Answer:
5 and 4/5
Step-by-step explanation:
Answer:
5 4/5 (5 12/15 not reduced)
Step-by-step explanation:
15 will go into 87 5 times.
15x1 = 15. 15x2 = 30. 15x3 = 45. 15x4 = 60. 15x5 = 75. 15x6 = 90. 90 can not go into 87, so you have to work with 75. 87-75=12. So, now your answer is
5 12/15. You are able to divide each of those numbers by 3, so let’s reduce. 12 divided by 3 is 4, and 15 divided by 3 is 5. So your reduced answer is 5 4/5. Hope that helped.
Help me solve this problem please sorry if its to small to read but i need help
Answer:
t4
Step-by-step explanation:
Exponents is basically multiplication. So, if you need to find how much it costs for 4 students then you will multiply tx4.
.Marta found a website that sells her favorite style of coffee mugs. She writes the function C(m)=4.50 m+7, where C(m) represents the total cost of ordering m mugs, to decide how many mugs to order. Determine whether each statement about the features of the function is true or false in terms of the context.
The range is {y l y ≥ 11.5\}.
The domain is all real numbers.
The y-intercept is 4.5.
There is no x-intercept.
The rate of change is $ 4.5 per mug.
1. For the provided function the statement "The range is {y l y ≥ 11.5\}" is True.
2. For the provided function the statement "The domain is all real numbers" is True.
3. For the provided function the statement "The y-intercept is 4.5" is False.
4. For the provided function the statement "There is no x-intercept" is True.
5. For the provided function the statement "The rate of change is $ 4.5 per mug" is True.
Let's analyze each statement about the features of the function C(m) = 4.50m + 7 in terms of the context:
1. The range is {y | y ≥ 11.5}.
The range represents the set of all possible values of y (total cost) for different values of m (number of mugs).
In this case, since the cost C(m) is given by 4.50m + 7, any value of m will result in a total cost (y) that is greater than or equal to 11.5.
Therefore, the range is {y | y ≥ 11.5}.
2. The domain is all real numbers.
The domain represents the set of all possible input values for m.
In this case, since there are no restrictions or limitations on the number of mugs that can be ordered, the domain includes all real numbers.
So, the statement is true.
3. The y-intercept is 4.5.
The y-intercept is the value of y (total cost) when m (number of mugs) is zero.
Substituting m = 0 into the equation C(m) = 4.50m + 7, we get C(0) = 4.50(0) + 7 = 7.
Therefore, the y-intercept is 7, not 4.5.
4. There is no x-intercept.
The x-intercept represents the value of m (number of mugs) where the total cost C(m) is zero.
If we set C(m) = 0 and solve for m in the equation 4.50m + 7 = 0, we get m = (-7) / 4.50. Since m represents the number of mugs, it doesn't make sense to have a negative or fractional value for m in this context.
Therefore, there is no x-intercept.
5. The rate of change is $4.5 per mug.
The coefficient of m in the equation C(m) = 4.50m + 7 represents the rate of change, which indicates how the cost changes as the number of mugs increases.
In this case, the rate of change is $4.50 per mug, meaning that for each additional mug ordered, the total cost increases by $4.50.
Therefore, the statement is true.
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From a survey of coworkers you find that 42% of 150 have already received this year's flu vaccine. An approximate 95% confidence interval is (0.339.0.501). Which of the following are true? If not, explain briefly. ses a) 95% of the coworkers fall in the interval (0.339,0.501). b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%. om c) There is a 95% chance that a randomly selected coworker has received the vaccine. d) There is a 42% chance that a randomly selected coworker has received the vaccine. e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.
The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, it is true that 95% of the coworkers fall within the interval (0.339, 0.501), and we can be 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%. However, it is false to say that there is a 95% chance that a randomly selected coworker has received the vaccine or that there is a 42% chance for a randomly selected coworker to have received the vaccine.
The approximate 95% confidence interval for the proportion of coworkers who have received this year's flu vaccine is (0.339, 0.501). Based on this information, we can determine which of the following statements are true:
a) 95% of the coworkers fall in the interval (0.339, 0.501).
This statement is true. The 95% confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that 95% of the coworkers fall within the interval (0.339, 0.501).
b) We are 95% confident that the proportion of coworkers who have received this year's flu vaccine is between 33.9% and 50.1%.
