mexico has made it more expensive to travel there.
Learn more about Cost of traveling in Mexico here:https://brainly.com/question/33385154
#SPJ11
On a coordinate plane, a line with negative slope goes through (negative 8, 6) and (4, negative 4). A point is at (negative 6, 10).
Which is the ordered pair for the point on the x-axis that is on the line parallel to the given line and through the given point (–6, 10)?
(6, 0),(-6,10)
Step-by-step explanation:Find the slope of the first line.
Points:
A(-8, 6), B(4, -4)
m = Slope = change in y over the change in x = [tex]\frac{y2-y1}{x2-x1} = \frac{-4-6}{4-(-8)} =\frac{-10}{12} = -\frac{5}{6}[/tex]
Plug (-6, 10) into y = mx + b to get your y intercept using the same slope
Additional info: Because its parallel the slopes are the same but the only thing we need to find is the y intercept to find the equation to the second line.
y = -5/6x + b
10 = -5/6(-6) + b
10 = 5 + b
-5 -5
5 = b
Write the equation
y = -5/6x + 5
Plug in 0 for y to get your x-intercept and solve to get your second point of the ordered pair
0 = -5/6x + 5
-5 -5
-5 = -5/6x
6 = x
Your ordered pair is:
(6, 0)
Answer:
(6, 0),(-6,10)
Step-by-step explanation:
(6, 0),(-6,10)
Step-by-step explanation:
Find the slope of the first line.
Points:
A(-8, 6), B(4, -4)
m = Slope = change in y over the change in x =
Plug (-6, 10) into y = mx + b to get your y intercept using the same slope
Additional info: Because its parallel the slopes are the same but the only thing we need to find is the y intercept to find the equation to the second line.
y = -5/6x + b
10 = -5/6(-6) + b
10 = 5 + b
-5 -5
5 = b
Write the equation
y = -5/6x + 5
Plug in 0 for y to get your x-intercept and solve to get your second point of the ordered pair
0 = -5/6x + 5
-5 -5
-5 = -5/6x
6 = x
Your ordered pair is:
(6, 0)
John practices the trumpet 35 minutes each day. How many minutes does he practice in 2 weeks?
Answer:
490 minutes
Step-by-step explanation:
There are 7 days in a week, and he practices 35 minutes every day
We can multiply 7 and 35 to find how long he practices for in 1 week
7*35=245
He practices for 245 minutes in 1 week.
To find 2 weeks, multiply his time for 1 week by 2
245*2=490
So, he practices for 490 minutes in 2 weeks
Answer:
490
Step-by-step explanation:
its 35 times 14, each day he does 35 mins for 2 weeks, in 2 weeks you have 14 days. ;)–2x + 2y = -4
3х + Зу = -18
Answer:
(-2, -4)
Step-by-step explanation:
–2x + 2y = -4
3х + Зу = -18
Divide the first equation by 2
–2x/2 + 2y/2 = -4/2
-x +y = -2
Divide the second equation by 3
3х/3 + Зу/3 = -18/3
x + y = -6
Add these equation together
-x +y = -2
x + y = -6
-------------------
0x + 2y = -8
2y = -8
Divide each side by 2
2y/2 = -8/2
y = -4
Now we need x
x+y = -6
x-4 = -6
Add 4 to each side
x-4+4 = -6+4
x = -2
Consider the triangles.
Answer the questions about these triangles.
What is the measure of angle C? _____ A.35.5 B.37.2C.51.8D.57.2
Which angle corresponds to angle C?A. D. B. r C. s or D. t
What can be concluded about the triangles? The triangles are congruent, similar, or not similar.
I need help right away
Answer:
1. Angle C is 57.2
2. Which angle corresponds to angle C? The answer is angle S
3. The angles are similar
Step-by-step explanation:
Edge.
Hence angle Cis 57degrees
What is angle sum property of triangle?
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°
How to solve?
