(a) [tex]\( P(X = 5) \approx 0.234 \)[/tex]
(b) [tex]\[ P(X \geq 6) \approx 0.892 \][/tex]
(c) [tex]\[ P(X < 4) \approx 0.020 \][/tex]
To solve this problem, we can use the binomial probability formula since each man's response (considering themselves a baseball fan or not) is independent and there are only two possible outcomes (success or failure).
Given:
- Probability of success (considering themselves a baseball fan) [tex]\( p = 0.57 \)[/tex]
- Probability of failure (not considering themselves a baseball fan) [tex]\( q = 1 - p = 1 - 0.57 = 0.43 \)[/tex]
- Number of trials [tex]\( n = 10 \)[/tex]
We'll calculate the probabilities for each case:
(a) To find the probability that exactly five men consider themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{10 - 5} \][/tex]
(b) To find the probability that at least six men consider themselves baseball fans, we can find the probability of six, seven, eight, nine, and ten men being baseball fans, and then sum them up.
(c) To find the probability that less than four men consider themselves baseball fans, we need to find the probabilities of zero, one, two, and three men being baseball fans, and then sum them up.
Let's calculate each probability:
(a) [tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
We'll use these formulas to find the probabilities for each case. Let me do the calculations.
(a) To find the probability that exactly five men consider themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]
Using the binomial coefficient formula [tex]\(\binom{n}{k} = \frac{n!}{k!(n - k)!}\)[/tex], where [tex]\(n = 10\)[/tex] and [tex]\(k = 5\)[/tex]:
[tex]\[ \binom{10}{5} = \frac{10!}{5!(10 - 5)!} = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 252 \][/tex]
Now, we plug in the values:
[tex]\[ P(X = 5) = 252 \times (0.57)^5 \times (0.43)^{5} \][/tex]
[tex]\[ P(X = 5) \approx 0.234 \][/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
For each [tex]\(k = 6, 7, 8, 9, 10\)[/tex], we calculate [tex]\(P(X = k)\)[/tex] using the binomial formula and sum them up.
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Similarly, for each [tex]\(k = 0, 1, 2, 3\)[/tex], we calculate [tex]\(P(X = k)\)[/tex] using the binomial formula and sum them up. Let me do the calculations.
(a) [tex]\( P(X = 5) \approx 0.234 \)[/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
Using the binomial formula for each [tex]\( k = 6, 7, 8, 9, 10 \)[/tex] and summing the probabilities:
[tex]\[ P(X \geq 6) \approx 0.892 \][/tex]
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Using the binomial formula for each [tex]\( k = 0, 1, 2, 3 \)[/tex] and summing the probabilities:
[tex]\[ P(X < 4) \approx 0.020 \][/tex]
The third term of an arithmetic sequence is 21, and the eighth term is 56. The first term is _____.
The first term of the given arithmetic sequence is 7. This can be determined by finding the common difference and moving backwards from the third term using this value.
Explanation:The subject of this question is Arithmetic Sequence which is a topic in mathematics. An arithmetic sequence is defined by a common difference (d) between consecutive terms.
To solve this problem, we have to find the common difference first. The difference between the 8th term (56) and the 3rd term (21) is 35. But since there are 5 steps from the 3rd term to the 8th term, each step (or the common difference) must be 35 ÷ 5 = 7.
Now that we have the common difference (7), we can reverse it from the 3rd term (21) back to the 1st term which gives us: 21 - 2(7) = 7. So, the first term is 7.
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Jason deposits $5,000 in a bank account that will pay him 4% simple interest annually. If Jason deposits no more than the initial 5,000 , how much money will be in the account at the end of 5 years ?
One serving of granola provides 4% of the protein you need daily. You must get the remaining 48 grams from other sources. How many grams of protein do you need daily?
A tape that records one hour and 30 minutes on each side moves at cm a second through the tape player. How long, in metres, is the tape?
16. Tamara’s dosage of medication has recently decreased 20 milligrams per day. What is the total decrease in Tamara’s medication at the end of the week? Show your work.
Compare the 3 in 536 to the 3 in 1,36 7.
Draw number 536 using base ten block?
Grape juice comes in a 64 oz bottle. Apple juice comes in a 80 ounce bottle. Both juices will be poured into cups of equal size so that no juice remains in either bottle. How many ounces is the largest possible cup that can be used for both juices?
Find AB if BC = 4 , BD = 5, and AD =4
The area of a rectangle is 27 m^2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.
Length: ___m
Width: ____m
The volume of a rectangular prism is b3 + 8b2 + 19b + 12 cubic units, and its height is b + 3 units. The area of the base of the rectangular prism is square units.
