The dot plot shows the number of books lent by a school library during a 10-day period.
What was the mean absolute deviation of the number of books?
F. 0
G.
H.
J.
1.04
1.96
..
23 24 25 26 27 28 29 30 31 32 33
2.19
Answers
The mean absolute deviation of the number of books is 1.84
How to determine the mean absolute deviation?The dot plot of the number of books is in the attached figure.
From the figure, we have:
x f
1 1
2 2
3 2
4 3
5 1
6 2
7 3
8 1
Start by calculating the mean using:
[tex]\bar x= \frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x= \frac{1 * 1 + 2 * 2 + 2 * 3 + 3 * 4 + 1 * 5 + 2 * 6 + 3 *7 + 1 * 8}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the sum and products
[tex]\bar x= \frac{69}{15}[/tex]
Divide
[tex]\bar x= 4.6[/tex]
The mean absolute deviation is then calculated as:
[tex]|\bar x| = \frac{\sum f|x - \bar x|}{\sum f}[/tex]
So, we have:
[tex]|\bar x|= \frac{1 * |1 -4.6|+ 2 * |2 -4.6| + 2 * |3 -4.6|+ 3 * |4 -4.6|+ 1 *| 5 -4.6|+ 2 * |6 -4.6|+ 3 *|7 -4.6|+ 1 * |8-4.6|}{1 +2+2+3+1+2+3+1}[/tex]
Evaluate the absolute difference
[tex]|\bar x|= \frac{1 * 3.6+ 2 * 2.6 + 2 * 1.6+ 3 * 0.6+ 1 *0.4+ 2 * 1.4+ 3 *2.4+ 1 * 3.4}{15}[/tex]
Evaluate the sum of products
[tex]|\bar x|= \frac{27.6}{15}[/tex]
Divide
[tex]|\bar x|= 1.84[/tex]
Hence, the mean absolute deviation of the number of books is 1.84
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Related Questions
Evaluate each expression for r=9 n t=14 enter in your numerical answer
Answers
Answer:
1764
Step-by-step explanation:
[tex]from \: the \: question \: rt {}^{2} \\ were \: r =9 \\ and \: t = 14 \\ rt {}^{2} = 9 \times (14) {}^{2} = 9 \times 196 = 1764[/tex]
Hii!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer.}\circ \leftharpoonup[/tex]
1764
[tex]\rightsquigarrow\circ\boldsymbol{Explanation.}\circ\leftharpoonup[/tex]
Stick in the values: 9 for r and 14 for t, and simplify.
[tex]\twoheadrightarrow\sf 9\cdot14^2}[/tex]
[tex]\bullet[/tex] Square 14 first
[tex]\twoheadrightarrow\sf 9\cdot196}[/tex]
[tex]\bullet[/tex] Multiply the numbers
[tex]\twoheadrightarrow\sf 1764}[/tex]
[tex]\bullet[/tex] Great job! We found the answer
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
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PLS HELP ME WITH THIS PROBLEM
Answers
[tex]y=200(0.5)^2^t[/tex] is Decay
[tex]y=\frac{1}{2}(2.5)^\frac{t}{6}[/tex] is Growth
[tex]y=(0.65)^\frac{t}{4}[/tex] is Decay
Ayuda por favor
Sea ABC un triángulo equilátero de la 2a y altura h
como se muestra en la figura. Si se traza una línea
horizontal que divide la altura del triángulo en dos
partes iguales formando 2 figuras geométricas de
igual altura, entonces el cociente entre el área del
triángulo AMN y el cuadrilátero BMNC es:
Answers
A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.
¿Cómo determinar la medida de un lado de un triángulo desconocido?
En este problema tenemos un sistema formado por dos triángulos similares, la semejanza entre los dos triángulos se debe a la colinealidad entre los segmentos de línea AP' (triángulo pequeño) y AP'' (triángulo grande), así como de los lados AM y AB, así como los lados AN y AC, así como los mismos ángulos en la misma distribución. (Semejanza Lado - Ángulo - Lado)
En consecuencia, obtenemos las siguientes proporciones:
AP'/AP'' = MN/BC = 1/2 (1)
Finalmente, la proporción entre el triángulo AMN y el cuadrilátero BMNC es:
[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)}{\frac{1}{2}\cdot (2\cdot a) \cdot h - \frac{1}{2}\cdot a \cdot \left(\frac{1}{2}\cdot h \right)} = \frac{\frac{1}{4}\cdot a\cdot h }{a\cdot h - \frac{1}{4}\cdot a \cdot h }[/tex]
[tex]\frac{AMN}{ABC - AMN} = \frac{\frac{1}{4} }{\frac{3}{4} } = \frac{1}{3}[/tex]
A partir de la definición de razón y la teoría de semejanza entre triángulos, la razón del área del triángulo AMN y el área del cuadrilátero BMNC es equivalente a 1/3.
