A new car is tested on a 290m-diameter track. If the car speeds up at a steady 1.2ms−2 , how long after starting the engine will the magnitude of its centripetal acceleration be equal to its tangential acceleration?
Answers
The new car will take 14.3 seconds after starting the engine for the magnitude of the car's centripetal acceleration to be equal to its tangential acceleration.
How we find the magnitude of its centripetal acceleration?Calculation of time when centripetal acceleration is equal to tangential acceleration
The given problem can be solved using the equations for centripetal acceleration and tangential acceleration:
Centripetal acceleration (a_c) = v^2/rTangential acceleration (a_t) = aWe are given that the car speeds up at a steady 1.2 m/s^2, so the tangential acceleration is a_t = 1.2 m/s^2.
To find the time when the centripetal acceleration is equal to the tangential acceleration, we need to equate the above two equations:
v^2/r = a v = √(ar)We know that the diameter of the track is 290 m, so the radius is r = 145 m.
Substituting the value of r, we get:
v = √(1.2 m/s^2 × 145 m)= 17.15 m/s
Now, we can find the time taken to reach this speed:
t = v/a_t= 17.15 m/s / 1.2 m/s^2
= 14.3 s
The problem involves finding the time at which the magnitude of the car's centripetal acceleration becomes equal to its tangential acceleration. To solve the problem, we use the equations for centripetal and tangential acceleration, and equate them to find the velocity at which the two accelerations become equal.
Once we have found the velocity, we use the equation for tangential acceleration to find the time taken to reach this velocity. Finally, we get the answer that the time taken for the magnitude of the car's centripetal acceleration to be equal to its tangential acceleration is 14.3 seconds after starting the engine.
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Related Questions
the ends of a water trough are 8 feet long are equilateral triangles whose sides are 2 feet long. if water is being pourd into the trough at a rate of 5 ft^3 / min, find the rate at which the water level is rising when the depth is 8 inches
Answers
If water is being poured into the trough at a rate of 5 ft^3/min, the rate at which the water level is rising when the depth is 8 inches is 15√3/32 ft/min.
Length (L) = 8 feet
Side = 2 feet
If water is being poured into the trough at a rate of 5 ft^3/min. So
dV/dt = 5 ft^3/min
The depth is 8 inches.
h = 8 inches = 2/3 feet
The formula of volume (V) = √3/4 b^2 · L
Now putting the value
V = √3/4 b^2 · 8
Simplify
V = 2√3b^2
Using the Pythagorean Theorem
b/h = 2/√3
So b = 2/√3 h
Now putting the value of h in the volume V
V = 2√3(2/√3 h)^2
V = 2√3 × 4/3 × h^2
V = 8/√3 × h^2
Differentiating the equation with respect to t
dV/dt = 8/√3 d/dt(h^2)
dV/dt = 8/√3 × 2h dh/dt
dV/dt = 16h/√3 × dh/dt
As dV/dt = 5. So
5 = 16h/√3 × dh/dt
Multiply by √3 on both side, we get
16h dh/dt = 5√3
Divide by 16h on both side, we get
dh/dt = 5√3/16h
As h = 2/3. So
dh/dt = 5√3/(16×2/3)
After solving
dh/dt = 15√3/32 ft/min
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what is the probability you will $100 in the vent from the last question
A. about 2% unlikely
B. about 6% unlikely
C. about 10% unlikely
D. about 16% unlikely
Answers
Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9), A = { 1, 2, 3, 4, B= {2, 4, 6, 8} and
C= {3, 4, 5, 6). Find (i) A (ii) An C (iii) (An CY (iv) A UB (V) BIC
Answers
Answer:
yo i coy to ghost minder
Which term describes the red curve in the figure below?
A.
Circle
B.
Ellipse
C.
Parabola
D.
Hyperbola
Answers
Answer:
D
Step-by-step explanation:
A Hyperbola looks like a Parabola and its reflection, each Parabola curving opposite directions.
