The meaning of the situation involving the camp director and the sack lunches, is D. The number of lunches left over after packing the boxes.
What does the remainder show ?The remainder in this instance, shows the number of lunches that the camp director will not be able to fit in boxes and so will be left over after the boxes have been packed.
There are 85 sack lunches and yet only 3 lunches can go into a single box. The number of boxes would be:
= 85 / 10
= 10 boxes remainder 5 lunches
10 boxes will be filled with lunch sacks and 5 lunches will be leftover.
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The full question is:
The camp director is putting 85 sack lunches in boxes for a picnic. She can fit 8 lunches in each box. She does the division problem shown to find out how many boxes she will need. 85 divided 8 = 10 remainder 5
What is the meaning of the remainder in this situation?
A. The number of extra boxes needed.
B. The number of extra lunches needed.
C. The number of boxes left over after packing the lunches.
D. The number of lunches left over after packing the boxes.
Students at a high school were polled to determine the type of music they preferred. There were students who completed the poll. Their responses are represented in the circle graph.
What percent of students preferred music?
A circle graph titled Music Preferences consists of a circle divided into 6 regions with labels and sizes as follows: rap, 945; alternative, 462; rock and roll, 275; country, 168; jazz, 15; other, 85.
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
The percent of students that preferred alternative music is 23.7%
How to determine the percentage?The music type and the preference are given as:
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85
From the above table, we have:
Alternative = 462
Total = 945 + 462 + 275 + 168 + 15 + 85
Total = 1950
The percentage is then calculated as:
Percentage = Alternative/Total * 100%
This gives
Percentage = 462/1950 * 100%
Evaluate
Percentage = 23.7%
Hence, the percent of students that preferred alternative music is 23.7%
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If f(x) = x and g(x) = 2, what is (fog)(x)?
Step-by-step explanation:
=fog(x)
−2x=0
x(x−2)=0
x=0,2
The following data show the height, in inches, of 11 different plants in a garden:
9
4
10
9
5
2
22
10
3
3
5
After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.
What does the mean absolute deviation represent?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.
Mean absolute deviation = (1/n) x ∑ l x - m(x) l
Mean without the outlier : (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6
(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = 3.2
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What is the domain of the function given below
Answer:
c. [-1, infinity)
Step-by-step explanation:
the domain the interval or set of valid x values (while the range is the same for the valid y values).
what is the smallest value of x we see for the graph ?
for x values we need to look left and right.
and the more left the value, the smaller it is.
so, in other words, what is the left-most x value e can find ?
x = -1
that is the "starting point" of the function. there is no functional value for any smaller x.
and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.
therefore the answer.
keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).
If cot theta = 3/2, what is the value of csc theta?
The value of csc theta is [tex]\frac{3. 61}{2}[/tex]
How to determine the valueIt is important to note that the ratio for cot is given as;
Cot theta = adjacent/opposite
cosec theta = hypotenuse/opposite
If cot theta = 3/2, then
Adjacent = 3
Opposite = 2
Using Pythagoras theorem, we have
Hypotenuse square = opposite + adjacent square
[tex]H = \sqrt{2^2 + 3^2}[/tex]
[tex]H = \sqrt{4 + 9}[/tex]
[tex]H = 3. 61[/tex]
Cosec theta = [tex]\frac{3. 61}{2}[/tex]
Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]
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Answer:
3.16/2
Step-by-step explanation:
Have a great day
Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6
Answer:
Step-by-step explanation:
eq. of any line perpendicular to 5x+6y=-6 is
5y-6x=c
where c is a constant.
it passes through (-2,-1) so
5(-1)-6(-2)=c
c=-5+12=7
so reqd. eq. is 5y-6x=7
or 6x-5y=-7
or
slope of given line =-5/6
slope of reqd. line=6/5
eq. of line through (-2,-1) with slope 6/5 is
y+1=6/5(x+2)
5y+5=6x+12
5y=6x+12-5
or 5y=6x+7
or
6x-5y=-7
The median household in the United States increased by a rate of 0.25% each year between 1980 and 1985. If the median household income was $42,050 in 1980, what was the median household income after 5 years? Round answer to the nearest whole dollar.
