I don't have a diagram, but here's the key info:
There is a sector of a circle:
The radius is 5.2
The arc length is 6π
You are not given the angle of the sector
Find the area of the sector, and give your answer in terms of pi I got 49π, let me know if I'm right ty. I've attached my working out
Answers
Answer:
Area of sector is 15.6π========================
Let the central angle be α.
Arc length equations = 2πr × α/360, if α in degreess = 2πr × α/2π = αr, if α in radiansWe have s = 6π and r = 5.2Find the central angles = αr6π = 5.2αα = 6π/5.2Area of sectorA = r²α/2, when α in radiansSubstitute the value of αA = 5.2² × 6π/5.2 × 1/2 = 5.2 × 3π = 15.6πNote: You could get it more easily if considered 360° = 2π in your calculations.
Answer:
[tex]\dfrac{78}{5} \pi = 15.6 \pi[/tex]
Step-by-step explanation:
Given values:
Radius (r) = 5.2Arc length = 6πAs the arc length is given in terms of pi, use the formulas where the angle is measured in radians.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the given values into the arc length formula to calculate the central angle (in radians):
[tex]\implies 6\pi=5.2\; \theta[/tex]
[tex]\implies \theta=\dfrac{6\pi}{5.2}[/tex]
[tex]\implies \theta=\dfrac{15}{13}\pi[/tex]
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Area of a sector of a circle}\\\\Area of a sector = $\dfrac12 r^2 \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]
Substitute the radius and the found angle into the formula and solve for area:
[tex]\begin{aligned}\implies \textsf{Area of the sector}&=\dfrac{1}{2}(5.2)^2 \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{1}{2}(27.04) \left(\dfrac{15}{13}\pi\right)\\\\&=(13.52) \left(\dfrac{15}{13}\pi\right)\\\\&=\dfrac{78}{5}\pi \\\\&=15.6 \pi\end{aligned}[/tex]
Related Questions
X
-1
0
1
3
Y
10
7
4
-2
find the slope and y-intercept
m =
b =
Answers
Slope of the line is - 3 and y-intercept is 6
Slope - intercept form of line is y = mx + b where m is slope of the line and b is intercept on y-axis
taking any two points from the table
A(-1 ,10) , B(0,7)
calculating slope by y₂-y₁/x₂-x₁
putting x₁ = -1 , x₂ = 10 and y₁ =0 , y₂=7
m = 7-10 / 0 + 1 = -3/1
m = -3
equation of line will be y = -3x + b
calculating intercept b by putting one point in equation of line
10 = -3(-1) + b
10 = 4 + b
b = 6
substituting value of b in the equation
y = -3x + 6 is our equation of line
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PLEASE HELP!!!
A line passes through the point (4, 8) and has a slope of 3/2.
Write an equation in slope-intercept form for this line.
Answers
Answer:
y=1.5x+2
Step-by-step explanation:
The equation for a line in slope-intercept form is written as y=mx+c where m is the slope and cis the y-intercept.
We know the slope is 3/2 or 1.5, so we can write
y=1.5x+c
We know the line contains the point (4,8), so we can sub this in to find c:
8=1.5(4)+c
8=6+c
c=2
Having found m and c, we can write the equation:
y=1.5x+2
Answer: [tex]\text{y}=\frac{3}{2}\text{x}+2\\\\[/tex]
This is the same as writing y = (3/2)x + 2
=====================================================
Work Shown:
[tex]\text{y}-\text{y}_1=\text{m}\left(\text{x}-\text{x}_1\right)\\\\\text{y}-8=\frac{3}{2}\left(\text{x}-4\right)\\\\\text{y}-8=\frac{3}{2}\text{x}+\frac{3}{2}(-4)\\\\\text{y}-8=\frac{3}{2}\text{x}-6\\\\\text{y}=\frac{3}{2}\text{x}-6+8\\\\\text{y}=\frac{3}{2}\text{x}+2\\\\[/tex]
I used point-slope form as the first step. The 'm' is the slope, and [tex](x_1,y_1) = (4,8)[/tex] is the point on the line.