Answer:
b^2 + 5b +4
Step-by-step explanation:
An investigator wants to estimate caffeine consumption in high school students. how many students would be required to estimate the proportion of students who consume coffee? suppose we want the estimate to be within 5% of the true proportion with 95% confidence.
We can solve this problem by referring to the standard probability distribution tables for z.
We are required to find for the number of samples given the proportion (P = 5% = 0.05) and confidence level of 95%. This would give a value of z equivalent to:
z = 1.96
Since the problem states that it should be within the true proportion then p = 0.5
Now we can find for the sample size using the formula:
n = (z^2) p q /E^2
where,
p = 0.5
q = 1 – p = 0.5
E = estimate of 5% = 0.05
Substituting:
n = (1.96^2) 0.5 * 0.5 / 0.05^2
n = 384.16
Around 385students are required.
a commercial jet airplane climbs at takeoff with slope m=4/9. How far in the horizontal direction will the airplane fly to reach am altitude of 20,000 ft above the takeoff point?
The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A commercial jet airplane climbs at takeoff with slope m = 4/9.
Then the equation of the line will be given as,
y = (4/9)x
The y-intercept is zero.
The horizontal direction will the airplane fly to reach an altitude of 20,000 ft above the takeoff point will be
20,000 = (4/9)x
180,000 = 4x
x = 180,000 / 4
x = 45,000 feet
The horizontal direction in will the airplane flies to reach an altitude of 20,000 ft above the takeoff point will be 45,000 feet.
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If the revenue for the week is $2000, and labor cost consist of two workers earning $8 per hour who works 40 hours each, whay is labor cost aa percentage of revenue?
The function f(x)=log[7]x is increasing. True or false
The given function increases as x increases, so the statement is true.
Is the function increasing?Here we have the function:
[tex]f(x) = log_7(x)[/tex]
To see if it is increasing, we can evaluate in two values, 10 and 15, this will serve to see if the function is increasing or not:
[tex]f(10) = log_7(10) = 1.18\\\\f(15) = log_7(15) = 1.39[/tex]
As you can see, when x increases also does f(x), so the function is increasing.
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The volume of a prism is the product of its height and area of its base, V = Bh. A rectangular prism has a volume of 16y4 + 16y3 + 48y2 cubic units. Which could be the base area and height of the prism? a base area of 4y square units and height of 4y2 + 4y + 12 units a base area of 8y2 square units and height of y2 + 2y + 4 units a base area of 12y square units and height of 4y2 + 4y + 36 units a base area of 16y2 square units and height of y2 + y + 3 units
Answer:
D!
a base area of 16y2 square units and height of y2 + y + 3 units
The formula for finding the circumference of a circle is C=2πrC=2πr . Rearrange the formula to solve for the radius (r).
Simplify x^2-4x-32/x^2+7x+12
Three students simplified the expression 2x- 3(y-2x) +-5times -2y.
Amber -4y + 7y
Butch 4x + 7y
Carl 8x + 7y
Who is correct? Explain the error the other students made
A square is inscribed in a circle. A point in the figure is selected at random. Find the probability that the point will be in the shaded region.
The probability of the point will be in the shaded region is 0.64 or 64%.
A square is inscribed in circle. Probability of point to be pick from the square to be find out.
Venn diagram are the Figures of probabilities to understand better.
Here, diameter of circle = d and radius r =d/2, edge of the square = a
By Pythagorean theorem,
a²+a²=d²
2a²= (2r)²
a²=2r²
Area of the square =2r²
Area of the circle = πr²
Now probability = Area of the square/Area of the circle
= 2r²/πr²
= 2/π
= 0.64
Thus, The probability of the point will be in the shaded region is 0.64 or 64%.
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Find the volume of the wedge-shaped region contained in the cylinder x2 + y2 = 49, bounded above by the plane z = x and below by the xy-plane.