Using an exponential function, the median household income after 5 years was of $42,578.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.For this problem, the parameters are:
A(0) = 42050, t = 5, r = 0.0025[/tex]
Hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]A(t) = 42050(1.0025)^t[/tex]
[tex]A(5) = 42050(1.0025)^5 = 42578[/tex]
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Which of the following functions best describes this graph?
Answer:
C
Step-by-step explanation:
We can use process of elimination
D is incorrect because the roots are 3 and -4 and there are no negative roots visible
B is wrong because the roots -3 and -6 are both negative
You can factor A into (x-2)(x-3) and the roots are 2 and 3 but the roots on the graph look closer to 3 and 6
For C it can be factored as (x-6)(x-3) so the roots are 3 and 6 which look accurate
Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equations that can be used to find the lengths of the legs of the triangle are as follows:
100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,
Therefore,
c² = a² + b²
where
c = hypotenuse sidea and b are the other legsTherefore,
10² = (x + 2)² + x²
100 = (x + 2)² + x²
Therefore, using the area of a triangle,
area of a triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × (x + 2)(x)
24 = 0.5 × (x + 2)(x)
24 = x² + 2x / 2
cross multiply
48 = x² + 2x
x² + 2x - 48 = 0
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How many fewer people live in Elmira than White Plains
Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.
Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.
Thus in the given question, it can be deduced that;
The population of people living in White Plains =56,853
The population of people living in Elmira = 29,200
So, the difference in the population between the two cities can be determined as;
= 56,853 - 29,200
= 27,653
Thus, the number of fewer people living in Elmira than in White Plains is 27,653
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Select all of the following that are quadratic equations.
5x-1=3x+8
5 x- 3 = 0
x²-2x = 4x+1
2x²+12 x = 0
x³-6x² + 8 = 0
9x²+6x-3=0
The quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
Given six equations as under:
5x-1=3x+85 x- 3 = 0x²-2x = 4x+12x²+12 x = 0x³-6x² + 8 = 09x²+6x-3=0We are required to find the quadratic equations among the above equations.
Quadratic equations are those equations in which the highest power of the variable present in the equation is 2.
It is in form of [tex]ax^{2} +bx+c=0[/tex].
In our options quadratic equations are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
5x-1=3x+8: It is not a quadratic equation as the highest power is 1.
5 x- 3 = 0:It is also a linear equation not quadratic equation.
x³-6x² + 8 = 0:It is a cubic equation not a quadratic equation.
Hence the quadratic equations among all the options given are [tex]x^{2} -2x=4x+1[/tex],[tex]2x^{2} +12x=0[/tex] and [tex]9x^{2} +6x-3=0[/tex].
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In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?
Using it's concepts, we have that:
The absolute change was of $15,153 million.The relative change was of 60.60%.What is the absolute change of two values?The absolute change between two values is given by the absolute value of the difference between two values.
In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:
A = 40,156 - 25,003 = $15,153 million.
What is the relative change?The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:
(15,153/25,003) x 100% = 60.60%.
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What are the fourth roots of -3+3√3i?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.
By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].
How to determine a fourth root of a complex numberAccording to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:
[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)
Where:
r - Magnitude of the complex number.θ - Direction of the complex number, in radians.First, we find the magnitude and direction of the complex number:
[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]
r = 6
[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]
[tex]\theta = \frac{2\pi}{3} \,rad[/tex]
Now we find the four quartic roots of the complex number:
[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]
[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]
[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]
[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]
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A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following.
1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute.
2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses.
Mark's method is correct, because even though it is impossible to deliver mail to 1.2 houses in minute, it represents the unit rate of houses per minute .
Is Mark's method correct?The first step is to determine the unit rate of houses per minute. This can be done by dividing 36 houses by 30 minutes.
36/30 = 1.2 houses per minute
The second step is to multiply 1.2 by 7.5: 1.2 x 7.5 = 9 houses
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Find the area of the figure.
You get a raise of 3.5% each year.
a. What is the approximate doubling time of your salary?
b. If you are currently 25 years old and are making $40,000 per year, use the approximate doubling time to find your annual salary when you retire at the age of 65.
Using an exponential function, it is found that:
a) The doubling time of the salary is of approximately 20 years.
b) The salary will be of $160,000.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the growth rate, as a decimal.The growth rate for this problem is:
r = 0.035.
The doubling time is t for which A(t) = 2A(0), hence:
[tex]A(t) = A(0)(1 + r)^t[/tex]
[tex]2A(0) = A(0)(1.035)^t[/tex]
[tex](1.035)^t = 2[/tex]
[tex]\log{(1.035)^t} = \log{2}[/tex]
[tex]t\log{1.035} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{\log{1.035}}[/tex]
t = 20 years.
You retire in 40 years, which is 2 doubling periods, hence the salary will be of:
40000 x 2 x 2 = $160,000.
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SKETCHPAD
Question 5
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro (T(-4,3)(ABC))
90°
Draw AA'B'C'' if
You may use different colors for the separate transformations. Indicate your final
answer. Feel free to use the Dynamic Geometry Tool to complete the
transformations.
The attached figure represents the image of A"B"C" after the transformation
How to transform the triangle?The transformation rule is given as:
A"B"C" = Ro90° (T(-4,3)(ABC))
This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle
From the figure, the coordinates of ABC are
A = (-1, 2)
B = (1, 4)
C = (3, -1)
The rule of 90 degrees clockwise rotation is
(x,y) ⇒ (y,-x)
So, we have
A' = (2, 1)
B' = (4, -1)
C' = (-1, -3)
The translation of the triangle by T(-4,3) is
(x,y) ⇒ (x - 4, y + 3)
So, we have
A'' = (-2, 4)
B'' = (0, 2)
C'' = (-5, 0)
See attachment for the image of the transformation
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10 - 13x + 2 in words
The simplification of the equation above in words is = Twelve minus thirteen X.
Simplification of an equationIn mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.
The equation given is,
10 - 13x + 2
Arrange the digits without a coefficient together.
That is ,
10+2 -13x
12 - 13x
Therefore the simplification of the given equation in words is Twelve minus thirteen X.
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What is the y-intercept of the liner function? (y=3x-2)
The y-intercept of the linear function y = 3x - 2 is -2
How to determine the y-intercept?The function is given as
y = 3x - 2
The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)
As a general rule, linear functions are those functions that have constant rates or slopes
Next, we set x to 0, and calculate y to determine the value of the y-intercept
y = 3(0) - 2
Remove the bracket in the above equation
y = 3 * 0 - 2
Evaluate the product of 3 and 0 i.e. multiply 3 and 0
y = 0 - 2
Evaluate the difference of 0 and -2 i.e. subtract 0 from 2
y = -2
The above means that the value of y when x is 0 is -2
Hence, the y-intercept of the linear function y = 3x - 2 is -2
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A jar contains 100ml of a mixture of oil and water in the ratio 1:4. Enough oil is added to make the ratio of oil to water 1:2. How much water must be added to make the ratio oil to water 1:3?
Answer:
40 ml of water must be added.Step-by-step explanation:
Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.
First, let's find the volume of each component.
If the oil is x then water is 4x according to ratio and their sum is 100 ml:
x + 4x = 1005x = 100x = 20So, we have 20 ml of oil and 80 ml of water.
Now, let's added volume of oil be y. Then we have the ratio:
(20 + y)/80 = 1/220 + y = 40y = 20So, we have 40 ml of oil and 80 ml of water.
Lastly, let's added water be z. Then we have the ratio:
40/(80 + z) = 1/380 + z = 120z = 40We must add 40 ml of water.
Need help with that I don’t understand it
The answer is no. b.
Step-by-step explanation:
The answer is no b. u just take common
Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).
Which statements correctly compare the sum and product? Check all that apply.
Both functions have a constant rate of change.
The sum is linear and the product is quadratic.
The x-intercepts are the same.
The sum has one y-intercept and the product has two x-intercepts.
Both functions decrease for x ≥ 2.
The statements that correctly compare the sum and product of the function are:
The sum is linear and the product is quadratic.The sum has one y-intercept and the product has two x-intercepts.What is a linear function?A linear function simply means a function that represents a straight line on the coordinate plane.
In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.
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Find the axis of symmetry:
Picture is below.
Answer:
x = -3
Step-by-step explanation:
Axis of symmetry:Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.
From the graph, Vertex (-3, 4)
Axis of symmetry: x = -3
Solve the logarithmic equation by writing in exponential form or by
graphing.
log (5-2x) = 0
Answer:
Hello,
Step-by-step explanation:
[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]
how can i got 24.8 show your work
9. For Investment Plan A to C, solve for the future value at the end of the term based on the
information provided.
Investment Plan Principal
A
$7,500
B
$53,000
C
$19,000
Interest Rate
8% compounded quarterly
6% compounded monthly
5.75% compounded semi-annually
Term
3 years
4
years and 3 months
6 years and 6 months
The future value of Investment A is 9511.81
The future value of Investment B is 68,351.02
The future value of Investment C is29.067.07.
What are the future values?When an amount earns a compound interest, it means that both the amount invested and the interest rate already accrued increases in value at the next compounding date. For example, if interest is compounded quarterly, both the amount invested and the interest accrued increases every quarter.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInvestment A = 7500 x [(1 + (0.08/4)]^(4 x 3) = 9511.81
Investment B = 53,000 x [(1 + (0.06/12)]^[(4 x 12) + 3) = 68,351.02
Investment C = 19,000 x [(1 + (0.0575/2)]^{6 x 2) + 6/2) = 29.067.07
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If n = 140 and X = 112, construct a 95% confidence interval for the population proportion, p.
Give your answers to three decimals
The confidence interval for the population proportion, p is (0.766, 0.833)
Confidence intervalThe formula for calculating the confidence interval for proportion is expressed as:
CI = p±√pq/n
Given the following
p = 112/140 = 0.8
q = 1-p = 0.2
Substitute
CI = 0.8±√(0.8)(0.2)/140
CI = 0.8±0.0338
CI = (0.766, 0.833)
Hence the confidence interval for the population proportion, p is (0.766, 0.833)
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Express the confidence interval (0.065,0.143) in the form of p - E
The confidence interval expressed in the form p - E is:
(0.104 - 0.039, 0.104 + 0.039).
What are the mean and the margin of error of a confidence interval?The mean is the mean of the bounds, hence:
p = (0.065 + 0.143)/2 = 0.104.
The margin of error is the difference between the bounds and the mean, hence:
E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.
Hence the interval in the desired format is:
(0.104 - 0.039, 0.104 + 0.039).
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A national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile. Brian's sales
are at the 33rd percentile.
(If necessary, consult a list of formulas.)
(a) Which of the following must be true about Karen's sales?
The value of Karen's sales were about 26% of the chain's total.
O The value of Karen's sales was in the top half of all of the salespeople.
O Karen sold $2600 in merchandise.
O Karen had sales lower in value than about 74% of the salespeople.
(b) Which of the following must be
true about Karen's and Brian's sales?
The value of Brian's sales were $700 more than Karen's.
O The value of Karen's sales were $700 more than Brian's.
O Both Karen and Brian had sales higher in value than the median.
O Both Karen and Brian had sales lower in value than the median.
(a) The truth about Karen's sales is that Karen had sales lower in value than about 74% of the salespeople. So, the correct option is D.
(b) The truth about Karen's and Brian's sales is that both Karen and Brian had lower sales in value than the median. So, the correct option is D.
Given that department stores rank their 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile and brian's sales are at the 33rd percentile.
A percentile is a measure used in statistics that indicates the value below which a certain percentage of observations in a group of observations falls.
(a) Karen had sales lower in value than about 74% of the salespeople because the 26% percentile represents his relative position among all the employees in terms of sales.
(b) Both Karen and Brian had sales lower in value than the median because the Median represents the 50th percentile. Since Karen's sales are at the 26th percentile and Brian's sales are at the 33rd percentile it implies their sales are less than the median value.
Hence, the truth about Karen's sales is Karen had sales lower in value than about 74% of the salespeople, and true about Karen's and Brian's sales is both Karen and Brian had lower sales in value than the median.
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Explain how to determine if Carlos’s allowance is directly proportional to the number of chores he completes.
A 2-column table with 3 rows. Column 1 is labeled number of chores with entries 10, 13, 15. Column 2 is labeled Allowance with entries 75 dollars, 97 dollars and 50 cents, 112 dollars and 50 cents.
Using a proportional relationship, it is found that Carlos earns an allowance of $7.5 for each chore that he completes.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the constant is:
k = 75/10 = 97.5/13 = 112.5/15 = 7.5.
Hence Carlos earns an allowance of $7.5 for each chore that he completes.
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