Answer:
2.) P(Chocolate, sprinkles)
Step-by-step explanation:
A lot of people choose chocolate ice cream over other flavors, and a lot of people also like sprinkles on their ice cream.
Miguel is a golfer, and he plays on the same course each week. The following table shows the probability distribution for his score on one particular hole, known as the Water Hole. Score 3 4 5 6 7 Probability 0.15 0.40 0.25 0.15 0.05 Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better. (a) Suppose one of Miguel’s scores from the Water Hole is selected at random. What is the probability that Miguel’s score on the Water Hole is at most 5 ? Show your work.
Answer:
a. p(x<= 5) = .15 + .4 + .25 = .8
C. .4(4.2) = 1.68
5.4(1-.4) = 3.24
3.24 + 1.68 = 4.92 ,, 4.92 > 4.55 so short is better
Step-by-step explanation:
The probability that Miguel’s score on the Water Hole is at most 5 is 80%.
Given that,
Miguel is a golfer, and he plays on the same course each week.
The following table shows the probability distribution for his score on one particular hole, known as the Water Hole.
Score 3 4 5 6 7
Probability 0.15 0.40 0.25 0.15 0.05.
We have to determine,
The probability that Miguel’s score on the Water Hole is at most 5.
According to the question,
Let the random variable X represent Miguel’s score on the Water Hole. In golf, lower scores are better.
Suppose one of Miguel’s scores from the Water Hole is selected at random.
Then,
The probability that Miguel’s score on the Water Hole is at most 5 is,
At most 5 means scores which are equal or less than 5.
P(at most 5) = P(X ≤ 5) = P(X = 3) + P(X = 4) + P(X = 5)
P(X ≤ 5) = 0.15 + 0.40 + 0.25
P(X ≤ 5) = 0.80
P(X ≤ 5) = 80%
Therefore,
There is 80% chance that Miguel’s score on the Water Hole is at most 5.
Hence, The probability that Miguel’s score on the Water Hole is at most 5 is 80%.
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A fire truck parks 30 feet
away from a building. The
fire truck extends its ladder
45 feet to the very top of
the building. How tall is the
building?
Answer:
34 ft. tall
Step-by-step explanation:
Your first step should to draw a diagram. When you do that, your diagram should look like a right triangle, the leg, or the distance from the firetruck to the building, (we'll call this a) should be 30ft. and the hypotenuse, or the ladder (we'll call this c), should be 45ft.
Now we have a visual so it'll be easier.
We know that this problem is a right triangle and we know that to solve for a missing side of a right triangle you use pythagorean theorem: a^2+b^2=c^2
We know one leg 'a' and the hyp. 'c' and we just need to find 'b' the other leg (aka the building):
Plug in numbers and simplify:
30^2+b^2=45^2
900+b^2=2025
b^2=1125
≈33.54 OR 34 ft. tall
Answer:
about 33.5 feet tall
Step-by-step explanation:
use pythagorean's theorem:
a^2+b^2=c^2
plug in values:
30^2 + b^2 = 45^2
(we know the ladder extends diagonally so 45 is the hypotenuse meaning we plug it in for c)
rearrange the equation:
b^2= 45^2 - 30^2
b^2= 2025 - 900
b^2 = 1125
b= [tex]\sqrt{1125} \\[/tex]
b= 33.5
in his first year, a math teacher earned $32,000. Each successive year, he
earned a 5% raise. How much did he earn in his 20th year? What were his total
earnings over the 20-year period?
Explain steps by step
Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
The math teacher's salary in the 20th year, with a 5% annual raise, is approximately $85,200. Over the 20-year period, the total earnings amount to about $1,068,753.
The calculation also includes finding the total earnings over the 20-year period.
The salary in the 20th year can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount (salary in this case), P is the principal amount (initial salary), r is the rate of increase (5% expressed as 0.05), and n is the number of years.
Using the formula: A = 32000(1 + 0.05)^19, since the first year salary is given and we calculate the increase starting from the second year,
the salary in the 20th year is approximately $85,200.
To calculate the total earnings over 20 years, we sum all annual salaries over the 20 years which involve a geometric series. The sum of a geometric series can be found using the formula S = P(1 - (1+r)^n) / (1 - (1+r)), where S is the total sum, P is the initial amount, r is the rate, and n is the number of terms.
