f(x)
X
(b)
Use the graph to determine the limit visually (if it exists). (If an answer does not exist, enter DNE.)
(a)
lim f(x)
X--1
-2
lim f(x)
x 0
Write a simpler function that agrees with the given function at all but one point.
q(x) =
Answers
a) Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
b) The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
How to determine whether a limit exists or not
According to theory of limits, a function f(x) exists for x = a if and only if [tex]\lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x)[/tex]. This criterion is commonly used to prove continuity of functions.
Rational functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following lateral limits:
[tex]\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty[/tex]
[tex]\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty[/tex]
Since both limits are distinct and do not exist, we conclude that x = - 1 is not part of the domain of the rational function.
In addition, we can simplify the function by algebra properties:
[tex]\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}[/tex]
[tex]g(x) = \frac{1}{x + 1}[/tex]
The function [tex]f(x) = \frac{x}{x^{2}+ x}[/tex] is equivalent to the function [tex]g(x) = \frac{1}{x + 1}[/tex].
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Related Questions
Cual es el valor de A si 900 es el 130% de A
Answers
El valor del número A es 692.31.
PercentageThe percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:
[tex]\frac{50}{100} =0.5*100=50%[/tex]
The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks etc.
The exercise asks you the value of A and it gives you the value (900) that represents 130%A. Thus, you should write an equality between the division the percentage and the variable A by 100 with the value 900.
You should follow the steps below.
[tex]\frac{130*A}{100}=900\\ \\ 130A=90000\\ \\ A=\frac{90000}{130} =692.31[/tex]
You can check the result : [tex]\frac{692.31*130}{100} =\frac{90000.3}{100} =900.003=900[/tex]
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Which net can be folded to form a pyramid? A net has a square at the center. Squares are on 2 sides and triangles are on 2 sides. A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side. A net has a square at the center. 3 triangles are on 1 side. A net has a square at the center. A triangle and square are on 1 side and a square and triangle are on another side.
Answers
The net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.
What is a net?A net is a two-dimensional representation of a three dimensional solid object showing its faces.
Examples of material which can have nets are
cubes, cuboids prisms etcWhat is a pyramid?Now, for a pyramid, we know that a pyramid is a three dimensional solid object that has one square base and four triangular sides.
So, when a pyramid is split into its net, it will have one square at the center and four triangles on the sides of the squares.
So, the net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.
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Answer:
B
Step-by-step explanation:
You need to use the net that only have 1 square because a pyramid only has 1 square, it also has all the triangle sides needed which is 4. You can use a model to make a pyramid out of this net
Please help! Solve this
Answers
The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
How to solve the equation?The equation is given as:
[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]
Split the equation as follows:
[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]
[tex]y = 1 + x^2[/tex]
Next, we plot the graph of both equations (see attachment)
From the attached graph, the intersection point is (1, 2)
Remove the y value
x = 1
Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1
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find the product. simplify your answer
Answers
cancel by 3
8/21Answer:
[tex]\sf \dfrac{8}{21}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]
When multiplying fractions, simply multiply the numerators and multiply the denominators:
[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]
Cancel the common factor x:
[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]
Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:
[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]
Cancel the common factor 3:
[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]
PLS HELP I WILL GIVE YOU 100 POINTS… Question 4 (True/False Worth 4 points)
(07.07)
True or False?
When temperature rises, the number of people who go to the beach increases. Temperature is the independent variable in this situation.
True
False
Answers
Answer:
True
Number of people is dependent
Answer:
true because it's hots and people cool of by getting by getting the water
Savings account at a bank pays 5% simple interest in account at Bank B pays 2% compounded interest the table shows the balance in each account after an initial deposit of $1000 which describes the balance after a long period of time
Answers
Answer:
The balance in Bank B will be greater.
Step-by-step explanation:
Because simple interest is just interest on the principle only which is 50 every year doesn't change but with compound interest you will get 2% Interest every year. principle+interest
10 points please help with calculus HW
Find equations for the tangent line and the normal line to the graph of the equation at the given point. (The normal line at a point is perpendicular to the tangent line at the point.)
x^2 + y^2 = 10, (1, 3)
(a)Tangent Line = ___?____
(b)Normal Line=____?____
(c) Select a graph from the graph pictures attached
Answers
a. The equation of the tangent at (1,3) is y = -x/3 + 10/3
b. The equation of the normal at (1,3) is y = 3x
c. Find the graph in the attachment
a. How to find the equation of the tangent at (1, 3)?Since x² + y² = 10, we differentiate the equation with respect to x to find dy/dx which the the equation of the tangent.
