ou want to conduct a survey with a Margin of Error of 4% or less at the 95% confidence level. But you don't know what the proportional values will be. What should you assume the proportional value, p*, to be? a) p*= 25%. b) p* = 50%. c) p*= 75%. d) p* = 100%.
Answers
The correct answer to this question is Option B - p* = 50%. Using 50% as the proportional value, you can then calculate the minimum sample size needed for your survey to be at a 95% confidence level and with a margin of error of 4% or less.
To determine the appropriate assumed proportional value (p*) for calculating the sample size needed to achieve a specific margin of error, we generally use the conservative estimate of p* = 50%.
Assuming p* = 50% for calculating the sample size is a conservative approach as it ensures a larger sample size, which leads to a more accurate estimation. By assuming p* = 50%, we account for the maximum possible variability in the population proportion, resulting in a more robust survey design. This approach is widely adopted in situations where the actual proportion is unknown, providing a margin of error that is more likely to capture the true population proportion.
Therefore, in this case, you should assume p* = 50%.
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Related Questions
HELP! NEED ANSWER ASAP
Answers
The Area of the figure below is composed of a rectangle and semicircles that will be 56.1 unit sq.
The semicircles can be composed into a circle with a radius 3,
The area of a circle is πr² where r is the radius.
πr²= 3 x 3 /2 π
A ≈ = 99/7
A = 14.1
The area of the rectangle = Length x width
= 7 x 6
= 42
Total area of a figure = 14.1 + 42 = 56.1
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y=x-5
y = x2 – 5x + 3
Answers
Answer:
Step-by-step explanation:
\(x^{2} -5x+3=x-5\\x^{2} -5x-x+3+5=0\\x^{2} -6x+8=0\\(x-4)(x-2)=0\\x-4=0\\or\\x-2=0\\\)
x=4 or x=2
when x=4
y=(4)-5
y=-1
and when x=2
y=(2)-5
y=-3
meaning we have pairs
(4,-1) and (2,-3)
HELP ME ASAP!!! PLS!!
The Chu family can hike 3 miles per hour. How long will it take them to hike 15 miles?
A- 3.75 hours
B- 4 hours
C- 4.5 hours
D- 5 hours
Answers
Answer:
D- 5hrs
Step-by-step explanation:
If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.
Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours
Answer:
D. 5 hours
Step-by-step explanation:
3 miles per 1 hour so 3/1
15 miles per x hours so 15/x
3/1 = 15/x or 3 = 15/x
get x by itself so
3 divided by 3 and 15 divided by 3
x = 5 hours
i need help i will give brainliest
Answers
Step-by-step explanation:
triangles angles added up=180
180=58+3x+7x+2
=60+10x
120=10x
12=x
angle A=3x
=36
angle c=7x+2
=86
Re-write the following system of equations in matrix format and solve them by using Cramer's rule. z+5x= 24 3x+2z+3y=7 -x+2y=-9
Answers
The solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
The given system of equations is given as,z + 5x = 243x + 2z + 3y = 7-x + 2y = -9
To solve the given system of equations by using the Cramer's rule, we have to first represent the given system in matrix format.
Matrix format: ⎡1 0 5⎤ ⎡x⎤ ⎡24⎤ ⎢0 3 2⎥ ⎢y⎥=⎢7⎥ ⎣-1 2 0⎦ ⎣z⎦ ⎣-9⎦
Using the formula for Cramer's rule, we know that,
x = Dx / D, y = Dy / D, z = Dz / D, whereD is the determinant of the coefficient matrix, Dx is the determinant of the matrix obtained by replacing the x column with the constant matrix, Dy is the determinant of the matrix obtained by replacing the y column with the constant matrix, and Dz is the determinant of the matrix obtained by replacing the z column with the constant matrix.
Calculation of D: D = | A | = ⎡1 0 5⎤ ⎡0 3 2⎥ ⎣-1 2 0⎦
Applying the Laplace expansion along the first column, D = 1 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦| D = 6 Calculation of Dx: Dx = ⎡24 0 5⎤ ⎡3 2⎤ ⎢7 3 2⎥ ⎢-1 2⎥ ⎣-9 2 0⎦ ⎣2 0⎦
Applying the Laplace expansion along the first column, Dx = 24 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-9 2⎤| |⎣3 2⎦| |⎣3 2⎦| |⎣3 2⎦|
Dx = -18
Calculation of Dy: Dy = ⎡1 24 5⎤ ⎡0 2 2⎤ ⎢0 7 2⎥ ⎢-1 -1 0⎥ ⎣-1 -9 0⎦ ⎣2 0 0⎦
Applying the Laplace expansion along the second column, Dy = 0 |⎡1 5⎤| - 24 |⎡0 2⎤| + 5 |⎡0 2⎤| |⎣-1 0⎦| |⎣-1 0⎦| |⎣-1 0⎦|
Dy = 10
Calculation of Dz: Dz = ⎡1 0 24⎤ ⎡0 3 2⎥ ⎢0 3 7⎥ ⎢-1 2 -1⎥ ⎣-1 2 -9⎦ ⎣3 2 0⎦
Applying the Laplace expansion along the third column,
Dz = 24 |⎡3 2⎤| - 10 |⎡-1 2⎤| + 0 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦|
Dz = -24
Now we have the values of D, Dx, Dy and Dz.
Therefore, x = Dx / D, y = Dy / D, z = Dz / D,x = -18/6 = -3 y = 10/6 = 5/3 z = -24/6 = -4
Hence, the value of x, y, and z is (-3, 5/3, -4) respectively.
Therefore, the solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
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Find a power series representation for the function and determine the radius of convergence, R . f ( x ) = ln ( 5 − x ) We must first recognize that f ( x ) = ln ( 5 − x ) is an anti-derivative of a more familiar function. To find this function, we find d d x [ ln ( 5 − x ) ] = . Since d d x [ ln ( 5 − x ) ] , ∫ − 1 5 − x d x = + C . Now, our goal is to find a power series for − 1 5 − x and then integrate it. Factor -1 from the numerator and 5 from the denominator. This will give us − 1 5 − x = − 1 5 ( ) . Therefore, we get − 1 5 − x = − 1 5 [infinity] ∑ n = 0 ( ) n . Now, we can say that ln ( 5 − x ) = − 1 5 ∫ 1 1 − x 5 d x = − 1 5 ∫ [ [infinity] ∑ n = 0 ( x 5 ) n ] d x . After the integrating the power series, we have C − 1 5 [infinity] ∑ n = 0 . We have ln ( 5 − x ) = C − 1 5 [infinity] ∑ n = 0 x n + 1 5 n ( n + 1 ) = C − [infinity] ∑ n = 1 x n n 5 n . In order to find C , we let x = 0 and get f ( 0 ) = ln ( ) = C − , and so C = Now, f ( x ) = ln ( 5 − x ) = ln 5 − [infinity] ∑ n = 1 . This series will converge for ∣ ∣ < 1 , and so the radius of convergence is R =
Answers
a. We must first recognize that f ( x ) = ln ( 5 − x ) is an anti-derivative of a more familiar function. To find this function, we find d d x [ ln ( 5 − x ) ] =d/dx[ln(5 - x)] = -1/(5 - x)
b. Since d d x [ ln ( 5 − x ) ] , ∫ − 1 /5 − x d x = -1/5 ∑ (1/n+1) * (x/5)^(n+1) + C
c. Factor -1 from the numerator and 5 from the denominator. This will give us − 1/5 − x = − 1/5 (x - 5) .
d. Therefore, we get − 1 5 − x = − 1 5 [infinity] ∑ n = 0 (x - 5)/5 n .
e. After the integrating the power series, we have C − 1/5 [infinity] ∑ n = 0 [x^(n+1)/(5^n * (n+1))]
f. In order to find C , we let x = 0 and get f ( 0 ) = ln (5 - x) = C − 1/5 ∑ [x^(n+1)/(5^n * (n+1))] , and so C = ln(5 - x) = ln(5) - 1/5 ∑ [x^(n+1)/(5^n * (n+1))]
g. Now, f ( x ) = ln ( 5 − x ) = ln 5 − [infinity] ∑ n = 1 [x^(n+1)/(5^n * (n+1))]
h. The series converges for |x - 5| < 5, and the radius of convergence is R = 5.
To find a power series representation for f(x) = ln(5 - x), we start by recognizing that f(x) = ln(5 - x) is an anti-derivative of the function 1/(5 - x). We can find this function by taking the derivative of ln(5 - x):
d/dx[ln(5 - x)] = -1/(5 - x)
Now, we aim to find a power series for -1/(5 - x) and then integrate it. To do this, we can factor out -1/5 from the numerator and write -1/(5 - x) as:
-1/(5 - x) = -1/5 ∞ ∑ n = 0 ((x - 5)/5)^n
Now, we can write ln(5 - x) as an integral of the power series:
ln(5 - x) = -1/5 ∫ [ ∞ ∑ n = 0 ((x - 5)/5)^n ] dx
Integrating the power series term by term, we get:
ln(5 - x) = C - 1/5 ∑ [x^(n+1)/(5^n * (n+1))]
To determine the constant C, we can evaluate ln(5 - 0):
ln(5) = C - 1/5 ∑ [0^(n+1)/(5^n * (n+1))]
Simplifying, we have:
ln(5) = C
Therefore, C = ln(5). Substituting this back into the power series representation, we have:
ln(5 - x) = ln(5) - 1/5 ∑ [x^(n+1)/(5^n * (n+1))]
This power series representation converges for |x - 5|/5 < 1, which simplifies to |x - 5| < 5. Therefore, the radius of convergence, R, is 5.
In summary, the power series representation for f(x) = ln(5 - x) is:
ln(5 - x) = ln(5) - 1/5 ∑ [x^(n+1)/(5^n * (n+1))]
The series converges for |x - 5| < 5, and the radius of convergence is R = 5.
Your question is incomplete but most probably your full question attached below
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represent the rational number in number line 7 /8
Answers
Answer:
7/8 in number line.
I have been stuck on this question please help
Answers
Answer:
3⁷Step-by-step explanation:
(3⁴)⁻² * (3⁵)³ =3⁴⁽⁻²⁾*3⁵⁽³⁾ =3⁻⁸*3¹⁵ =3⁻⁸⁺¹⁵ =3⁷Correct option is B. 3⁷
what is interval notation example ?
Answers
Interval notation is a way of representing a range of values on a number line. It is written using brackets and parentheses to indicate whether the endpoints are included or excluded from the interval.
For example, the interval notation for the range of values between 1 and 5 (inclusive) would be [1, 5]. The square brackets indicate that both 1 and 5 are included in the range.
If the endpoints are excluded, we use parentheses. For instance, the interval notation for the range of values between 1 and 5 (excluding 1 and 5) would be (1, 5).
In general, we use square brackets for closed intervals (where the endpoints are included) and parentheses for open intervals (where the endpoints are excluded).
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The average square footage in an apartment in a town is 1,800 square feet with a standard deviation of 120 square feet. the square footage is normally distributed. you randomly select 10 apartments in the town. what is the probability that the mean will be more than 1900 square feet?
Answers
If the average square footage in an apartment in a town is 1,800 square feet with a standard deviation of 120 square feet, the square footage is normally distributed and if you randomly select 10 apartments in the town, then the probability that the mean will be more that 1900 square feet is 0.46%
To find the probability, follow these steps:
We can use the Central Limit Theorem, which states that for large enough sample sizes, the distribution of sample means will be approximately normal, regardless of the shape of the population distribution. We can calculate the standard deviation of the sample mean using the formula:Standard deviation of the sample mean = population standard deviation / square root of sample size
In this case, the standard deviation of the sample mean = 120 / √10 ≈ 37.95Next, we need to find the z-score, which measures how many standard deviations the sample mean is from the population mean. The formula for the z-score is:
z = (sample mean - population mean) / standard deviation of the sample mean
In this case, the sample mean is 1900 square feet, the population mean is 1800 square feet, and the standard deviation of the sample mean is 37.95.
z = (1900 - 1800) / 37.95 ≈ 2.64To find the probability that the mean will be more than 1900 square feet, we need to find the area to the right of the z-score of 2.64 in the standard normal distribution table (also known as the z-table).
Using the z-table, we find that the area to the right of 2.64 is approximately 0.0046.
Therefore, the probability that the mean will be more than 1900 square feet is approximately 0.0046, or 0.46%.
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Help!!!!!!!!!!!!!!!!!!!!!!!!! and I'm giving brainly thxxxxx
Answers
Answer:
the 3 is in the hundred thousands
Step-by-step explanation:
calculate the surface area and then the volume
Answers
Answer:
46
Step-by-step explanation:
length x width x height
7 x 5 x 3
Answer: surface area = 142
Volume = 105
* make sure to add labels (units^2, etc.)
Step-by-step explanation:
Area = length x height
Volume = length x width x height
Write the augmented matrix for the following system of equations.
-2z=-4y-9x
0=4x+6z+2
2z=2+3y
Answers
The augmented matrix for the system of equations is given as follows:
\(\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right]\)
What is a system of equations?A system of equations is when multiple variables are related, and equations are constructed to find the values of each variable. There are multiple ways to solve a system, and one of the most usual is in a matricial way, as the augmented matrix of the system is constructed.
In standard notation, the system is given by:
9x + 4y - 2z = 0.4x + 0y + 6z = -2.0x - 3y + 2z = 2.The augmented matrix for a system with variables x, y and z is constructed as follows:
The first column contains the coefficients of x.The second column contains the coefficients of y.The third column contains the coefficients of z.The fourth column contains the results of the operations.Hence for this system, the matrix is given by:
\(\left[\begin{array}{cccc}9&4&-2&0\\4&0&6&-2\\0&-3&2&2\end{array}\right]\)
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In the diagram, TC represents a vertical building. The points, A and B, are on the same level as the foot C of the building such that ATC = 40° and BTC = 56°. If BT is 29 m longer than AT, find
(a) the height of the building,
(b) the distance AB.
Answers
Answer:
(a) The height of the building is 60.06 m
(b) The distance AB is 139.43 m
Step-by-step explanation:
The given parameters are
Given that segment BT = segment AT + 29
By trigonometric ratios, we have;
cos∠ATC = CT/AT
cos∠BTC = CT/BT
Therefore, we have;
cos(40°) = CT/AT.................................(1)
cos(56°) = CT/BT = CT/(AT + 29).....(2)
cos(56°) = CT/(AT + 29)......................(3)
From equation (1)
CT = AT×cos(40°)
From equation (3)
AT×cos(56°) + 29 × cos(56°) = CT
Therefore;
AT×cos(40°) = AT×cos(56°) + 29 × cos(56°)
AT×cos(40°) - AT×cos(56°) = 29 × cos(56°)
AT×(cos(40°) - cos(56°)) = 29 × cos(56°)
AT = 29 × cos(56°)/(cos(40°) - cos(56°)) = 78.4 m
TC = CT = AT×cos(40°) = 78.4×cos(40°) = 60.06 m
The height of the building = 60.06 m
(b) BT = AT + 29 = 78.4 m + 29 m= 107.4 m
AB = AT×sin(∠ATC ) + BT×sin(∠BTC) = 78.4×sin(40°) + 107.4×sin(56°) = 139.43 m
The distance AB = 139.43 m.
CAN SOMEONE PLEASE HELP ME!!!!!
Answers
9514 1404 393
Answer:
$7.00 per week
Step-by-step explanation:
The balance at the end of week 1 is $39-32 = $7.00 higher than at the start. The rate of change is $7.00 per week.
Answer:
$ 7.00 per weekStep-by-step explanation:
#CarryOnLearningSolve for x.6(x - 2) = 41.x=12.x=1 1/33.x= 2 2/3
Answers
The given equation is:
\(6(x-2)=4\)It is required to solve for x.
Distribute 6 into the expression in parentheses:
\(6x-12=4\)Add 12 to both sides of the equation:
\(\begin{gathered} 6x-12+12=4+12 \\ \Rightarrow6x=16 \end{gathered}\)Divide both sides of the equation by 6:
\(\begin{gathered} \frac{6x}{6}=\frac{16}{6} \\ \Rightarrow x=\frac{8}{3}=2\frac{2}{3} \end{gathered}\)Hence, the correct answer is 3) x=2 2/3.
The correct option is 3.
You deposit $6000 in an account that earns 3% annual interest. Find the balance after 6 years if this interest is
compounded with the given frequency.
Answers
A lake was closed because of an accidental pesticide spill. The concentration of the pesticide after the spill was 848 parts per million. Each day the water is tested, and the amount of pesticide is found to be about 75% of what was there the day before. Do you think the lake will ever be completely free of the pesticide? Explain.
Answers
Answer:
Step-by-step explanation:
\(a_{n}=a_{1}r^{n-1}\\0=848(0.75)^{n-1}\\or~(0.75)^{n-1}=0\\0.75<1\\so~(0.75)^{n-1} \rightarrow 0,if~n-1 \rightarrow ~\infty\)
\(or~n \rightarrow 1+\infty\\or~n \rightarrow \infty\)
Hence lake will never be free of pesticide.
what percentage of persons who lose weight are able to maintain it for more than a year?
Answers
Answer: 20%
Step-by-step explanation:
What is the 20th term of the expansion (c-d)^35
Answers
Answer:
Step-by-step explanation: T20 = (-1)^20 3520(c)^15(d)^20
= 35c20c^15 d^20
Enter the division problem 15 ÷11 as a fraction.
Answers
Answer: 15/11
Step-by-step explanation:
Answer:
15 ÷ 11 as a fraction is 15/11. As a mixed number it is 1 4/11.
Step-by-step explanation:
Say thanks! I just did this because I have 1,633 points (Now 1,533 I think) SOOO first comes first served
Answers
thanks for them regardless :)
What happens to the graph of f(x) when it is multiplied
by a number between - 1 and 0?
Answers
Can someone help me pls
Answers
Answer:
$8.30 per keychain
Step-by-step explanation:
15.5 is the price of one hat so we multiply by 3
15.5x3=46.5
Now we subtract this from 96.30
96.3-46.5=49.8
Now divide by 6 to get each key chain price
49.8/6= 8.3
$8.30 for each keychain
Claire’s answer is u reasonable because of the work I did above
Hopes this helps please mark brainliest
Assuming that all years have 365 days and all birthdays occur with equal probability, how large must n be so that in any randomly chosen group of n people, the probability that two or more have the same birthday is at least 1/2?
Answers
it is seen that if the number of people in the group is n = 23, the probability that at least two people will have the same birthday is at least 1/2.
Let P(A) be the probability that in a randomly selected group of n people, at least two people have the same birthday.
If we assume that the year has 365 days, then the number of ways to select n people with different birthdays is n x (n-1) x (n-2) x ... x (n-364).
the probability of selecting n people with different birthdays is P(A') = n(n - 1)(n - 2)...(n - 364)/365nThen, the probability that at least two people in a group of n have the same birthday is given by P(A) = 1 - P(A').
We need to find the smallest value of n such that P(A) ≥ 1/2.Let's solve for this.Let us find n such that P(A) ≥ 1/2.
By using the complement rule, 1-P(A') = P(A).Then:1 - n(n - 1)(n - 2)...(n - 364)/365n ≥ 1/2n(n - 1)(n - 2)...(n - 364)/365n ≤ 1/2(2)n(n - 1)(n - 2)...(n - 364) ≤ 365n/2Now, take the natural logarithm of both sides and simplify as follows:ln[n(n - 1)(n - 2)...(n - 364)] ≤ ln[365n/2]nln(n) - ln[(n - 1)!] - ln[(n - 2)!] - ... - ln[2!] - ln[1!] ≤ ln[365n/2]
Therefore, we need at least 23 people in the group for the probability of two or more people having the same birthday to be at least 1/2.
This is because n = 23 is the smallest number for which the inequality holds, and therefore, it is the smallest number of people required to ensure that the probability of two or more people having the same birthday is at least 1/2.
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What is the value of a?
Answers
Answer:
66
Step-by-step explanation:
The sum of all of the angles in a triangle is 180. So all three angles would add up to 180:
(a + 21) + 57 + (a - 30) = 180
Combine like terms:
2a + 48 = 180
2a = 132
a = 66
Answer:
a+21+57+a-30=180(angle of triangle)
2a+48=180
2a=180-48
2a=132
a=132/2
a=66
then,a+21=66+21 =87
a-30=66-30 =36
Step-by-step explanation:
I think this is the answer
Calculate the value of a in the triangle below
Answers
Answer:
127
Step-by-step explanation:
15 multiplied by 17 equals 255 now we divide 255 by 2 and the result would be 127
At party each guest receives five party favors. Write an expression that describes the total number of party favors bought if three favors are left. Let ' g' represent the number of guests.
Answers
Answer:
T = 5g + 3
Step-by-step explanation:
The information provided is summarized as follows:
At party each guest receives five party favorsThe variable "g" represent the number of guests.Only three favors are left at the end.Let T represent the total number of favors bought.
The expression representing the total number of favors given to the guests is:
5g.
Then the expression representing the total number of favors bought is:
T = 5g + 3
Plss Help Due Tomorrow Give Brainliset
Answers
Answer:
1=137 2=43 3=137 4=43 5=137 6=43
Step-by-step explanation:
Given the piecewise function shown below, select all of the following statements that are true
Answers
Answer:
A and C
Step-by-step explanation:
A
when x = 2 , that is x > 1 then f(x) = x² , that is
f(2) = 2² = 4 ← True
B
when x = 5, that is x > 1 then f(x) = x² , that is
f(5) = 5² = 25 ≠ 1 ← not true
C
when x = 1 then f(x) = 5 , that is
f(1) = 5 ← True
D
when x = - 2 , that is x < 1 , then f(x) = 2x , that is
f(- 2) = 2(- 2) = - 4 ≠ 4 ← not true