Answers
the result by 5 and adds 4 one last time to get the final output value. This can also be written in shorthand as:=(f o f o f) (X) = 5(5(5X + 4) + 4) + 4 = 125X + 124.
How to solve a function?
To find (f o f o f) (X), we need to apply the function f three times to X. Let's start by finding (f o f) (X):
(f o f) (X) = f(f(X)) = f(5X + 4) = 5(5X + 4) + 4 = 25X + 24
Now, we need to apply f to (f o f) (X) to get the final result:
(f o f o f) (X) = f((f o f) (X)) = f(25X + 24) = 5(25X + 24) + 4 = 125X + 124
Therefore, (f o f o f) (X) = 125X + 124.
In words, the function (f o f o f) (X) takes any input value X, multiplies it by 5, adds 4, multiplies the result by 5 again, adds 4, and finally multiplies the result by 5 and adds 4 one last time to get the final output value. This can also be written in shorthand as:
(f o f o f) (X) = 5(5(5X + 4) + 4) + 4 = 125X + 124.
This process of applying a function multiple times to an input value is known as function composition, and it is a fundamental concept in mathematics and computer science.
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Related Questions
lodine-131, a radioactive substance that is effective in locating brain tumors, has a half-life of only eight days. A
hospital purchased 16 grams of the substance but had to wait six days before it could be used. How much of the
substance was left after six days?
...
The amount of substance left after six days was
9.
(Round the final answer to three decimal places as needed. Round all intermediate values to seven decimal places as
needed.)
Answers
The mass of substance left after 6 days is 9 g
The mass of substance left, N is given by
N = N₀exp(-λt) where λ = decay constant and N₀ = initial mass of substance present = 24 g and t = time
Also, λ = 0.693/t' where t' = half-life of iodine = 8 days
So, λ = 0.693/t'
λ = 0.693/8
λ = 0.086625/day
Since the mass of substance left is N = N₀exp(-λt) and we require the mass of substance after t = 6 days,
N = N₀exp(-λt)
N = 16 gexp(-0.086625/day × 7 days)
N = 16 gexp(-0.606375)
N = 16 g × 0.5453
N = 8.72 g
N = 8.72 → 9 g
So, the mass of substance left after 7 days is 9 g
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QUESTION 5..... [1.5 marks]
The following data set represents the score distribution for the Final Exam in MATH 146:
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
Find the 85th percentile.
Solution. Please write your detailed solution here:
Answers
answer
82
steps
put data in numerical order
55, 56, 57, 58, 59, 60, 60, 61, 63, 65, 69, 71, 78, 78, 79, 79, 82, 82, 83, 83
there are 20 numbers = 20
85 is the percentile = p
percentile rank formula
PR = (p/100) * (n + 1)
PR = (85/100) * (20 + 1) = 17.85
round up 17.85 to 18
it's the 18th number which is
82
chatgpt
Write a rule for the translation.
(x-1, y + 2)
(x-2, y + 1)
(x+2, y - 1)
(x+1, y-2)
Answers
Answer: Step 1: Pick a pair of corresponding points: one point in the shape before the translation and the same point in the shape after the translation.
Step 2: Determine how many units, a, left or right the shape moved.
Step-by-step explanation:
Standard Deviation. Find the Standard Deviation of the following set of data. You must fill out the table and show the ending calculations in order to get full credit here.
7.2, 8.9, 2.7, 11.6, 5.8, 10.2
show ALL steps
Answers
The standard deviation of the data set is 1.03.
What is the standard deviation?
The standard deviation is a measure of the amount of variation or dispersion of a set of data values. It measures how spread out the data is from the mean or average value.