So, x² + y² = 10
d(x² + y²)/dx = d10/dx
dx²/dx + dy²/dx = 0
2x + 2ydy/dx = 0
2ydy/dx = -2x
dy/dx = -2x/2y
dy/dx = -x/y
At (1,3), dy/dx = -1/3
Using the equation of a straight line in slope-point form, we have
m = (y - y₁)/(x - x₁) where
m = gradient of the tangent = dy/dx at (1,3) = -1/3 and (x₁, y₁) = (1,3)So, m = (y - y₁)/(x - x₁)
-1/3 = (y - 3)/(x - 1)
-(x - 1) = 3(y - 3)
-x + 1 = 3y - 9
3y = -x + 1 + 9
3y = -x + 10
3y + x = 10
y = -x/3 + 10/3
So, the equation of the tangent at (1,3) is y = -x/3 + 10/3
b. The equation of the normal at the point (1, 3)Since the tangent and normal line are perpendicular at the point, for two perpendicular line,
mm' = -1 where
m = gradient of tangent = -1/3 and m' = gradient of normalSo, m' = -1/m
= -1/(-1/3)
= 3
Using the equation of a straight line in slope-point form, we have
m' = (y - y₁)/(x - x₁) where
m' = gradient of normal at (1, 3) and (x₁, y₁) = (1,3)So, m = (y - y₁)/(x - x₁)
3 = (y - 3)/(x - 1)
3(x - 1) = (y - 3)
3x - 3 = y - 3
y = 3x - 3 + 3
y = 3x + 0
y = 3x
So, the equation of the normal at (1,3) is y = 3x
c. Find the graph in the attachment
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Please answer this question for me
Answers
Answer: B
Step-by-step explanation:
The vertical asymptotes are at x=-4 and x=1, so the denominator needs to have factors of (x+4) and (x-1).
This eliminates everything except for B.
Instructions: Find the slope between the two points given. Then, use the slope and point ONE to write the
equation of the line in Point-Slope form. State the slope
Answers
Step-by-step explanation:
Find the slope between the two points given. Then, use the slope and point ONE to write the
equation of the
Verify which of the following are identities.
Answers
Answer:
C
Step-by-step explanation:
Equation 1:
[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]
Equation 2:
[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]
When the absolute value of slope gets bigger the graph of the line gets ???
Answers
how much y value changes with respect to the
change in × value. So the slope gives the
steepness of the line.
Slope O indicates there is no change in y when
the x value is changed and so the line with
slope 0 is a horizontal line. A line with slope 1
shows with 1 unit change in ×, y changes by 1
unit. Likewise slope equal 2 indicates with 1 unit
change in ×, y changes by 2 units.
We can see as the absolute value of slope is
increasing, the change in y with respect to x is
increasing i.e. the line is becoming more tilted or
steep.
Hence, we can conclude that:
The graph of a line gets Steeper as the absolute
value of the slope gets bigger.
C is the correct answer.
Evaluate the expression.
n =
If P(n, 5) = 2520, find n.
Answers
The value of n in the permutation equation P(n, 5) = 2520 is 7
How to evaluate the permutation expression?The expression is given as:
P(n, 5) = 2520
The above expression is a permutation expression.
The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula
P(n,r) = n!/(n - r)!
Substitute 5 for r in the above equation
P(n,5) = n!/(n - 5)!
Substitute the given values in the above equation
n!/(n - 5)! = 2520
Expand the above equation
n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520
Evaluate the quotient in the above equation
n(n-1)(n - 2)(n - 3)(n - 4) = 2520
Express 2520 as 7 * 6 * 5 * 4 * 3
n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3
By comparing the equation, we have
n = 7
Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7
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Solve the right triangle ABC, with C = 90°.
A = 38.5°, b = 43.5 cm. Find B, a, and c. Round to the nearest tenth.
Answers
B = 51.5
a = 34.6
c = 55.6
Alec starts up a monthly subscription potato box. It costs 18.20 dollars per month,
and comes with 16 potatoes in each box. Each subscriber may order any amount of
”luxury potatoes”, that are separate from the 16 that normally come in the box, for
an additional 5 dollars each.
(a) Write a formula for the monthly revenue, R in dollars, earned by Alec as a function
of s, the number of monthly subscribers, and n, the total number of luxury potatoes that his clients order. R(s, n) =
(b) Using your formula from above, find R(10, 3)
Answers
A. The formula (mathematical function) for the monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
B. Using the formula above, the value of R(10, 3) is $197.
What is a function?A function is an expression, rule, or law defining the relationship between an independent variable and a dependent variable.
Functions are used to define physical relationships between variables.
Data and Calculations:Cost monthly subscription = $28.20 per box
Number of normal potatoes in each box = 16
Cost of additional luxury potatoes = $5 per potato
If the monthly revenue function, R, is given as R(s, n) where:
s = number of monthly subscribers
n = total number of luxury potatoes ordered
The monthly revenue, R, earned by Alec, R(s, n) = $18.20s + $5n.
The value of R(10, 3) is $197 ($18.20 x 10 + $5 x 3)
Thus, using the formula above, the value of R(10, 3) is $197.
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80 1/4 is 5% of what number
Answers
Answer: 80 1/4 is 5% of 1605
Step-by-step explanation:
5 percent of some number = 80.25
let x = some number
[tex]\frac{5}{100} *x = 80.25[/tex]
[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]
[tex]=x=80.25*20[/tex]
[tex]=x=1605[/tex]
Can someone explain how to do this
Answers
The negative solution is -2.21 and positive solution is 12.21
Factorizing quadratic equationsGiven the quadratic equation expressed as:
x^2-10x-27 = 0
Find the solution using the general formula
x^2-10x-27 = 0
x = 10±√(10)²-4(1)(-27)/2
x = 10±√100+108/2
x = 10±√208/2
x = 10±14.422/2
Simplify
x = 10+14.422/2 and x = 10-14.422/2
x = 24.422/2 and -4.422/2
x = 12.21 and -2.21
Hence the negative solution is -2.21 and positive solution is 12.21
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A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below: Male Female Type A 65 85 Type B 38 12 Compare P(Male or Type B) with P(Male | Type B). (5 points) P(Male or Type B) > P(Male | Type B) P(Male or Type B) = P(Male | Type B) P(Male or Type B) < P(Male | Type B) There is not enough informatio
Answers
The correct statement regarding the probabilities is given as follows:
P(Male or Type B) > P(Male | Type B)
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there is a total of 200 people, of which 103 are males and 12 are Type B females, hence:
P(Male or Type B) = 115/200 = 0.575
Of the 103 males, 38 are Type B, hence:
P(Male|Type B) = 38/103 = 0.3683.
Hence:
P(Male or Type B) > P(Male | Type B).
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7. How would the net of a box with a closed top differ from the net of the same box with an open top?
Sketch the net for each case to demonstrate the difference.
Answers
The main difference between the two nets is the top face.
The net of a box with a closed top is a 3-dimensional figure that is made up of 6 faces. The faces are all rectangles, and they are connected to each other by flaps. The flaps are the parts of the net that fold over to create the closed top.
The net of a box with an open top is a 3-dimensional figure that is made up of 5 faces. The faces are all rectangles, and they are connected to each other by flaps. However, the top face of the net is not a rectangle. Instead, it is a trapezoid. The trapezoid is created by the flaps that fold over to create the open top.
As you can see, the main difference between the two nets is the top face. The top face of the net of a box with a closed top is a rectangle, while the top face of the net of a box with an open top is a trapezoid.
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Which of the following numbers is the greatest?
2.5
-2.5
0
-7
Answers
Answer:
2.5
Step-by-step explanation:
2.5 is the only positive number amongst the options, so it must be the greatest.
Find the x and y intercepts on the graph of the line, if they exist.
3x + 4y = 24
Answers
The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.
What are the intercepts of a line?The standard equation of a line is ax + by + c = 0.
Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.
In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.
Calculation:It is given that,
The equation of the given line is 3x + 4y = 24
Rewriting the given equation into the general form,
3x + 4y - 24 =0
On comparing with ax + by + c = 0,
a = 3, b = 4 and c = -24
So,
The x-intercept of the line (-c/a) = -(-24)/3 = 8 and
The y-intercept of the line (-c/b) = -(-24)/4 = 6
Therefore, the required x and y intercepts are 8 and 6 respectively.
(The graph showing the intercepts of the given line is shown below)
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Please help me with this I need the answers please
Answers
i think this is the answer
PLEASE IF ANYONE CAN HELP JUST ANSWERS 1-8 (giving brainliset)
Answers
The computation of the equations is illustrated below.
How to illustrate the equation?a. x - y = 1 .... i
x + y = -9 ..... ii
Subtract the equations
-2y = 10
y = 10/-2 = -5
Since x - y = 1
x - (-5) = 1
x + 5 = 1
x = 1 - 5 = -4
b. 3x + 2y = -9
x - y = -13
Multiply equation i by 1
Multiply equation ii by 3
3x + 2y = -9
- 3x - 3y = -39
5y = 30
y = 6
Since x - y = 13
x - 6 = 13
x = 13 + 6 = 19
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Select the correct answer from each drop-down menu. A hot tub is in the shape of a regular pentagon. To the nearest tenth, what is the area of the cover on the hot tub? 4 ft The apothem of the pentagon is approximately ft². ft, and the perimeter of the pentagon is Reset Next ft. Therefore, the area is
Answers
Answer:
27.53
Step-by-step explanation:
The apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.
What is Polygon?Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides
Given,
A hot tub is in the shape of a regular pentagon.
The side of polygon is 4ft.
We need to find the apothem of the pentagon, area and perimeter.
In the middle we will have 360 degrees.
If we divide the polygon to five triangles, then one of the verte will have 36 degree measure.
h=2/tan 36=2.7528
Perimeter of polygon=5 a
a is side of polygon
Perimeter=5×4=20 ft.
Area=1/2 perimeter ×apothem
=1/2×20×2.7528
=27.528 ft²
Hence the apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.
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1. Find the domain and range of the function
f(x)=√1-4x².
Answers
[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]
[tex]1 - 4x {}^{2} \geqslant 0[/tex]
[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]
[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]
[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]
[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]
Answer:
[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]
[tex]\textsf{Range}: \quad [0, 1][/tex]
Step-by-step explanation:
Domain: set of all possible input values (x-values)
Range: set of all possible output values (y-values)
Given function:
[tex]f(x)=\sqrt{1-4x^2}[/tex]
As negative numbers don't have real square roots:
[tex]\implies 1-4x^2\geq 0[/tex]
Therefore, to find the domain, solve the inequality.
Subtract 1 from both sides:
[tex]\implies -4x^2\geq -1[/tex]
Divide both sides by -1 (reverse the inequality):
[tex]\implies 4x^2 \leq 1[/tex]
Divide both sides by 4:
[tex]\implies x^2\leq \dfrac{1}{4}[/tex]
[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]
[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]
[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]
[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]
Therefore:
[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]
To find the range, input the endpoints of the domain into the function:
[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]
[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]
To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.
[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]
[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]
[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]
Setting it to zero and solving for x:
[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]
[tex]\implies -4x=0[/tex]
[tex]\implies x=0[/tex]
Substitute x = 0 into the function:
[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]
Therefore, the range is [0, 1]
A coin has two sides head and tails a die has six sides if you roll the die what is the probability that you flip heads and roll a number greater than 5
Answers
Using it's concept, the probability that you flip heads and roll a number greater than 5 is: [tex]\frac{1}{12}[/tex].
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
The probability of a head is 1/2.The probability of a number greater than 5 is 1/6.Hence the probability of both events is:
[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex].
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In a certain chemical, a ratio of zinc to copper is 4 to 11 . A jar of the chemicals contains 319 copper. How many grams of zinc does it contain?
Answers
Answer:
116
Step-by-step explanation:
zinc : copper
4 : 11
11 = 319
zinc = 4 / 11 * 319
Zinc = 116
Is -46x-23 = 46x+23 an infinite solution
Answers
Answer:
There is only 1 solution, and it is ½
Step-by-step explanation:
-46x - 23 = 46x + 23
46x + 46x = 23 + 23
92x = 46
x = 46 / 92
x = ½
Someone please help with this math problem.
Answers
Problem Set 3.1: Characteristics of the Mean Criterion: Explain a distribution. Instructions: Read the following and answer the questions. Data: To study perception, a researcher selects a sample of participants (n = 12) and asks them to hold pairs of objects differing in weight, but not in size, one in each hand. The researcher asks participants to report when they notice a difference in the weight of the two objects. Below is a list of the difference in weight (in pounds) when participants first noticed a difference. Answer the following questions based on the data given in the table. Difference in Weight 4 8 9 5 12 7 6 15 10 4 8 8 1. State the following values for this set of data: a) Mean ___8____ b) Median ___8____ c) Mode(s) ___8____ 2. What is the shape of this distribution? Hint: Use the values of the mean, median, and mode to infer the shape of this distribution. _____________
Answers
1a.The mean is 8.
b. The median is 8.
c. The mode is 8.
2. The shape of the data is: perfectly symmetrical distribution.
How to Find the Mean of a Data Set?To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.
Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12
Mean = (96)/12
Mean = 8
How to Find the Median?The median is the center of the data when it is ordered.
Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15
The center (median) is the average of the two center values = (8 + 8)/2 = 16/2
Median = 8
How to Find the Mode?The mode of the data is 8, because 8 appeared most in the data set.
The mean is 8.
The median is 8.
The mode is 8.
Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.
Therefore the shape of the data is: perfectly symmetrical distribution.
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On the number line above, points A, B, C, and D are integers, and AB: BC: CD = 3:2:1. What is the length of AC?
Answers
Using proportions, it is found that the length of AC is of 15 units.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The ratios in this problem are given as follows:
[tex]\frac{AB}{BC} = \frac{3}{2}[/tex].[tex]\frac{BC}{CD} = \frac{2}{1}[/tex].[tex]\frac{AB}{CD} = \frac{3}{1}[/tex].The entire length is of 18 units, AB is half of that, hence:
AB = 0.5 x 18 = 9 units.
BC is two thirds of the length from 6 to 15, hence:
BC = 2/3 x (15 - 6) = 6
Thus, the length of AC is:
AC = 9 + 6 = 15 units.
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