The final step shows us the line has a y intercept of b = 2, which is at the location (0,2).
To graph this, draw a straight line through (0,2) and (4,8)
--------------
Check:
Plug x = 4 into the equation we found. We should arrive at y = 8.
[tex]\text{y}=\frac{3}{2}\text{x}+2\\\\\text{y}=\frac{3}{2}*4+2\\\\\text{y}=\frac{12}{2}+2\\\\\text{y}=6+2\\\\\text{y}=8\\\\[/tex]
This confirms (4,8) is indeed on this line and confirms the answer is correct.
You can also use graphing tools like Desmos or GeoGebra to quickly and visually confirm the answer.
The function B(t) 17,550(0.88) models the value of a boat. t years after it was purchased. Which statement is true about the value of the boat? A The value of the boat is increasing by 12% each year. B. The value of the boat is increasing by 88% each year. C. The value of the boat is decreasing by 12% each yearD. The value of the boat is decreasing by 88% each year.
Answers
Answer:
Explanation:
The function that models the value of the boat is given as:
[tex]B\mleft(t\mright)=17,550\mleft(0.88\mright)^t[/tex]We can rewrite this as:
[tex]B(t)=17,550(1-0.12)^t[/tex]This is in the form of an exponential decay
Shane bought 36 gallons of gas this week this amount is 6 gallons more than twice the amount of gas he bought last week how many gallons of gas in Shane by last week
Answers
so, she bought 15 gallons of gas last week
Explanation
Step 1
Let
36 gallons this week
x= number of gallons of gas Shane bought las week
this amount is 6 gallons more than twice the amount of gas he bought last week , then
[tex]36=2x+6[/tex]Step 2
solve for x
[tex]\begin{gathered} 36=2x+6 \\ \text{subtract 6 in both sides} \\ 36-6=2x+6-6 \\ 30=2x \\ \text{divide each side by 2} \\ \frac{30}{2}=\frac{2x}{2} \\ x=15 \end{gathered}[/tex]so, she bought 15 gallons of gas last week
A school assembly had 40 students in attendance, and 80% of them were first-graders. How many first-
graders were at the assembly?
Answers
Answer: 32 first graders were at the assembly
Step-by-step explanation:
80% of 40 can be written as 80% × 40
= 80/100 × 40
= 32
Thus, 80% of 40 is 32.
which angle is congruent to
Answers
The angle congruent to ∠CGD is the angle ∠AGF as they are vertical angles.
Danielle is trying to solve the equation 25^x+3=176 Explain in detail how Danielle should solve this problem. Then solve it step by step showing all your work and tell Danielle what the answer should be.
Answers
Given:
Equation is:
[tex]\begin{gathered} 25^x+3=176 \\ \end{gathered}[/tex]Find-:
Solve the equation
Explanation-:
Simplify the equation then,
[tex]\begin{gathered} 25^x+3=176 \\ \\ 25^x=176-3 \\ \\ 25^x=173 \\ \\ 5^{2x}=173 \end{gathered}[/tex]Taking ln both sides then,
[tex]\ln5^{2x}=\ln173[/tex]Use logarithmic property
[tex]\ln a^b=b\ln a[/tex]Then the value is:
[tex]\begin{gathered} \ln5^{2x}=\ln173 \\ \\ 2x\ln5=\ln173 \\ \\ 2x=\frac{\ln173}{\ln5} \\ \\ x=\frac{\ln173}{2\ln5} \end{gathered}[/tex]The value of "x" is:
[tex]\begin{gathered} x=\frac{\ln173}{2\ln5} \\ \\ x=\frac{5.1533}{2\times1.6094} \\ \\ x=\frac{5.1533}{3.2189} \\ \\ x=1.601 \end{gathered}[/tex]So, the value of "x" is 1.601
There are 16 ounces in 1 lb juwan is mailing a package that weighs 10 lb he wants to know the weights of the package and the ounces
Answers
Juwan is mailing a package that weighs 10lb