To find the standard deviation, we first need to find the mean of the data set:
Mean = (7.2 + 8.9 + 2.7 + 11.6 + 5.8 + 10.2) / 6 = 7.4
Next, we calculate the deviations from the mean for each data point:
| x - mean | (x - mean)²
0.2 0.04
1.5 2.25
4.7 22.09
4.2 17.64
1.6 2.56
2.8 7.84
To find the variance, we add up the (x - mean)² values and divide by the number of data points:
Variance = (0.04 + 2.25 + 22.09 + 17.64 + 2.56 + 7.84) / 6 = 6.36/6 = 1.06
Finally, we take the square root of the variance to get the standard deviation:
Standard deviation = √(1.06) = 1.03 (rounded to two decimal places)
Therefore, the standard deviation of the data set is 1.03.
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Find the centre and radius of 364+28y+y^2+x^2=-26x
Answers
Step-by-step explanation:
hope it will help you , and give some clue to do typical qno..
Bill's father can paint a room in 3 hours less than Bill can paint it. Working together they cam
complete the job in 2 hours. How much time would each require working alone?
Answers
Answer: Bob 3 Hours Jack 2 Hours
Step-by-step explanation:
Two cars leave towns 320 kilometers apart at the same time and travel toward eachother. One car's rate is 12 kilometers per hour less than the other's. If they meet in 2 hours, what is the rate of the slower car?
Do not do any rounding.
Answers
Answer:
74 kilometers per hour.
Step-by-step explanation:
Let's call the speed of the faster car "x" (in kilometers per hour). Then, according to the problem, the speed of the slower car is "x - 12" (in kilometers per hour).
The two cars are traveling towards each other, so the distance between them decreases at a rate equal to the sum of their speeds. In other words, the relative speed between the two cars is:
x + (x - 12) = 2x - 12
According to the problem, they meet after 2 hours of travel, so the total distance they cover is:
distance = speed × time
For the faster car, the distance it covers is:
distance = x × 2
For the slower car, the distance it covers is:
distance = (x - 12) × 2
Since they are both traveling towards each other, the sum of the distances covered by both cars should be equal to the total distance between them at the start of the trip (320 kilometers):
x × 2 + (x - 12) × 2 = 320
Simplifying this equation:
2x + 2x - 24 = 320
4x = 344
x = 86
Therefore, the speed of the faster car is 86 kilometers per hour.
To find the speed of the slower car, we can use the expression we found earlier:
x - 12 = 86 - 12 = 74
Therefore, the speed of the slower car is 74 kilometers per hour.
i need help to do spiral review 5 on lesson 9.7 pls help
Answers
Answer: wheres the page/diagram
Step-by-step explanation:
In the year 2000, the number of snakes in a certain forest was 280.
Since that year the number of snakes in that forest has increased at a
rate of 12% per year. Write a function, f(x), that models the number of
snakes x years after the year 2000.
Answers
Step-by-step, explanation/work/how to solve:
The initial number of snakes in the year 2000 is 280. If the number of snakes increases at a rate of 12% per year, then the number of snakes x years after the year 2000 can be modeled by the following equation:
f(x) = 280 * (1 + 0.12)^x
Where x is the number of years after the year 2000.
So, if you want to know the number of snakes after, say, 5 years from the year 2000, you can plug in x = 5 into the equation and get:
f(5) = 280 * (1 + 0.12)^5
f(5) = 280 * 1.76234
f(5) = 493.24
Could someone help answer Number 22 please
Answers
Area of the first triangle is 582.86 square units
Area of the second triangle is 694 square units
How to find the area of the trianglesThe formula for area of a triangle is solved by
= 1/2 * b * h
For the first figure, we solve for h first using trigonometry
tan 68 = 48 / h
h = 48 / tan 68
h = 19.39
The other side of the base is solved using tan 58
tan 58 = 43.22 / b
b = 43.22 / tan 58
b = 12.12
base of the triangle = 48 + 12.12 = 60.12
Area of the first triangle = 0.5 * 60.12 * 19.39 = 582.86 square units
22. Solving for h
cos 64 = h / 50
h = 50 * cos 64 = 21.92
the other part of the base
sin 64 = b / 50
b1 = 50 * sin 64 = 44.94
tan 50 = h / b2 = 21.92 / b2
b2 = 21.90 / tan 50 = 18.38
base = b1 + b2 = 44.94 + 18.38 = 63.32
Area of the second triangle = 0.5 * 21.92 * 63.32 = 693.99 square units
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please help me on this question
Answers
Answer:
x = 30 cm
Perimeter = 72 cm
Step-by-step explanation:
By Pythagoras theorem,
x² = 18² + 24²
x² = 324 + 576
x² = 900
x² = 30²
x = 30 cm
Perimeter of a triangle is just the sum of its sides,
Perimeter = 18 + 24 + 30
Perimeter = 72 cm
Answer:
30cm, 72cm
Step-by-step explanation:
c²=a²+b²
x²=18²+24²=900
x=√900
x=30cm
p=a+b+c
p=18+24+30
p=72cm
A chain was calibrated to be of exact length 30.00 m at 200C. When this chain was used for chain surveying in field, the temperature was recorded to be 45oC. If the coefficient of linear expansion of steel used in chain is 8x 10-6 per oC, find the true total distance chained if measured distance on ground is 6000 m.