So, total earnings over 20 years is approximately $1,068,753.
Dena is going to construct a paper box. She will make the box x inches wide. The height of the box is 3 inches greater than the width, and the box is twice as deep as it is high. The volume of the box is 6464 in33. Which equation correctly describes the volume of the box?
Final answer:
The equation to describe the volume of the box, given its dimensions in terms of x, is 6464 = [tex]x(x + 3)^2[/tex](x + 3), where x represents the width of the box.
Explanation:
The question asks us to find an equation that represents the volume of a box where the width is x inches, height is x + 3 inches (since it's 3 inches greater than the width), and depth is 2(x + 3) inches because the box is twice as deep as it is high. The volume is given to be 6464 in3. The formula to calculate the volume of a rectangular box is volume = length × width × height.
In this scenario, the width is x, the height is x + 3, and the depth (or length) is 2(x + 3). So, the volume equation can be expressed as:
V = x × (x + 3) × 2(x + 3)
Since we know the volume is 6464 in3, we can set up the equation as:
6464 = [tex]x(x + 3)^2[/tex](x + 3)
jen buys 4 tires for $272. what is the cost of 1 tire?
Answer:
68
Step-by-step explanation:
Take the cost of all 4 tiers and divide by 4
272/4 =68
The cost of 1 tire is 68
What 4 numbers adding give you a sum of 15
Answer: 6 and 9, 7 and 8. 69, 78, 87, 96. So, there are only 4 combinations which would result in 15.
Step-by-step explanation:
Therefore the average sum of three numbers is 45:3=15. The number 15 is called the magic number of the 3x3 square. You can also achieve 15, if you add the middle number 5 three times. The odd numbers 1,3,7, and 9 occur twice in the reductions, the even numbers 2,4,6,8 three times and the number 5 once.
9+1+3+2= 15
Hope this helps you:)
using trig to find a side. help please !
Answer:
The length of LM to the nearest tenth of a foot would be 11.7
Step-by-step explanation:
Using the law of sines (b = c·sin(B)/sin(C)) you would plug in your missing values
x=7*sin(59)/sin(31)
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.1degreesf and a standard deviation of 0.56degreesf. construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6degreesf as the mean body temperature?
Answer:
The 99% confidence interval estimate for the mean is 97.9576 ≤ μ ≤ 98.246
A) This suggests that the mean body temperature could very possibly be 98.6 °F
Step-by-step explanation:
The number of body temperatures, n = 103
The mean body temperature, [tex]\bar x[/tex] = 98.1
The standard deviation, s = 0.56
Confidence interval required = 99%
Confidence interval, CI is given by
[tex]CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Plugging in the values we get;
z = 2.56 at 99%
[tex]CI=98.1}\pm 2.56\times \frac{0.56}{\sqrt{103}}[/tex]
Therefore, we have
[tex]\mu_{min} = 97.9579 , \ \mu_{max} = 98.242[/tex],
The statistical result suggest that at 99% confidence level, the sample mean temperature is likely to be 98.1 °F
i need the answer for this
Answer:
535.9 ft²
Step-by-step explanation:
Since there are 360° in a circle, and 240° is 2/3 of 360°, we can say that the area of the bolded sector is 2/3 the area of the whole circle. The area of a circle with a radius of r is πr², or approximately 3.14r², so the area of the whole circle is ≈ 3.14(16)² = 3.14(256) = 803.84 ft². Taking 2/3 of this gets us 803.84 * (2/3) ≈ 535.9 ft²
If the mean of x and 4x is 10, the x = ?
Please explain how you got your answer.
Answer: x = 4
Step-by-step explanation: The mean is the average of the given numbers, so take the numbers add them up and divide by the quantity of numbers. To get the answer to this question, you know the mean is 10 and you have two numbers. You take the 10, multiply it by 2 and you get how much the numbers add up to. You can combine x and 4x to get 5x. 5x=20. Divide 20 by 5 and you get the answer of x=4
Answer:
x = 4
Step-by-step explanation:
To find the mean of two numbers, you have to add the numbers, then divide by 2.
So, if 10 is equal to the mean of x and 4x, it is equal to the sum of 4x and x divided by 2. If we put this in the form of an equation, we get:
[tex]\frac{x + 4x}{2} =10[/tex]
Now we can multiply both sides by 2, and get:
[tex]x + 4x = 20[/tex]
Simplify the left side to:
[tex]5x = 20[/tex]
And lastly, divide both sides by 5:
[tex]x = 4[/tex]
What is the prime factorization of 72?