for every 1 lb you have 16 ounces inside the package
if 1 lb ------- 16 ounces
10lb ------- x ounces
reason why we have x ounces is because we dont know how many ounces 10 lb we give us
cross multiplication
1 * x = 10 x 16
x = 10 x 16
x = 160 ounces
10lb we give us a total of 160 ounces
therefore, there are 160 ounces in the 10 lb package juwan is mailing
The answer is 160 ounces
I need the answer! I snap a pic to try n get it but no answer lol someone help!!! I’m on the clock
Answers
The given equation is
x^2 + 7x = 8
By subtracting 8 from both sides, it becomes
x^2 + 7x - 8 = 0
We would find two terms such that their sum or difference is 7x and the product is - 8x^2. The terms are - x and 8x. Replacing 7x with - x and 8x, we have
x^2 - x + 8x - 8 = 0
By factorising, we have
x(x - 1) + 8(x - 1) = 0
Since x - 1 is common, it becomes
(x + 8)(x - 1) = 0
x + 8 = 0 or x - 1 = 0
x = - 8 or x = 1
Option C is correct
9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
Answers
Answer:
Step-by-step explanation:
For some of the questions there are multiple answers that could be correct. Here’s some of the possible answers. Hope that helps!
a. 3 & 5
b. 3 & 4
c. 4 & 5
d. 4 & 5
e. 1 & 2
Brianna is buying a house for $210,000. She plans to make a 14% down payment. Closing costs include $650 for 6 months of homeowners insurance, $600 for 6 months of property tax, $125 for the title fee, and $350 in transaction fees. Brianna also agreed to pay two points in exchange for a 0.5% reduction in interest rate. Determine the amount of money Brianna needs to cover closing costs. Round your answer to the nearest cent.
Answers
To change a fraction into a decimal do you, divide the denominator by the numerator.
Answers
To change a fraction into a decimal do you, divide the denominator by the numerator. FALSE. You should divide the numerator by the denominator (the top by the bottom).
Answer:
No.
You divide the numerator by the denominator.
Step-by-step explanation:
No.
You divide the numerator by the denominator.
For example, 8/2 = 8 divided by 2 = 4
1/5 = 1 divided by 5 = 0.2
4. Maliyah has 3 54 cups of dough for baking bread. Each loaf of bread requires96 of a cup of dough. What is the exact number of loaves that Maliyah canmake from the dough?
Answers
Write 3 3/4 as a fraction:
[tex]3\frac{3}{4}=3+\frac{3}{4}=\frac{12}{4}+\frac{3}{4}=\frac{15}{4}[/tex]Use conversion factor to find the exact number of loaves that Maliyah can make with 3 3/4 (15/4) cups of dough.
1 loaf requires 1/6 of cup of dough.
[tex]\frac{15}{4}\text{cups}\cdot\frac{1\text{loaf}}{\frac{1}{6}\text{cup}}=\frac{15}{4}\text{cups}\cdot6\frac{\text{loaf}}{\text{cup}}=\frac{90}{4}\text{loaves}=\frac{45}{2}\text{loaves}[/tex]You can write the answer as a mixed number:
[tex]\frac{45}{2}=\frac{44}{2}+\frac{1}{2}=22\frac{1}{2}[/tex]Then, with 3 3/4 cups of dough Maliyah can make 22 1/2 (45/2) loaves of bread.
Which set of ordered pairs does not represent a function?
O {(6, 7), (-4,-5), (-1, 7), (-9, -7)}
O{(-6, 1), (-9, -6), (6, 7), (1, -8)}
O {(5,9), (7,2), (1,6), (-6,9)}
O {(-1, 1), (4, -6), (-3,0), (-3, 8)}
Answers
Answer:
it's 4
Step-by-step explanation:
#4 because we can see how x repeats its self 2 times such as (-3,0) and (-3,8)
It takes `20` tomato slices to make `2` of Ivan's pizzas.
How many does it take to make 10 pizzas?
