Solutions refers to the answer to the problem, The example of real solution can be the solution for the value of 'x' in a equation.
What do you mean by a solution?In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.
What are ideal and real solutions?In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.
example:
x+2=0
x=-2
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Write an exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12.
The exponential function f so that the slope of a line from the point (0, f(0)) to the point (2, f(2)) is equal to 12 is defined as follows:
f(x) = 5^x.
How to define the exponential function?The general format of an exponential function is given as follows:
y = ab^x.
In which:
a is the initial value.b is the rate of change.The slope of a line, given two points, is given by the division of the change in the output by the change in the input of these two points.
Considering that the slope of points (0, f(0)) and (2, f(2)) is equals to 12, we have that:
[f(2) - f(0)]/(2 - 0) = 12
f(2) - f(0) = 24.
One case that satisfies this involves these two following points.
(0,1) -> f(0) = 1.(2,25) -> f(2) = 25.Hence the parameter a is given as follows:
a = 1.
When x = 2, y = 25, meaning that the parameter b is calculated as follows:
b² = 25
b = 5.
Hence the exponential function is:
f(x) = 5^x.
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. Solve for x in the equation log (7x+5) -log(x - 1) = 1(with full working
Answer:
Step-by-step explanation:
To solve this equation, we can start by using the logarithm property that states: log(a) - log(b) = log(a/b).
Then, we can apply this property to the left side of the equation:
log (7x+5) - log(x - 1) = log((7x+5)/(x - 1)) = 1
Next, we can rewrite the right side of the equation as:
log((7x+5)/(x - 1)) = log(7x+5) - log(x - 1) = 1
Now, we can use the inverse property of logarithms, which states: log(a) = b, then a = 10^b, to solve for x.
This gives us: (7x+5)/(x - 1) = 10
We can then cross-multiply and simplify to get: 7x+5 = 10x - 10
This equation simplifies to: 3x = -5
Dividing both sides by 3 gives us: x = -5/3
Therefore, the solution to the equation is x = -5/3.
In tenpin bowling, the height of each bowling pin must be 15 inches with an absolute deviation of 0.03125 inches find the minimum and maximum possible heights of the bowling pin.
The minimum and maximum possible heights of the bowling pin are 14.96875 inches and 15.03125 inches
How to find the minimum and maximum possible heights of the bowling pin.From the question, we have the following parameters that can be used in our computation:
Absolute deviation = 0.03125 inches
Height = 15 inches
The minimum is calculated as
Minimum = Height - Absolute deviation
Substitute the known values in the above equation, so, we have the following representation
Minimum = 15 - 0.03125 inches
Minimum = 14.96875 inches
The maximum is calculated as
Maximum = Height + Absolute deviation
Substitute the known values in the above equation, so, we have the following representation
Maximum = 15 + 0.03125 inches
Minimum = 15.03125 inches
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Jump to level 1
Housing prices in a small town are normally distributed with a mean of
$142,000 and a standard deviation of $7. 0. Use the empirical rule to
complete the following statement.
Approximately 95% of housing prices are between a low price of
$ Ex: 5000 and a high price of $
Modul Three Assignment Gui.
4. 2. Normal distribution - Goog.
By standard deviation, 68% housing price are between a low price of $135000 and a high price of $149000.
What is standard deviation in math?
The variability in your dataset is measured by its standard deviation. It reveals the average deviation between each result and the mean.
A low standard deviation denotes that values are grouped close to the mean, whereas a large standard deviation shows that values are often far from the mean.
Given,
mean (μ) = 142000
standard deviation (σ ) = 7000
By using empirial rule,
P( μ - σ ≤ X ≤ μ + σ ) ≈ 68%
Then,
P(142000 - 7000 ≤ x ≤ 142000 + 7000 ) ≅ 68%
P( 135000 ≤ x ≤ 149000 ) ≅ 68%
68% housing price are between a low price of $135000 and a high price of $149000.
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What is the slope of the line passing through the points
(-8, 5) and (7,0)?
Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.
The slope of the line passing through the points (-8, 5) and (7,0) can be found by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
So, using the coordinates (-8, 5) and (7,0), we have:
m = (0 - 5) / (7 - (-8)) = -5 / 15 = -1/3
Therefore, the slope of the line passing through the points (-8, 5) and (7,0) is -1/3.