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The inverse of the function f(x) =
f(x) = x + 10 is shown.
h(x) = 2x-0
What is the missing value?
0 1
05
O 10
O 20
Answers
Answer: 20
Step-by-step explanation:
Let [tex]f(y)=x[/tex]
[tex]x=\frac{1}{2}y+10\\\\x-10=\frac{1}{2}y\\\\y=h(x)=2x-\boxed{20}[/tex]
Express 10/4 as a mixed fraction
Answers
Hey there!
10/4
≈ 10 ÷ 2 / 4 ÷ 2
≈ 5/2
≈ 2 1/2
Therefore, your answer should be:
2 1/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
find the value of x? thanks
Answers
Answer:
x=1
Step-by-step explanation:
20(3x-3/5) = 20(2x-2/4)
12x-12= 10x-10
12x-10x =12-10
x= 1
Answer:
Step-by-step explanation:
Solution
3x - 3 2x - 2
===== = ====== Cross Multiply
5 4
4(3x - 3) = 5(2x - 2) Remove the brackets. Distributive Property
12x - 12 = 10x - 10 Subtract 10 x from both sides
12x-10x - 12 = 10x-10x - 10 Combine
2x - 12 = - 10 Add 12 to both sides
2x-12+12 = -10 + 12 Combine
2x = 2 Divide by 2
2x/2 = 2/2
Answer
x = 1
[tex]3.135x 789[/tex]
Answers
Answer:
Step-by-step explanation:
How do you write 16/25 as a percentage?
Answers
Answer:
64%
Step-by-step explanation:
Convert 16/25 to Percentage by Converting to Decimal
With this method, we first need to divide the numerator by the denominator:
16 ÷ 25 = 0.64
Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:
0.64 × 100 = 64%
We can see that this gives us the exact same answer as the first method: 16/25 as a percentage is 64%.
Note, the final percentage is rounded to 2 decimal places to make the answer simple to read and understand.
A parallelogram has an area of 160 square meters and a height of 4 meters. What is the length of the base of the parallelogram?
Answers
The length of the base is 40 meters
How to determine the length of the base?We have:
Area= 160 square meters
Height = 4 meters
The area is calculated using:
Area = Base * Height
So, we have:
160 = Base * 4
Divide both sides by 4
Base = 40
Hence, the length of the base is 40 meters
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Can someone help me? I’ll give Brainliest to whoever answers correctly first
Answers
Answer:Angle C=68 degrees
Step-by-step explanation:
The solution is in the
what is the value of the rational expression below when is equal to 5?
Answers
Answer:
[tex]\boxed {C. -2}[/tex]
Step-by-step explanation:
[tex]\textsf {Substitute x = 5 in the expression :}[/tex]
[tex]\longrightarrow \mathsf{\frac{15 - x}{x - 10}}[/tex]
[tex]\longrightarrow \mathsf{\frac{15 - 5}{5 - 10}}[/tex]
[tex]\longrightarrow \mathsf{\frac{10}{-5}}[/tex]
[tex]\longrightarrow \mathsf{-2}[/tex]
for the function f(x)=5(x+2) find f (2)
Answers
Answer:
20
Step-by-step explanation:
To calculate f(2), just replace x in the equation of f(x) with 2:
[tex]f(x) = 5(x + 2)\\\\f(2) = 5(2+2)\\\\f(2) = 5(4)\\\\f(2) = 20[/tex]
A
Find the value of x.
6
X
B
D
x = [?]
8
4
C
Answers
Answer:
x = 3
Step-by-step explanation:
8/2 = 4
6/2 = 3
x = 3
Johann is 60 and Chad is 34 years younger. How many years
ago was Johann three times as old as Chad?
Answers
Answer: 6 years ago
Step-by-step explanation: Since Chad is 34 years younger than Johann, Chad is currently 26. 60 divided by 3 (since the question says three times) is 20, and 26 (Chad’s current age) minus 20 is 6. So, 6 years is the correct answer.
Answer:
21 years
Step-by-step explanation:
Let x represent the number of years since Johann was 3 times Chad's age. The given relation can be written as the equation ...