Answer:
D. Hyperbola
Step-by-step explanation:
A conic is the intersection of a plane and a right circular cone.
CircleFormed when a cone is intersected by a plane so that the plane is parallel to the circular base.
EllipseFormed when a cone is intersected by a plane so that the plane is at an angle with respect to the circular base.
ParabolaFormed when a cone is intersected by a plane so that the plane is parallel to an edge.
HyperbolaFormed when a double-cone is intersected by a plane so that the plane is perpendicular to the circular bases.
Triangle BCD, with vertices B(4,-7), C(6,-8), and D(7,-2), is drawn on the coordinate
grid below.
S
Answer: A =
6
7
D
9
What is the area, in square units, of triangle BCD?
units
Submit Answer
K
Answers
Answer: The area is 6.5
How do I find the measurement of Angle x?
Answers
Answer:
26°
Step-by-step explanation:
The angle 123° is on a straight line. All angles on a straight line add up to 180°, so the first thing you should do is subtract 123 from 180.
(180-123)
Now, your answer should be 57°, and that is equal to angle W.
You now know two angles. Angles in a triangle add up to 180°, too, so all you do now is the following:
97 + 57 = 154
180- 154 + 26
And there's your answer!
The average weight of ten bulls is 500kg and the standard deviation of the weight is 30kg. What would be the weight of a bull that is 6 standard deviations above the mean weight
Answers
Answer:
680kg
Step-by-step explanation:
The average weight of ten bulls is 500kg and the standard deviation of the weight is 30kg. What would be the weight of a bull that is 6 standard deviations above the mean weight
The formula to solve for the weight that is 6 standard deviation above the mean weight =
μ + 6σ = w
Where
μ = Mean weight = 500kg
σ = Standard deviation = 30kg
Hence:
w = 500kg + 6(30kg)
w = 500kg + 180kg
w = 680kg
Therefore, the weight of a bull that is 6 standard deviations above the mean weight is 680 kg
Using the normal distribution, it is found that the weight of a bull that is 6 standard deviations above the mean weight is of 680 kg.
Normal Probability DistributionIn a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, the mean and the standard deviation are, respectively, of \(\mu = 500\) and of \(\sigma = 30\).
The weight of a bull that is 6 standard deviations above the mean weight is X when Z = 6, hence:
\(Z = \frac{X - \mu}{\sigma}\)
\(6 = \frac{X - 500}{30}\)
\(X - 500 = 6 \times 30\)
\(X = 680\)
The weight of a bull that is 6 standard deviations above the mean weight is of 680 kg.
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T/F of the range, the interquartile range, and the variance, the interquartile range is least influenced by an outlying value in the data set.
Answers
false :) thats ur answer
A line with a slope of 7 passes through the points (2,–8) and (4,z). What is the value of z?
Answers
Answer:
z : 6
Step-by-step explanation:
points: (2,-8) and (4, 6)
write an equation in slope-intercept form tha is parallel to y=4x-2 and has a y-intercept of -2
Answers
Answer:
y = 4x - 2
Step-by-step explanation:
Formula: y = mx + b
Parallel means same slope as original and b is -2.
Find the slope of the following equation. Simplify your answer.
5x + 2y = -10
m= -5/2
m= 5
m= 2
m= 2/5
Answers
Answer:
1st option
Step-by-step explanation:
theequation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
5x + 2y = - 10 ( subtract 5x from both sides )
2y = - 5x - 10 ( divide terms by 2 )
y = - \(\frac{5}{2}\) x - 5 ← in slope- intercept form
with slope m = - \(\frac{5}{2}\)
What is the range of the function f(x) = -3x + 1 when the domain is {-2, 0, 3}?
