The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x
Given, a number line is moving from ₋3 to ₊5 .
Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.
When we mark the point and shade the left part of it then we can start applying the inequality expressions.
And from that we can match the applicable inequalities while observing the graph.
For the first inequality ₋1.5 ≥ x.Here,x value ranges from ₋1.5 to ₊5, hence we take this as an inequality expression.Next, if we consider x ≤ ₋1.5, then here x value will range from ₋1.5 to ₋3. where the region is shaded. Hence this expression doesn't satisfy the graph.the next expression is ₋1.5 ≤ x. here the value will again range in the shaded area so it is not applicable.₋1.5 ≥ x, here the values will satisfy the graph.remaining inequality expressions does not support the graph.Therefore the only inequalities the graph represents is x ≥ ₋1.5 and ₋1.5 ≤ x
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2
Drag each number or expression to the correct location on the table. Each number or expression can be used more than once, but not all
numbers or expressions will be used.
Complete the empty cells in the table by determining all terms, constants, and coefficients for both algebraic expressions.
-5 7 5
Expressions
Terms
Constants
Coefficients
-5a
11
Reset
4a2
4a2. -5a-3
Next
7(-3x + 5) + 1ly
7(-3x + 5)
11y
5
The empty cells in the table by determining all terms, constants, and coefficients for both algebraic expressions will be:
Constant = -3Coefficient = -4, -5How to illustrate the information?In the first expression, the equation is given as 4a² - 5a - 3 while in the second expression, the equation is given as 7(-3x + 5) + 11y.
In this second expression, the term is 7(3x + 5), 11y. The constants are -7 and 5. Lastly, the coefficients are -3, and 11.
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What is the solution set for this inequality? 5x − 4 < 11 + 8x
Answer: x>-5
Step-by-step explanation:
add 4 to both sides
5x-4+4<11+8x+4
simplify
5x<8x+15
subtract 8x from both sides
5x-8x<8x+15
simplify
-3x<15
divide both sides by -3 and switch inequality sign
-3x/-3>-15/-3
x>-5
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 11+8x \end{gathered}$}[/tex]
Simplify both sides of the inequality.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4 < 8x+11 \end{gathered}$}[/tex]
Subtract 8x from both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 5x-4-8x < 8x+11-8x \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4 < 11 \end{gathered}$}[/tex]
Add 4 to both sides.
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x-4+4 < 11+4 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf -3x < 15 \end{gathered}$}[/tex]
Divide both sides by -3.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{-3x}{-3} < \frac{15}{-3} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x > -5 \ \ \iff \ \ \ Answer \end{gathered}$}[/tex]
{ Pisces04 }how do i factor f(x)= x^4 - 4x^3 +3x^2 + 4x -4 into linear terms?
The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the function f(x) = x⁴ - 4x³ + 3x² + 4x -4. The factor of the polynomial f(x) = x⁴ - 4x³ + 3x² + 4x -4 are x = -1, x = 1 and x = 2.
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TIME REMAINING
59:23
Jessie graphed one of the lines in a system of equations: y = 3 x minus 2. If the system has an infinite number of solutions, which statements are true? Check all that apply.
On a coordinate plane, a line goes through (0, negative 2) and (1, 1).
Any point in the coordinate plane is a solution because it has an infinite number of solutions.
Point (1, 1) is a solution because it is one of the points on the line already graphed.
It is impossible to tell if (–1,–5) is a solution without seeing the other line graphed.
Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.
When the other line in the system is graphed, it will share all points with the line already graphed.
Answer:
a & c
Step-by-step explanation:
Answer:
B) Point (1, 1) is a solution because it is one of the points on the line already graphed.
D) Point (20, 58) is a solution because it results in a true statement when the point values are substituted into the equation of the line.
E) When the other line in the system is graphed, it will share all points with the line already graphed.
Step-by-step explanation:
For a certain company, the cost for producing x items is 60x+300 and the revenue for selling x items is 100x−0.5x2 .
The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $50 .
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
x=
Preview
Part c: Is it possible for the company to make a profit of $2,500 ?
The answers are
A. The equation for the profit from selling the items is P = 40x-0.5x²-300. b. The values of x are 10 and 70.c. It is not possible to have the profit of 2500How to solve for the expressionWe have the cost function in this question to be
C(x) = 60x+300
We have the function of the revenue to be
Revenue = 100x−0.5x²
A. The formula for revenue function is given
revenue - cost
This is expressed as
= (100x−0.5x²)-60x+300
We have to collect like terms and open the equation above.
This given us:
40x-0.5x²-300B. when profit = 50$
We have p = 40x-0.5x²-300
50 = 40x-0.5x²-300
Multiply the two sides by 10
This gives
500 = 400x - 5x² - 3000
This gives a quadratic equation
5x² - 400x - 3500 = 0
To solve the equation you have to make use of a quadratic calculator.
This gives us the values
x = 10x = 70c. We have P = 40x-0.5x²-300.
at P = 2500
2500 = 40x-0.5x²-300.
Multiply the equation by 10
25000 = 400x - 5x² - 3000
collect like terms
400x - 5x2 - 3000 +28000
400x -5x2 +28000
We have to take the discriminant
-400² - 4*5*28000
= -400000
The discriminant is negative hence it is not possible.
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What is the range of the function shown on the graph above HELP
Answer:
C. 0 ≤ y ≤ 7
Step-by-step explanation:
Range is the interval of the numbers on the y-axis. The numbers go from y-value 1 to y-value 7. Since the circles at the ends are closed, this means 0 and 7 are included in the range, so ≤ is included instead of <.
What is the range of the averages in this class? histogram group of answer choices 65 points 80 points 30 points none of the above
The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Range is the difference between the maximum value and minimum value of a data set. Hence:
Range = Maximum - Minimum
Let us assume that the maximum point is 100 point and the minimum point is 20 point, hence:
Range = 100 - 20 = 80 points
The range of the averages in a class with a maximum point of 100 point and a minimum point of 20 point is 80 points
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Find the exponential function that contains the points (3,24) and (4,48).
The required exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x
Exponential functionsThe standard exponential function is expresses as y = ab^x
Given the coordinate points (3,24) and (4,48), the equivalent equations are:
24 = ab^3 ......... 1
48 = ab^4
Take the ratios
48/24 = b^4/b^3
2 = b
Substitute b = 2 into equation 1
24 = a(2)^3
8a = 24
a = 3
Hence the required exponential function that contains the points (3,24) and (4,48) is y = 3(2)^x
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Instructions: Solve the quadratic equation and simplify your answer(s).
7x2=−12−5x
x=
-5
+
√
,
-5
−
√
14
14
[tex]7x^2 = -12-5x\\\\7x^2 + 5x+12=0\\\\x=\frac{-5 \pm \sqrt{5^{2}-4(7)(12)}}{2(7)}\\\\\boxed{x=\frac{-5 \pm i \sqrt{311}}{14}}[/tex]
If f(x) = x2 + x and g(x) = x − 3, find f(g(7)).
The value of f(g(7)) is 20
How to determine the composite functions?The functions are given as:
f(x) = x^2 + x
g(x) = x - 3
Start by calculating g(7)
g(7) = 7 - 3
Evaluate
g(7) = 4
So, we have:
f(g(7)) = f(4)
Substitute 4 for x in f(x) = x^2 + x
f(4) = 4^2 + 4
Evaluate
f(4) = 20
Hence, the value of f(g(7)) is 20
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Vernon Taber deposits $600 into an ordinary annuity after each quarter for 4 years. The account pays 4% interest compounded quarterly. Find the a) future value, and b) total interest earned.
The future value is $10,354.72.
The total interest earned is $754.72.
What is the future value and the interest earned?When an amount is compounded quarterly, it means that both the amount deposited and interest already earned increases in value every quarter.
The future value = quarterly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate = 4% / 4 = 1%n = number of years = 4 x 4 = 16Annuity factor = [1.01^16) - 1 ] / 0.01 = 17.26
17.26 x 600 = $10,354.72
Total interest earned = future value - total amount deposited
Total amount deposited = $600 X 4 X 4 = 9600
$10,354.72 - 9600 = $754.72
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In stats would a test looking at gender & holiday preference would I do a Chi-squared test? Which is the explanatory & which is the response variable?
Any help provided is appreciated. Thanks!
In statistics, a Chi-squared test may be used to determine holiday choice and gender and α (alpha) is the response variable.
What is the Chi-squared test?A statistical technique called the chi-square test is used to compare actual outcomes with predictions.
The goal of this test is to establish if a discrepancy between actual and predicted data is the result of chance or a correlation between the variables you are researching.
Whether there is a statistically significant association between categorical variables is determined by the Chi-square test of independence.
This issue is addressed by a hypothesis test. The chi-square test of association is another name for this assessment.
Hence,in stats would a test looking at gender & holiday preference yes you can do a Chi-squared test and α(alpha) is the response variable.
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Write an equation of the line passing through the point (6,4) that is perpendicular to the line y=- 1/2x +4
Hello,
"perpendicular to the line y= - 1/2x +4 "
so y = -1/2x + p
-1/2 × 6 + p = 4 ⇔ -3 + p = 4 ⇔ p = 4 + 3 = 7
y = -1/2x + 7
what is the percentage of change from 12 to 19
Answer:
(19-12):12*100 =
(19:12-1)*100 =
158.33333333333-100 = 58.33
4. The parents made pies for the school bake sale to pay for the next field trip.
They made 55 apple pies and 45 blueberry pies. How many pies did they make
altogether? Estimate first, then solve.
The total number of pies they made altogether is 100.
How many pies did they make altogether?
In order to determine this value, add the number of blueberry pies with the number of apple pies. Addition is the mathematical operation that is used to determine the sum of two or more numbers.
The total number of pies = 55 + 45 = 100 pies
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what to write it here
Answer:
84 degrees
Step-by-step explanation:
Angle A = 83 degrees
Angle B = x degrees
Angle C = 135 degrees
Angle CDE = 122 degrees
We know that the four inner corners of a quadrilateral should add up to 360 degrees. Two supplementary angles will add up to 180 degrees. Adjacent angles on a straight line will always be supplementary. Knowing this, just solve for <ADC and add that amount to <A and <C. Then, subtract that sum from 360 degrees.
<ADC = 180-122 = 58
58+83+135 = 276
360-276 = 84 degrees
A convenience store recently started to carry a new brand of soft drink. Management is interested in estimating future sales volume to determine whether it should
continue to carry the new brand or replace it with another brand. The following table provides the number of cans sold per week. Use both the trend projection with
regression and the exponential smoothing (let a=0.4 with an initial forecast for week 1 of 574) methods to forecast demand for week 13. Compare these methods by
using the mean absolute deviation and mean absolute percent error performance criteria. Does your analysis suggest that sales are trending and if so, by how much?
2
5
Period 1
3 4
574 635 652 739 679
Sales
with regression forecast.
(Enter your response rounded to the nearest whole number.)
(1) Obtain the trend projection
The forecast for week 13 is
6
637
7
723
8
691
9
773
10
718
11
656
12
729
The forecast for week 13 is 9.7%
a) MAD without the forecast = 43.71
MAD with the forecast = 45.59
b) MAPE = 0.097
MAPE= 9.7%
642 602 656 747 663 618 731 726 679 737 664 740
Mean Absolute deviation is given as
MAD = [Σ|x - μ|]/N
We first calculate the mean
Mean = Σx/N
Mean = (642+602+656+747+663+618+731+726+679+737+664+740)/12
Mean = (8205/12)
Mean= 683.75
absolute deviations from the mean
|642-683.75| + |602-683.75| + |656-683.75| + |747-683.75| + |663-683.75| + |618-683.75| + |731-683.75| + |726-683.75| + |679-683.75| + |737-683.75| + |664-683.75| + |740-683.75|
Absolute deviations from the mean
41.75+81.75+27.75+63.25+20.75+65.75+47.25+42.25+4.75+53.25+19.75+56.25= 524.5.
What is the formula for absolute mean deviation?MAD = [Σ|x - μ|]/N
MAD = (524.5/12)
MAD = 43.71
If we include the forecast for the 13th week
642 602 656 747 663 618 731 726 679 737 664 740 747
Mean = (8205+747)/13
Mean = 688.62
absolute deviations from the mean
|642-688.62| + |602-688.62| + |656-688.62| + |747-688.62| + |663-688.62| + |618-688.62| + |731-688.62| + |726-688.62| + |679-688.62| + |737-688.62| + |664-688.62| + |740-688.62| + |747-688.62|
Absolute deviations from the mean
=46.62+86.62+32.62+58.38+25.62+70.62+42.38+37.38+9.62+48.38+24.62+51.38+58.38
= 592.62
MAD = (592.62/13)
MAD = 45.59.
b) MAPE is used to check forecast errors
MAPE = (1/N) Σ [|x-f|/x]
where N = Sample size = 12
x = each variable
f = the forecasted value = 747
x = 642, 602, 656, 747, 663, 618, 731, 726, 679, 737, 664, 740
Σ[|xf|/x]=0.164+0.241+0.139+0+0.112+0.209+0.022+0.029+0.100+0.014+0.125+0.009
Σ [|x-f|/x] = 1.164
MAPE = (1.164/12)
MAPE = 0.097
MAPE=9.7%
The forecast for week 13 is 9.7%.
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How many 4-character passwords can you generate if the first character can be any letter of the English alphabet, the next two characters can be any two digits from 0 to 9, and the last one can be any of the characters %,*, or #? (Repetition is allowed!)
There are 7,800 different passwords.
How many different passwords can be generated?
Here we need to count the number of options for each of the digits of the password.
The first character has 26 options (26 letters in the alphabet).
The second character has 10 options (ditis from 0 to 9), and also does the third character
The fourth character has 3 options (%,*, or #)
The total number of different passwords that can be generated is given by the product between the numbers of options, so we have:
C = 26*10*10*3 = 7,800
There are 7,800 different passwords.
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Solve the mathematical puzzle.
Determine the digits of Y
from these clues.
The digits of Y
add to 16.
The first digit is 4 times the third digit.
The second digit is 3 times the third digit.
Y is a three digit number.
Answer:
862
Step-by-step explanation:
4 x 2 = 8
3 x 2 = 6
8 + 6 + 2 = 16
A particular sawdust pile has a base diameter of 25 feet when the height is 20 feet. Find the volume of this sawdust pile when it is 30 feet high.
The volume of the sawdust pile is 11,039.06 ft³.
What is the volume of the pile?The shape of the sawdust pile would be a cone. The diameter is always proportional to its height.
Diameter = k x height
where k is equivalent to the rate of increase of the diameter with respect to the increase in height.
25= k20
k = 25 / 20
k = 1.25
Diameter when height is 30 ft = 1.25x 30 = 35.50 feet
Volume of the sawdust = [tex]\frac{1}{3}[/tex]πr²h
Where:
π = 3.14 r = radius = diameter / 2 = 35.50 / 2 = 18.75h = 30[tex]\frac{1}{3}[/tex] x 3.14 x 18.75² x 30 = 11,039.06 ft³
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What is the greatest common factor of 6, 42, and 18?
Answer:
Step-by-step explanation:
1) List the factors of each number.
Factors of 6 : 1, 2, 3, 6
Factors of 42 : 1, 2, 3, 6, 7, 14, 21, 42
Factors of 18 : 1, 2, 3, 6, 9, 18
2) Find the largest number that is shared by all rows above. This is the GCF.
GCF = 6
please find the inverse of this
y=log base 4 x^4
Step-by-step explanation:
[tex]y = log_{4}( {x}^{4} ) [/tex]
Swap x and y.
[tex]x = log_{4}( {y}^{4} ) [/tex]
Solve for y.
[tex]x= 4 log_{4}(y) [/tex]
[tex] \frac{1}{4} x = log_{4}(y) [/tex]
[tex]4 {}^{ \frac{1}{4}x } = y[/tex]
So the inverse is
[tex]4 {}^{ \frac{x}{4} } = f {}^{ - 1} (x)[/tex]
Pls Help! Geometry
Find the area of the shaded region.
Answer: 112.5 square cm
Step-by-step explanation:
The area of the rectangle is [tex](20)(9)=180[/tex] square cm.
The area of the white triangle is [tex]\frac{1}{2}(9)(20-3-2)=67.5[/tex] square cm.
So, the area of the shaded region is [tex]180-67.5=112.5[/tex] square cm.
A bus travels from Boston to New York 220 miles. The bus departs at 2pm and arrives at new York at 7pm. what's the average speed?
Each side of a hexagon is 10 inches longer than the previous side. What is the length of the shortest side of this hexagon if its perimeter is 401 inches?
Answer:
41.83 inches
Step-by-Step Explanation:
You have to trust me. I helped my brother with this.
The length of the shortest side of the hexagon is approximately 41.83 inches
Let's denote the length of the shortest side of the hexagon as "x" inches. According to the given information, each side of the hexagon is 10 inches longer than the previous side.
So, the lengths of the sides of the hexagon can be expressed as follows:
First side: x inches
Second side: (x + 10) inches
Third side: (x + 20) inches
Fourth side: (x + 30) inches
Fifth side: (x + 40) inches
Sixth side: (x + 50) inches
To find the perimeter of the hexagon, we sum up the lengths of all the sides:
Perimeter = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)
We know that the perimeter is given as 401 inches, so we can set up the equation:
401 = x + (x + 10) + (x + 20) + (x + 30) + (x + 40) + (x + 50)
Simplifying the equation:
401 = 6x + 150
Subtracting 150 from both sides:
251 = 6x
Dividing both sides by 6:
x = 251/6
Therefore, the length of the shortest side of the hexagon is approximately 41.83 inches (rounded to two decimal places).
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Find the Equation of the Perpendicular Line
Instructions: Find the equation of the line through point (-1, 2) and perpendicular to x + 3y = 3.
y =
Answer:
y = 3x +5
Step-by-step explanation:
The equation of a perpendicular line can be formed by swapping the x- and y-coefficients, and negating one of them. The constant in the equation will be chosen to make the equation true at the given point.
Coefficients swappedThe desired equation in the given standard form will be ...
3x -y = c . . . . . . for some new constant c
Note that we have kept the x-coefficient positive, and have negated the y-coefficient.
Constant valueThe new constant will make the equation true at the point (-1, 2):
3(-1) -(2) = c = -5
So, the standard-form equation is ...
3x -y = -5
Slope-intercept formThe answer form suggests you want to solve this for y. Adding y+5 to both sides will give the form you want:
3x -y +(y+5) = -5 +(y+5)
3x +5 = y
y = 3x +5
Which of the following examples illustrates ordinal numbers?
A. Marie counted the number of chips on her plate and said, " I have eight".
B. Gracie told Bradly she would be the first one to go down the slide.
C. Bennett said he had more blocks than anyone.
Answer:
30-5×2 of 3+(19-3) ÷8
Step-by-step explanation:
30-5×6+(19-3)÷8
30-5×6+16÷8
30-30+8
38-30
8
Answer:
Step-by-step explanation:
b
which expressions are equivalent to 3x
x is powering both numbers so it can be outside the parenthesis.
We have given that 3^x.
What is the expression?An expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
The first one isn't an answer because 3^x is exponential while x^3 is a cubic function.
If you draw them you will see that they are very different.
B is correct because we can divide both numerator and denominator by 6 and we get 3^x.
C is not correct because x is not powering 3 so we cannot divide both by 6D is correct because 3^(x-1) is the same as
and when multiplied by 3 we get 3^x
3^x*3^(-1) = 3^x/3
E is not correct.
will understand after the explanation in DF is correct.
x is powering both numbers so it can be outside the parenthesis.
The question is incomplete the complete question is,
Which expressions are equivalent to the one below? Check all that apply.
3^x
A. x^3
B.(18/6)^x
C.18^x/3
D.3(3^(x-1))
E.3(3^(x+1))
F.18^x/6^x
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FOR 50 POINTS!
In great detail, describe how to solve the advanced function below.
4^(8 - 2x) = 256
I understand the solution to the problem is (2). I would like a detailed description of how exactly to solve this problem.
The value of x in the equation is 2.
What is indices?Indices singular index is a branch of algebra that deals with the power or exponent of variables.
Laws of indices help us to evaluate indicial expressions and equations.
Analysis:
[tex]4^{8-2x}[/tex] = 256
Here 4 is the base number while 8-2x is the exponent or index.
So for us to evaluate this, we need to write 256 in its index form having its base as 4 also.
so 256 in base 4 index form is [tex]4^{4}[/tex]
[tex]4^{8-2x}[/tex] = [tex]4^{4}[/tex]
since both sides have the same base number, we equate only their exponent
8-2x = 4
-2x = 4 - 8
-2x = -4
x = -4/-2 = 2
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In survey of 100 students in the institute of Language Studies at Addis Ababa University,
the numbers of students studying various languages were found to be English 28,
Amharic 30, Afan Oromo 42, English and Afan Oromo 10, English and Amharic 8,
Amharic and Afan Oromo 5, and all the three languages 3. How many students
a. were studying none of the languages?
b. had Afan Oromo as their only language?
c. studied Amharic if they studied Afan Oromo?
Answer:
a. 17
b. 30
c. 5
Step-by-step explanation:
English (E) = 28 - 15 (10+8-3) = 13
Amharic (A) = 30 - 10 (8+5-3) = 20
Afan Oromo (AO) = 42 - 12(10+5-3) = 30
E+AO = 10
E + A = 8
A + AO = 5
A + AO + E = 3
a. 13 people spoke just English+ 20 people who just spoke Amharic + 30 people who just spoke Afan Oromo+ The multilingual people (10+8+5-3=20) which is 83, so that means that 17 learned no language.
b. 42 People learned Afan Oromo, but only 30 of them learned that language separately. 10 People learned it along with English, and 5 learned it with Amharic. However, 3 of those people were the same, so 12 people of those 42 spoke multiple languages. Therefore, only 30 people spoke just Afan Oromo.
c. This one is kinda just a trick question, they want you to overthink it because of the 3 who learned all, but it's just 5 like it says in the question.