A softball player's batting average is defined as the ratio of hits to at bats. Suppose that a player has a 0.250 batting average and is very consistent, so that the probability of a hit is the same every time she is at bat. During today's game, this player will be at bat exactly three times.
(a) What is the probability that she ends up with two hits?
(b) What is the probability that she ends up with no hits?
(c) What is the probability that she ends up with exactly three hit?
(d) What is the probability that she ends up with at most one hit?
Answers
(a) The probability of ending up with two hits is approximately 0.1406.
(b) The probability of ending up with no hits is approximately 0.4219.
(c) The probability of ending up with exactly three hits is approximately 0.0156.
(d) The probability of ending up with at most one hit is approximately 0.8438.
To solve the given problem, we need to use the concept of binomial probability since each at-bat is independent and has the same probability of a hit. We'll use the batting average of 0.250 to calculate the probabilities.
The probability of a hit is given by the batting average, which is 0.250.
(a) To find the probability that she ends up with two hits:
Using the binomial probability formula, the probability of getting exactly two hits in three at-bats can be calculated as follows:
P(X = 2) = (3 choose 2) * \((0.250)^2 * (1 - 0.250)^(^3^ -^ 2^)\)
Calculating the values:
P(X = 2) = (3 choose 2) * \((0.250)^2 * (0.750)^1\)
P(X = 2) = 3 * 0.0625 * 0.750
P(X = 2) ≈ 0.1406
Therefore, the probability that she ends up with two hits is approximately 0.1406.
(b) To find the probability that she ends up with no hits:
Using the same binomial probability formula, the probability of getting no hits in three at-bats can be calculated as follows:
P(X = 0) = (3 choose 0) *\((0.250)^0 * (1 - 0.250)^(^3^ -^ 0^)\)
Calculating the values:
P(X = 0) = (3 choose 0) *\((0.250)^0 * (0.750)^3\)
P(X = 0) = 1 * 1 * 0.4219
P(X = 0) ≈ 0.4219
Therefore, the probability that she ends up with no hits is approximately 0.4219.
(c) To find the probability that she ends up with exactly three hits:
Using the same binomial probability formula, the probability of getting three hits in three at-bats can be calculated as follows:
P(X = 3) = (3 choose 3) \(* (0.250)^3 * (1 - 0.250)^(^3^ -^ 3^)\)
Calculating the values:
P(X = 3) = (3 choose 3) *\((0.250)^3 * (0.750)^0\)
P(X = 3) = 1 * 0.0156 * 1
P(X = 3) ≈ 0.0156
Therefore, the probability that she ends up with exactly three hits is approximately 0.0156.
(d) To find the probability that she ends up with at most one hit:
We can find this probability by calculating the sum of the probabilities of getting 0 hits and 1 hit.
P(X ≤ 1) = P(X = 0) + P(X = 1)
Substituting the calculated values:
P(X ≤ 1) ≈ 0.4219 + P(X = 1)
To calculate P(X = 1), we can use the binomial probability formula as before:
P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^(^3^-^1^)\)
Calculating the values:
P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^2\)
P(X = 1) = 3 * 0.250 * 0.5625
P(X = 1) ≈ 0.4219
Substituting back into the equation:
P(X ≤ 1)
≈ 0.4219 + 0.4219
P(X ≤ 1) ≈ 0.8438
Therefore, the probability that she ends up with at most one hit is approximately 0.8438.
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Related Questions
Please help ASAP Use the screenshot answer the question
Answers
Answer:
0.35, 0.40
Step-by-step explanation:
a firework is fired into the air from a location 8 yards away. if height of the firework is increasing at a rate of 25 yards per second, then how fast is the distance from you to the firework changing when the firework is 6 yards above the ground?
Answers
Answer:
15 yd/s
Step-by-step explanation:
You want to know the rate of change of distance to a firework when it is 8 yards away horizontally, 6 yards high, and its height is increasing at 25 yards per second.
GeometryThe geometry of the problem can be modeled by a 3-4-5 right triangle scaled by a factor of 2 yards. The straight-line distance to the firework is ...