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HELPPPPPPP MEEEEE
If a trapezoid has an area of 135cm^2 and it’s height is 10cm and one base is 12 cm, find the other base length.
thxxx <333
The length of other base is 15 cm.
The area of a trapezoid can be found by using the formula:
Area = (b1+b2) * h / 2 where b1 and b2 are the lengths of the bases, and h is the height.
Given that the area of the trapezoid is 135 cm^2, the height is 10 cm, and one base is 12 cm, we can substitute these values into the formula to find the length of the other base.
Area = (b1+b2) * h / 2 = 135cm^2
We can solve for the other base length by isolating b1
b1 = 2*Area/h - b2
b1 = 2*135/10 - 12 = 27 - 12 = 15
So, the other base length is 15 cm.
Therefore, The length of other base is 15 cm.
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Each grid square is 1 square unit. Find the area, in square units, of the shape without counting every square. Be prepared to explain your reasoning.
The total area of the two rectangles is given by the equation A = 33 units²
What is the Area of a Rectangle?The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle
Area of Rectangle = Length x Width
Given data ,
Let the total area of the 2 rectangles be A
Now , each grid square represents = 1 square unit
Now , let the first rectangle be represented as P
The length of P = 4 grid squares
The width of P = 3 grid squares
Let the second rectangle be represented as Q
The length of Q = 7 grid squares
The width of Q = 3 grid squares
So , Area of Rectangle = Length x Width
The area of rectangle P = 4 x 3
The area of rectangle P = 12 units²
The area of rectangle Q = 7 x 3
The area of rectangle Q = 21 units²
So , the total area of figure A = area of P + area of Q
On simplifying the equation , we get
Total area of figure A = 12 units² + 21 units²
Total area of figure A = 33 units²
Therefore , the value of A is 33 units²
Hence , the area is 33 units²
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Find m (angle) 1 . Then classify the triangle by its angles.
M (angle) 1 =
Answer:
right triangle m=5
Step-by-step explanation:
because it has a 90 degree angle
If a partical traveled a distance of 9.0×1012 meters at a rate of 1.8×105 meters per second. If distance = rate x time, how many seconds did it take the particle to travel the specified distance?
A particle traveled a distance of 9.0×10¹² meters in 5.0 × 10⁷ seconds.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
If a particle traveled a distance of 9.0×10¹² meters at a rate of 1.8×10⁵meters per second.
And the distance,
= rate x time.
Rearranging the formula,
Time = Distance / rate
Time = 9.0×10¹² / 1.8×10⁵
Simplifying by using division operation,
Time = (9.0/1.8) × 10¹² × 10⁻⁵
Time = 5.0 × 10⁷
Therefore, the required specified time is 5.0 × 10⁷ seconds.
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45. Sliding Down a Hill
Ojemba is sitting on a sled on the side of
a hill inclined at 60°. The combined weight of Ojemba and the
sled is 160 pounds. What is the magnitude of the force required
for Mandisa to keep the sled from sliding down the hill?
If Ojemba is sitting on a sled on the side of a hill inclined at 60° and weight of Ojemba and sled is 160 pounds , then magnitude of force needed for Mandisa to keep sled from sliding down the hill is 355.59 N .
the inclination angle of the the side of the hill is = 60° ;
the compound mass of Ojemba and Sled is = 160 pounds ,
On conversion we get the mass in Kg is = 72.57 Kg .
the acceleration due to gravity is , [tex]g = 9.8 m/s^{2}[/tex] ;
The force required for Mandisa to keep sled from sliding down the hill can be calculated by the formula ;
[tex]F = mgSin\theta[/tex] , Substituting the values ,
we get ;
[tex]F = 72.57\times 9.8\times Sin(30\textdegree)[/tex]
[tex]F = 72.57\times 9.8\times \frac{1}{2}[/tex] ;
So , [tex]F = 355.59 N[/tex] .
The required magnitude of the force is 355.59 N .
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PLEASE HELPP!!! picture attached
Which diagram shows an obtuse scalene triangle?
Option D. is an obtuse scalene triangle in the given lists of diagrams.
What is obtuse scalene triangle?In terms of geometry, an obtuse scalene triangle is one in which one of the angles is less than 90 degrees and the other two are less than 180 degrees, with the one angle measuring greater than 90 degrees but less than 180 degrees. Measurement differences exist for each of the three sides and angles.