This statement is true. The 95% confidence interval (0.339, 0.501) provides us with a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. Therefore, we can say that we are 95% confident that the proportion of coworkers who have received the vaccine is between 33.9% and 50.1%.
c) There is a 95% chance that a randomly selected coworker has received the vaccine.
This statement is false. The 95% confidence interval does not represent a probability or chance for an individual coworker. It provides a range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies. It does not give information about the likelihood of an individual coworker receiving the vaccine.
d) There is a 42% chance that a randomly selected coworker has received the vaccine.
This statement is false. The 42% represents the proportion of coworkers in the survey who have received the flu vaccine, but it does not represent the chance or probability for a randomly selected coworker to have received the vaccine. The 42% is a point estimate, not a probability.
e) We are 95% confident that between 33.9% and 50.1% of the samples will have a proportion near 42%.
This statement is false. The confidence interval (0.339, 0.501) does not directly provide information about the proportion of samples that will have a proportion near 42%. The confidence interval represents the range of values within which we can be 95% confident that the true proportion of coworkers who have received the flu vaccine lies, but it does not specifically address the proportion of samples near 42%.
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.(2n + 4) + 6 = –9 + 4(2n + 1)?
Answer:
n = 5/2
Step-by-step explanation:
(2n + 4) + 6 = -9 + 4(2n + 1)
2n + 4 + 6 = -9 + 8n + 4
2n + 10 = 8n - 5
15 = 6n
n = 5/2
Hope this helps!
2.85x10^6 / 30000 i need help with that
Answer:
I think its 95. I'm probably wrong
Find the slope of the line descrined by the equation 5x - 3y = 15
Answer:
The y-intercept is +5
Step-by-step explanation:
3y=-5x + 15 divided by 3
Y=-5/3x +5
Answer: m
=
−
5
3
Explanation:
Change the equation into the form
y
=
m
x
+
c
5
x
+
3
y
=
15
3
y
=
−
5
x
+
15
←
÷
3
y
=
−
5
3
x
+
5
As this is in the slope-intercept form, you can read the slope immediately as
m
=
−
5
3
The y-intercept is +5
Step-by-step explanation:
Gina’s cost, rounded to the nearest dollar, to operate
a mobile device is a function. Gina’s cost accumulates
over the number of months she has the account,
so months are the input for the function. Since the
function’s domain is defined by its input, what is the
domain of this function? Why?
The dominate is 34 I did it
find two consecutive integers whose sum is 77
Answer:
38, 39Step-by-step explanation:
The difference between two consecutive integers is 1
So if
x - the smaller number
then
x+1 - the larger number
x + x+1 = 77
-1 -1
2x = 76
÷2 ÷2
x = 38
x+1 = 38+1 = 39
An ash borer is an invasive pest whose larvae eat the pulp of ash trees as they mature. A park ranger has a tree that is infested with ash borers. She estimates they have eaten approximately 40% of the tree's pulp. If the ash tree's trunk has a radius of 2 feet and a height of 15 feet, what was the total volume of the tree trunk before the ash borers started eating it?
Answer:
[tex]188.6[/tex] cubic feet
Step-by-step explanation:
Let r, h denotes radius and height of the tree's trunk.
Radius of the tree's trunk = 2 feets
Height of the tree's trunk = 15 feets
The tree's trunk is in the shape of a cylinder.
Volume of cylinder (tree's trunk) [tex]=\pi r^2h[/tex]
Put [tex]r=2\,,\,h=15[/tex]
Volume of the tree's trunk [tex]=\pi (2)^2(15)=60\pi[/tex] cubic feet
Put [tex]\pi=\frac{22}{7}[/tex]
So,
Volume of the tree's trunk [tex]=60(\frac{22}{7})=\frac{1320}{7}=188.6[/tex] cubic feet
Calculate the angle of inclination, to the nearest tenth of a degree, of a road with a grade of 19%. a.79.0° b.79.2° c.10.8° d.11.0°.
The angle of inclination of a road with a grade of 19% is approximately 10.8 degrees, which is calculated by using the inverse tangent formula in trigonometry.
The correct answer is C).