5 × (2 yd) = 10 yards
The vertical distance is given as 6 yards, increasing at 25 yd/s. Then the cosine of the angle from the line of sight to the direction of travel is ...
cos(α) = adjacent/hypotenuse = (6 yd)/(10 yd) = 0.6
Speed made goodThe speed in the direction of the line of sight is the speed of the firework, multiplied by the cosine of the angle between its direction and the line of sight:
rate of change of distance away = (25 yd/s) × cos(α) = (25 yd/s)(0.6)
rate of change of distance away = 15 yd/s
__
Additional comment
The rate of change can also be found using calculus. The distance away can be expressed using the distance formula, and its derivative found. The value of that derivative at the time of interest will give the rate of change of distance to the firework. This is shown in the second attachment, using a graphing calculator to find the derivative.
There are 6 red marbles, 5 green marbles, and 4 yellow marbles in a bag. If Joe picks 2 marbles one after the other without replacement, then what is the probability that both are red in color? P(R,R)
Pilihan jawaban
2/5
1/21
5/35
1/7
Answers
Answer:
1/7
Step-by-step explanation:
6 + 5 + 4 = 15
There are 15 marbles to start with.
p(event) = (number of desired outcomes)/(total number of outcomes)
First pick (there are 6 desired outcomes out of a total of 15 possible outcomes):
p(r) = 6/15
Now there are 5 red marbles left and a total of 14 marbles left.
Second pick (there are 5 desired outcomes out of a total of 14 possible outcomes):
p(r) = 5/14
These events are independent, so we multiply the two probabilities.
p(r, r) = 6/15 × 5/14
p(r, r) = 3/7 × 1/3
p(r, r) = 1/7
[25] 1251 3) Fit the data given in the table of problem (2) to an exponential equation of the form y = 1 + aebx by linearizing the equation and using linear regression to determine the coefficients a and b. Use this result to estimate the value of y at x =
Answers
Using the exponential regression feature of the calculator to find the equation of the regression line, we get that \($$y = 0.8996 e^{1.3759x}.$$\)
Given data, $$\begin{array}{|c|c|} \hline x & y\\ \hline 1 & 2.20\\ 2 & 3.60\\ 3 & 5.90\\ 4 & 9.70\\ 5 & 15.90\\ 6 & 26.00\\ \hline \end{array}.$$
The equation of the form is y = 1 + aebx;
Thus, the required equation is \($$y = 1 + 0.8996 e^{1.3759x}.$$\)
Finally, putting x = 7, we get
\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)
Thus, the required equation is\($$y = 1 + 0.8996 e^{1.3759x}.$$\)Finally, putting x = 7, we get
\($$y = 1 + 0.8996 e^{1.3759(7)} \approx 156.76.$$\)
So, the value of y at x = 7 is approximately 156.76.
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in a survey of 282 college students, it is found that 64 like brussels sprouts, 94 like broccoli, 58 like cauliflower, 26 like both brussels sprouts and broccoli, 28 like both brussels sprouts and cauliflower, 22 like both broccoli and cauliflower, and 14 like all three vegetables. how many of the 282 students do not like any of these vegetables?
Answers
There are 128 students who do not like any of these vegetables.
How to solve this problem?
To solve this problem, we can use the principle of inclusion-exclusion. We start by adding up the number of students who like each vegetable:
Number who like brussels sprouts = 64
Number who like broccoli = 94
Number who like cauliflower = 58
Next, we subtract the number of students who like more than one vegetable once:
Number who like both brussels sprouts and broccoli = 26
Number who like both brussels sprouts and cauliflower = 28
Number who like both broccoli and cauliflower = 22
We can't just subtract the number who like all three vegetables once, since we have now subtracted them twice (once for each pair of vegetables). So we need to add them back in once:
Number who like all three vegetables = 14
Now we can calculate the number of students who like at least one vegetable:
Number who like at least one vegetable = 64 + 94 + 58 - 26 - 28 - 22 + 14
Number who like at least one vegetable = 154
Finally, to find the number of students who do not like any of these vegetables, we subtract this from the total number of students:
Number who do not like any of these vegetables = 282 - 154
Number who do not like any of these vegetables = 128
Therefore, there are 128 students who do not like any of these vegetables.