Both the obtuse triangle and the scalene triangle's characteristics are present in an obtuse scalene triangle. A scalene triangle has all three sides and angles that are of a different size, whereas an obtuse triangle only has one obtuse angle. The following are the characteristics of an obtuse scalene triangle:
Two of its angles are acute, while the other is obtuse.Measurement varies across all sides and angles.Three interior angles added together result in a 180° angle.Learn more about obtuse triangle
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Morgan bought 95 roses from the florist for her wedding. The roses cost $1.75 each, including sales tax. If Morgan gives the florist $200, how much change should she get back?
Answer:
33.75
Step-by-step explanation:
1.75*95 = 16 6.25
200 - 166.25 = 33.75
Parker could pay 45% of his college tuition with his scholarship. The remaining $10,500 he paid for a with a student loan. What was the cost of Parker's tuition? Show your work.
Answer:
5,775 for the cost of parking tuition
Step-by-step explanation:
45% = 0.45
0.45(10,500)= 4,725
10,500 - 4,725 = 5,775 for the cost of parking tuition
A news website is interested in knowing which other sites its users visit for their technology news, so it sends an email survey to 10,000 of its registered users selected at random. For what type of bias are the survey results at risk
10,000 randomly chosen registered users receive an email survey from the company. The survey findings are most susceptible to nonresponse bias.
What type of bias are the survey results at risk for?A news website sends an email survey to 10,000 randomly chosen registered users in order to learn which other websites its readers visit for their technology news. The most common sort of bias that the survey results are vulnerable to is nonresponse bias. Because convenience sampling, which many researchers engage in, frequently leads to undercoverage bias in survey research, it is a widespread problem.
Coverage bias, like many other potential problems in survey research and data gathering in general, can significantly change your survey results and compromise the integrity of your research. This phrase describes the several circumstances and biases that may affect survey results. Regardless of whether the bias was deliberate or unintentional, erroneous survey results make the information less helpful.
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(a+b+c)(a-b+c)=a2+b2+c2 prove
Answer:
There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.
(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
Step-by-step explanation:
(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)
Since ab = ba, ac = ca and bc = cb,
-ab and ba can be cancelled out
bc and -cb can be cancelled out
Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
This is what I have obtained through expansion, then simplification by cancelling out the common terms.
Could you help check the question again?
11. Which of the following is a solution to the
inequality c + 4 <-7?
(1) -15
(2) -10
(3) -5
(4) O 0
(5) 10
Answer:
-15
Step-by-step explanation:
That's the answer because
-15+4=-11
-15+4=-11-11<-7
1
Which line is pointing to the cell body?
A. 1
B. 2
C. 4
D. 5
2
3
4
5
Image by Dhp 1080
The line 2 is pointing towards the body of the cell, in the given image of a neuron.
What is cell body?The soma, or cell body, is the spherical part of the neuron that houses the nucleus. The cell body is linked to the dendrites, which transport information to the neuron, and the axon, which sends information to other neurons.
When one neuron receives information from another, the dendrites send it to the cell body. Depending on the signal strength, the cell body may then send the information to the axon.
The cell body's role is to regulate all of the cell's functions. It has several important organelles that aid in this process. Organelles are tiny organelles found within cells that each perform a specific function. The nucleus is the most important organelle within the cell body.
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raph of the function f(x) = (x+2)(x+6) is shown
-4 2
4
2+
N
-2
-6
2
4 6
X
What is true about the domain and range of the function?
O The domain is all real numbers, and the range is all
real numbers greater than or equal to -4.
O The domain is all real numbers greater than or equal
to
-4, and the range is all real numbers.
O The domain is all real numbers such that -6 ≤x≤-2,
and the range is all real numbers greater than or equal
to-4.
O The domain is all real numbers greater than or equal
to
-4, and the range is all real numbers such that -6 sx
≤-2.
The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). In this case, the function f(x) = (x+2)(x+6) is defined for all real numbers, so the domain is all real numbers.
What do a function example's range and domain mean?
A straightforward function, such as f(x) = x2, can have a domain (what goes in) of just the counting numbers 1, 2, 3, etc., and a range (what comes out) of the set 1, 4, 9, etc. Another function, g(x) = x2, may have an integer domain of..., -3, -2, -1, 0... 1, 2, 3, and its range is..., 1, 4, 9,...
The range of a function is the set of all possible output values (y-values) produced by the function. The function f(x) = (x+2)(x+6) is a polynomial, and all polynomials of the form (ax^2 + bx + c) with real coefficients (a,b,c) have range is all real numbers. The range of the function f(x) = (x+2)(x+6) is also all real numbers.
So the answer is
The domain is all real numbers, and the range is all
real numbers.
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Tammy has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Which equation can be
used to determine the length and the width of the rug?
A 21 - -W² - 4W
B. 21 = 42
C. 21 - W2 + 4w
D. 21 - W2 + 4
The equation to determine the length and the width of the rug is
21 = W² - 4W.
What is a rectangle ?A rectangle is a quadrilateral with four right angles in the Euclidean plane. It may alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal. A square is a rectangle with four equally long sides.
A quadrilateral is a rectangle.
A rectangle's opposing sides are equal and parallel to one another.
Each vertex of a rectangle has a 90° internal angle.
360° is the total of all interior angles.
The diagonals cut each other in half.
The diagonals are all the same length.
The Pythagorean theorem may be used to determine the length of the diagonals.
A rectangle is also referred to as a parallelogram since its sides are parallel.
While all parallelograms are rectangles, not all rectangles are parallelograms.
The length of the rug is l ft
Then the width of the rug will be l-4 ft
So the are will be l*(l-4) = [tex]l\x^{2} - 4l[/tex]
We know area is 21
so the equation is 21 = [tex]l\x^{2} - 4l[/tex] (Option a)
And after solving the equation the lenght is7m and breadth is 3 m.
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Select the correct answer.
The class sizes of the Introductory Psychology courses at a college are shown below.
121, 134, 106, 93, 149, 130, 119, 128
The college adds a new Honors Introductory Psychology course with 45 students. What effect does the new class size have on the center and spread of the class sizes of the Introductory Psychology courses at the college?
A. The value of the center increases and the distribution has a larger spread.
B. The value of the center decreases and the distribution has a smaller spread.
C. The value of the center decreases and the distribution has a larger spread.
D. The value of the center increases and the distribution has a smaller spread.
Center : Mean Before the introduction of the new course, center = average(121,134,106,93,149,130,119,128) = 122.5 After the introduction of the new course, center = average(121,134,106,93,149,130,119,128,45) = 113.9 The center has moved to the left (if plotted in a graph) because of the low intake for the new course. Spread before introduction of the new course : Arrange the numbers in ascending order: (93, 106,119, 121), (128, 130,134, 149) Q1=median(93,106,119,121) = 112.5 Q3=median(128,130,134,149) = 132 Spread = Interquartile range = Q3-Q1 = 19.5 After addition of the new course,
(45,93, 106,119,) 121, (128, 130,134, 149)
Q1=median(45,93,106,119)=99.5
Q3=median (128, 130,134, 149)= 132
Spread = Interquartile range = 132-99.5 =32.5
We see that the spread has increased after the addition of the new course.
please show your work
A certain paint is to be mixed with 3 parts yellow to 2 parts blue. What is the ratio of yellow paint to the total amount of mixed paint
The ratio of yellow paint to mixed paint is 3/5.
What are ratio and proportion?A ratio is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is written as a/b or a: b. An equality of two ratios is a proportion. In order to write equivalent ratios, proportions are used, which aids in resolving the unknown quantities. As an illustration, a proportion is written as a: b = c: d.
Solution:-
Given,
Amount of yellow paint=3
Amount of blue paint=2
Ratio=yellow paint/total mixed paint
Ratio=3/(3+2)
Ratio=3/5
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The graph of y = x2 has been translated 7 units to the left. The equation of the resulting parabola is _____.
The equation of the parabola after the translation is:
g(x) = (x - 7)^2
What is the equation for the resulting parabola?We know that we start with a parabola of the form:
y = x^2
Now we know that the parabola has been translated 7 units to the left.
Remember tht for a general function y = f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.if N <0, the translation is to the right.So a translation of 7 units to the left is written as:
g(x) =f(x - 7)
g(x) = (x - 7)^2
That is the equation of the parabola after the translation.
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What is 3 6 equivalent to in fractions?
Answer:
1/2
Step-by-step explanation:
(0,4) (2,-6) find the slope
Answer:
Slope = -5
Step-by-step explanation:
Slope Formula:
y2-y1/x2-x1
So
-6-4/2-0=
-10/2
Therefore -5 is the Answer
Hope this helps
The volume of a cylinder is 60 cubic centimeters. What is the number of cubic centimeters in the volume of the sphere it circumscribes
Call the radius of the cylinder and sphere, r And the height of the cylinder = 2r
How to Calculate Volume in Cubic Centimeters?Calculating volume is just another way of saying that you're measuring the amount of space inside a three-dimensional object. You can use standardized formulas for calculating the volume of shapes like cubes, cylinders and spheres, as long as you know their basic measurements.So60 = pi * r^2 * 2r30 = pi * r^330/pi = r^3[30/pi]^1/3 = rSo...the volume of the sphere is(4/3)pi [ (30/pi)^1/3 ]^3 =(4/3) pi * 30/pi =40 cm^3A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm. One cubic centimetre corresponds to a volume of one millilitre.How to Work out Volume with Cubic Centimetres. If a container was filled with water and it had a length of 20 cm, a height of 5 cm and a depth of 4 cm to work out the volume of water you would need to multiply all 3 numbers together. 20 cm x 5 cm x 4 cm = 400 cm³To learn more about Volume in Cubic Centimeters refers to:
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What is the measure of ∠A if it is congruent to ∠B?
If measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.
Define the term congruent angles?Angles that really are identical to each other are referred to as congruent angles (and to themselves).
Angles that are congruent can also be acute, obtuse, exterior, and interior. No matter what kind of angle you have, if indeed the measure for angle one and angle two are the same, the angles are congruent.Two or more angles must have equal measurements in degrees as well as radians to be considered congruent. Congruent angles don't have to be created with the same figures or face the same direction (rays, lines, or the line segments). Both angles are congruent if the two measurements of the angles are equivalent.Thus, if measure of angle A is congruent to measure of angle B, then angle will be equal to angle B.
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five plus two times a number n is less than or equal to eleven. select all of the representation's that are solutions.
1) n less than or equal to 3
2) 3 less than or equal to n
3) n less than or equal to 8
4) 3 greater than or equal to n
Answer:
The worded problem translates to n ≤ 3
The options that are solutions to the problem are 1 and 4:
1) n less than or equal to 3, and
4) 3 greater than or equal to n (since 3 ≥ n)
Step-by-step explanation:
Let's translate the e=words into expressions:
"five plus two times a number n" becomes 5 + 2n
"is less than or equal to eleven" becomes ≤ 11
Put the two expressions together, with the word "is" and the "=" sign:
5 + 2n ≤ 11
Solving:
2n ≤ 11 - 5
2n ≤ 6
n ≤ 3
The options are:
1) n less than or equal to 3 Correct
2) 3 less than or equal to n Incorrect. 3 is greater than or equal to n
3) n less than or equal to 8 Incorrect. n is less than or equal to 3
4) 3 greater than or equal to n Correct 3 ≥ n
I really need help!! Find the value of..
Answer:488441
Step-by-step explanation:
Jay and kevin are shoveling the snow off a driveway. working together, they can clear the driveway of snow in 14 minutes. working alone, it would take kevin 21 minutes longer to clear the driveway of snow than it would take jay working alone. when j is the number of minutes it would take jay to clear the driveway of snow when working alone, the situation is modeled by this rational equation: how long would it take jay to clear the driveway of snow working alone?
a. 7 minutes
b. 21 minutes
c. 35 minutes
d. 42 minutes
Therefore, As a result, the answer to the given equation problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.
Define equation .
A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.
Here,
The formula is: 1/j +1/j+ 21 = 11/ 4.
LCM = j+21+j / j(j+21)=1/14
Thus, 2j+21 / j(j+21) = 1/14 is obtained.
14(2j+21) times itself yields j(j+21).
28j+294 expanded to j²+21j
Gather comparable terms
j²+21j-28j-294=0
j²- 7j-294=0
With the use of a graphing calculator, we have:
j = 21 or j= -14
Due to the context,
j's value cannot be negative.
As a result, the answer to the given equation's problem is Jay would need to work alone for 21 minutes to remove the snow from the driveway.
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