A. all real numbers
B. {-31, -29, -32}
C. {7, 1, -8}
D. {-5, 1, -8}
Answers
Answer:
Solution given:
f(x) = -3x + 1
f(-2)=-3×-2+1=7
f(0)=-3×0+1=1
f(3)=-3×-3+1=-8
So
Range is {7,1,-8) is a required answer
let r be the relation r = {(1, 1),(1, 2),(2, 3),(3, 1),(3, 4) (4,2)}. find −r2
Answers
Given the relation, value of −r2 is {(3, 1), (3, 3), (2, 3), (1, 4)}.
To find −r2, we first need to find r2, which is the composition of the relation r with itself. The composition of r with itself is given by:
r2 = {(a, c) | ∃b ∈ A, (a, b) ∈ r and (b, c) ∈ r}
where A is the set of all elements in the relation r.
Using this definition, we can calculate r2 as follows:
r2 = {(1, 3), (3, 3), (3, 2), (4, 1)}
Next, to find −r2, we simply take the inverse of each ordered pair in r2 and reverse the order of the pairs. Thus, we have:
−r2 = {(3, 1), (3, 3), (2, 3), (1, 4)}
Therefore, the relation −r2 is {(3, 1), (3, 3), (2, 3), (1, 4)}.
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Which ordered pairs are solutions to the inequality y−3x<10?
Answers
(0,-4) , (0,-1) , (4,-1) are the ordered pairs are solutions to the inequality
y − 3x < 10 which is option (A) , (D) and (E) .
An inequality compares two values and indicates whether one is less than, greater than, or equal to another. a ≠ b indicates that a is not equal to b a < b indicates that a is less than b a > b indicates that a is greater than b (These two are known as strict inequalities) a ≤ b means that a is less than or equal to b a ≥ b means that a is greater than or equal to b.
We have to check whether the given options are the solutions to the inequality y− 3x < 10 . ...(1)
(A) If (0,-4) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -4 in equation (1) , we get
\(-4-3(0) < 10\\-4 < 10\)
As the above condition is true so (0,-4) is the solution of given inequality
(B) If (-6,0) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -6 and y = 0 in equation (1) , we get
\(0-3(-6) < 10\\18 < 10\)
As the above condition is not true so (-6,0) is not the solution of given inequality .
(C) If (-1,7) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = -1 and y = 7 in equation (1) , we get
\(7-3(-1) < 10\\7+3 < 10\\10 < 10\)
As the above condition is not true so (-1,7) is the not the solution of given inequality .
(D) If (0,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 0 and y = -1 in equation (1) , we get
\(-1-3(0) < 10\\-1 < 10\)
As the above condition is true so (0,-1) is the solution of given inequality.
(E) If (4,-1) is the solution of given inequality y− 3x < 10 then it must satisfy the equation .
Putting x = 4 and y = -1 in equation (1) , we get
\(-1-3(4) < 10\\-1-12 < 10\\-13 < 10\)
As the above condition is true so (4,-1) is the solution of given inequality.
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Question 2 To achieve better software, one viewpoint aims to have the right product. What does having the right product mean?
Answers
Having the right product means that the software being developed meets the needs and requirements of its intended users.
This involves identifying the target audience, understanding their needs, and designing the software in a way that meets those needs. In addition to functionality, having the right product also means ensuring the software is user-friendly, reliable, and efficient. Achieving the right product requires effective communication between developers and stakeholders, as well as ongoing testing and feedback to ensure that the software meets its intended purpose.
Ultimately, having the right product leads to greater user satisfaction, increased productivity, and improved overall performance of the software.
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In Exercises 8-10, find the domain and range of the function. 8. y = x + 2 9. y = -x + 1 10. y = - |x| -3
Answers
The domain and the range of the functions are
1. The domain is (-∝, ∝) and the range is (-∝, ∝)2. The domain is (-∝, ∝) and the range is (-∝, ∝)3. The domain is (-∝, ∝) and the range is (-∝, -3]How to determine the domain and the range?Equation 1
The equation is given as
y = x + 2
The above equation is a linear equation
So, the domain is (-∝, ∝) and the range is (-∝, ∝)
Equation 2
The equation is given as
y = - x + 1
The above equation is a linear equation
So, the domain is (-∝, ∝) and the range is (-∝, ∝)
Equation 3
The equation is given as
y = -|x| - 3
The above equation is an absolute value function
An absolute value function represented as
y = a|x - h| + k
Where
Vertex = (h, k)
So, we have
Vertex = (0, -3)
Remove the x value
y = -3
Because the leading coefficient is negative, then the vertex is a maximum
i.e.