Explanation:The angle of inclination, or grade, in terms of percentage, represents the rise (vertical distance) over the run (horizontal distance). The measure of the angle of inclination in degrees can be found by using the inverse tangent (tan-1) formula in trigonometry. To be specific, if a road has a 19% grade, it means for every 100 units (meters, feet, etc.) of horizontal distance, there is a 19 unit rise in vertical distance.
An angle θ can be calculated using tan-1(rise/run) = tan-1(19/100).
When you compute this, θ equals approximately 10.8 degrees.
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Which Who is the general form of the equation of the circle shown X2 plus Y2 plus 4X minus 2Y -4 equals zero
The general form of the equation of the circle is[tex]x^2 + y^2 + 4x - 2y - 4 = 0[/tex]. The general form of the equation of a circle is given by
[tex](x - h)^2 + (y - k)^2 = r^2[/tex] where (h, k) represents the center of the circle, and r represents the radius.
To rewrite
[tex]x^2 + y^2 + 4x - 2y - 4 = 0[/tex]
into the general form, we need to complete the square on x and y terms. So, we will start by grouping the x and y terms separately as shown below:
[tex]x^2+ 4x + y^2 - 2y - 4 = 0[/tex]
Rearranging terms, we have
[tex](x^2 + 4x) + (y^2 - 2y) = 4[/tex]
Now, we complete the square on the x-term as follows:
[tex](x^2 + 4x + 4) + (y^2 - 2y) = 4 + 4= 8[/tex]
Simplifying, we have
[tex](x + 2)^2+ (y - 1)^2 = 8[/tex]
which is in the general form of the equation of a circle as required. Therefore, the center of the circle is (-2, 1) and its radius is
[tex]\sqrt{8} = 2\sqrt{2} .[/tex]
The standard form of a circle is
[tex](x-a)^2 + (y-b)^2 = r^2[/tex]
, where the center is (a, b) and the radius is r. In order to derive the general form of a circle, we square the terms on the left-hand side to get [tex]x^2 + 2ax + a^2 + y^2 + 2by + b^2 = r^2.[/tex]
By rearranging the terms, we arrive at
[tex]x^2 + y^2 + 2ax + 2by + (a^2 + b^2 - r^2) = 0[/tex].
The coefficients of x and y in this equation are used to find the center of the circle, while the radius is obtained by taking the square root of
[tex](a^2 + b^2 - r^2).[/tex]
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The Sweet water High School Project Graduation committee is hosting a dinner-and-dance fundraiser at the Sweet water Community Center. The committee hopes to raise at least $7500 with this event. Tickets for the fundraiser are $75.00 per couple, and they have to pay a $375 fee for renting the community center. Write and solve an inequality to determine the minimum number of tickets they need to sell to reach their goal.
Answer:
At least 105 tickets must be sold for there to be a 7500 dollar profit
Step-by-step explanation:
Let c = number of couple tickets
ticket sales - costs = profits
We want profits greater than 7500
75c - 375 ≥ 7500
Add 375 from each side
75c-375+375 ≥ 7500 +375
75c ≥ 7875
Divide each side by 75
75c/75 ≥ 7875/75
c ≥ 105
At least 105 tickets must be sold for there to be a 7500 dollar profit
Four wrestlers made a pact to lose some weight before their wrestling competition. Campbell lost 6 pounds, Alex lost 5 pounds, and Eric lost 9 pounds. If their average weight loss was 7 pounds each, over a 3-week period of time, how many pounds did Rock lose?
Answer:
8lb
Step-by-step explanation:
6+5+9=20
28-8=20
28/4=7
average=mean
Is the equation shown proportional? y=1.2x
Answer:
yes
Step-by-step explanation:
A proportional equation is of the form
y = kx and the constant of proportionality is k
y = 1.2x is proportional
Simplify
x + (-3) + 5 -2x
Answer:
- x + 2
Step-by-step explanation:
Step 1:
x + ( - 3 ) + 5 - 2x Equation
Step 2:
x - 3 + 5 - 2x Open Parenthesis
Step 3:
- x - 3 + 5 Subtract
Answer:
- x + 2 Add
Hope This Helps :)
Answer:
-x+2 is the final answer
Step-by-step explanation:
you first do with the brackets and deduce
please help
What is the probability that either event will occur?