22 × 32
22 × 33
23 × 32
23 × 33
Answer: its C
Step-by-step explanation:
Answer:
Its C on Edge 2021
Step-by-step explanation:
what are the coordinates of point A if it is rotated 90 degrees counterclockwise about the origin?
Answer:-5
Step-by-step explanation:
A painter uses the expression 35h + 30c to determine how much he charges a customer for a job that takes h hours and c cans of paint. His last job required 3 cans of paint and took 15 hours to complete. How much did the painter charge? a) $540 b) $555 c) $615 d) $638
Final answer:
The painter charged $615 for a job that took 15 hours and required 3 cans of paint, which is answer choice (c).
Explanation:
To calculate the total charge for a painting job that took 15 hours and used 3 cans of paint, we need to plug these values into the painter's pricing formula, 35h + 30c.
Substituting the given values into the equation, we get:
Total charge = 35(15) + 30(3)
Total charge = 525 + 90
Total charge = $615
Therefore, the painter charged $615 for the job, which corresponds to answer choice (c).
What is 7 And what is 8 ?
Answer:
7. 23.7
8. option 2
Step-by-step explanation:
Brainliest?
100 points and brainliest
Which statement best describes the faces that make up the total surface area of this composite solid? A triangular prism on top of a rectangular prism. 9 faces, 5 rectangles, and 4 triangles 9 faces, 7 rectangles, and 2 triangles 11 faces, 7 rectangles, and 4 triangles 11 faces, 9 rectangles, and 2 triangles
Answer:
Step-by-step explanation:
1: SA = bh + (s1 + s2 + s3)H
2: A = lw
3: A = lw
Answer:
The answer is B) 9 faces, 7 rectangles, and 2 triangles
Step-by-step explanation:
There are five identical blue books, two identical green books, and three identical black books. How many different patterns can the books be arranged on a shelf?
Answer:
2520 patterns
Step-by-step explanation:
In 'n' 10! ways, books can be arranged. But, there are also 5! permutation of blue books 'n1', 2! permutation of identical green books 'n2', and 3! permutation identical black books 'n3'.
Therefore, for non identical arrangements:
[tex]\frac{n!}{n1!n2!n3!}[/tex]
[tex]\frac{10!}{5!2!3!}[/tex] = 2520
Therefore, the books can be arranged on a shelf in 2520 patterns
There are 3,024 different patterns in which the books can be arranged on the shelf.
Explanation:To calculate the number of different patterns the books can be arranged on a shelf, we can use the concept of permutations. We have 5 identical blue books, 2 identical green books, and 3 identical black books, so the total number of books is 5 + 2 + 3 = 10.
The number of different patterns is given by the formula:
n! / (n1! * n2! * n3! * ...)
where n is the total number of books and n1, n2, n3, ... are the numbers of books of each type. Substituting the values, we get:
10! / (5! * 2! * 3!) = 3,024 patterns.
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A chef combines 5 quarts of pineapple juice, 4 pints of milk, and 4 cups of apple juice to make smoothies. How many cups can be filled with smoothies? Explain.
The chef can fill 32 cups with smoothies by converting all liquids into cups, resulting in 20 cups from pineapple juice, 8 cups from milk, and adding the 4 cups of apple juice.
To calculate how many cups can be filled with smoothies, we first need to convert all quantities of liquids into the same unit of measurement, which is cups in this case.
We have 5 quarts of pineapple juice, 4 pints of milk, and 4 cups of apple juice.
First, we convert quarts to cups. The conversion is:
1 quart = 4 cups
Therefore, 5 quarts of pineapple juice equals:
5 quarts imes 4 cups/quart = 20 cups
Next, we convert pints to cups. The conversion is:
1 pint = 2 cups
Therefore, 4 pints of milk equals:
4 pints x 2 cups/pint = 8 cups
Adding the apple juice to the mix:
20 cups (pineapple juice) + 8 cups (milk) + 4 cups (apple juice) = 32 cups of smoothie
Todd wants to paint a design on the wood along the diagonal shown. If each tile is 15 centimeters on each side, what is the length of the diagonal shown?
