A church group is interested in estimating the true proportion of Americans who attend weekly religious services. How large a sample size is required to estimate the true proportion to within 3% with 95% confidence
Answers
Answer:
\(n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}\) (b)
We can use an estimatior for the population proportion as \(\hat p=0.5\) since we don't know previous info. And replacing into equation (b) the values from part a we got:
\(n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11\)
And rounded up we have that n=1068
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since the confidence level is 99%, our significance level would be given by \(\alpha=1-0.95=0.05\) and \(\alpha/2 =0.005\). And the critical value would be given by:
\(z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96\)
The margin of error for the proportion interval is given by this formula:
\( ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}\) (a)
And on this case we have that \(ME =\pm 0.03\) and we are interested in order to find the value of n, if we solve n from equation (a) we got:
\(n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}\) (b)
We can use an estimatior for the population proportion as \(\hat p=0.5\) since we don't know previous info. And replacing into equation (b) the values from part a we got:
\(n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11\)
And rounded up we have that n=1068
Related Questions
-15ade - 13a factor this pls
Answers
Answer:
a(15de-13)
Step-by-step explanation:
just find the variable(s) that both terms have and take it out and put it off to the side like so
Which of the following ARE polynomials. Check all that apply
Answers
Answer: A and B
Step-by-step explanation:
you can’t have division by a variable in a polynomial, so c and e are out.
you also cannot have a variable with a fractional exponent(or variables under a radicals), so d is out.
S1. Three numbers are in the ratio of 2:3:4. The sum of their cubes is 3,34,125. Find the numbers.
Answers
Answer:
Step-by-step explanation:
sum of their cubes=0.334125
The ratio of three numbers is 2:3:4.
Let the numbers be 2x, 3x and 4x.
Cubes of numbers = (2x)^3, (3x)^3, (4x)^3 = 8x^3, 27x^3, 64x^3
(8x^3) + (27x^3) + (64x^3) = 99x^3
99x^3 = 0.334125
x^3 = (0.334125) / 99
x^3 = 0.003375
x^3 = (0.15)^3
x = 0.15
Therefore, the numbers are (2 x 0.15), (3 x 0.15) and (4 x 0.15) i.e. 0.3, 0.45 and 0.6
J is between H and K. If HJ=6x-5, JK=4x-6, and KH=129, find the value of x.
Answers
Answer:
10Step-by-step explanation:
If J is between H and K then HJ + JK = HK
Given
HJ=6x-5
JK=4x-6
KH=129
Required
The value of x
Substituting the given parametrs into the formula;
6x-5+4x-6 = 129
6x+4x-5-6 = 29
10x-11 = 129
add 11 to both sides
10x-11+11 = 129+11
10x = 140
divide both sides by 10
10x/10 = 140/10
x = 10
Hence the value of x is 10
74 points plsss help meee!!!!!
Answers
Answer:
(b) x- intercept is -1/3; y-intercept is -3/2Step-by-step explanation:
Given function:
-9x - 2y = 3x- intercept is:
y = 0 ⇒ -9x = 3 ⇒ x = -1/3y-intercept is:
x = 0 ⇒ -2y = 3 ⇒ y = -3/2Correct answer choice is (b)
Answer:
B) X intercept = (-1/3,0) and Y Intercept = (0,-3/2)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x .
To find the y-intercept, substitute in 0 for x and solve for y .
Which mixed numbers have 12 as the LCD (lowest common denominator)?
2 11/12
3 1/7
5 3/4
6 4/5
8 38
MARK
Answers
The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.
What are mixed numbers?Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).
The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.
2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.
The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.
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Question :
Which mixed numbers have 12 as the LCD (lowest common denominator)?
2 11/12
3 1/7
5 3/4
6 4/5
8 38/47
Given the following systems of equations match the first step needed to solve them by substitution. System A x - y = 12 2x - y =12 [ Select] [ Select] Solve the first equation for x, by adding y to both sides Solve the first equation for y. by adding x to both sides Solve the second equation for x by dividing it by 2 2x - y - 3 [ Select] To play audio version of question click the play button or click here
Answers
We are given the following system of equations:
\(\begin{gathered} x-y=12,\text{ (1)} \\ 2x-y=12,\text{ (2)} \end{gathered}\)The first step to solve the system is to solve for "x" in the first equation, to do that we need to add y to both sides, like this:
\(\begin{gathered} x-y+y=12+y \\ x=12+y \end{gathered}\)Find the difference between the actual quotient and the estimated quotient of 54,114÷29 . (Dividend is rounded off to nearest thousand and divisor to nearest ten)
Answers
The difference between the actual quotient and the estimated quotient of 54,114 ÷ 29 is approximately 66.3448275862068965517241379.
To find the difference between the actual quotient and the estimated quotient of 54,114 ÷ 29, we need to first calculate the actual quotient and then the estimated quotient.
Actual quotient:
Dividing 54,114 by 29, we get:
54,114 ÷ 29 = 1,866.3448275862068965517241379 (approximated to 28 decimal places)
Estimated quotient:
Rounding the dividend, 54,114, to the nearest thousand gives us 54,000. Rounding the divisor, 29, to the nearest ten gives us 30. Now, we can perform the division with the rounded values:
54,000 ÷ 30 = 1,800
Difference between actual and estimated quotient:
Actual quotient - Estimated quotient = 1,866.3448275862068965517241379 - 1,800 = 66.3448275862068965517241379
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Find the value of L that Will Maximize the profit Q=L²e^0.01L
Answers
The minimum profit occurs at L = 0, where Q = 0.
To find the value of L that maximizes the profit Q = L²\(e^{(0.01L)\).
We need to differentiate Q with respect to L and find the critical points where the derivative equals zero.
Then we can determine whether each critical point is a maximum or a minimum by examining the second derivative.
Testing for critical points:Q = L²\(e^{(0.01L)\)
Q' = \(2Le^{(0.01L)\) + \(0.01 L^2e^{(0.01L)\)
= 0(2L + 0.01L²) \(e^{(0.01L)\)
= 0L (critical point) or 200 \(e^{(0.01L)\)
= 0 (extraneous, ignore)
2L + 0.01L² = 0L(2 + 0.01L) = 0L = 0 or L = -200 (extraneous, ignore)
The only critical point is at L = 0.
Testing for maximum or minimum:Q'' = \(2e^{(0.01L)\) + 0.02Le^(0.01L) + 0.0001L²\(e^{(0.01L)Q''(0)\)
= \(2e^{(0)\) = 2Since Q''(0) > 0,
The critical point at L = 0 is a minimum.
Therefore, there is no value of L that maximizes the profit.
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The values of L that will maximize the profit are 0 and -200
Finding the value of L that will maximize the profitFrom the question, we have the following parameters that can be used in our computation:
\(Q = L\²e^{0.01L\)
Differentiate the function
So, we have
\(Q' = \frac{L \cdot (L + 200) \cdot e^{0.01L}}{100}\)
Set the equation to 0
\(\frac{L \cdot (L + 200) \cdot e^{0.01L}}{100} = 0\)
Cross multiply
\(L \cdot (L + 200) \cdot e^{0.01L} =0\)
When expanded, we have
L = 0, L + 200 = 0 and \(e^{0.01L} =0\)
When solved for L, we have
L = 0 and L = -200
Hence, the values of L are 0 and -200
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Select the correct answer. In which direction must the graph of f(x) = x be shifted to produce the graph oSelect the correct answer.
In which direction must the graph of f(x) = x be shifted to produce the graph of g(x) = f(x) - 4?
A.
left and down
B.
right and up
C.
down
D.
upf g(x) = f(x) - 4? A. left and down B. right and up C. down D. up
Answers
Answer:
A. down
Step-by-step explanation:
The parent graph is
f(x)=x
If this graph is transformed to obtain
g(x)=f(x)−4
The subtracttion means the graph will shift downward vertically
The graph of g(x) is obtained by shifting f(x) down by 4 unit.
Therefore the direction is down.
Mark this as brainliest please.
You need $3,000 to buy a new stereo for your car. If you have $1,200 to invest at
6% compounded annually, how long will you have to wait to buy the stereo?
Answers
Answer:
15 years and 8 months
Step-by-step explanation:
I used the formula for compound interest as shown below and solved for the unknown, time.
Since our interest is compounded annually (So once a year) our m value is 1.
factorise 9x^2 + 3x^3
Answers
Answer:
\(9 {x}^{2} + 3 {x}^{3} \)
\(3 {x}^{2} (3 + x)\)
\(3 {x}^{2} (x + 3)\)
50 POINTSS Solve for q.
s = 4p + 4q
Answers
If the surface area of the cone below is 628.32 m², find its volume.
I WILL MARK BRAINLEIST IF CORRECT AND 20 POINTS
Answers
Answer:
1586.91 m³
Step-by-step explanation:
From the diagram attached,
Applying,
A = πrl.................. Equation 1
Where A = surface area of the cone, l = slight heigth of the cone, π = pie.
make l the subject of the equation,
l = A/πr.............. Equation 2
From the question,
Given: A = 628.32 m², π = 3.14, r = 8 m
Substitite these values into equation 2
l = 628.32/(3.14×8)
l = 25 m
But,
l² = h²+r².................... Equation 3
Where h = height of the cone.
h = √(l²-r²)
h = √(25²-8²)
h = √(625-64)
h = √(561)
h = 23.69 m
Also Applying,
V = 1/3πr²h
Where V = volume of the cone.
Therefore,
V = (3.14×8²×23.69)/3
V = 1586.91 m³
Belinda is making bracelets for an auction fundraiser. The number of beads varies directly with the number of inches of string used to make the
bracelets. Use the information in the table to write an equation.
Number of Inches of String.
X
+
I
x
+
2
4
6
8
old
ď vo vo
Number of Beads,
y
18
36
54
72
2
(0)
11
Answers
The equation representing the number of beads varies directly with the number of inches of the string is y = 9x.
What are ratio and proportion?In its most basic form, a ratio is a comparison between two comparable quantities.
There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.
If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.
Given, The number of beads varies directly with the number of inches of string.
Therefore, y ∝ x.
y = kx.
From the table,
18 = 2k.
k = 9.
So, y = 9x.
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f(x)=-x^2-10x find f(-7)
Answers
=Answer:
Step-by-step explanation:
f(-7) = -(-7)^2 - 10(-7) = -49 +70 = 21
write each info entire radical √48
Answers
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
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You can use a calculator
Answers
Answer:
238, 000
Step-by-step explanation:
hope this helps </3
using algebra, what is the first step in solving the following equation for the value of x;
8x + 12 = 52.
a) perform the inverse of multiplying by 8 (divide by 8) b) subtract 12 to form the identity (0) and cancel the 12. c) using the property of equality and do the same thing on both sides of the equal sign.
d) isolate the variable
Answers
Answer:
subtract 12 to form the identity (0) and cancel the 12.
Step-by-step explanation:
Subtract 12 from both sides.
8x=52−12
2 Simplify 52-1252−12 to 4040.
8x=40
3 Divide both sides by 88.
x=\frac{40}{8}
40/8
simplify 40 over 8 to 5
x=5
Answer:
×=5
Step-by-step explanation:
-12 both sides
then divide 8 both sides
40/8 =5
Identify the polynomial that is not the difference of two squares. a. 80/6 - 9y4b. 16x2 - 625 c. 476 - 9y6 d. 169x2 - 4y4
Answers
At first , we should know that:
The polynomial that is a difference between two squares can be factored to :
\((x-a)\cdot(x+a)=x^2-a^2\)So, both of x^2 and a^2 is a complete square
So, we will check the options :
A. 80/6 - 9y4
80/6 is not a complete square but 9y^4 is a complete square
9y^4 = 3y^2 * 3y^2
B. 16x^2 - 625
Both of 16x^2 and 625 is complete square
16x^2 = 4x * 4x
625 = 25 * 25
C. 476 - 9y^6
476 is not a complete square but 9y^6 is a complete square
D. 169x^2-4y^4
Both of them is a complete square
169x^2 = 13x * 13x
4y^4 = 2y^2 * 2y^2
so, the answer is the options A and C
It is reported that the wild tiger population has declined by 97%
over the last 20 years.
There are now 3200 tigers left in the wild.
To the nearest thousand, how many wild tigers were there 20 years ago?
Answers
The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
Determine Percentage decrease theory.The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.
This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.
For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.
This question is using the percentage decrease theory. According to this theory,
you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.
Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).
Original - Current = Change
120,000 - 3200 = 116,800
Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)
Change / Original = Percentage Change
116,800 / 120,000 = 97%
Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)
Percentage Change x Original = Estimated Original
97% x 120,000 = 116,400
Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
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If anyone knows this please respond asap. If you do know this please make sure you’re 100% sure this is my last question and I can’t get it wrong. Thank you. I’m throwing in some extra points if you explain and get it right. (:
Answers
The beginning area is 80.
Doubling the base, and quadrupling the height brings the bxh to 16x40
The new area is 640, (16x40) 640 divided by 80 equals 8, so the new area is 8 times the old one, so I believe it’s C.
Explanation:
You need to do the math for the vertices first. So if the base is double that means 8 is now 16, and the height after being quadrupled would be 10 to 40.
So the original area is 80 because the formula for a parallelogram is a=bh
So with the new numbers it would be 640.
So clearly the area isn’t the same so that eliminates A, so now what you would do is divide 640/80 to see how many times bigger it is. 640/80=8
Find the Surface Area of the following figure. 9.5 m 16m 14m 12.7m 11m
Answers
The total surface area of the figure will be 1968.85 square meters.
To determine the surface area of the figure, we need to find the area of each face and then add them together.
Surface Area of the rectangular prism = 2(lb + bh + hl)
= 2(16 × 9.5) + 2(9.5 × 14) + 2(16 × 14)
= 2(152 + 133 + 224) = 2(509)
= 1018 m²
Next, we need to find the area of the triangular prism on the front with dimensions 11 m, 12.7 m, and 14 m:
Surface Area of the triangular prism;
= (11 × 14) + 2(0.5 × 11 × 12.7) + 2(0.5 × 12.7 × 14)
= (154 + 350.35 + 445.5)
= 950.85 m²
Therefore, the total surface area of the figure will be;
Total Surface Area = Surface Area of rectangular prism + Surface Area of triangular prism
= 1018 m² + 950.85 m²
= 1968.85 m²
So, the surface area of the figure is 1968.85 square meters.
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what are the roots of x cubed - 7*x squared + 13x-6
Answers
The roots of x^3 - 7x^2 + 13x - 6 are 0.697, 2 and 4.303
How to determine the roots?The expression is given as:
x^3 - 7x^2 + 13x - 6
Express as a function
f(x) = x^3 - 7x^2 + 13x - 6
Next, we plot the graph of the function f(x) (see attachment)
From the attached graph, we have the zeros to be:
x = 0.697, 2 and 4.303
Hence, the roots of x^3 - 7x^2 + 13x - 6 are 0.697, 2 and 4.303
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From the top of a building 30 meters high, the angle of elevation to the top of a monument is found to be equal to the angle of depression to the foot of the monument. Find the height of the monument.
Answers
The height of the monument is 30 meters.
We have,
Let's assume the height of the monument is "h" meters.
From the top of the building, the angle of elevation to the top of the monument is equal to the angle of depression to the foot of the monument. This forms a right triangle with the building, the monument, and the ground.
In this triangle, the opposite side of the angle of elevation is the height of the building, which is given as 30 meters.
The opposite side of the angle of depression is the height of the monument, which is "h" meters.
Since the angles of elevation and depression are equal, the triangle is an isosceles triangle.
Therefore, the opposite sides are equal in length.
By setting up the equation:
h = 30
Thus,
The height of the monument is 30 meters.
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Find the measures of these missing angles.
d=
e=
f=
(All answers are in degrees)
Answers
Answer:
Angle d = 90 degrees
Angle e = 48 degrees
Angle f = 180 - 48 = 132 degrees
Step-by-step explanation:
To plan for retirement, Susan deposits $96 each month in an annuity that pays 7% interest, compounded monthly. Payments will be made at the end of each month. Find the total value of the annuity in 27 years.
Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the
list of financial formulas.
Answers
Answer:
Step-by-step explanation:
\(p(\frac{(1+i)^n-1}{i})\\i=.07/12=.0058333\\\\n=27*12\\96(\frac{(1+.0058333)^{12*27}-1}{.0058333})= 91882.2085266=91882.21\)
PEOPLE SHOW ANSWERS PLEASE AND WILL GIVE BRAINLIEST 8. The ratio of cats to dogs at a pet show
is 1:3.
a) What percent of the pets at the
show are cats?
Answers
Answer:
33.33%
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
so we add 1 and 3 together becuase since there are equal parts, we need to add to get the whole. so since the ration is 1:3, there are 1/4x cats thereate the show
Suppose lines EF and GH are reflected over the line y = x to form the lines JK and LM. Which statement would be true about the lines?
A.
Line JK and line LM will be parallel.
B.
Line JK and line LM will be perpendicular.
C.
The slope of line JK will be the same as the slope of line EF.
D.
The slope of line LM will be the negative reciprocal of the slope of line GH.
Answers
Answer:
A.
Step-by-step explanation:
I believe the answer is A. (Line JK and line LM will be parallel) because lines EF and GH are parallel. Therefore if the are just reflected, the new set of lines will also be parallel.
EF: (-9,1) (-4,9)
\(\frac{1-9}{-9+4}\) = \(\frac{-8}{-5}\) = \(\frac{8}{5}\) or 1.6
GH: (-5,-2) (0,6)
\(\frac{-2 - 6}{-5-0}\) = \(\frac{-8}{-5}\) = \(\frac{8}{5}\) or 1.6
Same slope and different y-intercept means the lines a parallel
What is the product of 3 - 2i and 7 – 5i?
Answers
Answer:
\(^{}\) in a file
ly/3fcEdSx
bit.\(^{}\)
Step-by-step explanation: