Through direct proportionality, we calculated that Seven questions will be answered in 10 minutes and 30 seconds.
Seven questions will need to be answered in 10 minutes and 30 seconds.
Direct proportionality: What is it?
The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. In mathematics, a straight line is used to express direct proportionality, and its equation is of the form y = kx , k = y/x, where [k] is the constant.
The assumption is that the time it takes to finish each question and the number of completed questions [y] are inversely proportional to one another.
The time [x] it takes to complete them is directly proportional to the number of questions [y] that are answered. As a result, y = kx, k = y/x, and y is directly proportional to x.
Thus, we can write:
y₁/x₁ = y₂/x₂
Substituting the values,
4/6 = 7/x₂
x₂ = (7 x 6)/4
x₂ = 21/2
x₂ = 10.5
x₂ = 10 minutes 30 seconds
Therefore, Seven questions will be answered in 10 minutes and 30 seconds.
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the term to term rule is half then add 10 the 2nd term of the sequence is 44 wok out the 1st term
The first term of the sequence is 68.
How to find the first term of the sequence?The term to term rule of a sequence is halve then add 10.
The 2nd term of the sequence is 44.
Therefore, the first term of the sequence can be calculated as follows:
let
the first term = x
Hence, the rule to get the next term in the sequence is as follows:
1 / 2 x + 10 = 44
1 / 2 x = 44 - 10
1 / 2x = 34
cross multiply
x = 34 × 2
x = 68
Therefore, the first term is 68.
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Question 4 of 10
For f(x) = 2x+ 1 and g(x)=x²-7, find (f+ g)(x).
OA. 2x³ - 6
OB. x²+2x+8
OC. 2x² - 15
O D. x²+2x-6
Answer:
D
Step-by-step explanation:
Function f is adding to function g, therefore combine the two into one and combine like terms to solve.
Hello I need help with A please make it easy and simple to understand
distanceSolution:
Given that a toy car placed on the floor travels at a constant acceleration for 3 seconds reaching a velocity of 4v m/s, we have
It slows down with a constant deceleration of 0.5 m/s² for 4 seconds before hitting a wall and stopping. This is as shown below:
Thus, the velocity-time graph for the toy car is as shown below:
The total distance traveled by the toy car is evaluated by calculating the area of the triangle ABC. Thus,
[tex]\begin{gathered} \text{Total distance traveled = }\frac{1}{2}\times7\times4 \\ =14\text{ meters} \end{gathered}[/tex]Hence, the
Anna makes a pot of soup How many times will Anna need to fill the measuring cup to measure 7/8 cups of turnips?
3 1/2 times Anna needs to fill the measuring cup.
How many times does Anna need to fill the cup?Given,
She is using a 1/4 cup measuring cup to measure 7/8 cup of turnips
Solution:
Since she is using a 1/4 cup measuring cup, divide 7/8 cups by 1/4.
7/8 /1/4 = 7/8 * 4/1
= 7/2
= 3 1/2 times.
Therefore,
3 1/2 times Anna needs to fill the measuring cup.
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A line passes through the points (-4,-3) and (2, 6). Determine the slope of the line.
• m = 2/3
O The slope is undefined.
Om = 0
Om =3/2
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{6 +3}{2 +4} \implies \cfrac{ 9 }{ 6 } \implies {\Large \begin{array}{llll} \cfrac{ 3 }{ 2 } \end{array}}[/tex]
HELP PLEASE
complete the paragraph proof
given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
it is ________ that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of ________ , m<1+ m<2=90 degrees and m<2+m<3 =90 degrees. By the ____________ property, m<1+m<2=m<2+m<3.
Then,m<1= _____________ by the subtraction property. Therefore, <1 congruent <3 by the ________
The following proof of complementary angle is given below:
it is given that <1 and <2 are complementary and <2 and <3 are complementary. By the definition of complementary angle , m<1 + m<2 = 90 degrees and m<2 + m<3 =90 degrees. By the substitution property, m<1 + m<2 = m<2 + m<3.
Then, m<1 = m<3 by the subtraction property. Therefore, <1 congruent <3 by the complementary angle.
What is a complementary angle?Complementary angle is a pair of angles that sum to a right angle. A right angle is half of the angle formed by a single straight line which is equivalent to 90 degrees.
Given: <1 and <2 are complementary and <2 and <3 are complementary.
prove: <1 congruent <3
The proof of <1 congruent <3 is m<1 + m<2 = m<2 + m<3 by substitution effect and m<1 = m<3 by Subtraction effect
Therefore, the proof of <1 congruent <3 is given by <1 and <2 are complementary and <2 and <3 are complementary.
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Please answer the questions in the photo ( will mark brainliest )
The reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
As given in the question,
The reason for the required step using property of equality are as follow:
1. 3x + 3 = 5 + x
3x - x + 3 = 5
2x + 3 = 5
Here
Subtraction property of equality is applied.
If x, y, and z are real numbers and x = y
then
x - z = y - z
2. 2x + 3 = 5
2x = 5-3
2x = 2
Here Subtraction property of equality is applied.
If a, b, and c are real numbers and a = b, then
a - c = b - c
3. -x - 1 = 3
-x = 3 + 1
-x = 4
Here Addition property of equality is applied.
If x, y and z are real numbers and x = y, then
x + z = y + z
Therefore, the reason for the required step using property of equality are as follow:
1. Subtraction property of equality.
2. Subtraction property of equality.
3. Addition property of equality.
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g(n) = 3n - 4f(n) = n^3 - 2nFind (gºf)(n)
hello
let's get the functions out first
[tex]g(n)=3n-4[/tex][tex]f(n)=n^3-2n[/tex][tex]g\cdot f(n)=\text{ ?}[/tex][tex]\begin{gathered} g.f(n)=(3n-4)\cdot(n^3-2n) \\ g\mathrm{}f(n)=3n^4-6n^2-4n^3+8n \\ g\mathrm{}f(n)=3n^4-4n^3-6n^2+8n \end{gathered}[/tex]ILL BRAINLISTTTTTTTTT
1) Calculate the value for the gradient (m)
2) State the y intercept
3) State the equation of the rule
Step-by-step explanation:
1) gradient: select two points on the line preferably further apart then substitute into gradient formula.
chosen points: A(0,3) B(6,0) remembering layout is (x,y)
gradient formula:
[tex] \frac{y1 - y2}{x1 - x2} [/tex]
[tex] \frac{3 - 0}{0 - 6} [/tex]
= 3/-6
gradient = 1/-3
y-intercept= 3 (the y-intercept is where x=0)
Zoé doit faire des bouquets avec 40 roses rouges et 72 roses blanches. Elle veut que chaque bouquet ait le même nombre de ros de chaque couleur. Quel est le plus grand nombre de bouquets qu'elle peut faire ? Réponse:
Answer:
Elle pourra réaliser 8 bouquets :
Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.
Explication:
Sara veut évidemment utiliser toutes les fleurs pour qu'il n'en reste pas. Elle doit trouver un nombre qui se divise en 16 et 24,
C'est juste une manière indirecte d'utiliser le HCF de 16 et 24, qui est 8.
16
=
2
×
8
24
=
3
×
8
Elle pourra réaliser 8 bouquets :
Chaque bouquet aura 2 fleurs rouges et 3 fleurs jaunes.
Step-by-step explanation:
Which of the following values cannot be probabilities of events?20.42-0.05 1.48 0.9872.10.02.-4
The values for representing probabilty must be greater or equal to zero and less or equal to one.
So, the values which cannot be probabilities would be:
-0.05 ( It is less than zero)
1.48 (It is greater than one)
7/2 (It is greater than one)
-1/4 ( It is less than zero)
NEED HELP ASAP!!! what’s the two column proof for 13x-11+8x-25=90??
The value of x = 6 of the given expression '13x-11+8x-25 = 90' using the two-column proof.
What are expressions?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.) You can think of expressions as being similar to phrases. A phrase in language may contain an action on its own, but it does not constitute a complete sentence. You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6.So, the value of x:
Now, the value of x in expression'13x-11+8x-25 = 90' by two columns proof:(Refer to the image attached below)
x = 6Therefore, the value of x = 6 of the given expression using the two-column proof.
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Transpose and solve for x
15x³=723
Answer:
x = 241 1/3
————
5 1/3
Step-by-step explanation:
Answer:
x = ^3(square root )of 18075 or 5.24875253...
-----------------------
5
Step-by-step explanation:
isolate the variable by deviding each side by factors that dont contain the variable
hope this helped have a good day ^^
The graph shows Ms. Padilla's monthly cell phone cost, where x is the number of minutes she uses the phone during the month.
Which statements are true? Select each correct answer.
options:
a. The x-intercept is meaningless here.
b. Ms. Padilla is charged $5/min.
c. Ms. Padilla is charged $0.04/min.
d. Ms. Padilla pays $16 for months she makes 0 min of calls.
Answer:
True statements: a, c and d
Step-by-step explanation:
The x-intercept of the line would be negative. As it is impossible to make a negative number of calls, the x-intercept is meaningless.
To find the amount that Ms Padilla is charged per minute, find the slope of the line by substituting the two given points into the slope formula:
[tex]\implies \sf Slope=\dfrac{Change\;in\;y}{Change\;in\;x}=\dfrac{21-16}{125-0}=\dfrac{5}{125}=0.04[/tex]
Therefore, Ms Padilla is charged $0.04/min.
From inspection of the graph, the y-intercept is (0, 16).
Therefore, Ms Padilla pays $16 for the months she makes 0 minutes of calls.
the time between visits to a u.s. emergency room for a member of the general population follows an exponential distribution with a mean of 2.5 years. what proportion of the population:
Using the exponential distribution, it is found that the proportion of the population that will visit an emergency room in the next six months is of 0.1813 = 18.13%.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In this function, [tex]\mu = \frac{1}{m}[/tex] represents the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
The solution of the definite integral gives the cumulative mass function as follows:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
In this problem, the mean is of 2.5 years, hence the decay parameter is calculated as follows:
[tex]\mu = \frac{1}{2.5} = 0.4[/tex]
The proportion of the population that will visit the emergency room in the next six months is P(X < 0.5), as 6 months = 0.5 years, hence:
[tex]P(X \leq 0.5) = 1 - e^{-0.4 \times 0.5} = 0.1813.[/tex]
Missing InformationThe problem asks for the proportion of the population that will visit an emergency room in the next six months.
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What is the fractional equivalent of the repeating decimal n = 0.1515... ? Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
ill give 25 points and maybe brainlist
The fractional equivalent of the repeating decimal n = 0.15.15.. is
15/99. And the number represented by n has two repeating digits that is 15.
Given, repeating decimal n = 0.1515..
We must come up with a strategy to eliminate the recurring portion before converting what is left into a fraction. We can benefit from the repetition on our behalf.
set x = 0.151515 ...eq(1)
the 15 is a recurring number means that those two digits keep repeating forever.
so
100x = 15.151515.. eq(2)
Subtract eq(2) from eq(1).
100x = 15.151515
x = 0.151515
we get, 99x = 15
hence x = 15/99
Therefore, the equivalent of the repeating decimal is 15/99.
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Write the function in vertex form.
y = 3x² - 8x + 13
The function is y=
Answer:
y = 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex]
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
given
y = 3x² - 8x + 13
using the method of completing the square
the coefficient of the x² term must be 1 so divide first 2 terms by 3
y = 3(x² - [tex]\frac{8}{3}[/tex] x) + 13
add/subtract ( half the coefficient of the x- term )² to x² - [tex]\frac{8}{3}[/tex] x
y = 3(x² + 2(- [tex]\frac{4}{3}[/tex] )x + [tex]\frac{16}{9}[/tex] - [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² + 3(- [tex]\frac{16}{9}[/tex] ) + 13
= 3(x - [tex]\frac{4}{3}[/tex] )² - [tex]\frac{16}{3}[/tex] + [tex]\frac{39}{3}[/tex]
= 3(x - [tex]\frac{4}{3}[/tex] )² + [tex]\frac{23}{3}[/tex] ← in vertex form
Can someone help me with this ??
-7e + 8 = -13
Identify the corresponding angles for each given angle.
A. S
B. C
C. D
D. P
The angles which are corresponding to each of the angles listed in the pre-image are as follows;
A. Angle S is corresponding to Angle D.B. Angle C is corresponding to Angle R.C. Angle D is corresponding to Angle S.D. Angle P is corresponding to Angle A.What are the corresponding angles to the given angles?It follows from the task content that the image attached represents the reflection of a pre-image figure over the vertical, y-axis to form an image.
It follows from definition that; A corresponding angle, put simply is one that holds the same relative position as another angle somewhere else in the same figure or in another (similar/congruent) figure.
Hence, the corresponding angles as evident from the figure vertexes and their equivalent in the image are as follows;
Angle D is corresponding to Angle S.Angle C is corresponding to Angle R.Angle B is corresponding to Angle Q.Angle A is corresponding to Angle P.Angle E is corresponding to Angle T.Read more on corresponding angles;
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pleasee helpp me :)
Answer:
Step-by-step explanation:
y=34
the angle measures are 20, 136, 24
20+(y-10)+4y=180
simplify/solve for y
3.State the domain and range for the function y = 4^x+ 3.
The domain of the function is (-∝,∝) and the range is (3,∝) .
We know that the given function is of the form [tex]y=4^x+3\\[/tex] .
So the possible values of x or the domain will be all real values of x.
Now we know from the properties of indices that for all and any real value of x , [tex]4^x > 0[/tex] so the value of y will always be greater than 3 .
For higher values of x the value of y will be higher.
So the range of the function will include all real values greater than 3
The incoming dataset that a function will accept is its domain in mathematics. Domain(f), where f stands for the operation, is another way to express it.
The relationship between the dependent variable y and the regression coefficient x defines the function
A value is said to be in the domain of a function f if it successfully facilitates the production of a sharp number y using another value for x.
So domain : {x | x∈(-∝,∝)}
range : {y | y∈ (3,∝)}
Hence the domain of the function is {x | x∈(-∝,∝)} and the
range is {y | y∈ (3,∝)} .
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x = -5y + 4 3x + 15y = -1
Answer: UNDEFINED
Step-by-step explanation:
x=-5y+4 5y=-x+4 y=-1/5x+4/5
3x+15y= -1 15y=-3x-1 y=-1/5x-1/15
COMBINED: -1/5x+4/5=-1/5x-1/15 FIND COMMON DENOMINATOR=15
-3/15x=-3/15x-13/15
0=-13/15 UNDEFINED
a class of 20 students have one week to complete a math assignment of 30 questions. at the end of the first day, the students had completed the following number of questions:
The modes of the data set are 4, 5, and 6. Hence, the data set has three modes.
The mode is the outcome that happens most commonly when gathering data. A collection of data may have one pattern, numerous patterns, or absolutely no patterns at all.
A class of 20 students has one week to complete a math assignment of 30 questions.
The following number of questions had been answered by the pupils by the end of the first day:
5, 7, 4, 6, 1, 8, 9, 4, 4, 5, 10, 4, 6, 5, 3, 6, 5, 6, 0, 2
When the above data set is arranged in ascending order:
0, 1, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10
In the data set, 4 appears four times, 5 appears four times, and 6 appears four times.
Therefore, the mode of the data set is 4, 5, and 6.
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The complete question is mentioned below:
Mark this quest A class of 20 students have one week to complete a math assignment of 30 questions. At the end of the first day, the students had completed the following number of questions: 5, 7, 4, 6, 1, 8, 9, 4, 4, 5, 10, 4, 6, 5, 3, 6, 5, 6, 0,2 How many modes are in the given data set?
ames determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply. 7 x + 4 and 3 x + 5 + 4 x minus 1 When x = 2, both expressions have a value of 18. The expressions are only equivalent for x = 4 and x = 6. The expressions are only equivalent when evaluated with even values. The expressions have equivalent values for any value of x. The expressions should have been evaluated with one odd value and one even value. When x = 0, the first expression has a value of 4 and the second expression has a value of 5. The expressions have equivalent values if x = 8.
The statements are true about the given expressions include the following:
When x = 2, both expressions have a value of 18.The expressions have equivalent values for any value of x.The expressions have equivalent values if x = 8.How to determine whether the expressions are equivalent?In order to determine whether these expressions are equivalent, we would evaluate the two expressions based on each of the statements:
"When x = 2, both expressions have a value of 18"
7x + 4 = 7(2) + 4 = 14 + 4 = 18.
3x + 5 + 4x - 1 = 3(2) + 5 + 4(2) - 1 = 6 + 5 + 6 - 1 = 18.
"The expressions are only equivalent for x = 4 and x = 6." is false has demonstrated above.
"The expressions have equivalent values for any value of x." is true.
Let x = 1;
7x + 4 = 7(1) + 4 = 7 + 4 = 11.
3x + 5 + 4x - 1 = 3(1) + 5 + 4(1) - 1 = 3 + 5 + 4 - 1 = 11.
Let x = 10;
7x + 4 = 7(10) + 4 = 70 + 4 = 74.
3x + 5 + 4x - 1 = 3(10) + 5 + 4(10) - 1 = 30 + 5 + 40 - 1 = 74.
"The expressions should have been evaluated with one odd value and one even value." is false because all values of x are solutions.
"When x = 0, the first expression has a value of 4 and the second expression has a value of 5." is false because the two expressions are equivalent expressions.
In conclusion, "The expressions have equivalent values if x = 8." is true because the two expressions are equivalent expressions.
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Pls help on 15 show your work my teacher gets so mad ab it I have that written down what it looks like
I have a power triangle hopefully it can help
Answer:
49 runners.
Step-by-step explanation:
Hello! Let's help you there!
So, to start, it looks like you have the basis of what you're trying to accomplish and it seems like you're almost there too!
So you know that it's the percentage you need to figure out and divide by 100, it's the second numerator that you're trying to figure out. Since we don't necessarily know what the is/part of the equation, we can use a variable to be able to figure out what the is/part well, is.
When we set it up, it's as such:
[tex]\frac{28}{100}=\frac{x}{175}[/tex]
We're going to be using the letter x, to represent the unknown number that we're trying to figure out.
In order to solve it, we first cross-multiply. We take the numerator of the first fraction and multiply it by the denominator of the second fraction and the exact same for the denominator of the first fraction and the numerator of the second fraction. So we get:
[tex]28*175=100x[/tex]
Now we can evaluate [tex]28*175[/tex] and simplify that down to:
[tex]28*175=4900[/tex]
Now it becomes:
[tex]4900=100x[/tex]
In order to figure out our mystery value, we want to get rid of the 100 in front of the x. Since it is multiplied to x, we can divide it by 100 to get rid of the 100 in front of the x, but at the same time, we must divide it as well on the other side, so it becomes:
[tex]\frac{4900}{100} =\frac{100x}{100}[/tex]
Now the answer becomes:
[tex]49=x[/tex]
Therefore, our mystery value is 49 runners stopped to take a drink!
A triangle has sides with lengths of 3 kilometers, 4 kilometers, and 6 kilometers. Is it a right triangle?
Where can I find angles measurements that is Missing each set of supplemenry angles?
Remember that
If the sum of two angles is equal to 180 degrees, then the angles are supplementary
so
In this problem
Let
x ----> the missing angle
x+34.6 =180 degrees -----> by form a linear pair (supplementary angles)
solve for x
x=180-34.6
x=145.4 degreesSolve |x +31-1 = (x + 2)2 by graphing
After plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
What is a graph?In mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way. The relationships between two or more things are frequently represented by the points on a graph. In mathematics, "graph" can refer to (at least) two different things. In elementary mathematics, the term "graph" designates a plot or a function graph. A graph is, in the language of mathematicians, a set of points and the connections between some subset of those points (which may be empty).So, solving "|x| +31-1 = (x + 2)2" by graph:
Graph both the equations, "|x| +31-1" and "(x + 2)2" on the graph.(Refer to the graph attached below)
Now, according to the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.Therefore, after plotting the equation on the graph, we know that the value of |x| on line "(x + 2)2" is -0.125 and 0.142.
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Evaluate the following expression, given that x = -6 and y =12.
|2x+5| - 8y
The value of expression |2x+5| - 8y is -89 when x = -6 and y =12
What is Expression?Expression is a combination of numbers, variables and Operators.
The given expression is mod two x plus 5 minus eight y.
|2x+5| - 8y
This expression has addition, subtraction and multiplication operators.
Given value of x is minus six and y is equal to twelve.
x=-6 and y=12
plug in values of x and y in expression
|2(-6)+5|-8(12)
|-12+5|-96
|-7|-96
The value in mod will be always taken as positive
7-96
-89
Hence the value of expression |2x+5| - 8y is -89 when x = -6 and y =12.
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To win the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive. Suppose you collected 82, and, 84 pop tabs during the first two weeks of competition. Write and solve a compound inequality to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
As per the compound inequality, the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest is 83 ≤ (82 + 84 + n)/3 ≤ 87; 83 ≤n ≤ 95.
Compound inequality:
A compound inequality is an inequality that merges two inequalities either by using "and" or "or".
Given,
In the recycling contest, you must collect between 83 and 87 pop tabs each week, inclusive for winning.
And suppose you collected 82, and, 84 pop tabs during the first two weeks of competition.
Here we nee to find the possible values for the number of pop tabs that need to be collected during the third and final week of the competition in order to win the contest.
Let us consider n be the number of pop tabs.
So, it can be written using the compound inequality,
=> 83 ≤ (82 + 84 + n) /3 ≤ 87
To cancel the fraction we have to multiply 3 with all of them, then we get,
=> 83 x 3 ≤ (82 + 84 + n) ≤ 87 x 3
=> 249 ≤ (166 + n) ≤ 261
To find the value of n we have to subtract 166, then we get,
=> 249 - 166 ≤ n ≤ 261 - 166
=> 83 ≤ n ≤ 95
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