Answers
The true total distance chained if the measured distance on the ground is 6000 m would be 6001.8 m.
Linear expansivity problemThe measured distance on the ground is 6000 m. However, due to the increase in temperature during the surveying, the chain would have expanded, leading to an increase in the measured length.
The coefficient of linear expansion of steel is 8 x 10^-6 per oC. Therefore, for a temperature increase of 45 - 20 = 25 oC, the increase in length of the chain can be calculated as follows:
ΔL/L = αΔT
where ΔL is the increase in length, L is the original length (30.00 m), α is the coefficient of linear expansion (8 x 10^-6 per oC), and ΔT is the temperature increase (25 oC).Substituting the given values, we get:
ΔL/30.00 = (8 x 10^-6) x 25
ΔL = 0.006 m
This means that the actual length of the chain during the surveying was 30.006 m.
To find the true total distance chained, we need to correct the measured distance on the ground for the increase in chain length. Let D be the true total distance chained. Then we have:
D/30.006 = 6000/30.00
Solving for D, we get:
D = 6000 x 30.006 / 30.00
D = 6001.8 m
Therefore, the true total distance chained is 6001.8 m.
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Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
Answers
The equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7 = 4/3(x - 3).
Explain about slopes of parallel lines?The amount by which a line is inclined towards the horizontal axis is known as its slope. The slope can also provide a measure of a line's steepness and is helpful in assessing if two lines remain parallel or perpendicular.
Standard equation of line:
y = mx + c
m is the slope and c is the y intercept.
equation of a line: y = 4/3x + 4
On comparing both equation:
m = 4/3 and c is 4
Now, we know that : slopes of parallel lines are equal.
m = 4/3 and passing point is given as: (3,-7).
Using the point slope form:
y - y1 = m(x - x1)
y - (-7) = 4/3(x - 3)
y + 7 = 4/3(x - 3)
Thus, the equation of the new line which is parallel to the given line of equation y= 4/3x+4 is found to be: y + 7 = 4/3(x - 3).
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Suppose the probability of an IRS audit is 1.5 percent for U.S. taxpayers who file form 1040 and who earned $100,000 or more.
(a) What are the odds that such a taxpayer will be audited? (Round your answers to the nearest whole number.)
(b) What are the odds against such a taxpayer being audited? (Round your answers to the nearest whole number.)
Answers
(a) For every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited. (b) for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
(a) To calculate the odds that a taxpayer will be audited, we need to divide the probability of being audited by the probability of not being audited. The probability of being audited is given as 1.5 percent or 0.015. The probability of not being audited is the complement of the probability of being audited, which is 1 - 0.015 = 0.985. Therefore, the odds that a taxpayer will be audited are:
0.015/0.985 = 0.0152284264
To convert this to odds notation, we divide the probability of being audited by the probability of not being audited:
0.015/0.985 = 0.0152284264 = 0.0152 (rounded to four decimal places)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 2 of them will be audited.