Answer:
130 centimeters
Completed question;
Todd placed 32 square tiles along the edge of his wooden dining room table, as shown below.
Todd wants to paint a design on the wood along the diagonal shown. If each tile is 13 centimeters on each side, what is the length of the diagonal shown?
A. 182 centimeters
B. 169 centimeters
C. 130 centimeters
D. 91 centimeters
Step-by-step explanation:
To determine the length of diagonal, we have to first find the length of each side;
According to the attached image;
The length consist of 8 tiles
And breadth consist of 6 tiles
Length per tile = 13 centimeters
Length = 8 × 13 = 104 centimeters
Breadth = 6×13 = 78 centimeters
Using Pythagoras theorem;
diagonal length d = √(104^2 + 78^2)
d = 130 centimeters
Chris Paul is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 88\%88%88, percent of the time. What is the probability of Chris Paul making all of his next 9 free throw attempts?
Answer:
.88^9
Step-by-step explanation:
this is the only right answer on khan
The required probability of Chris Paul making all of his next 9 free throw attempts is 0.31
Given that,
Chris Paul is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 88\%88%88, percent of the time. The probability of Chris Paul making all of his next 9 free throw attempts is to be determined.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
According to the question,
Probability is given as,
P = [0.88]⁹
P = 0.31
Thus, the required probability of Chris Paul making all of his next 9 free throw attempts is 0.31
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Write an exponential equation to represent the situation and answer the question.
a. If the cost of a loaf of bread is now $2.75 and is increasing at 5% per year, what will it cost 10 years from now?
b. The population of Flood River City is now 42,000. Experts predict the population will decrease 25% each year for the next five years. What will be the population in five years?
c. A share of Orange stock that was worth $25 in 2000 was worth $60 in 2010. What is the multiplier and percent increase?
Answer:
a. $4.48¢
b. 9,967 people
ci. Multiplier: F = 25 × (1.09)^t
cii. Percent increase = 9.15%
Step-by-step explanation:
a. The equation we are going to use to calculate the future cost of bread in 5 years:
P = F/(1+r)^t
Where P is current cost, F = future cost(what we are required to calculate), r = percentage increase per year, t = time (years).
Where P = 2.75
r = 5/100 or 0.05
t = 10
F = ?
Substituting appropriately, we have:
2.75/1 = F/(1+0.05)^10
We then cross multiply
F = 2.75 × (1+0.05)^10
F = 2.75 × (1.05)^10
F = 2.75 × 1.62889
F = $4.48¢
Therefore, the bread will cost $4.48 in 10 years.
b. Here population is 42,000 people now. There's predicted 25% decrease in population every year for the next 5years. We are to calculate the expected population in 5 years. The equation that can be used to calculate the expected population:
P = F/(1 - r)^t
F = future population
P = present population
r = percentage of decrement
t = period.
Here P = 42,000
r = 25/100 = 0.25
t = 5
F = ?
Substituting accordingly:
42000 = F/(1 - 0.25)^5
Cross multiply
F = 42000 × [(1 - 0.25)^5]
F = 42000 × 0.2373
F = 9,967
The population in the next 5 years will decrease to 9,967 people.
c. Share of orange stock = $25 in the year 2000
The same share = $60 in 2010, we are required to determine the multiplier and percent increase.
Since the future value = $60, the present value = $25, the time = 2010 - 2000 = 10 years. Then we can use the formula:-
F = P × (1 + r)^t
60 = 25 × (1 + r)^10
(1 + r)^10 = 60/25
(1 + r)^10 = 2.4
1 + r = 10√2.4
1 + r = 1.0915
r = 1.0915 - 1
r = 0.0915
r = 9.15%
Therefore the multiplier is:
F = 25 × (1.09)^t
The percent increase = 9.15%
a. The cost of bread in 10 years will be approximately $4.48. b. Flood River City's population will drop to around 9,965 in 5 years. c. The Orange stock had a 2.4 multiplier, corresponding to a 140% increase over 10 years.
Let's address each part of the question with appropriate exponential equations:
a. Cost of a loaf of bread in 10 years:
We use the exponential growth formula:
Future Value = Present Value × (1 + growth rate)^number of years.
Here, the Present Value (P) is $2.75, the growth rate (r) is 5% or 0.05, and the number of years (n) is 10.