Answers
Answer:
100
Step-by-step explanation:
If you need 20 for every 2 pizzas, that means you would need 10 for 1 pizza. (tomato's) 10 x (pizzas)10 = 100
what is one important difference between a normal distribution and a t distribution? group of answer choices the t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
Answers
The t distribution has heavier tails than a normal distribution. the normal distribution has heavier tails than a t distribution. the two distributions have similar tails, it's just that the t distribution can be skewed, while the normal distribution may not be skewed.
There are a few important differences between a normal distribution and a t distribution. First, the t distribution has heavier tails than the normal distribution. This means that there is a greater chance of observing extreme values in the t distribution. Second, the t distribution can be skewed, while the normal distribution may not be. This means that the t distribution is more likely to have values that are not evenly distributed around the mean. Finally, the t distribution is more variable than the normal distribution. This means that the t distribution is more likely to have values that are far from the mean.
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Over the course of 5 hours, the temperature dropped 10°C.
The temperature dropped the same number of degrees each hour.
What operation represents
the change in temperature
each hour?
Answers
Using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operations which represent this is 10/5 = 2°C.
What are mathematical operations?Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."
The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.
In mathematics, addition, subtraction, multiplication, division, and modular forms are the five basic operations.
So, the operation that represents the change in temperature:
Time taken is 5 hours.
The temperature drop is 10°C.
The same amount of temperature in each hour.
Then, the operation will be:
10/5 = 2°C
Therefore, using mathematical operations, we know that the drop in temperature in each hour is 2°C, and the operation which represents this is 10/5 = 2°C.
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In two days, Mariposa drinks seven 16-ounce
bottles of water. She drinks the water in 4 equal
servings. How many ounces of water does
Mariposa drink in each serving?
Answers
Answer:
28 oz
Step-by-step explanation:
First, find the total amount of water that was drank.
7 × 16 oz = 112 oz total
Then, divide this by 4 to get the amount per one serving.
112 oz / 4 = 28 oz per serving
On a coordinate plane, PQ is translated 3 units up and 3 units to the right to create P'Q'. Line p is drawn through P and P', and Line q is drawn through Q and Q'. Which
statement about Lines p and q is true?
O Lines p and q are parallel.
O Lines p and q are perpendicular.
O Lines p and a have the same x-intercept.
Lines p and a have the same y-intercept.
Answers
The correct statement about line p and q is, Lines p and q are parallel.
What is translation of graph?
Any movement of the graph either horizontally or vertically parallel to the -axis is referred to as a translation.
In mathematics, a translation is the movement of a shape left, right, up, or down. The translated shapes are identical to the original ones in size, indicating that they are congruent. They simply changed positions in one or more directions. The shape is unchanged because it is simply being transferred from one location to another.
Let, On a coordinate plane, PQ is translated 3 units up and 3 units to the right to create P'Q'. Line p is drawn through P and P', and Line q is drawn through Q and Q'.
There is no change in the shape or size of p and q.
Hence, lines p and q are parallel.
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is shape A congruent to shape 82BA
Answers
Solution
For this case the answer would be:
yes
And the reason is because we have the same shape and with the smae structure so then are congruent
You have 26 video games in your collection.Some are for the X-Box system and someare for PlayStation. You have 4 fewerPlaystation games than X-Box games.Write a variable expression to model thesituation. How many of each type of gamedo you have?
Answers
Total number of videogames = 26
PLaystation games = y
x box games = x
x+y=26
You have 4 fewer (-4) PlayStation games than X-Box games.
y = x-4
The system is:
x+y=26 (a)
y = x-4 (b)
Puy (b) into (a)
x+ (x-4) =26
x+x-4 =26
Solve for x:
2x= 26+4
2x=30
x=30/2
x=15 (c)
(c) into (b)
y=15-4
y=11
X box games = 15
Playstation games = 11
2102 subscript 3 + 1001 subscript 3
Answers
Answer:
[tex]10110_3[/tex]Explanation:
Given the sum:
[tex]2102_3+1001_3[/tex]The sum (in base 3) is evaluated below:
The answer is 10110 (in base 3).