(b) The odds against a taxpayer being audited is the ratio of the probability of not being audited to the probability of being audited. We have already calculated the probability of not being audited to be 0.985, and the probability of being audited to be 0.015. Therefore, the odds against a taxpayer being audited are:
0.985/0.015 = 65.66666667
To convert this to odds notation, we divide the probability of not being audited by the probability of being audited:
0.985/0.015 = 65.66666667 = 66 (rounded to the nearest whole number)
This means that for every 100 taxpayers who file form 1040 and who earned $100,000 or more, about 66 of them will not be audited.
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A boxplot for a set of 80 scores is given below.
How many scores are represented in the blue section of the boxplot?
Answers
Answer: The number of scores represented in the blue section of the boxplot is 12.
A set of ten cards were labeled as E, X, P, R, E, S, S, I, O, N. What is the sample space for choosing one card? S = {E, P, X} S = {S, I, O, N} S = {E, X, P, R, E, S, I, O, N} S = {E, E, I, N, O, P, R, S, S, X}
QUICK
Answers
The sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.
What is sample space?Sample space refers to the set of all possible outcomes of a random experiment or a probability event. In the context of your card example, the sample space is the set of all possible cards that could be chosen from the labeled set.
In this case, the sample space would be {E, X, P, R, S, I, O, N}, as these are the possible outcomes when selecting one card from the set.
Therefore the sample space for chosing one card is S = {E, X, P, R, E, S, I, O, N}.
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How much do we need to invest each month at a rate of 8% compounded monthly so that we have a total of $600,000 saved in 25 years?
Will mark brainliest
Answers
we need to invest $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.
define rate of interestThe rate of interest is the percentage amount charged by a lender or financial institution for borrowing money or the percentage amount paid to an investor or saver for lending money. It represents the cost of borrowing or the return on investment over a period of time.
To calculate the monthly investment required, we can use the formula for future value of an annuity, which is:
FV = PMT x ((1 + r)ⁿ⁻¹) / r
where:
FV is the future value of the annuity
PMT is the monthly payment or investment
r is the monthly interest rate
n is the total number of periods (months)
In this case, we want to save $600,000 in 25 years, which is equivalent to 300 monthly payments (25 years x 12 months/year). The monthly interest rate is 8% / 12 = 0.00667.
Plugging in the values, we get:
$600,000 = PMT x ((1 + 0.00667)³⁰⁰⁻¹) / 0.00667
Solving for PMT, we get:
PMT = $600,000 x 0.00667 / ((1 + 0.00667)³⁰⁰⁻¹)
= $1,410.91 (rounded to the nearest cent)
Therefore, we need to invest approximately $1,410.91 each month at a rate of 8% compounded monthly to have a total of $600,000 saved in 25 years.
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The company bank account currently has a positive balance of R2195,00. You have to refund five clients an amount of R665,00 each, due to a sales discount not being applied to their recent purchases. What will the balance be on the company account after the refunds have been paid?
Answers
Step-by-step explanation:
The total amount to be refunded to the five clients is:
5 x R665,00 = R3325,00
To find the balance on the company account after the refunds have been paid, we need to subtract the total amount refunded from the current balance:
R2195,00 - R3325,00 = -R1130,00
Therefore, the balance on the company account will be negative and equal to -R1130,00 after the refunds have been paid.
A, B, C and D are 4 towns
B is 30km due east of A.
C is 30km due North of A.
D is 45km due South of A.
Calculate the bearing of D to B
Answers
The bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
We can start by drawing a diagram to represent the positions of the four towns. Let A be the origin of the coordinate system, B be located 30 km due east of A, C be located 30 km due north of A, and D be located 45 km due south of A. The diagram would look like this:
C (30 km)
|
|
|
A (0,0)---+---B (30 km)
|
|
|
|
D (45 km)
To calculate the bearing of D to B, we need to determine the angle that DB makes with the north-south axis (i.e., the y-axis) in a clockwise direction.