Future Value = 2.75 × (1 + 0.05)¹⁰
= 2.75 × (1.05)¹⁰
≈ 2.75 × 1.6289
≈ $4.48
So, in 10 years, the cost of the bread will be approximately $4.48.
b. Population of Flood River City in 5 years:
We use the exponential decay formula:
Future Value = Present Value × (1 - decay rate)^number of years.
Here, the Present Value (P) is 42,000, the decay rate (r) is 25% or 0.25, and the number of years (n) is 5.
Future Value = 42,000 × (1 - 0.25)⁵
= 42,000 × (0.75)⁵
≈ 42,000 × 0.2373
≈ 9,965
So, in 5 years, the population will be approximately 9,965.
c. Stock value multiplier and percent increase:
The stock value increased from $25 to $60 over 10 years. First, find the multiplier (M):
Multiplier (M) = Final Value / Initial Value
= 60 / 25 = 2.4
Next, calculate the percent increase:
Percent Increase = (Multiplier - 1) × 100
Percent Increase = (2.4 - 1) × 100 = 1.4 × 100 = 140%
So, the multiplier is 2.4 and the percent increase is 140%.
See the attachment to answer the question
Based on past experience, a bank believes that 4% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the mean of the sampling distribution of the proportion of clients in this group who may not make timely payments
Answer:
Mean = 0.04
Step-by-step explanation: given that P = 4%
n = 300
the mean of the sampling distribution of the proportion of clients in this group who may not make timely payments will be
4/ 100 = 0.04
The mean of the sampling distribution is 12 loans.
Explanation:Mean = 0.04
P = 4%
Loans = n = 300
To find the mean of the sampling distribution of the proportion of clients who may not make timely payments, we need to multiply the proportion of such clients by the total number of loans approved. In this case, the bank believes that 4% of the people who receive loans will not make payments on time. So, the mean is 4% of 300 loans.
Mean = (4/100) * 300
= 4 x 300/100
= 4 x 3
= 12 loans.
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The sum of four consecutive integers is 386. What is the fourth integer?
The 4 consecutive integers are 95, 96, 97 and 98.
The fourth integer is 98.
Step-by-step explanation:
Let us consider the 4 consecutive integers to be 'x' , 'x+1' , 'x + 2' , 'x + 3'
The sum of the 4 consecutive integers= 386
x + (x+1) + (x+2) + (x+3) = 386
4x + 6 = 386
4x = 380
x = 380/4
x = 95
x+1 = 96
x+2 = 97
x+3= 98
The 4 consecutive integers are 95, 96, 97 and 98.
The fourth integer is 98.
suppose a circle with center (1,-3) passes through point (1,-1). Which equation represents the circle ?
Answer:-4
Step-by-step explanation:
Answer:
The answer is C) (x − 1)^2 + (y + 3)^2 = 4
Step-by-step explanation:
The radius is the distance between the center and the point on the circle.
Center: (1, −3); Point: (1, −1)
Distance formula: d = square root of {(x2 - x1)^2 + (y2 - y1)^2}
r = square root of {(1 − 1)^2 + (−1 + 3)^2 }
r = square root of {0 + 4 } = 2
(x − h)^2 + (y − k)^2 = r2 ----> (x − 1)^2 + (y + 3)^2 = 4
Hope this isn't confusing and helps. I also know its right because I just did this on USA Testprep.
The parent function y = 0.5x is blank across its domain because its base, b, is such that blank
Answer: decreasing; 0 < b < 1
Step-by-step explanation: I got this question on edge
Answer:
Decreasing/ 0<b<1
Thank me later ;)
7/8 subtracted by 2/7
Find common denominators.
7/8 = 49/56
2/7 = 16/56
Subtract.
49/56 - 16/56 = 33/56
The fraction cannot be simplified any further.
Best of Luck!
Jackson invested $52,000 in an account paying an interest rate of 2.1% compounded
continuously. Assuming no deposits or withdrawals are made, how much money, to
the nearest dollar, would be in the account after 17 years?
Answer:
74310
Step-by-step explanation:
A=52000e ^0.021(17)
A=52000e^{0.357}
A=52000e^ 0.357
A=74309.8652324
A=74310
The amount in account after 17 years is $74032.4.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$52,000, rate of interest =2.1% and time period =17 years.