Write the equation of the line that passes through the points (8, -1) and (2, -5) inpoint-slope form.
Answers
First, we find the slope using the given points and the formula below
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-(-1)}{2-8}=\frac{-5+1}{-6}=\frac{-4}{-6}=\frac{2}{3}[/tex]Then, we use the point-slope formula to find the equation
[tex]y-y_1=m(x-x_1)_{}[/tex]Let's replace the point (8, -1) and the slope 2/3.
[tex]\begin{gathered} y-(-1)=\frac{2}{3}(x-8) \\ y+1=\frac{2}{3}x-\frac{16}{3} \\ y=\frac{2}{3}x-\frac{16}{3}-1 \\ y=\frac{2}{3}x+\frac{-16-3}{3} \\ y=\frac{2}{3}x-\frac{19}{3} \end{gathered}[/tex]Hence, the equation in point-slope form is[tex]y+1=\frac{2}{3}(x-8)[/tex]This relation is a function:{(5,-2), (6,-2),(7,-2), (8,-2)}A.TrueB.False
Answers
For the following exercise, write a formula for the function g that results when the graph of a given toolkit function is transformed as described.
The graph of f(x)=1/x is vertically stretched by a factor of 5 units, then shifted to the right 2 units and up 6 units.
g(x)=
Answers
The required transformed function is given by, g(x) = 5/(x-2) + 6
Given the parent function is, f(x) = 1/x
Now if we vertically stretched the function by a factor 5 units then the function becomes,
g(x) = 5/x
Again if we shifted to the right to 2 units then the function becomes,
g(x) = 5/(x-2)
Further if we shift up to 6 units then the function transformed to,
g(x) = 5/(x-2) + 6
Hence the ultimate transformed function is, g(x) = 5/(x-2) + 6.
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Rendering math...Five adults and four children go to the museum. They pay a total of $19 for admission. Theadult admission fee is three times the fee for a child. If an adult ticket costs x dollars and a ticket for a childcosts y dollars, which of the following statements are correct? Select all that apply.One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtainedThe adult fee is 3 dollars.The ticket for a child costs 2 dollars.5One of the equations to be used in solving the problem is x=3y.After a possible substitution, 53y+4y=19 can be obtained.One of the equations to be used in solving the problem is y=3x.After a possible substitution, 53x+4x=19can be obtained.The adult fee is 3 dollars.English (US)ere to searchE1515 +G
Answers
Let be "x" the cost in dollars of an adult ticket and "y" the cost in dollars of a child ticket.
You know that a 5 adults and 4 children went to the museum and the total cost was $19. Therefore, you can write the following equation:
[tex]5x+4y=19[/tex]The word "Three times" indicates a multiplication by 3. Therefore, "The
adult admission fee is three times the fee for a child" can be written as:
[tex]x=3y[/tex]In order to find the values of "x" and "y", substitute the second equation into the first one and solve for "y":
[tex]\begin{gathered} 5(3y)+4y=19 \\ 15y+4y=19 \\ 19y=19 \\ y=1 \end{gathered}[/tex]To find "x", substitute the value of "y" into the second equation. Then:
[tex]\begin{gathered} x=3(1) \\ x=3 \end{gathered}[/tex]Therefore, you can identify that the correct options are:
- One of the equations to be used in solving the problem is :
[tex]x=3y[/tex]- The adult fee is 3 dollars.
A medical clinic has a crew of 5, two of which have been infected with a virus althoughthey show no symptoms. If you select two crew members for a task, what is the probability that there is at least one infected person in group assigned for the task.