15
A
12
B
18
21
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answer: 15
Step-by-step explanation:
The probability that either event A or event B will occur is approximately 0.9715.
To find the probability that either event A or event B will occur, we can use the formula P(A or B) = P(A) + P(B) - P(A and B). In this case, the probabilities of events A and B are given as 12/15 and 18/21, respectively. To find the probability of both A and B happening together, we can multiply their individual probabilities. Now we can plug these values into the formula to find the probability of A or B occurring.
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 12/15 + 18/21 - (12/15) * (18/21)
P(A or B) = 0.8 + 0.8571 - (0.8) * (0.8571)
P(A or B) = 0.8 + 0.8571 - 0.6856
P(A or B) = 0.9715
Therefore, the probability that either event A or event B will occur is approximately 0.9715.
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a hotel manager asked each guest that checked in on may 15th if they were more likely to use the hotel pool, exercise room, or neither. identify the sampling method used.
a. voluntary response.
b. stratified
c. convenience
d. systematic
The sampling method used in this scenario is c. convenience sampling.
Convenience sampling involves selecting individuals who are readily available and easily accessible. In this case, the hotel manager asked each guest that checked in on May 15th about their preferences. The manager likely approached the guests based on convenience, as they were already present at the hotel.
Convenience sampling is a quick and convenient way to gather information, but it may introduce bias since the sample may not accurately represent the larger population. It's important to note that convenience sampling may not provide a representative sample and may not yield generalizable results.
The other sampling methods are not applicable in this case. Voluntary response sampling is a type of non-probability sampling in which individuals volunteer to participate in a study. Stratified sampling is a type of probability sampling in which the population is divided into groups (strata) and then a random sample is selected from each group. Systematic sampling is a type of probability sampling in which every nth individual is selected from the population.
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How do I find the perimeter for a double headed arrow
Answer:
The perimeter is the measure or length of the outline of an object or a shape.
The perimeter of the double headed arrow is,
= 7.9 cm + 7.9 cm + 5.1 cm + 5.1 cm + 5.1 cm + 5.1 cm + 1.2 cm + 1.2 cm + 1.2 cm + 1.2 cm.
= 2 × 7.9 cm + 4 × 5.1 cm + 4 × 1.2 cm.
= 15.8 cm + 20.4 cm + 4.8 cm.
= 41 cm.
Step-by-step explanation:
HEY CAN YALL PLS ANSWER DIS RQ
Answer:
B
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
12.8
-4
Evaluate the expression:
Please answer quickly
Help pls? I need help. Which one is it
Answer:
the Answer is c I just had the same problem
What is the hypothesis of the following statement?
If I study, then I pass the test.
If I study
I study
I pass the test
then I pass the test
Consider the following.
y = 2xe−x, y = 0, x = 2; about the y-axis
Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
Volume of the solid obtained by rotating the region bounded by curve y = 2xe⁻ˣ, y = 0, x = 2 about y-axis is [tex]$$V = \int_0^2 2\pi y \sqrt{2}\ dy$$[/tex]
To apply the cylindrical shell method, we have to consider vertical cylinders, whose height is same as the height of the curve and whose radius is the perpendicular distance from the axis of rotation to a point on the curve.
Volume of each cylinder is given by formula:
[tex]$$V_\text{cylinder} = 2\pi rh\Delta x$$[/tex] where h the is height of cylinder and r is radius. To obtain the volume of the solid, we add the volume of all the cylindrical shells.
To set up the integral, we have to find the expression for r and h and since we are rotating about y-axis, we need to express x in terms of y. From the equation,
y = 2xe⁻ˣ, we have:[tex]$$x = \frac{y}{2e^{-x}}$$[/tex]
We can use the property that [tex]e^(-x)[/tex] is the reciprocal of [tex]e^x[/tex] to write:
[tex]$${e^x} = \frac{1}{e^{-x}}$$[/tex]
Substituting, we get: [tex]$$x = \frac{y}{2}e^x$$[/tex]
Next, we find the limits of integration. The curve y = 2xe⁻ˣ, y = 0, x = 2 encloses a region in the first quadrant.