(-∝, -3]
So, the range is (-∝, -3]
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Mary is 63.5 inches tall and her sister Tonya is 70 inches tall . Tonya wants to know how many inches taller she is than Mary . Which equation and solution can be used to solve this problem? The answer is D 63.5 -x =70 subtract 63.5 from both sides . The answer is 6.5 inches
Answers
Answer: Tonya is 6.5 inches taller than Mary
Step-by-step explanation: Subtract 63.5 from 70 to get 6.5
Answer:
the answer is B :D
Step-by-step explanation:
got it right in edge
which estimating technique uses a statistical relationship between historical data and other variables (e.g., square footage in construction, lines of code in software development) to calculate an estimate for scope, cost and duration? group of answer choices bottom-up estimating analogous estimating monte carlo estimating parametric estimating
Answers
Parametric estimating is a valuable technique in project management that can save time and resources by using historical data to establish a statistical relationship and estimate the scope, cost, and duration of a project. (option d).
Estimating techniques are used in project management to calculate an estimate for the scope, cost, and duration of a project.
The keyword to note here is "statistical relationship". In parametric estimating, this relationship is established by analyzing historical data and identifying patterns and trends. Once a relationship has been established, it can be used to estimate the scope, cost, and duration of a similar project in the future.
Similarly, in software development, the lines of code can be used as a variable to establish a statistical relationship. By analyzing the historical data of similar projects, a relationship can be established between the lines of code and the duration of the project.
Hence the correct option is (d).
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1.
- I am a multiple of 3
- I am an odd number
- the sum of my digits is 6
- my ones is one more than my tens digit
- my hundreds digit is 5 times my one digit
what number am I?
2.
- all my digits are different
-my ones digit is 4 times my hundreds digit
- my thousands digit is a perfect square
-my ones digit is 3 more than my tens digit
what number am I?
Answers
Answer:
1. 501
2. 1258 or 4258 or 9258
Step-by-step explanation:
1. represent number (d3d2d1) in terms of x. let x = 10's digit (dxd) then
d2 = x
d1 = x + 1
d3 = 5(x + 1) = 5x + 5
d3 + d2 + d1 = 6
(5x + 5) + (x) + (x + 1) = 6
7x + 6 = 6
7x = 0
x = 0 SO
d3 = (5x + 5) = 5
d2 = 0
d1 = x + 1 = 1
501
2. d4d3d2d1 and d1 not = d2 not = d3 not = d4, let d3 = x and d2 = y then
d2 = y
d3 = x
d1 = 4x and d1 = y + 3 so 4x = y + 3 or y = 4x - 3
d4 = perfect square (1 or 4 or 9)
any d must be <= 9
d4d3d2d1 = (1 or 4 or 9)(x)(4x - 3))(4x) so x<3 (0,1,2) or d1 fails <= 9
(1,4,9)(0,1,2)((4x - 3 = (1,5))((4x = 0,4,8)
d3 (0,1,2) must be 2 because 0 does not work for d2 and 1 does not work for d1, so this make d1 (4x) = 8 so
(d4)(2)(4x - 3 = 5)(4x = 8) = d4 (1,4,9) and 258 so
1258 or 4258 or 9258
If answered I will give you brainliest.
Erica and Mario tested a toy car to see how fast it would travel. They recorded their results in the table below. What is the average speed of the toy car? Choose the best answer.
A 0.12 m/s
B 0.6 m/s
C 1.2 m/s
D 1.6 m/s
Answers
suppose that of the 14 customers selected, 9 have had their complaints resolved satisfactorily. using part b, do you believe the claim of 75 percent satisfaction? explain.