(60 -x) = 3(34 -x)
__
Solving this, we have ...
60 -x = 102 -3x . . . . . eliminate parentheses
2x = 42 . . . . . . . . . add 3x-60
x = 21 . . . . . . . . .divide by 2
21 years ago, Johann was 3 times as old as Chad.
_____
Additional comments
Their ages then were 39 and 13.
If you recognize the age difference is 60-34 = 26 years, and that J will be 3×C when C's age is half that difference, then you know C was 13 at that time. That was 34-13 = 21 years ago.
Given: m∠ELG = 124°
Prove: x = 28
3 lines are shown. A line with points D, L, G intersects a line with points E, L, H at point L. Another line extends from point L to point F between angle E L G. Angle D L E is (2 x) degrees.
Answers
Answer:
By using opposite angles of two intersecting straight lines are congruent we proved that x = 28°
Step-by-step explanation:
Opposite angles of two intersecting straight lines are congruent
Therefore ∠DLE = ∠GLH
Here ∠DLE = 2x = ∠GLH
Sum of all angles on a straight line is 180°
Therefore ∠ELG + ∠GLH = 180°
Given that ∠ELG = 124°
124° + ∠GLH = 180°
124° + 2x = 180°
2x = 180° - 124°
2x = 56°
x = 28°
hence proved that x = 28°
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Which Graph Represents A function ?
NEED ANSWER ASAP !!!!
Answers
Answer:
The very last one is a function
Step-by-step explanation:
The last one is a function because there are no y values that repeat. For example, If the points on one graph are like this; (1, 3) (2, 3); then it cannot be a function, the y values cannot repeat if it is a function.
To make things easier, just try to imagine vertical drawing lines through each point in every graph, if this imaginary vertical line passes more than one point in any graph, then that graph is not a function.
I hope this helps!! :D
Answer:
The last graph represents a function.
Explanation:
A function cannot be one-to-many, i.e., one value of x cannot produce multiple values of y.
In the first graph, when x = 1, y = 3 and y= -2, so it is not a function.
In the second graph, when x = 2, y = 2 and y = -2, so it's not a function.
In the third graph, when x = -3, y = 2 and y = -2, so it's not a function.
∴ In all the graphs except the last, single values of x give multiple values of y on the graph, so they are not functions.
144 to the 1/2 power
Answers
Answer:
(144)^1/2
(12^2)^1/2
12 is the answers
Step-by-step explanation:
please mark me as brainlest
Answer:
12
Step-by-step explanation:
Rewrite 144 as 12²
(12²)^1/2
Apply the power rule and multiply exponents, [tex](a^m)^n=a^{mn}[/tex].
12^2(1/2)
Cancel the common factor of 2.
Cancel the common factor.
Rewrite the expression
12^1
Evaluate the exponent.
12
If two triangles are congruent, which of the following statements must be true? Check all that apply. A. The corresponding sides of the triangles are congruent. B. The triangles have the same shape and size. C. The corresponding angles of the triangles are congruent. D. The triangles have the same shape, but not the same size. If two triangles are congruent , which of the following statements must be true ? Check all that apply . A. The corresponding sides of the triangles are congruent . B. The triangles have the same shape and size . C. The corresponding angles of the triangles are congruent . D. The triangles have the same shape , but not the same size.
Answers
Answer:
Step-by-step explanation:
A. Correct
B. Correct
C. Correct
D. False
2.
A. Correct
B. Correct
C. Correct
D. False
Hope I helped!
An entertainment company is opening a theme park in a nearby city. They are in the process of designing the theatre where a water show will take place. The following design is already under construction and will house the dolphins that perform in the show:
Main Show Tank Calculation:
The main show tank has a radius of 70 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally.) What is the volume of the quarter-sphere shaped tank? Round your answer to the nearest whole number. You must explain your answer using words, and you must show all work and calculations to receive credit.
Holding Tank Calculations:
The holding tanks are congruent. Each is in the shape of a cylinder that has been cut in half vertically. The bottom of each tank is a curved surface and the top of the pool is a flat surface. What is the volume of both tanks if the radius of tank #1 is 35 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit.
You must show all steps and provide any evidence needed in your solution to receive full credit.