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−8x 4y>3 6x−7y<−5 is (2,3) a solution of the system?
Answers
The ordered pair (2,3) is not a solution of the system
How to determine if (2,3) a solution of the system?From the question, we have the following parameters that can be used in our computation:
−8x + 4y > 3
6x - 7y < −5
The solution is given as
(2, 3)
Next, we test this value on the system
So, we have
−8(2) + 4(3) > 3
-4 > 3 --- false
This means that (2,3) is not a solution of the system
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Dell Computers receives large shipments of microprocessors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose Dell decides to test five microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned. Calculate the probability that the entire shipment will be kept by Dell even though the shipment has 10% defective microprocessors.
a 0.5905
b 0.3979
c 0.3995
d 0.4550
Answers
The probability that the entire shipment will be kept by Dell even though the shipment has 10% defective microprocessors is approximately 0.5905. Hence the correct answer is (a) 0.5905.
To calculate the probability that the entire shipment will be kept by Dell even though the shipment has 10% defective microprocessors, we can use the concept of binomial probability.
Let's denote the probability of a microprocessor being defective as p = 0.10 (10% defective) and the number of microprocessors Dell tests as n = 5.
We want to calculate the probability that all five tested microprocessors are non-defective, which is equivalent to the probability of having zero defective microprocessors in the sample.
Using the binomial probability formula, the probability of getting exactly k successes (non-defective microprocessors) in n trials is:
\(\[P(X = k) = \binom{n}{k} \cdot p^k \cdot (1 - p)^{n - k}\]\)
For this case, we want to calculate P(X = 0), where X represents the number of defective microprocessors.
\(\[P(X = 0) = \binom{5}{0} \cdot 0.10^0 \cdot (1 - 0.10)^{5 - 0} \\= 1 \cdot 1 \cdot 0.9^5 \\\\approx 0.5905\]\)
Therefore, the correct answer is (a) 0.5905.
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14. The equation of the line that passes through the
points (-2,2) and (3, -3) is
1. x + y = 5
2.x-y=5
3. y - x = 5
4. y = x
5. y = -X
Answers
Answer:
5. y = -x
Step-by-step explanation:
First, you need to find the slope of the line.
\(m = \frac{2 - (-3)}{-2 - 3} = \frac{5}{-5} = -1\)
Now, using either point substitute into the point-slope form for a line:
\(y - y_{1} = m(x - x_{1} )\)
Using (-2,2) for \((x_{1} , y_{1} )\) we get y - 2 = -1(x +2)
y - 2 = -x - 2
y = -x
Answer 5 is the correct answer
Consider the dictionary below: student ={ "name": "Em "class": 9, "marks": 75 "name": "Emma", Select all the correct methods to obtain the value(s) of the key marks from the dictionary m= student.get(2) m= student.get(’marks’) m=( student [2])
m=( student[’marks’])
none of the above A and C B and D
Answers
Method 4: Here, the square bracket notation is used with the key marks, which is enclosed within quotes. As the key marks is not enclosed within quotes in the dictionary, this method is incorrect.
Hence, the method is incorrect.
The correct methods to obtain the value(s) of the key marks from the given dictionary are as follows:a. `m= student.get('marks')`b. `m= student['marks']`.
Method 1: Here, we use the get() method to obtain the value(s) of the key marks from the dictionary. This method returns the value of the specified key if present, else it returns none. Hence, the correct method is `m= student.get('marks')`.
Method 2: Here, we access the value of the key marks from the dictionary using the square bracket notation. This method is used to directly get the value of the given key.
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Gold weighs 19.32 grams per cubic centimeter. If a gold coin contains 2.4 cubic centimeters
of gold, how much does it weigh in grams? Show your work.
Answers
Answer:
46.368 grams
Step-by-step explanation:
19.32g per 1 cubic cm
?g per 2.4 cubic cm
19.32 x 2.4 = 46.36800
When performing a statistical analysis, why do we usually work with a sample rather than an entire population?
