Complete Question
How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?
Exercise 9.53
A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.
B. What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?
Answer:
The First question
[tex] n = 1879 [/tex]
A
The 96% confidence interval is
[tex]0.51 < p < 0.63 [/tex]
B
The possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is
[tex]E = 0.06 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]E = 0.02[/tex]
The sample size is n = 200
The number that supported the annexation suit is k = 114
Considering the first question
Generally our sample in Exercise 9.53 is [tex]\^ p = 0.57[/tex]
From the question we are told the confidence level is 96% , hence the level of significance is
[tex]\alpha = (100 - 96 ) \%[/tex]
=> [tex]\alpha = 0.04[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.751 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.751}{0.02 } ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.751}{0.02 } ]^2 * 0.57 (1 -0.57 ) [/tex]
=> [tex] n = 1879 [/tex]
Considering question B
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.751 * \sqrt{\frac{ 0.57 (1- 0.57 )}{200} } [/tex]
=> [tex]E = 0.06 [/tex]
Considering question A
Generally the sample proportion of the number that supported the annexation suit is mathematically represented as
[tex]\^ p = \frac{114}{200}[/tex]
=> [tex]\^ p = 0.57[/tex]
Generally 96% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.57 - 0.06 < p < 0.57 + 0.06 [/tex]
=> [tex]0.51 < p < 0.63 [/tex]
Simplify 8x + 9d + 3x -5d
Please Do Show Your Work Explanation
Answer:
The answer is =4d+11x
Step-by-step explanation:
8x + 9d + 3x -5d
=9d-5d+8x+3x
=4d+11x
Answer:
putting in arranged and sum the like terms
8x+3x+9d-5d
11x+4d
What is the simple interest earned when the principal is $500 at a rate of 10% held in the ban for 8 months?
S.I= PRT /100
where,
P = price $500
R = rate 10%
T = time =8months
= $500*10*8/100
= $40,000/100
S.I = $400
Pls help 2 and 3!!!!!!!!!
Answer:
2)
d. -1 1/2
3)
c. 21 1/2
Step-by-step explanation:
14) The value of y varies directly with x, and y = 3.6 when x = 6. Find y when x= 48.
Please and thank you. I needed now. Please help
Answer: y = 28.8
Step-by-step explanation:
By using ratios
if the values vary with each other, then they will increase the same amount. 6x8 is 48. So 3.6 x 8 is your answer, 28.8
PLEASE HELP ME!
100 POINTS!
A cylinder has a volume of 20x®y4 units cubed. If the base of the cylinder has an area of
5x"y2 units squared, which of the following expressions represent the height of the cylinder?
(Hint: V = Bh)
O 100x®y
O 15wy?
o 4x®y?
O 4xy?
Answer:
100xy
Step-by-step explanation:
The height of the cylinder is 4x³y² unit.
The correct option is A.
What is a cylinder?A cylinder is a 3D solid form made up of two bases that are parallel and identical and are connected by a curving surface. These bases resemble spherical disks. The axis of the cylinder form is a line drawn through the center or connecting the centers of two circular bases.
Given:
A cylinder has a volume of 20x⁶y⁴ units cubed.
The base of the cylinder has an area of 5x³y² units squared.
And the volume of the cylinder V = Base area x height.
So, 20x⁶y⁴ = 5x³y² (height).
The height of the cylinder = 20x⁶y⁴/ 5x³y²
The height of the cylinder = 4x³y²
Therefore, 4x³y² is the height of the cylinder.
To learn more about the cylinder;
https://brainly.com/question/16134180
#SPJ5
The complete question is given in the attached image.
i need help with this question please
Answer: it C
Step-by-step explanation: if it not incorrect sorry for the wrong answer
A ladder 20 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. Find the rate at which the angle between the ladder and the wall of the house is changing when the base of the ladder is 16 feet from the wall.
Answer:
0.17 °/s
Step-by-step explanation:
Since the ladder is leaning against the wall and has a length, L and is at a distance, D from the wall. If θ is the angle between the ladder and the wall, then sinθ = D/L.
We differentiate the above expression with respect to time to have
dsinθ/dt = d(D/L)/dt
cosθdθ/dt = (1/L)dD/dt
dθ/dt = (1/Lcosθ)dD/dt where dD/dt = rate at which the ladder is being pulled away from the wall = 2 ft/s and dθ/dt = rate at which angle between wall and ladder is increasing.
We now find dθ/dt when D = 16 ft, dD/dt = + 2 ft/s, and L = 20 ft
We know from trigonometric ratios, sin²θ + cos²θ = 1. So, cosθ = √(1 - sin²θ) = √[1 - (D/L)²]
dθ/dt = (1/Lcosθ)dD/dt
dθ/dt = (1/L√[1 - (D/L)²])dD/dt
dθ/dt = (1/√[L² - D²])dD/dt
Substituting the values of the variables, we have
dθ/dt = (1/√[20² - 16²]) 2 ft/s
dθ/dt = (1/√[400 - 256]) 2 ft/s
dθ/dt = (1/√144) 2 ft/s
dθ/dt = (1/12) 2 ft/s
dθ/dt = 1/6 °/s
dθ/dt = 0.17 °/s
Find the distance from San Antonio to El Paso.
633 mi
344 mi
558 mi
261 mi
Answer:
558
Step-by-step explanation: I just took the quiz!
Distance from San Antonio to El Paso in Miles is 558 miles
Find:Distance from San Antonio to El Paso in Miles
Computation:
We know that
Distance from San Antonio to El Paso is 888 km
So,
1 km = 0.621371 miles
Distance from San Antonio to El Paso = 888 × 0.621371
Distance from San Antonio to El Paso in Miles = 558 miles
Learn more:https://brainly.com/question/19679508?referrer=searchResults
60 POINTS PLEASE SEND ME A COMPLETED COPY OF THIS "linear functions worksheet: child's growth and prosperity
Answer:
give it to me now and then I'll do it
Answer:
Step-by-step explanation:
How many solutions does the equation 4x + 8 = -2 - 2 + 5x have? (5 points)
Two
One
None
Infinitely many
Answer:
i believe it only has one solution, which would be x=12.
Step-by-step explanation:
Answer:
write Then finding matrix the system as a matrix equation, solve a matrix equation by the inverse of the coefficient , S 4X-5v=lle 25x-ley=19 X-ley= 19
Step-by-step explanation:
its in answer
1. The National Football League (NFL) has been finding new ways to reduce the risk of its players
getting concussions. For example, helmets have changed to keep players more safe. In the 2017-
2018 season, 190 athletes reported concussions out of 1700 total players. In the 2018-2018
season, 135 concussions were reported out of total 1650 players.
a. Make a two way table displaying this information.
TOTAL
b. Calculate the risk of a football player reporting a concussion in 2017-2018 and 2018-2019.
C. Find the absolute risk reduction.
Answer:
Reduced/depressed
courageously/daringly
Boost/inflate
Explanation:
The following statement displays the recommendation of National Football League's(NFL) rule to wear new and lighter helmets by the players to diminish the chances of head injury during collisions between players. However, it has led the players to play more brazenly and fearlessly that eventually may cause the expansion of the number of collisions suffered by NFL players due to the valiant behavior of the players. This equates the ratio and leading to no improvement in the reduction of injuries among them even after this rule.
the area of the square is 36 cm. 2 what is the formula that shows the length or side b
Answer:
36=b^2 or b=the square root of 36
Step-by-step explanation:
The sides of a square are all equal in length. To find the area of a square you can multiply the two sides together. Considering that they are the same length, you can just square one of the side lengths to get your answer. To find a side length you can take the square root of the area.
Answer:
Step-by-step explanation:
b · b = 36
Find the degree measure of the angle with the given radian measure. (Round your answer to one decimal place.)
Answer:
108 degrees
Step-by-step explanation:
Since we are not given the radian measure. Let the radian measure be 3π/5 rad;
Using the conversion;
πrad = 180°
3π/5 rad = x
Cross mulriply;
π * x = 180 * 3π/5
x = 180 * 3/5
x = 36 * 3
x = 108 degrees
Hence the degree measure is 108 degrees
Note that the same conversion can be used to convert other values in radians
Please give me the correct answer
Answer:
i dont think so.
Step-by-step explanation:
A 5-kilogram bag of cat food costs $18.90. What is the unit price?
$
per kilogram
Answer:
3.78
Step-by-step explanation:
Acellus help slope intercept
Greetings.
The answer is y = 2x + 7.
Explanation:
If you are an expert in graph then you are able to find the slope without calculating. (Rise over Run by looking at the graph.)
We can also find the slope by calculating m-value.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] ---> Rise Over Run
But how are we gonna calculate if we don't have any two given ordered pairs?
The answer is, we can just pick two ordered pairs that are part of the graph, or rather say that the graph passes through.
The graph passes through (-3,1) and (-2,3).
Then we can calculate the slope by using rise/run.
[tex]m=\frac{3-1}{-2-(-3)}\\m=\frac{2}{-2+3}\\m=\frac{2}{1}\\m=2[/tex]
Thus, the slope is m = 2.
However, we are not done yet. We just only found out the slope. We need to find the y-intercept too.
From Linear Function - [tex]y=mx+b[/tex]
Where m = slope and b = y-intercept.
Since b = y-intercept, we don't need to calculate/substitute x = 0. We simply find which number the graph has y-intercept at.
Which is (0,7), the y-intercept.
Then we substitute b = 7 as y-intercept.
Thus the answer is [tex]y=2x+7[/tex]
given: 2c=d-2b, c=a-b, d=a+b prove: a=b
Answer:
D
Step-by-step explanation:
Your friend says that there are 36 feet in 12 yards. Is your friend correct? Explain your reasoning?
Answer:
Your friend is correct.
Step-by-step explanation:
3 feet - 1 yard
36 / 12 = 3
Find the value of the power 6 to the -4th
Answer:
6 to the -4th is 7.716 x 10^-4
Step-by-step explanation:
A T-shirt company charges a design fee of $25 and then sells the shirts for $10 each. The total cost y can be represented by the equation y = 10x + 25, where x represents the number of T-shirts. The graph of the equation is shown. Describe what the slope and y-intercept represent.
Answer:
y-intersept is the design fee
What is an equation if the line that passes thriugh the point (-4,-6) and is parallel to the line 3x - y = 6
Answer:
the desired equation is 3x - y = -6
Step-by-step explanation:
Recall that parallel lines have the same slope. Thus, the desired line has an equation of the form 3x - y = C, where C is determined by the coordinates of the point (-4, -6).
3x - y = C becomes 3(-4) - (-6) = C after substitution of -4 and -6 for x and y respectively. Then -12 + 6 = C, and C = -6.
Thus, the desired equation is 3x - y = -6
PLZZZ HELP GIVING BRAINLIST Match each expression to its value.
1. 7 - 5
-2
2. -7 + 5
2
3. -7 - 5
12
4. 7 - (-5)
-12
Answer:
1. 0
2. 5
3. 0.416666667
4.0
Find 4cos2a, if
[tex] \cos(a) = \frac{ \sqrt{3} }{2} [/tex]
If you mean to find 4 cos(2a), then recall the double angle identity for cosine:
cos(2x) = 2 cos²(x) - 1
so that
4 cos(2a) = 4 (2 cos²(x) - 1) = 4 (√3 - 1)
What is the recursive formula for this sequence? 12, 16, 20, 24, 28, ...
Answer:
A
Step-by-step explanation:
first term is 12, and following terms are obtained adding 4 to previous term.
Factor the expression using the GCF.
4x + 8
Answer:
The common factors for 4,8 are −4,−2,−1,1,2,4 - 4 , - 2 , - 1 , 1 , 2 , 4 .
Step-by-step explanation:
There ya go, mate.
The greatest common factor of the expression 4x + 8 will be 4.
What is the highest common factor?The Highest Common Factor (HCF) of two numbers is the highest possible number that is divisible by both numbers.
In other words, the highest common factor is the common factor between the two numbers but it should be the highest among all common factors.
As per the given expression,
4x + 8
The highest number that can be take common in the above expression is 4 as,
4(2x + 2)
Thus, 4 will be the GCF.
Hence "The greatest common factor of the expression 4x + 8 will be 4".
To learn more about the highest common factor,
https://brainly.com/question/128394
#SPJ2
6. Lars walks his dog 4 times farther than Michelle
walks her dog. Michelle walks her dog 0.23 mile.
How far does Lars walk his dog?
Answer:
0.92
Step-by-step explanation:
What is |-8|?
-16
-8
08
16
Answer:
it's 8
Step-by-step explanation:
lol girl I did this in the first day of school in 6th and I got the same answer , -8 is a negative, your supposed to put it back to a non negative when something is negative change it back to positive it's 8!
Arrange the integers 1,4,8,12,17,32 so that all consecutive integers add to a perfect square. Enter your answer with numbers separated by commas.
One possible answer is: 1, 8, 17, 32, 4, 12
I don't know if there's a methodical way to get this answer. I used trial and error. I started with 1 and looked through the list to see what adds to 1 to get a perfect square. That would be 8 since 1+8 = 9 = 3^2
The process is repeated but this time for 8. After a bit of guess and checking, we see that 8+17 = 25 = 5^2.
Then after 17 is 32 because 17+32 = 49 = 7^2.
Keep doing this until all of the values are used up. If you get stuck, then try backtracking to a previous branch/path where everything worked and try another fork in the road. If that doesn't work, then try starting the sequence with a completely different value (instead of 1).
Other answers may be possible. I haven't checked all possible permutations.
please answer to the above question
Answer:
b
Step-by-step explanation:
I did this assignment and got the highest grade
What equation does this map show?
Answer:
Oh, it's y=3x-4.
Because it's slope is 3 and it crosses through -4 on the y axis, we know that that would be the equation.
Good luck with the assignment man, let me know of anymore questions. :)