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from above answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answers
1) The volume of the quarter sphere shaped tank is; V = 20510 ft³
2) The volume of the smaller mock-up tank is; 230790 ft³
How to find the area and volume of a composite shape?1) The volume of the quarter sphere shaped tank is;
V = ⁴/₃πr²
V = ⁴/₃π * 70 * 70
V = 20510 ft³
2) We multiply dimensions by 2 not radius to make 1 whole cylinder. Thus
r = 35 feet remains the same as radius can only be half of a joined circle,
Since vertically cut, we have;
h = 125 * 2 = 250ft
Let's find the Area;
A = πr²
A = π * 35 * 35
A = Surface Area = 3846.5 ft²
Volume = Surface area * h
V = 3846.5 * 120 = 461580 combined.
For each; V = 461580/2 = 230790 ft³
3) Volume of smaller mock-up tank is;
V = (1/6) * 20510
V = 3418.33 ft³
4) 5/6 * 20510 = 17091.66 ft³
For the larger tank the increase is 17092 ft rounded up (0.165 value) of that of the smaller mock up tank. Therefore percentage is 1/6 = 16.67% and 5/6 = 83.33%
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Complete the statements below with the process used to achieve steps 1-4.
Select the correct answer from each drop-down menu.
Consider the equation below.
-2(5x+8)=14+6x
The equation was solved using the following steps.
Answers
The statements can be completed by using the following :
1) -2 is multiplied with (5x+8)
2) transposing of numeral values and variable values
3) The numerical values are taken one side and added to each other
4) 30 is divided by -16
5) The numerator and denominator are cancelled to the lowest possible value
x= -15/8
Given: -2(5x+8)=14+6x
and steps for solving them have also been given
In the first step, -2 is multiplied with (5x+8) and we get
-10x -16 = 14 +6x
In step 2, transposing of numeral values and variable values is done and we get -16x - 16 = 14
In step 3,
The numerical values are taken one side and added to each other and we get -16x=30
In step 4, 30 is divided by -16
In step 5, they are cancelled to the lowest possible value and we get
x= -15/8
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he area of a circle is 153.86 square meters. What is the diameter of the circle? Use 3.14 for π.
Answers
Answer:
14m
Step-by-step explanation:
Area = πr²
A = 153.86m²
153.86 = 3.14 *r²
r² = 153.86/3.14
r = √49
r = 7
d = 2r
d = 2*7
d = 14
If x is 0 what is 1/3 times as large
Answers
Answer:
0
Step-by-step explanation:0 times anything is still 0
Help please I need it now!
Answers
Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]
Step-by-step explanation:
This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].
The sequence has 7 terms, so the sigma notation is:
[tex]\sum^{7}_{n=1} (-2+9n)[/tex]
Solve for x : 2/5x -9 < 3/5x+3
X < 60
X > -60
-x < -60
-x < 60
Answers
Answer:
x>-60
Step-by-step explanation:
Combine multiplied terms into a single fraction
2/5x - 9 < 3/5x + 3
2x/5 - 9 < 3/5x + 3
Find common denominator
2x/5 - 9 < 3/5x + 3
2x/5 + 5(-9)/5 < 3/5x + 3
Combine fractions with the common denominator
2x + 5(-9)/5 < 3/5 + 3
I HOPE YOU GOT THE ANSWER JUST SIMPLIFY IT (2x + 5(-9)/5 < 3/5 + 3) AND YOU WILL GET THE ANSWER YOURSELF AS I HAVE GIVEN ABOVE PLS MARK ME AS THE BRAINLILEST IF YOU LIKE TO AND MY ANSWER HELPED YOU:)
Answer:
[tex]\boxed {x > -60}[/tex]
Step-by-step explanation:
2/5x - 9 < 3/5x + 3
-1/5x < 12
x > -12 x 5
x > -60
what is the probability that s+d>3 and s.d>3? write your answer as a decimal rounded to hundreth place
Answers
The probability that s+d > 3 and sd > 3 is 0.03.
SolutionPlot the inequalities
The region -5 ≤ s,d ≤ 5 is the square shaded in grey.
The region s + d > 3 is the region Q shaded to the right of the straight line.
The region sd > 3 is the region R shaded to the right of the curve d = 3/s.
Find the intersection of the three regions
From the figure, the region satisfying all the above three inequalities is the region to the left of the curve d = 3/s, bounded by the square region, i.e. the region R.
Probability of region R
The required probability is the Geometric probability of the intersection region R. It is calculated as
P(R) = ar(region R) / ar(square region P).
Calculate the areas of the regions
ar(region R) = area of the rectangle to the right in the first quadrant formed by dropping a vertical from point F - area under the curve d = 3/s in the first quadrant
[tex]\[\Rightarrow \;\; \mathrm{ar(\mathbf{R}) =} \int_{3/5}^5\frac{3}{s}ds = 25-3-3\ln\frac{25}{3} = 15.64.\][/tex]
ar(region P) = 25 × 25 = 625.
Calculate P(R)
The probability of the region R, P(R) = 15.64 / 625 = 0.025.
Rounding it to the hundredth place of decimal, P(R) = 0.03.
The probability that s+d >3 and sd>3, where -5 < s,d < 5, is 0.03.
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Disclaimer: The question was incomplete. Please find the full content below.
What is the probability that s + d > 3 and sd > 3, where -5 ≤ s,d ≤5? Write your answer as a decimal rounded to the hundredth place.
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A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
Answers
Answer:
51
Step-by-step explanation:
let's set the starting number as x
1. x times 2 = 2x
2. 2x- 138
3. result = 102
So, 2x-138 = 102
Now lets work backwards to solve for x.
1. 2x = 102
x = 51
So the starting number was 51.
2x - 138 = 102
+138 +138
(x=the missing number)
2x =240
240\2 = 120
x=120
With the information given, can you prove this quadrilateral is a parallelogram?
Could someone help me with this problem? I'm not sure if those lines are parallel, congruent, or both, because there are two arrows on each line instead of one.
Will give Brainliest for the best answer.
Answers
Answer:
it it a parallelogram
Step-by-step explanation:
it has 2 sets of 2 parallel lines
With the information given, we can not prove this quadrilateral is a parallelogram. Explanation is given.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
In order to prove, quadrilateral is a parallelogram:
We can prove either one of these following method;
1. Establish the congruence of the two pairs of opposing sides.
2. Show that the two opposing side pairs are parallel.
3. Show that one pair of opposed sides is parallel and congruent.
Here, we have AB = CD
And we have line AD and BC.
Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
AD and BC are at equal distance.
That means, AD II BC.
And to solve further, we do not have any statements.
Therefore, with given information, we can not prove this quadrilateral is a parallelogram.
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A section of a tessellated plane is shown. Which type of symmetry does the tessellated plane have? translational and rotational rotational and reflectional reflectional and translational glide reflectionalA section of a tessellated plane is shown. Which type of symmetry does the tessellated plane have?
translational and rotational
rotational and reflectional
reflectional and translational
glide reflectional
Answers
Answer:
The given tessellated plane has translational and rotational symmetry. From the given options, we find that option A is correct.
Step-by-step explanation:
Concept: The symmetry has to be decided in such a way that when it applies to a figure, we get exactly the next figure. In the given figure, we have translational and rotational symmetries. We can translate the triangles to the next position and get the same triangle. Or we can rotate the triangle about the point of contact and get the same triangle.
For example, take the top left triangle. If it is translated towards approximately 30° direction, then we will get the triangle present at the top.
Or when we turn that triangle about the point of contact of that and the topmost triangle, then we can get the topmost triangle.
But there is no reflectional symmetry due to the absence of symmetry line.
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An equivalent ratio to the tape diagram shown is
to pls i need a answer
Answers
An equivalent ratio to the tape diagram shown is 1 to 2
How to determine the equivalent ratio?From the tape diagram, we have:
Red = 2
Blue = 4
Express as a ratio
Red : Blue = 2 : 4
Divide by 2
Red : Blue = 1 : 2
Hence, an equivalent ratio to the tape diagram shown is 1 to 2
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Given the function h(x) = 3(5)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3. Part A: Find the average rate of change of each section. (4 points) Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points) (10 points)
Answers
Answer:
For section A, the average rate of change is 12. For section B, the average rate of change is 300. The average rate of change in Section B is greater than Section A by 25. The rate of change keeps on increasing because the slope of the function is increasing.
Step-by-step explanation:
Concept: For a function f(x), the rate of change is given by [tex]\frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1} }[/tex]. Given function is h(x) = 3(5∧x).
For x = 0 to x = 1, the value of function would be f(0) = 3 to f(1) = 15.
The rate of change would be (15-3) / (1-0) = 12.
For x = 2 to x = 3, the value of function would be f(2) = 75 to f(3) = 375.
The rate of change would be (375-75) / (3-2) = 300.
The average rate of change in Section B is greater than Section A by
300 / 12 = 25.
Looking at the function, that is h(x) = 3(5∧x), we see that this function is an increasing function. The slope of an increasing function keeps on increasing with the value of x. The rate of increase is also a slope. That is why the rate keeps on increasing.
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