Select one:
a. The p-values only work with samples, not populations.
b. A t-test doesn't produce results when a population is used.
c. We don't work with samples, we only work with entire populations.
d. We often lack the manpower and resources to gather an entire population for a statistical analysis
Answers
When performing a statistical analysis, we work with sample rather than the entire population because, we often lack manpower or resources to gather data. So option D is correct.
Statistical work is usually done with a sample. This is done because, if we try to include and collect data from the whole population, it will be very time consuming and need more manpower and resources. It will become a much tedious process.
So a sample which is representative of the whole population is needed. Selecting a sample size and determining the sample must follow certain criteria. They are population parameters we want to estimate, Cost of sampling, Variability of the population, how hard is it to collect data and how precise we want the final estimates to be. All these are taken into consideration and a sample that properly represent the population is determined without bias.
So, option D is the correct answer.
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I need help please help
Answers
Answer:
21u-16v+18w
Step-by-step explanation:
(7u-4v+4w) 14u-12v+14w
21u-16v+18w
Answer:
= 21u−16v+18w
Step-by-step explanation:
Let's simplify step-by-step.
7u−4v+4w−2(−7u+6v−7w)
Distribute:
=7u+−4v+4w+(−2)(−7u)+(−2)(6v)+(−2)(−7w)
=7u+−4v+4w+14u+−12v+14w
Combine Like Terms:
=7u+−4v+4w+14u+−12v+14w
=(7u+14u)+(−4v+−12v)+(4w+14w)
=21u+−16v+18w
Answer:
=21u−16v+18w
A bat travels 100 miles in 3 hours. What is the unit rate?
Answers
Answer:
33.33 mph
Step-by-step explanation:
Haley made 88% on a history test. The
test had 50 questions of equal point value.
How many questions did Haley miss?
Answers
Answer:
She missed 6 questions.
Step-by-step explanation:
88% can be written as (88/100) or as 0.88.
You can set this as a ratio problem which is,
88/100 = correct/50
correct = (88/100)*50 (multiply both sides by 50)
correct = 44
So, 50 (total questions) - 44 = 6 incorrect questions
distributive property to write an equation that's equivalent to -2(-6 +3y -1)
Answers
Answer:
-2(-6+3y-1) = -6y+14
Step-by-step explanation:
Need help pleaseeeeeeee
Answers
The volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.
What is pyramid?Pyramid is a structure with a polygonal base and triangular sides that meet at a point. Pyramids have been used throughout history as tombs, temples and monuments. Many of the most famous pyramids are located in Egypt, such as the Great Pyramid of Giza.
The volume of a right square pyramid is equal to one-third of the base area multiplied by the height. To find the volume of this pyramid, we first need to calculate the base area.
The base area of a square pyramid is equal to the length of one side (s) squared. Since the length of one side of this pyramid is 6m, the base area is 6m x 6m, which equals 36m².
Now that we know the base area, we can calculate the volume of the pyramid. The volume is equal to one-third of the base area multiplied by the height. In this case, the volume of the pyramid is one-third of 36m² multiplied by 4m, which equals 48m³.
Therefore, the volume of the right square pyramid with the dimensions e = 5m, h = 4m, and s = 6m is 48m³.
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What is the domain of the function shown on the graph?
A. -10 < x < 2
B. x ≤ 1
C. -∞ < x < ∞
D. x ≤ 2
Answers
Answer:
C. -∞ < x < ∞
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
We see that our x-values can be any number. Therefore, we have all real numbers as our domain:
(-∞, ∞) or -∞ < x < ∞
Answer:
C. -∞ < x < ∞
Step-by-step explanation:
Plato
Can someone help me find the domain and range?
Answers
domain is x
range is y
domain is time
range is distance
domain is between 0 & 170 seconds
range is 0 & 60 meters
meters per seconds is like
miles per hour so
this graph is about SPEED !
speed is usually indicated by the graph's
SLOPE !
Does the following graph represent a function, Yes or No
Answers
Answer:
no
Step-by-step explanation:
Use the vertical line test to determine if it is a function
Since a vertical line touches more than one point on the graph, it is not a function
Maryama bought 45 plain cookies for $2.20 each. She decorated them with icing and sold them for $3.75 each. How much profit did she make selling her decorated cookies?
Answers
45x2.20=99
meaning she spent $99
45x3.75=168.75
shows how much she made
168.75-99=69.75
shows what she profited
your answer is $69.75
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The cross section of rectangular prism A measures 6 units by 4 units. The cross section of triangular prism B has a base that measures 8 units and a height of 6 units. If the length of each prism is 7. 22 units, which statement is true? rectangular prism A , with a cross-section that is parallel to its respective basetriangular prism B, with a cross-section that is parallel to its respective base Volume A = one half(Volume B) Volume A = 2(Volume B) Volume A = one third(Volume B) Volume A = Volume B.
Answers
The statement "Volume A = Volume B" is true. The cross section of rectangular prism A measures 6 units by 4 units.
To determine the relationship between the volumes of rectangular prism A and triangular prism B, we need to calculate their volumes and compare them.
For rectangular prism A:
Cross-sectional dimensions: 6 units by 4 units
Length: 7.22 units
Volume of A = Length * Width * Height
= 7.22 units * 6 units * 4 units
= 173.28 units³
For triangular prism B:
Base dimensions: 8 units by 6 units
Height: 7.22 units
Volume of B = (Base * Height) / 2
= (8 units * 6 units * 7.22 units) / 2
= 173.28 units³
Comparing the volumes of A and B, we find that the volume of rectangular prism A is equal to the volume of triangular prism B.
Therefore, the statement "Volume A = Volume B" is true.
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Line r passes through the points (1,1) and (8,9) . line s is perpendicular to r what is the slope of line s?
Answers
Answer: \(\frac{-7}{8}\)
Step-by-step explanation:
First, we will need to find the slope of line r.
\(\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1}} =\frac{9-1}{8-1}=\frac{8}{7}\)
Next, we know that perpendicular slopes are negative reciprocals of one another. To find the slope of line s, we will find the negative reciprocal of line r's slope.
\(\displaystyle \frac{8}{7} \rightarrow \frac{-7}{8}\)
PLEASE HELP!!!
ABC maps the outline of a new park. What is the area of the park?
the multiple choice answers are in the photo
Answers
Answer:
\(Area = 10\)
Step-by-step explanation:
Given
\(A = (2,1)\)
\(B =(4,7)\)
\(C =(6,3)\)
Required
The area of the park
The outline is a triangle and as such, the area is calculated using:
\(Area = \frac{1}{2}|(x_1y_2 - x_2y_1) + (x_2y_3 - x_3y_2) + (x_3y_1 - x_1y_3)|\)
This gives:
\(Area = \frac{1}{2}|(2*7 - 4*1) + (4*3 - 6*7) + (6*1 - 2*3)|\)
Using a calculator, we have:
\(Area = \frac{1}{2}|-20|\)
Remove absolute bracket
\(Area = \frac{1}{2}*20\)
\(Area = 10\)
Jenna borrows $8,000 for college at a yearly simple interest rate of 6%. She takes
15 years to pay off the loan and interest. How much interest does she pay? What is
the total amount she pays?
Answers
Answer:
The interest will rack up to $7,200
The total will be $15,200
Step-by-step explanation:
the interest she pays is $7,000
the total amount she pays is $15,200
Jenna borrows $8,000 for college at a simple interest rate of 6%
she has 15 years to pay back the loan and interest
the interest can be calculated as follows
= 6/100 × 8,000
= 0.06 × 8000
= 480
= 480 × 15
= $7200
the total amount she pays can be calculated as follows
= $7200 +$8000
= $15,200
Hence the interest she pays is $7200 and the total amount is $15,200
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if sin(θ) = x 7 for − π 2 < θ < π 2 , find an expression for cos(2θ) in terms of x.