Here, Amount =52000(1+2.1/100)¹⁷
= 52000(1+0.021)¹⁷
= 52000(1.021)¹⁷
= 52000×1.4237
= $74032.4
Therefore, the amount in account after 17 years is $74032.4.
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Paula can pick 5 quarts of strawberries in 30 minutes. At this rate,How many quarts of strawberries can she pick in 4.5 hours
Paula can pick 45 quarts of strawberries in 4.5 hours.
Explanation:To find out how many quarts of strawberries Paula can pick in 4.5 hours, we need to convert the time into minutes for easier calculation. There are 60 minutes in 1 hour, so 4.5 hours equals 4.5 x 60 = 270 minutes.
Given that Paula can pick 5 quarts of strawberries in 30 minutes, we can set up a ratio to find the number of quarts she can pick in 270 minutes. The ratio is 5 quarts / 30 minutes = x quarts / 270 minutes.
Cross multiplying, we get 30x = 5 * 270. Solving for x, we find x = 5 * 270 / 30 = 45 quarts.
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Paula can pick 45 quarts of strawberries in 4.5 hours at her current picking rate.
Explanation:First, we need to understand the time frames we're working with. Paula picks 5 quarts of strawberries in a half an hour, and we want to know how much she can pick in 4.5 hours.
We are given that Paula can pick strawberries for a total of 4.5 hours. Now, we know that each hour has 60 minutes, so to get the total picking time in minutes, we multiply 4.5 (hours) by 60 (minutes per hour). This gives us a total of 270 minutes.
Next, we also know that Paula picks 5 quarts of strawberries in 30 minutes. If we want to find out how many 30-minute intervals are in 270 minutes, we simply divide 270 by 30. This gives us 9 intervals.
Finally, knowing that Paula can pick 5 quarts in each half-hour, we multiply this rate by the number of half-hour intervals. Therefore, 5 (quarts per half-hour) multiplied by 9 (half-hour intervals) equals 45 quarts.
So, Paula can pick 45 quarts of strawberries in 4.5 hours.
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Exhibit 5-8 The student body of a large university consists of 60% female students. A random sample of 8 students is selected. Refer to Exhibit 5-8. What is the probability that among the students in the sample exactly two are female?
Answer:
P(X=2)=0.04129
Step-by-step explanation:
-This is a binomial probability problem whose function is expressed as;
[tex]P(X=x)={n\choose x}p^x(1-p){n-x}[/tex]
-Given that p=0.6, n=8 , the probability that among the students in the sample exactly two are female is calculated as:
[tex]P(X=x)={n\choose x}p^x(1-p)^{n-x}\\\\P(X=2)={8\choose2}0.6^2(1-0.6)^6\\\\=0.04129[/tex]
Hence, the probability of exactly two females is 0.04129
To find the probability that exactly two students are female in a sample of 8 students, we can use the binomial probability formula. The probability is approximately 43.008%.
Explanation:To find the probability that exactly two students are female, we can use the binomial probability formula. The formula is:
P(X = k) = C(n, k) * pk * (1-p)n-k
where:
P(X = k) is the probability that exactly k events occurn is the number of trialsp is the probability of the event occurring in a single trialn-k is the probability of the event not occurring in a single trialIn this case, n = 8, k = 2, and p = 0.6 (since 60% of the students are female). Plugging these values into the formula:
P(X = 2) = C(8, 2) * 0.62 * (1-0.6)8-2
Simplifying:
P(X = 2) = 28 * 0.62 * 0.46
P(X = 2) = 28 * 0.36 * 0.4096
P(X = 2) = 0.43008
Therefore, the probability that exactly two students are female in the sample is approximately 0.43008 or 43.008%.
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A survey in one middle school showed that 3 out of 5 students
enjoy biking on the weekends. Predict how many of the 485
students in the school would say they enjoy biking on the
weekends.
To predict how many out of 485 students enjoy biking on the weekends, set up a proportion and solve for the missing value.
Three out of five students enjoy biking on the weekends, so to predict how many out of 485 students would say they enjoy biking, we can set up a proportion.
3 students out of 5 enjoy biking
Set up a proportion: 3/5 = x/485
Cross-multiply to find x: 5x = 3 × 485
Solve for x: x = (3 × 485) / 5
x = 291 students would be predicted to enjoy biking on the weekends.