Answers
P(at least 1 infected person) = 0.7
Explanation:Note that:
Probability = (Number of possible outcomes) / (Number of total outcomes)
The crew members = 5
Number of infected crew members = 2
Number of uninfected crew members = 3
We want to select two crew members for a task out of 5
Number of total outcomes = 5C2 (Selecting 2 out of 5)
Note that:
[tex]nCr=\frac{n!}{(n-r)!r!}[/tex][tex]\begin{gathered} 5C2=\frac{5!}{(5-2)!2!} \\ \\ 5C2=\frac{5!}{3!2!} \\ \\ 5C2=\frac{5\times4\times\cancel{3!}}{\cancel{3!}\times(2\times1)} \\ \\ 5C2=\frac{20}{2} \\ \\ 5C2=10 \end{gathered}[/tex]Number of total outcomes = 10
That is, there are 10 ways of selecting 2 crew members from 5
Number of ways of selecting 1 infected person means how we can select two people out of 5 such that 1 one of them will be infected. This means that we will select 1 from the two infected persons, and select the second one from the 3 uninfected persons
Number of ways of selecting 1 infected persons = 2C1 x 3C1
[tex]\begin{gathered} 2C1=\frac{2!}{(2-1)!1!}=\frac{2!}{1!1!}=\frac{2\times1}{1\times1} \\ 2C1=2 \\ \\ 3C1=\frac{3!}{(3-1)!1!}=\frac{3!}{2!1!}=\frac{3\times2\times1}{2\times1\times1}=\frac{6}{2} \\ 3C1=3 \end{gathered}[/tex]Number of ways of selecting 1 infected persons = 2 x 3
Number of ways of selecting 1 infected persons = 6
Number of ways of selecting 2 infected persons = 2C2
[tex]2C2=\frac{2!}{(2-2)!2!}=\frac{2!}{2!}=1[/tex]Number of ways of selecting 2 infected persons = 1 way
Probability of selecting 1 infected person = 6/10 = 0.6
Probability of selecting 2 infected person = 1/10 = 0.1
P(at least 1 infected person) = P(1 infected person) + P(2 infected persons)
P(at least 1 infected person) = 0.6 + 0.1
P(at least 1 infected person) = 0.7
A local produce stand has eight pumpkins on display the diameters of the pumpkin in inches are given in the table
Answers
SOLUTION
We will be pairing the pumpkins as follows
AB, CD, EF and GH
For AB, we have
[tex]\begin{gathered} 16\frac{1}{2}\div5\frac{1}{2} \\ \frac{33}{2}\div\frac{11}{2} \\ \frac{33}{2}\times\frac{2}{11} \\ =\frac{33}{11} \\ =3 \end{gathered}[/tex]Hence B is 3 times larger than A
For C and D, we have
[tex]\begin{gathered} 41\frac{1}{4}\div8\frac{1}{4} \\ \frac{165}{4}\div\frac{33}{4} \\ \frac{165}{4}\times\frac{4}{33} \\ =\frac{165}{33} \\ =5 \end{gathered}[/tex]Hence D is 5 times larger than C
E and F, we have
[tex]\begin{gathered} 13\frac{3}{4}\div3 \\ \frac{55}{4}\div\frac{3}{1} \\ \frac{55}{4}\times\frac{1}{3} \\ =\frac{55}{12} \\ =4.5833333333 \\ =4.583 \end{gathered}[/tex]Hence E is 4.583 times larger than F
And the last G and H, we have
[tex]\begin{gathered} 22\frac{3}{4}\div10\frac{1}{2} \\ \frac{91}{4}\div\frac{21}{2} \\ \frac{91}{4}\times\frac{2}{21} \\ =\frac{91}{21\times2} \\ =\frac{91}{42} \\ =2.167 \end{gathered}[/tex]Hence G is 2.167 times larger than H
How do I find the feet in a 9 inch board
Answers
Answer:
3/4 of a foot.
Step-by-step explanation:
In order to find how many feet are in 9 inches, we simply divide 9 by 12. We use the number 12, because that is how many inches are in a foot. 9 divided by 12 = 0.75 or 3/4 of a foot.
May I have Brainliest please? I am so close to getting my next ranking! I just need 3 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
The mean of the data set shown in the table is 57. What is the mean absolute deviation?699.512
Answers
To find the mean absolute deviation of the data set, first, you have to calculate the absolute value of the difference between each value of the data set and the mean.
The data set is
[tex]\mleft\lbrace6,9,9.5,12\mright\rbrace[/tex]The mean of the data set is 57