First, we can use the Pythagorean theorem to find the distance between B and D:
BD² = AB² + AD²
BD² = 30² + 45²
BD² = 2025
BD = √2025
BD = 45 km
Next, we can use trigonometry to find the angle that DB makes with the north-south axis. Let θ be the angle we are looking for. Then:
tan θ = (opposite / adjacent) = (AB / AD) = (30 / 45) = 2/3
Taking the arctangent of both sides, we get:
θ = tan⁻¹(2/3) ≈ 33.7°
Therefore, the bearing of D to B is approximately 33.7°, measured in a clockwise direction from the north-south axis.
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A glass of cold milk is sitting on the counter, warming up to room temperature. Currently, the milk is 16°C below room temperature. However, that temperature difference is shrinking by 7% every minute. What will the temperature difference be in 14 minutes? If necessary, round your answer to the nearest tenth.
Answers
Answer: it's 8.6 or 1.4
Step-by-step explanation:
Turn 10% into a decimal form... .10
.10 x 14 = 1.4
10 - 1.4 = 8.6
I have a queston can you answer it pls
Answers
Answer:
0.1 gallons per second or 6 gallons per minute
Step-by-step explanation:
Unit rate =measurement/time
Measurement=
42
gallons
Time=
7
42/7=6
Or if you want in seconds, change the mins to seconds. There are 60 seconds in a minute
7
×
60
=
420
seconds
Unit rate =
42
420
=
0.1
gallons per second
The diameter of a cone's circular base is 12 inches. The height of the cone is 12 inches.
What is the exact volume of the cone?
Enter your answer in the box.
in³
Answers
Answer: It is 144 but add pi symbol
Step-by-step explanation:
In conclusion the exact volume of the cone is 144π cubic inches.
How to solve and what does volume mean?
The radius of the circular base is half the diameter, which is 12/2 = 6 inches.
The volume of a cone can be found using the formula V = (1/3)πr²2h, where r is the radius and h is the height.
Substituting the given values, we get:
V = (1/3)π(6²2)(12)
V = (1/3)π(36)(12)
V = (1/3)(432π)
V = 144π
Therefore, the exact volume of the cone is 144π cubic inches.
Volume is a measure of the amount of space occupied by a three-dimensional object, such as a solid, liquid, or gas. It is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³). The volume of an object can be determined by measuring its dimensions, such as length, width, and height, and applying the appropriate formula for the shape of the object.
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Please help me answer these two questions!!!
Answers
in the alphabetical order A-B SO I THINK IT IS 10
y = 3x + 1
y = 8x - 4
with solution pls, i would rlly appreciate it
Answers
Answer:
si y = a 55 es 5.7
Step-by-step explanation:
la otra es 3.9
Equal to which of the following?
Answers
The expression for the difference quotient is option C and the simplified form of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.
What is the expression of the difference quotient?We are asked to find the expression for the difference quotient of the function f(x) when evaluated at x and x + h. The difference quotient is given by:
[tex]$\frac{f(x+h) - f(x)}{h}$[/tex]
where h is a small nonzero number representing the change in the input.
Substituting f(x) with its expression, we get:
[tex]$\frac{(2(x+h)^2 + 4(x+h) - 3) - (2x^2 + 4x - 3)}{h}$[/tex]
Expanding and simplifying the numerator, we get:
[tex]$\frac{2x^2 + 4xh + 2h^2 + 4x + 4h - 3 - 2x^2 - 4x + 3}{h}$[/tex]
Simplifying further, we get:
[tex]$\frac{2x^2 + 4xh + 2h^2 + 4h}{h}$[/tex]
Canceling the common factors of h, we get:
[tex]$2x + 4 + 2h$[/tex]
Therefore, the expression for the difference quotient of the function f(x) when evaluated at x and x + h is 2x + 4 + 2h.
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Solve the expression 7 + (one-fifth x 18 – 3) using the order of operations.
Answers
The solution to the expression 7 + (one-fifth x 18 – 3) using the order of operations is 7.6 .
What is order of operations?The order of operations is:
Perform any calculations inside parentheses first.
Exponents (ie powers and square roots, etc.)
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
To solve the expression 7 + (one-fifth x 18 – 3), we need to apply the order of operations, which is a set of rules that determines the sequence in which we perform mathematical operations.
Using the order of operations simplifies the expression as follows:
Calculate what's inside the parentheses:
one-fifth x 18 – 3 = (1/5) x 18 – 3
= 3.6 - 3
= 0.6
Add 7 to the result:
7 + 0.6 = 7.6
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for the function graphed, determine the interval(s) where the derivative is (a) positive; (b) negative; and the x-value(s) at which the derivative is (c) equals zero; (d) does not exist.'
Answers
(a) Positive derivative interval: From x = -∞ to x = -4, and from x = 0 to x = 3.
(b) Negative derivative interval: From x = -4 to x = 0, and from x = 3 to x = ∞.
(c) x-value(s) where derivative equals zero: At x = -3 and x = 2.
(d) x-value(s) where derivative does not exist: At x = -4 and x = 3.
To find the intervals where the derivative of the function is positive, negative, or equals zero, we first need to find the critical points by setting the derivative equal to zero and solving for x. We can see from the graph that there is only one critical point at x = -2. We then test each interval between the critical points and endpoints to determine if the derivative is positive or negative.
From x = -infinity to x = -2, the derivative is negative. From x = -2 to x = 3, the derivative is positive. From x = 3 to x = infinity, the derivative is negative. Therefore, the answer is (a) the derivative is positive on (-2, 3); (b) the derivative is negative on (-infinity, -2) and (3, infinity); (c) the derivative equals zero at x = -2; (d) the derivative exists for all x.
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51. For which of the following values of L will the lines whose equations are 2x+3y=8
and 8x+12y = L be parallel?
I. L = 0
II. L = 8
III. L = −8
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
Answers
explanation
Graph the first equation then graph the 2nd equation substituting 0, 8 and -8 for L.
All three show a parallel line to the first equation.
2x + 3y = 8
x = 4, y= 2.666…
8x + 12y = 0
x= 0, y=0
8x + 12y = -8
x = -1, y = -.66666….
PLEASE HELP!!! URGENT 60 POINTS!!!!!
1. Construct the 99% confidence interval estimate of the population proportion p if the sample size is n=100 and the number of successes in the sample is x=66.
Give your answers to 4 decimal places, and use at least 3 decimal places in your critical value.
______ < p < ______
2. In a random sample of 710 Americans, 37.2% indicated that they have a cat for a pet. Estimate with 95% confidence the proportion of all Americans that have cats as pets. Give the confidence interval in interval notation, (LCL,UCL) . Give your answer as percentages, to at least 2 decimal places, and use at least 3 decimal places in your critical value.
Confidence Interval:
3. Refer to the following scenario.
An epidemiologist is worried about the prevalence of the flu in East Vancouver and the potential shortage of vaccines for the area. She will need to provide a recommendation for how to allocate the vaccines appropriately across the city. She takes a simple random sample of 336 people living in East Vancouver and finds that 39 have recently had the flu.
Suppose that the epidemiologist wants to re-estimate the population proportion and wishes for her 95% confidence interval to have a margin of error no larger than 0.04. How large a sample should she take to achieve this? Please carry answers to at least six decimal places in intermediate steps, and use at least 3 decimal places in your critical value.
Sample size =
4. Refer to the following scenario.
A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 126 people living in Gastown and finds that 21 have an annual income that is below the poverty line.
Suppose that the government official wants to re-estimate the population proportion and wishes for his 90% confidence interval to have a margin of error no larger than 0.05. How large a sample should he take to achieve this? Please carry answers to at least six decimal places in intermediate steps, and use at least 3 decimal places in your critical value.
Sample size =
Answers
The 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.
What is confidence interval?
A confidence interval is a range of values calculated from a sample of data that is used to estimate an unknown population parameter with a certain level of confidence.
1.To construct a 99% confidence interval estimate of the population proportion p, we can use the following formula:
CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
where:
[tex]$\hat{p}$[/tex] is the sample proportion (x/n)
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 99% confidence level, which is 2.576
n is the sample size
Substituting the given values, we have:
[tex]$\hat{p}$[/tex] = x/n = 66/100 = 0.66
[tex]\item $z_{\alpha/2}$[/tex] = 2.576 (from the standard normal distribution table or calculator)
n = 100
Plugging these values into the formula, we get:
CI = 0.66 ± 2.576 * [tex]\sqrt{(0.66)\frac{(1-0.66)}{100}}[/tex]
CI = 0.66 ± 0.1277
Therefore, the 99% confidence interval estimate of the population proportion p is (0.5323, 0.7877) to 4 decimal places.
2.To estimate the proportion of all Americans that have cats as pets with 95% confidence, we can use the following formula:
CI=[tex]$\hat{p}$[/tex]±[tex]\item $z_{\alpha/2}$[/tex]×[tex]\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }[/tex]
where:
[tex]$\hat{p}$[/tex] is the sample proportion (0.372)
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level, which is 1.96
[tex]\item $n$[/tex] is the sample size (710)
Substituting the given values, we have:
CI=0.372±1.96×[tex]\sqrt{0.372\frac{(1-0.372)}{710} }[/tex]
CI=0.372±0.0325
Therefore, the 95% confidence interval estimate of the proportion of all Americans that have cats as pets is [tex]$(0.3395, 0.4045)$[/tex] to 4 decimal places.
Expressing this in interval notation, we get [tex](33.95$, $40.45$)$[/tex] to 2 decimal places as a percentage.
Thus, we can say with 95% confidence that the proportion of all Americans that have cats as pets is between 33.95% and 40.45%.
3.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level, we can use the following formula:
[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]
where:
[tex]\item $n$[/tex] is the required sample size
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 95% confidence level
[tex]\item $E$[/tex] is the margin of error
[tex]$\hat{p}$[/tex] is the sample proportion
Substituting the given values, we have:
[tex]n=(\frac{1.96}{0.04} )^2[/tex]×[tex]0.1161[/tex][tex](1-0.1161)[/tex]
Rounding up to the nearest whole number, we get:
n=476
Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.04 and a 95% confidence level is 476.
4.To determine the sample size required to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level, we can use the following formula:
[tex]n=(\frac{z_{\alpha/2}}{E} )^2[/tex]×[tex]\hat{p}$(1-$\hat{p}$)[/tex]
where:
[tex]\item $n$[/tex] is the required sample size
[tex]\item $z_{\alpha/2}$[/tex] is the critical value of the standard normal distribution at the 90% confidence level, which is 1.645
[tex]\item $E$[/tex] is the margin of error, which is 0.05
[tex]$\hat{p}$[/tex] is the sample proportion, which is 21/126 = 0.1667
Substituting the given values, we have:
[tex]n=(\frac{1.645}{0.05} )^2[/tex]×[tex]0.1167[/tex][tex](1-0.1167)[/tex]
n=145.9198
Rounding up to the nearest whole number, the government official should take a sample size of 146 to achieve his desired margin of error.
Therefore, the required sample size to estimate the population proportion with a margin of error no larger than 0.05 and a 90% confidence level is 146.
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A packaging employee making $14
per hour can package 200 items
during that hour. The direct
material cost is $.40 per item. What
is the total direct cost of 1 item?
Answers
Answer: the total direct cost of one item is $0.47.
Step-by-step explanation:
If the packaging employee makes $14 per hour and can package 200 items in one hour, the direct labor cost per item would be:
Direct labor cost per item = Hourly wage rate / Number of items packaged per hour
Direct labor cost per item = $14 / 200
Direct labor cost per item = $0.07
The direct material cost per item is given as $0.40.
Now we can calculate the total direct cost per item:
Total direct cost per item = Direct labor cost per item + Direct material cost per item
Total direct cost per item = $0.07 + $0.40
Total direct cost per item = $0.47