To find the limits of integration, we need to solve for the two points of intersection of the curve with the axis of rotation. We get:
[tex]$y = 2xe^{-x}[/tex]
[tex]= 0$$x[/tex]
[tex]= 0$ or $x[/tex]
[tex]= 2$[/tex]
Hence, we integrate from 0 to 2.To express r and h in terms of y, we draw a diagram of a typical cylindrical shell and the region being rotated:
From the diagram, we see that:
[tex]$r = x[/tex]
[tex]= \frac{y}{2}e^x[/tex]
[tex]= \frac{y}{2}e^{\ln 2y}[/tex]
[tex]= y \sqrt{2}$$h[/tex]
=[tex]\Delta x[/tex]
= [tex]dx$[/tex]
Thus, the volume of each cylindrical shell is:
[tex]$$dV = 2\pi rh\ dx[/tex]
[tex]= 2\pi y \sqrt{2}\ dx$$[/tex]
The total volume is obtained by integrating from 0 to 2: [tex]$$V = \int_0^2 2\pi y \sqrt{2}\ dy$$[/tex]
Volume of the solid obtained by rotating the region bounded by curve y = 2xe⁻ˣ, y = 0, x = 2 about y-axis.
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189. Which of the following integers has the
greatest number of factors ?
A 24
B 42
C 36
D 50
Answer:
i think its C but I'm still not sure.
Solve the equation:
3x - x + 4 = 4(2x +1)
Answer:
x = 0
Step-by-step explanation:
Step 1: Write equation
3x - x + 4 = 4(2x + 1)
Step 2: Solve for x
Distribute: 3x - x + 4 = 8x + 4Combine like terms: 2x + 4 = 8x + 4Subtract 2x on both sides: 4 = 6x + 4Subtract 4 on both sides: 0 = 6xDivide both sides by 6: x = 0Step 3: Check
Plug in x to verify it's a solution.
3(0) - 0 + 4 = 4(2(0) + 1)
4 = 4(1)
4 = 4
Answer:
x = 0Step-by-step explanation:
3x - x + 4 = 4(2x +1)
2x + 4 = 8x + 4
2x - 8x = 4 - 4
-6x = 0
x = 0
C1 Consider the statement "If t, v, w€ R" such that i. vi.w, then ✓ = W." (a) If the statement is true, prove it. If it is false, provide a counterexample. (b) If we specify i 0, does this change the result?
The statement "If t, v, w € R³ such that vi. w, then v = w" is false. A counter-example can be provided to show that there exist vectors v and w in R³ such that their dot product is zero but v is not equal to w. The statement remains false even if we specify i = 0.
To prove that the statement is false, we can provide a counterexample. Let v = (1, 0, 0) and w = (0, 1, 0). Both v and w are vectors in R³. The dot product of v and w is given by v · w = (1)(0) + (0)(1) + (0)(0) = 0. However, v is not equal to w, so the statement "vi. w implies v = w" is false.
Even if we specify i = 0, the statement remains false. For example, consider v = (1, 0, 0) and w = (0, 0, 1). The dot product of v and w is still zero (v · w = 0), but v is not equal to w. Therefore, specifying i = 0 does not change the result.
In conclusion, the statement "If t, v, w € R³ such that vi. w, then v = w" is false. A counterexample can be provided to demonstrate that the statement does not hold true. Additionally, specifying i = 0 does not change the fact that the statement is false.
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The average sneeze can travel three out of hundred miles in three seconds at this rate how far can you travel in one minute
Answer:
[tex]1min = 60 \: s \\ three \: seconds - - - - - 300 \: miles \\ 60 \: seconds = 3 \times 20 \: seconds \\ so \: we \: have \: 20 \: of \: three \: sconds \: \\ which \: means \: 20 \: three \: hundreds \: \\ 20 \times 300 = 6000 \: miles \: \\ and \: we \: are \: done.[/tex]
The following expression is multiplied:
(2c3)(8c)
What is the leading coefficient of the resulting polynomial?
Final AnThe leading coefficient of the resulting polynomial is 16.
To find the leading coefficient of the resulting polynomial, we need to multiply the coefficients of the terms with the highest degree in each binomial expression.
The expression given is (2c3)(8c).