In ΔEDC=∠E+∠D+∠C=180degree
=35.5+87.3+∠E=180
∠E=180-87.3-35.5=57
earn more about Angle sum property of trianglehttps://brainly.com/question/25215131
#SPJ2
How to find the θ in this equation: tan(θ+16°)=1/tan(θ+60°) by using the trigonometric identities?thanks
Answer:
[tex] \huge \theta =7°[/tex]
Step-by-step explanation:
[tex]tan( \theta + 16 \degree) = \frac{1}{tan( \theta + 60 \degree) } \\ tan( \theta + 16 \degree) =cot( \theta + 60 \degree) \\ tan( \theta + 16 \degree) = tan \{90 \degree - (\theta + 60\degree) \} \\ \theta + 16 \degree = 90 \degree - \theta - 60\degree \\ \theta +\theta = 30 \degree - 16\degree \\2 \theta = 14 \degree \\ \theta = \frac{14 \degree}{2} \\ \huge \red{ \boxed{\theta =7 \degree}}[/tex]
Final answer:
To solve the given trigonometric equation, convert tan(θ + 60°) to cot(θ + 60°) and then to cos(θ + 60°)/sin(θ + 60°). Next, cross-multiply and simplify using trigonometric identities to find θ. The correct θ value satisfying the equation is 32°.
Explanation:
To solve the equation tan(θ+16°) = 1/tan(θ+60°) using trigonometric identities, we first convert the right side of the equation using the identity that tan(α) = 1/cot(α).
This gives us tan(θ+16°) = cot(θ+60°). Now we use the identity for cotangent, which is cot(α) = cos(α)/sin(α), and write the equation as tan(θ+16°) = cos(θ+60°)/sin(θ+60°).
In terms of sine and cosine, tangent can be written as tan(α) = sin(α)/cos(α), so our equation becomes sin(θ+16°)/cos(θ+16°) = cos(θ+60°)/sin(θ+60°).
Next, cross-multiply to get sin(θ+16°) × sin(θ+60°) = cos(θ+16°) × cos(θ+60°). Using trigonometric identities for sine and cosine of sum of angles, we get an equation that can be simplified.
After simplification, the only θ values that satisfy the equation between 0° and 360° are found to be 31° 58.6' and 78° 31.5'. However, the given solution to the problem is θ = 32°, which closely matches one of the correct angles found.
What is the quotient of 8.832 x 106 and 9.6 x 102 expressed in scientific notation?
Final answer:
To calculate the quotient of 8.832 x 10^6 and 9.6 x 10^2 in scientific notation, divide the coefficients and subtract the exponents to get 0.92 x 10^4.
Explanation:
The student is asking to divide two numbers expressed in scientific notation and then to express the quotient in scientific notation.
To find the quotient of 8.832 x 10⁶ and 9.6 x 10², we divide the coefficients (8.832/9.6) and subtract the exponents (6-2).
First, divide the coefficients: 8.832/9.6 = 0.92.
Next, subtract the exponents: 6 - 2 = 4.
Now combine the result in scientific notation: 0.92 x 10⁴.
We can leave the result as 0.92 x 10⁴ because in scientific notation, it's acceptable for the coefficient to be less than 1 as long as it's at least 0.1.
So, the quotient expressed in proper scientific notation is 0.92 x 10⁴.
The quotient of [tex]\( 8.832 \times 10^6 \)[/tex] and [tex]\( 9.6 \times 10^2 \)[/tex] expressed in scientific notation is [tex]\( 9.2 \times 10^3 \).[/tex]
To find the quotient of two numbers in scientific notation, divide the coefficients and subtract the exponents. Here's the step-by-step process:
1. Divide the coefficients (the numbers without the exponents):
[tex]\[ \frac{8.832}{9.6} = 0.92 \][/tex]
2. Subtract the exponents (the powers of 10):
[tex]\[ 10^6 \div 10^2 = 10^{6-2} = 10^4 \][/tex]
3. Combine the result of the division of the coefficients with the result of the subtraction of the exponents:
[tex]\[ 0.92 \times 10^4 \][/tex]
4. To express the result in proper scientific notation, the coefficient must be greater than or equal to 1 and less than 10.
Therefore, we need to adjust the coefficient and the exponent accordingly.
Since 0.92 is less than 1, we multiply the coefficient by 10 and decrease the exponent by 1:
[tex]\[ 9.2 \times 10^{4-1} = 9.2 \times 10^3 \][/tex]
So, The quotient of [tex]\( 8.832 \times 10^6 \)[/tex] and [tex]\( 9.6 \times 10^2 \)[/tex] expressed in scientific notation is [tex]\( 9.2 \times 10^3 \).[/tex]
Which costs more per gallon? 5 gallons for $12.50 or 11 gallons for $26.40
Please answer ASAP PLEEEEEASE
Answer: 5
Step-by-step explanation:
If;
5 gallons = $12.50 / 5 = $2.50/gallon
11 gallons = $26.40 / 11 = $2.40/gallon
In conclusion, 5 gallons cost more per gallon than 11.
You serve a volleyball with a mass of 2 kg. The ball leaves your hand with a speed of 30 m/s. The ball has kinetic energy. Calculate it.
Answer:
900 j
Step-by-step explanation:
KE=1/2mv^2
so:
1/2x(2kg)x(30m/s)^2
is 900 joules. :)
The kinetic energy should be900 j
Given that,
You serve a volleyball with a mass of 2 kg. The ball leaves your hand with a speed of 30 m/s.Based on the above information, the calculation is as follows:
[tex]KE=1\div 2mv^2\\\\\\= 1\div 2\times (2kg)\times (30m/s)^2[/tex]
= 900 joules.
Learn more: https://brainly.com/question/25914450?referrer=searchResults
A triangle had side measures of 7, 7, and 14. Does this form a triangle?
-79,000 + 45,34444444444=5.65
Jay bought 15 tee shirts for $68.40. What was the unit price of the tee shirts?????????????????????????????????????? HELP PLEASE I WILL MARK BRAINLEST
4.56
Step-by-step explanation:
Hope this helps :)
The unit price of the tee shirts that Jay bought is calculated by dividing the total cost ($68.40) by the number of tee shirts (15), coming to a unit price of $4.56 per tee shirt.
Explanation:The question is asking for the unit price of the tee shirts that Jay bought. To find the unit price, you'll divide the total price by the number of units (tee shirts) purchased. This is a straightforward division of the total cost by quantity.
So, Jay's total cost is $68.40 for 15 tee shirts. To calculate the unit price:
Divide the total cost ($68.40) by the number of tee shirts (15).The result will be the cost per shirt (unit price).So, $68.40 / 15 = $4.56.
Therefore, the unit price for the tee shirts that Jay bought is $4.56.
Learn more about Unit price here:https://brainly.com/question/34061692
#SPJ12
solve the inequality 9 - 7x < 6
3 (4y + 1) + 2y what is the answer?
Step-by-step explanation:
12y + 3 + 2y
14y + 3
If you have to find the value of y then
14y = - 3
y = - 3/14
Does anyone know the answer? (I need help ASAP please)
Answer:
D. (-10, -3), (-3, -10)
Step-by-step explanation:
For a question like this, it is easiest to check the offered answers in the given equations.
The first equation requires the sum of the x- and y-values to be -13. Adding two numbers is pretty easy, so you can rapidly determine that choice D is the only reasonable choice.
_____
Comment on the process
Answering multiple-choice questions is as much about test-taking skill as it is about math skill. First, you eliminate choices that don't answer the question.
Then you see if there is a way to identify the "correct" answer from the remaining "reasonable" answers. Often, that requires you only solve part of the problem, or you check for consistency between parts of the answer. (Here, if (a, b) is an answer, then (b, a) will be the other answer. Again, only choice D has that characteristic.)
You can see if the answer choices satisfy the details of the problem requirements.
Finally, as a last resort, you actually work the problem to determine your own answer to the question. (Here, you can substitute for y: x^2 +(-13-x)^2 = 109, then solve the quadratic, 2x^2 +26x +60 = 0 to find x=-3 or -10.) When you're done with this, you also need to check your answer against the above criteria.
Jack's mother gave him 505050 chocolates to give to his friends at his birthday party. He gave 333 chocolates to each of his friends and still had 222 chocolates left. Write an equation to determine the number of friends (x)(x)(, x, )at Jack's party. Find the number of friends at Jack's party.
Answer:
There are 16 friends at Jack's party.
Step-by-step explanation:
We are given the following in the question:
Let x be the number of friends at Jack's party.
Total number of chocolates Jack have = 50
Number of chocolates given to each friend = 3
Number of chocolates left = 2
Thus, we can write the equation:
Total number of chocolate - Total number of chocolates given = Total number of chocolates left
[tex]50 - 3x = 2[/tex]
Solving the equation, we get,
[tex]50 - 3x = 2\\3x = 48\\\\\Rightarrow x = \dfrac{48}{3} = 16[/tex]
Thus, there are 16 friends at Jack's party.
draw a quadrilateral that does not belong, then explain why. What should I draw and write?
Answer
do u have a demonstration
picture
Step-by-step explanation:
What is not a requirement of the binomial probability distribution?
Answer:
B. the trials must be dependent
Step-by-step explanation:
The image for the question is attached.
The missing options are;
A. The probability of a success remains the same in all trials.
B. The trials must be dependent.
C. Each trial must have all outcomes classified into two categories.
D. The procedure has a fixed number of trials.
For a binomial distribution probability, the event must be repeated for a number of time (n) and the probability of success (q) must be the same during each trial.
Binomial distribution probability has two possible outcome: success (p) or failure (q). The event are also independent of each other.
The formula for a binomial distribution probability is given as:
P(X=x) = nCx (p ^ x) (q ^ (n-x))
From the above, we can see that the answer is:
B. the trials must be dependent
Final answer:
The requirement that is not necessary for a binomial distribution is for the probabilities of success (P) and failure (Q) to be equal. This misconception arises because the binomial probability applies even if P ≠ Q. The use of technology has made calculating binomial probabilities for large values of n convenient without the need for normal approximation.
Explanation:
What is not a requirement of the binomial probability distribution? This question pertains to specific characteristics that define a binomial distribution. In the context of probability and statistics, a binomial distribution has several key requirements, including the presence of a fixed number of trials, each trial being independent, a dichotomy of outcomes (success/failure), and a constant probability of success across trials.
However, something that is not a requirement for a binomial distribution is that the probabilities of success (P) and failure (Q) must be equal. This is a common misconception because of the symmetry seen in fair coin tosses, where the probability of heads (P) and tails (Q) is the same. However, the binomial probability applies even if P ≠ Q. An example of this could be having a biased coin where the probability of getting heads (PH) differs from getting tails (PT).
It is also important to note that using the Poisson distribution may be more appropriate in some cases, such as modeling the number of events occurring within a fixed interval if the probability of success is very low, and the number of trials is very high. Moreover, when dealing with trials that are not independent, such as selecting a chairperson and a recorder from a committee without replacement, the conditions for a binomial distribution are not met, and we cannot apply binomial probability.
Given the equation f(x) = (x + 3)2 – 8, fill in the blanks: Axis of symmetry: x = _______a0 Vertex: ( _______a1, _______a2) Number of real solutions: ________a3
We have been given an equation [tex]f(x)=(x+3)^2-8[/tex]. We are asked to fill in the blanks using our given equation.
The axis of symmetry will be the vertical line passing through vertex.
First of all, we will convert our given equation in standard vertex form of parabola as:
Standard vertex form of parabola: [tex]y=(x-h)^2+k[/tex], where (h,k) is vertex of parabola.
[tex]f(x)=(x-(-3))^2-8[/tex]
Upon comparing our function with standard vertex form, we can see that vertex of parabola is at [tex](-3,-8)[/tex].
The axis of symmetry will be vertical line passing through point [tex](-3,-8)[/tex]. The vertical line will pass through [tex]x=-3[/tex], therefore, the axis of symmetry is [tex]x=-3[/tex].
Since our given parabola is an upward opening parabola, so it has a minimum at [tex](-3,-8)[/tex]. This means that parabola will intersect the x-axis at two points. Therefore, there are two real solutions for the given function.
Jason filled his 52 ounce mug full of his favorite soda at the gas station it cost a total of $1.07 to fill his mug how much did Jason pay per ounce to fill his mug
Answer:
2 cents per ounce
Step-by-step explanation:
divide 1.07 by 52 to get 2 cents
What is the volume of a cylinder with a radius of five and a height of three