We have that
Volume of the wedge-shaped region
[tex]W=228.65[/tex]
Attached below is a picture of the wedge-shaped region contained in the cylinder
Bearing in mind this shape, we have that the coordinates identifying the cylinder are as follows
Co-ordinates
[tex]0 \leq r \leq 7,\frac{\pi}{2} \leq 0 \leq \frac{\pi}{2},0 \leq z \leq x[/tex]
Where
[tex]0 \leq z \leq x =rcos \phi[/tex]
Generally the equation for the volume of the wedge-shaped region W is mathematically given as
[tex]\int \int \int_W 1dv=\int^{7}_{0} \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \int^{rcos \phi}_{0}[/tex]
[tex]\int \int \int_W 1dv=\int^{7}_{0} r (\int^{\frac{\pi}{2}}_{-\frac{\pi}{2}}rcos\phi dv))dr[/tex]
[tex]\int \int \int_W 1dv=(\frac{(7)^3}{3}+\frac{(0)^3}{3})(sin {\pi/2}+sin{-\pi/2})[/tex]
[tex]\int \int \int_W 1dv=228.67[/tex]
Therefore
Volume of the wedge-shaped region
[tex]W=228.65[/tex]
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Given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
(A ) - {}
(B) - {a,e}
(C ) - {a, b, e, g, i, l, o, r, u}
A ratio is a rate. Sometimes always or never true
In a recent local taste contest testing Coke against Pepsi it was found that 3/5 of all people surveyed preferred to taste the Coke. if 7,500 people were in the survey how many chose Pepsi ?
Answer: 3,000
Step-by-step explanation:
Given : In a recent local taste contest testing Coke against Pepsi it was found that [tex]\dfrac{3}{5}[/tex] of all people surveyed preferred to taste the Coke.
If 7,500 people were in the survey , then the number of people chose coke will be :-
[tex]\dfrac{3}{5}\times7500=3\times1500=4500[/tex]
Now, the number of people chose Pepsi = 7,500-4,500=3,000
Hence, there are 3,000 people who chose Pepsi.
Explain why you would want to keep some, but not all, receipts as part of your financial records.
You or we keep only those receipts
1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.
2. We keep those receipts of goods,which are under warranty period or for which you are paying EMI.
3. Receipt of those goods which has very high amount printed on it, and it mismatch with our income ,i.e not correlated with our income Someone can make false claim to entangle you.
Answer:
1. The receipt of those goods which has high transaction value, so that if there is a mismatch, at that time you can help the financial authorities or System.
Step-by-step explanation:
1) Which number rounds up when rounded to the nearest tenth?
55. 24
170.93
0.12
8.15
___________
2)
Estimate the value of 2968 + 9912 by rounding each number to the thousands.
14,000
13,000
12,000
7000
___________
3)
Which statement below shows the best use of friendly numbers to estimate the value of 27 ·times 4
25 times 4 = 100
30 times 5 = 150
27 times 4 = 108
20 times 4 = 80
_____________
4)
Marcus has 78 baseball cards and 45 basketball cards. Estimate the total number of cards Marcus has.
30
33
123
130
___________
5)
Determine which answer is reasonable for 4. 8 times 9.2.
14
45.36
432
870.4
Answer:
1)8.15
2)13,000
3)25 x 4 =100
4) 130
5)45.3
Step-by-step explanation:
What is the estimate of 462,809+256,738
Find the taylor polynomial t3(x) for the function f centered at the number
a. f(x) = e^(â3x) sin(2x), a = 0
Most teachers enjoy teaching students. Most teachers are college graduates. Assuming these two statements are true, do some college graduates enjoy teaching students?
Answer:
yes some some college graduates enjoy teaching students.
Step-by-step explanation:
This question is based on reasoning.
Most teachers enjoy teaching students.
Most teachers are college graduates.
A syllogism is a form of logical reasoning formed by the joining of two or more premises to arrive at a conclusion.
So, here we can say that yes some some college graduates enjoy teaching students.
Valerie predicts she will be able to hold her breath for 31 second while underwater. If she actually held her breath for 34 seconds, what was Valerie's percent error? Round your answer to the nearest tenth of a percent.
If she actually held her breath for 34 seconds. Then the percentage error will be 8.82%.
What is the percentage error?The amount of error is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Valerie predicts she will be able to hold her breath for 31 seconds while underwater.
If she actually held her breath for 34 seconds.
Then the percentage error will be
[tex]\rm error \ \% = \dfrac{34-31}{34} \times 100\\\\\\error \ \% = \dfrac{3}{34} \times 100\\\\\\error \ \% = 8.82 \%[/tex]
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The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?The scores on an exam are normally distributed, with a mean of 74 and a standard deviation of 7. What percent of the scores are less than 81?
We are given the following variables:
Normal distribution
u = sample mean = 74
s = standard deviation of the samples = 7
x = sample value = 81
Since we are asked to find percent of the scores less than 81, this means we have to find the proportion using the z-score. The formula for z score is:
z = (x – u) / s
Substituting the given values:
z = (81 – 74) / 7
z = 1
Using the standard normal distribution tables for z, we find that:
P = 0.8413 at z = 1
Therefore this means that 84.13% of scores are less than 81.
The Answer is the two small boxes just got it right For Plato
FAR LEFT FAR RIGHT