Answers
An expression for cos(2θ) in terms of x is cos(2θ) = 1 - 2x²
To find an expression for cos(2θ) in terms of x, we can use the double angle identity for cosine:
cos(2θ) = 2cos²(θ) - 1
Since we know sin(θ) = x, we can use the Pythagorean identity for sine and cosine to find cos(θ):
cos²(θ) = 1 - sin²(θ) = 1 - x²
Now we can substitute this expression for cos²(θ) into the double angle identity:
cos(2θ) = 2(1 - x²) - 1 = 1 - 2x²
Therefore, an expression for cos(2θ) in terms of x is:
cos(2θ) = 1 - 2x²
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does anyone know how to do this?
Answers
Answer:
100
Step-by-step explanation:
I thinks it 100 cuz 15x20= 300 and ⅓ of 300 is 100
15×20 = 300
1/3 × 300 =100
Step-by-step explanation:
15 rows multiplied by 20 seats to find out total number of seats and then you multiply by a third to find one third of the total seats
Pls halp due today >_<. Thank you
Answers
Answer:
<
Step-by-step explanation:
Step 1: Evaluate 2√40
2√40 = 12.6491
Step 2: Evaluate 7 + √63
7 + √63 = 14.9373
Step 3: Fill in inequality symbol
12.6491 < 14.9373
The surface area of a small toy ball is 10 square inches. If the radius of the ball is doubled, what will be the surface area of the new, larger ball in square inches?.
Answers
The surface area of the new, larger ball is 160 square inches.
What is surface area?
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere with radius r is given by:
A = 4πr²
If the radius is doubled to 2r, the surface area of the new sphere is:
A' = 4π(2r)² = 4π(4r²) = 16πr²
So the new surface area is 16 times the original surface area.
Since the original surface area is 10 square inches, the new surface area is:
A' = 16(10) = 160 square inches
Therefore, the surface area of the new, larger ball is 160 square inches.
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colleen has 12 coins in her pocket. the mix of quarters, nickles and dimes add up to two dollars, and she has three times as many quarters as nickles
How many of each coin does Colleen have in her pocket
(solve this problem using Gaussian elimination)
Answers
By solving a system of equations we conclude that Collen has 6 quarters, 4 dimes, and 2 nickels.
How many of each coin does Colleen have in her pocket?
First, let's define the variables:
x = number of quarters.y = number of nickels.y = number of dimes.There are 12 coins, so:
x + y + z = 12
She has 2 dollars in total, so:
x*0.25 + y*0.05 + z*0.10 = 2
And she has 3 times as many quarters as nickels.
x = 3y
Then we can write the system of equations (or matrix, depending on how you like to see it):
x + y + z = 12
x*0.25 + y*0.05 + z*0.10 = 2
x - 3y = 0
To use the elimination method we just need to add/subtract these equations to remove variables.
If we subtract the third equation to the first one:
(x + y + z) - (x - 3y) = 12 - 0
4y + z = 12
Now we have two equations:
x*0.25 + y*0.05 + z*0.10 = 2
4y + z = 12
If we multiply the first one by 4:
x + y*0.20 + z*0.40 = 8
Subtracting the third eq:
x + y*0.20 + z*0.40 - (x - 3y) = 8 - 0
y*3.20 + z*0.40 = 8
Now the remaining equations are:
4y + z = 12
y*3.20 + z*0.40 = 8
On the top one, we can rewrite: z = 12 - 4y
Replacing that in the other equation:
y*3.20 + (12 - 4y)*0.40 = 8
Now we eliminated the variables x and z, so we can solve this for y:
y*1.60 + 4.8 = 8
y*1.60 = 3.2
y = 3.2/1.6 = 2
Now that we know the value of y, the values of x and z are:
x = 3y = 3*2 = 6
z = 12 - 4y = 12 - 4*2 = 4
Then we conclude that Collen has 6 quarters, 4 dimes, and 2 nickels.
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25 points and brainliest whoever gives right answer
Answers
Answer: D
Step-by-step explanation: Disregard the $ and solve algebraically.
\(4x+36\leq 52\)
\(4x\leq 52-36\)
\(4x\leq 16\)
\(x\leq 4\)
Answer: Choice D is the correct answer :)
Step-by-step explanation: