Answer: the length of an arc intercepted by an angle in a circle is L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.
Using this formula, we can find the length of the arc intercepted by an angle of π radians in a circle with radius 7:
L = rθ = 7π/1 = 7π
Therefore, the length of the arc is 7π units. This is already in its simplest form since π is a constant that cannot be simplified further.
Step-by-step explanation:
please help me on this question
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
If 4x-3=5, what is the value of x
Answer: the answer is two :)
Step-by-step explanation:
4x=5+3
4x=8
x= 8/4
x=2
Please help me answer these two questions!!!
in the alphabetical order A-B SO I THINK IT IS 10
A boxplot for a set of 80 scores is given below.
How many scores are represented in the blue section of the boxplot?
Answer: The number of scores represented in the blue section of the boxplot is 12.
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.
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.
18 students decide they don't want to be rescued and want to continue to live in the jungle if this represents 40 of the students how many students want to be rescued. The answer is 45 right?
Mel's cat eats 3/4 of a bag of cat food each month. How many
bags of cat food does Mel's cat eat in 10 months? Show your
work
Step-by-step explanation:
3/4 bag / months * 10 month = 30/ 4 bags = 7 1/2 bags
Could someone help answer Number 22 please
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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Write a rule for the translation.
(x-1, y + 2)
(x-2, y + 1)
(x+2, y - 1)
(x+1, y-2)
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:
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:
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
50pts!!!!!!!!!!!!!!!!!
she has a gross income of $105500
. If she pays $26982
in income tax and $2110
for the Medicare levy, what is her net income?
Answer:
Step-by-step explanation:
Claro que sí. El ingreso neto es el ingreso que queda después de restar los impuestos y otros gastos del ingreso bruto. La fórmula del ingreso neto es:
Ingreso neto = Ingreso bruto – Impuestos – Comisiones – Intereses – Créditos – Otros Gastos
En tu caso, el ingreso bruto es $105500 y los impuestos son $26982 por el impuesto sobre la renta y $2110 por el impuesto de Medicare. No sé si tienes otros gastos que debas restar, pero si no los tienes, entonces el ingreso neto sería:
Ingreso neto = $105500 - $26982 - $2110 Ingreso neto = $77408
Espero que te haya servido de ayuda.
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.)
(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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Pls help !! Find the equation of a line parallel to that passes y= 4/3x+4 through the point (3,-7).
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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helo I don't understand show work please
Answer:
a = 4.5 , b = 7.5
Step-by-step explanation:
using Pythagoras' identity in the two right triangle
outer right triangle
b² + 10² = (8 + a)² = 64 + 16a + a² → (1)
inner right triangle
a² + 6² = b² → (2)
substitute b² = a² + 6² = a² + 36 into (1)
a² + 36 + 100 = 64 + 16a + a² ( subtract a² from both sides )
136 = 64 + 16a ( subtract 64 from both sides )
72 = 16a ( divide both sides by 16 )
4.5 = a
----------------------------------------
substitute a = 4.5 into (2)
4.5² + 6² = b² , that is
20.25 + 36 = b²
56.25 = b² ( take square root of both sides )
[tex]\sqrt{56.25}[/tex] = b , then
b = 7.5
y = 3x + 1
y = 8x - 4
with solution pls, i would rlly appreciate it
Answer:
si y = a 55 es 5.7
Step-by-step explanation:
la otra es 3.9
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 =
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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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
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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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
i need help to do spiral review 5 on lesson 9.7 pls help
Answer: wheres the page/diagram
Step-by-step explanation:
I have a queston can you answer it pls
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
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
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 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
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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Solve the expression 7 + (one-fifth x 18 – 3) using the order of operations.
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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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.)
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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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.
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
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
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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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?
Answer: Bob 3 Hours Jack 2 Hours
Step-by-step explanation:
Help, solve this pls
Which set has an average of 8?
A) A
B) B
C) A and B
D) none of the above
Answer:
IT IS B hope this helped
Step-by-step explanation:
Find the centre and radius of 364+28y+y^2+x^2=-26x
Step-by-step explanation:
hope it will help you , and give some clue to do typical qno..
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
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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