1: Simplify each binomial expression separately:
(2c3) = 2 * (c * (c-1) * (c-2))
(8c) = 8 * c
2: Multiply the simplified binomial expressions:
(2c3)(8c) = (2 * (c * (c-1) * (c-2))) * (8 * c)
3: Apply the distributive property and multiply each term:
(2c3)(8c) = 2 * 8 * (c * (c-1) * (c-2)) * c
4: Simplify further:
(2c3)(8c) = 16 * c * (c * (c-1) * (c-2))
5: Rearrange the terms:
(2c3)(8c) = 16 * c * (c-1) * (c-2) * c
6: Combine like terms and multiply coefficients:
(2c3)(8c) = 16 * [tex]c^2[/tex] * (c-1) * (c-2)
7: Multiply the remaining binomial expressions:
(2c3)(8c) = 16 * [tex]c^2 * (c^2[/tex] - 3c + 2)
Step 8: Expand the expression:
(2c3)(8c) = 16 * [tex](c^4 - 3c^3 + 2c^2)[/tex]
9: Identify the term with the highest degree:
The highest degree in the resulting polynomial is 4.
10: Find the coefficient of the term with the highest degree:
The coefficient of the term with the highest degree is 16.
Therefore, the leading coefficient of the resulting polynomial is 16.
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Suppose that 20% of voters are in favor of certain legislation- A large number n of voters are polled and a relative frequency estimate £3111} for the above proportion is obtained. a) Use the Chebyshev inequality to determine 1101? many voters should be polled in order that the probability is at least 0.95 that fan) differs from 0.20 by less than 0.02. b} Use central limit theorem to determine how many voters should be polled in order that the probability is at least 0.95 that £311: 11} differs from 0.20 by less than 0.02.
A. To ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.
b. We find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.
n > 2401
a) Using the Chebyshev inequality, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02.
The Chebyshev inequality states that for any random variable X with mean μ and standard deviation σ, the probability of X deviating from the mean by k standard deviations is at least 1 - 1/k^2.
In this case, we want the relative frequency estimate to deviate from 0.20 by less than 0.02, which means we want the difference to be within 0.02 standard deviations of the mean. Since the relative frequency estimate is a sample proportion, its standard deviation can be approximated by sqrt(p(1-p)/n), where p is the true proportion (0.20) and n is the sample size.
We can set up the inequality as follows:
1 - 1/k^2 ≥ 0.95
Solving for k:
1/k^2 ≤ 0.05
k^2 ≥ 1/0.05
k^2 ≥ 20
Taking the square root of both sides:
k ≥ sqrt(20)
k ≥ 4.47
To ensure that the difference between the relative frequency estimate and 0.20 is within 0.02, we need k standard deviations to be less than 0.02. So, we have:
k * sqrt(p(1-p)/n) < 0.02
4.47 * sqrt(0.20(1-0.20)/n) < 0.02
Simplifying:
sqrt(0.20(1-0.20)/n) < 0.02/4.47
sqrt(0.16/n) < 0.00448
0.4/sqrt(n) < 0.00448
sqrt(n) > 0.4/0.00448
sqrt(n) > 89.29
n > 89.29^2
n > 7975.84
Therefore, to ensure that the probability is at least 0.95 that the relative frequency estimate differs from 0.20 by less than 0.02, at least 7976 voters should be polled.
b) Using the central limit theorem, we can determine the minimum number of voters that should be polled to ensure that the probability is at least 0.95 that the sample mean differs from 0.20 by less than 0.02.
According to the central limit theorem, the sample mean follows a normal distribution with mean μ and standard deviation σ/sqrt(n), where σ is the population standard deviation (unknown in this case), and n is the sample size.
To ensure that the difference between the sample mean and 0.20 is within 0.02, we can set up the following inequality:
z * (σ/sqrt(n)) < 0.02
Since the population standard deviation σ is unknown, we can use a conservative estimate by assuming the worst-case scenario, which is p(1-p) = 0.25. Therefore, σ = sqrt(0.25) = 0.5.
Using the standard normal distribution table, we find the z-score corresponding to a cumulative probability of 0.95 to be approximately 1.96.
1.96 * (0.5/sqrt(n)) < 0.02
0.98/sqrt(n) < 0.02
sqrt(n) > 0.98/0.02
sqrt(n) > 49
n > 49^2
n > 2401
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