Answers
No, the claim of 75 percent satisfaction is not supported by the data provided.
To determine if the claim of 75 percent satisfaction is true, we need to compare the number of customers who had their complaints resolved satisfactorily to the total number of customers.
In this case, we have 9 out of 14 customers who had their complaints resolved satisfactorily.
To calculate the percentage of satisfaction, we divide the number of customers with resolved complaints by the total number of customers and then multiply by 100.
Number of customers with resolved complaints = 9
Total number of customers = 14
Percentage of satisfaction = (9/14) * 100 ≈ 64.29%
The actual percentage of satisfaction based on the given information is approximately 64.29%.
Therefore, the claim of 75 percent satisfaction is not supported by the data provided.
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The total price of a shirt and a cap is $11. If the price of the shirt was doubled and the price of the cap was three times its original price, the total price of a shirt and a cap would be $25. The following system of equations models this scenario:
x + y = 11
2x + 3y = 25
What is the price of each shirt and cap?
Price of a shirt is $9, and price of a cap is $2.
Price of a shirt is $10, and price of a cap is $1.
Price of a shirt is $8, and price of a cap is $3.
Price of a shirt is $7, and price of a cap is $4.
Answers
Answer:
the shirt is 8 dollars and the cap is 3
Step-by-step explanation:
This is because 8 times 2 is 16 which is the new price of the shirt then 3 times 3 is 9 which would be the new cap price and 16 plus 9 is 25
Answer:
The answer is C
Step-by-step explanation:
I took the test
Data are drawn from a bell-shaped distribution with a mean of 120 and a standard deviation of 5. There are 900 observations in the data set. a. Approximately what percentage of the observations are less than 130? (Round your answer to 1 decimal place.) Percentage of observations 0 b. Approximately how many observations are less than 130? (Round your answer to the nearest whole number.) Number of observations
Answers
The percentage of observations less than 130 is 97.7%, and the number of observations less than 130 = 879
The question asks about the percentage and number of observations that are less than 130 in a data set that follows a bell-shaped distribution with a mean of 120 and a standard deviation of 5.
a. To find the percentage of observations that are less than 130, we can use the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Plugging in the given values, we get:
z = (130 - 120) / 5
z = 10 / 5
z = 2
Using a standard normal table or calculator, we can find that the probability of a z-score being less than 2 is approximately 0.9772. This means that approximately 97.7% of the observations are less than 130.
b. To find the number of observations that are less than 130, we can multiply the percentage by the total number of observations:
Number of observations = 0.9772 * 900
Number of observations = 879.48
Rounding to the nearest whole number, we get that approximately 879 observations are less than 130.
Therefore, the answers are:
a. Percentage of observations less than 130 = 97.7%
b. Number of observations less than 130 = 879
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Please help I will give brainliest and a lot of points :)
Answers
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
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Jen Butler has been pricing Speed-Pass train fares for a group trip to New York. Three adults and four children must pay $136. Two adults and three children must pay $97. Find the price of the adults
ticket and the price of a child's ticket.
Answers
The price of an adult ticket is $20
The price of a child's ticket is $19
How to calculate the price of an adult and child ticket ?Let x represent the price of a child ticket
Let y represent the price of an adult ticket
Three adults and four children must pay 136
3y + 4x= 136.........equation 1
Two adults and three children must pay $97
2y + 3x= 97.........equation 2
From equation13 1
3y+4x= 136
3y= 136-4x
y= 136-4x/3
Substitute 136-4x/3 for y in equation 2
2(136-4x) + 3x= 97
272-8x/3 + 3x/1= 97
272-8x+9x/3= 97
cross multiply
272-8x+9x=291
collect the like terms
-8x+9x= 291-272
x= 19
Substitute 19 for x in equation 1
3y+4x= 136
3y + 4(19)= 136
3y+ 76= 136
3y= 136-76
3y=60
y= 60/3
y= 20
Hence children tickets cost $19 and adult tickets cost $20
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Which of the following is the correct point-slope equation for the line that
passes through the point (-4,-2) and is parallel to the line given by
y = 5x + 44?
Ay+2= 5(x+4)
OB. y-4-5(x-2)
OC. y+4= 5(x+2)
OD. y-2= 5(x-4)
Answers
The correct point-slope equation for the line that passes through the point (-4,-2) and is parallel to the line given by y = 5x + 44 is: A. y + 2 = 5(x + 4)
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.Since the line is parallel to y = 5x + 44, the slope is equal to 5.
At data point (-4, -2) and a slope of 5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-2) = 5(x - (-4))
y + 2 = 5(x + 4)
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6. A lighting fixture manufacturer has daily production costs of c=0.25n²-10n+800, where C is the total
daily cost in dollars and n is the number of light fixtures produced.
a) Is the manufacturer's cost increasing or decreasing when they produce between 10 and 15 light fixtures?
Prove your claim with math. (2 pts)
b) Is the manufacturer's cost increasing or decreasing when they produce between 20 and 25 light fixtures?
Prove your claim with math. (2 pts)
Answers
By finding the average rate of change, we can see that:
a) The cost decreases.
b) The cost increases.
How to know when the cost is increasing or decreasing?
To check that, we need to find the average rate of change on the interval.
Remember that for function f(x) on an interval (a, b), the average rate of change is:
R = (f(b) - f(a))/(b - a)
Here the cost function is:
c(n) = 0.25*n² - 10n + 800
a) In the interval [10, 15] the average rate of change is given by:
R = (c(15) - c(10)/(15 - 10)
Where:
c(15) = 0.25*15^2 - 10*15 + 800 = 706.25
c(10) = 0.25*10^2 - 10*10 + 800 = 725
Then the average rate of change is:
R = (706.25 - 725)/(15 - 10) = -3.75
This means that between 10 and 15 light fixtures, the cost is decreasing.
b) Now we have the interval [20, 25], so let's do the same ting:
c(20) = 0.25*20^2 - 10*20 + 800 = 700
c(25) = 0.25*25^2 - 10*25 + 800 = 706.25
Here the average rate of change is:
R = (706.25 - 700)/(25 - 20) = 1.25
It is positive, which means that the cost is increasing.
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AN EMPTY SET IS EQUIVALENT TO ZERO?
Answers
Answer:
In mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
Hope this helps!
Step-by-step explanation:
What is a solution on a graph?
Answers
Answer:
The solution on a graph is the point where two lines interesect
Step-by-step explanation:
Suppose that 40% of voters in Okeechobee county support a proposed property tax. Consider the sampling
distribution of the sample proportion of supporters with sample size n = 135. Determine the mean and
standard deviation of the sampling distribution of p. Round solutions to four decimal places, if necessary.
Answers
The mean of the sampling distribution of p is 0.40 and the standard deviation of the sampling distribution of p is 0.0409.
What is standard deviation?Standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated by taking the square root of the variance of the data set. It is a commonly used measure to assess the variability in a data set.
The mean of the sampling distribution of p is 0.40, which is the same as the proportion of supporters in the population of Okeechobee County. This is due to the fact that the sample proportion estimates the population proportion. The standard deviation of the sampling distribution of p is equal to the square root of the product of p (0.40) and q (1-p, or 0.60) divided by the sample size (135). In this case, the standard deviation of the sampling distribution of p is 0.0409.
The mean and standard deviation of the sampling distribution of p can be used to understand what values of p are likely when samples of size n = 135 are drawn from the population of Okeechobee County. If a sample is drawn from the population, the sample proportion of supporters is likely to be close to 0.40, which is the mean of the sampling distribution of p. Furthermore, most of the sample proportions of supporters are likely to be within two standard deviations (or 0.0818) of the mean. This means that the sample proportion of supporters is likely to be between 0.3182 and 0.4818 when samples of size n = 135 are drawn from the population.
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