The simplified expression of 8x + 4 - 6y - 3x + y is 5x - 5y + 1
Expression:
An expression is any mathematical statement that consists of numbers, variables and an arithmetic operation between them.
Given,
Here we have the expression 8x + 4 - 6y - 3x + y.
Now, we have to simplify the expression.
To simplify the expression, first we have to write the given expression,
=> 8x + 4 - 6y - 3x + y
Now, we have to combine the like terms, then we get,
=> (8x - 3x) + (-6y + y) + (4 - 3)
Now, we have to perform the appropriate arithmetic operations on it, then we get,
> 5x + (-5y) +1
Therefore, the simplified form of the given expression is 5x - 5y + 1
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Rachel has 79 books in her collection. The average size
of each book is shown below. She wants to buy shelves
for her book collection. Each shelf is 34.5 inches wide
and costs $12.95. How much will it cost Rachel to shelve
her book collection? Explain how you found your
answer.
1.5 in.
9.2 in.
6 in.
The amount it would cost Rachel to shelve her book collection is $51.80.
What is the cost ?The first step is to determine the total width of the 79 books in the collection.
Total width = width of one book x total number of books
Total width = 1.5 x 79
Total width = 118.50 inches
The second step is to calculate the number of shelves that would be needed for the book collection.
Number of shelves that would be needed = total width of the collection / width of one shelf
Number of shelves that would be needed = 118.50 / 34.50
Number of shelves that would be needed = 3.4 ≈ 4
Total cost to shelve the book collection = cost of one shelf x total number of shelves needed
Total cost to shelve the book collection = 4 x $12.95 = $51.80
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Adjusted exponential smoothing forecasting includes an adjustment factor (T) which adjusts the exponential smoothing forecast for a:
Group of answer choices
a. Trend
b. Cycle
c. Seasonal Pattern
d. Random Variation
The adjustment factor (T) which adjusts the exponential smoothing forecast , does this adjustment for a. Trend.
What is the adjustment factor?A big part of the Adjusted exponential smoothing forecasting method is the use of an adjustment factor which has the purpose of adjusting the smoothing forecast for a trend.
If this trend is found, then there is a need to smoothen it out of the data so that the model is more trustworthy. It is important that this trend is removed to ensure that the forecast does not have a time bias.
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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
A line that represent the "rise" and the "run" of the line is shown in the image attached below. Also, a slope of this line in simplest form is equal to 0.25.
How to determine the slope of a line?Mathematically, the slope of a line is also referred to as pitch or gradient and can be calculated by using this formula:
Slope, m = V/H
Where:
V represents the rising vertical distance (rise) of an object.H represents the horizontal distance (run) an object runs through.From the graph of this line, we would choose the following data points to represent both the rise and run:
Rise (x, y) = (-5, 0)
Run (x, y) = (7, 3)
Substituting the selected data points into the slope formula, we have;
Slope (pitch), m = (3 - 0)/(7 - (-5))
Slope (pitch), m = (3 - 0)/(7 + 5)
Slope (pitch), m = 3/12
Slope (pitch), m = 0.25
At point (-5, 0), the equation of this line would be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the data points.Substituting the parameters into the formula, we have;
y - 0 = 0.25(x - (-5))
y - 0 = 0.25(x + 5)
y = 0.25x + 1.25
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Solve x² - 4x+1=0.
O x=2±2√5
O x=4± √√3
O x=2± √√3
Ox
x=-2± √3
Answer: x=2±√3
Step-by-step explanation:
[tex]\displaystyle\\x^2-4x+1=0\\\\ax^2+bx+c=0\\\\a=1\ \ \ \ \ b=-4\ \ \ \ \ c=1\\\\D=b^2-4ac\\\\D=(-4)^2-4(1)(1)\\\\D=16-4\\\\D=12\\\\\sqrt{D} =\sqrt{12}\\\\\sqrt{D}=\sqrt{3(4)} \\\\\sqrt{D}=2\sqrt{3}\\\\ Hence,\\\\x=\frac{-bб\sqrt{D} }{2c} \\\\x=\frac{-(-4)б2\sqrt{3} }{2(1)} \\\\x=\frac{4б2\sqrt{3} }{2} \\\\x=\frac{2(2б\sqrt{3}) }{2} \\\\x=2б\sqrt{3}[/tex]
The value of solution of equation is,
⇒ x = (2 ± √3)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
Quadratic equation is,
⇒ x² - 4x + 1 = 0
Now, We can simplify as;
⇒ x² - 4x + 1 = 0
⇒ x = - (-4) ± √(-4)² - 4×1×1 / 2
⇒ x = (4 ± √16 - 4) / 2
⇒ x = (4 ± √12) / 2
⇒ x = (4 ± 2√3) / 2
⇒ x = (2 ± √3)
Thus, The value of solution of equation is,
⇒ x = (2 ± √3)
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Tiffany, Gary and Noland start at the same time walking around a circular track in the same direction. Tiffany takes ½ hour to walk around the track. Gary takes 5/12 hour, and Noland takes 1/3 hour.
1) How many minutes does it take each person to walk around the track?
2) How many times will each person go around the track before all three meet again at the starting line?
3) Explain how you arrived at the solution for question 2.
The 1/2, 5/12, and 1/2 hour duration it takes Tiffany, Gary, and Noland to walk round the park provides the following;
1) The time in minutes it takes Tiffany to walk round the park is 30 minutes
Gary takes 25 minutes and Noland takes 20 minutes to walk round the park
2) Tiffany will go round 12 times, Gary will go round 12 times and Noland will go round the park 15 times before all three will meet again.
3) The solution to question 2 is arrived at by dividing the least common multiple of 30, 25, and 20, which is 300 by 30, 25, and 20 respectively
What is the least common multiple of two or more numbers?The least common multiple also known as the L.C.M. is the least number two or more numbers have as their multiples.
The time it takes Tiffany to walk around the track = 1/2 hour
The time it takes Gary to walk round the park = 5/12 hour
The time it takes Noland to walk round the park = 1/3 hour
1) The duration in minutes it takes each person to walk round the park are found using the conversion factor for minutes and hours as follows;
60 minutes = 1 hour
Therefore;
1/2 hour = 30 minutes
It takes Tiffany 30 minutes to walk around the track
5/12 hour = 25 minutes
It takes Gary 25 minutes to walk around the track
1/3 hours = 20 minutes
It takes Noland 20 minutes to walk round the park
2) The number of times each person will go round the track before all three meet again is given by the least common multiple of 30, 25, and 20, which is 300
Therefore;
The number of times Tiffany would walk round the park before all three meet again is 300 ÷ 30 = 10
The number of times Gary would walk round the park = 300 ÷ 25 = 12
The number of times Noland walks round the park = 300 ÷ 20 = 15
When all three meet again, Tiffany will halve walked 10 times, Gary would have walked 12 times and Noland would have walked 15 times round the park.
3) The solution for question 2 was arrived at by looking for the lowest common multiple of the durations it takes each of the three persons to walk round the park. The least common multiple provides the time at which all three will have made complete cycles simultaneously.
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Question 7(Multiple Choice Worth 2 points)
(Constant of Proportionality MC)
The equation g equals three fifths times m represents the proportional relationship of the number of gallons of water (g) used by a washing machine over a certain period of time, in minutes (m).
Create a written description for the equation.
For each minute the washing machine runs, it uses five thirds gallons of water.
For each minute the washing machine runs, it uses three fifths of a gallon of water.
For each gallon of water the washing machine uses, it runs for three fifths of a minute.
For each gallon of water the washing machine uses, it runs for 8 minutes.
The proportionality is a relation between two quantities. The equation for the given cases can be written as 3g = 5m, 5m = 3g, 5g = 3m and g = 8 m.
What is Proportionality?When two quantities have some dependence in their values they can be said to be proportional to each other.
It can be of two types such as direct and indirect.
The direct proportionality means the values of both the quantities are increasing or decreasing at the same time while the indirect proportionality implies that the value of one quantity is increasing while the other is decreasing.
Given that,
The number of gallons of water = g,
The number of minutes = m,
And, the equation for the given condition as,
g = 3 / 5 m
The equation for each minute the washing machine runs, it uses five thirds gallons of water is given as,
g = 5 / 3 m
=> 3g = 5m
The equation for each minute the washing machine runs, it uses three fifths of a gallon of water is given as,
m = 3 / 5 g
=> 5m = 3g
The equation for each gallon of water the washing machine uses, it runs for three fifths of a minute is given as,
g = 3 / 5 m
=> 5g = 3m
The equation for each gallon of water the washing machine uses, it runs for 8 minutes is given as,
g = 8 m
Hence, the equation for the given conditions can be written as,
3g = 5m, 5m = 3g, 5g = 3m and g = 8 m.
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About what percent of Davon's monthly budget was NOT spent on his mortgage?
A) 59%
B) 50%
C) 25%
D) 41%
How can i graph y=x+3
Answer:
The x-intercept is -3
Step-by-step explanation:
Answer:
x = -3, y = 3 ----> (-3,0) and (0, 3)
Step-by-step explanation:
Required: Find the X-intercept.
1) Let y = 0 to find the x-intercept (s):
0 = x + 3
2) Subtract 3 from both sides.
-3 = x
3) Switch sides.
x = -3
Just to find the y-intercept.
1) Let x = 0 to find the y-intercept (s):
y = 0 + 3
2) Simplify:
y = 3
What is an equation of the line that passes through the point (-6,-7)(−6,−7) and is perpendicular to the line 6x+5y=306x+5y=30? math
The equation of the line that passes though the point (-6,-7) and is perpendicular to the line 6x + 5y = 30 is y = (5/6)x -2 .
In the question ,
it is given that
the required line is perpendicular to the line 6x + 5y = 30 ,
rewriting the line we get
5y = -6x + 30
y = (-6/5)x + 6
the slope of perpendicular is -6/5 ,
the slope of the required line will be 5/6 .
The equation of the line passing through (-6,-7) with slope 5/6 is written as
(y - (-7)) = (5/6)(x - (-6))
y + 7 = (5/6)(x + 6)
y + 7 = (5/6)x + 5
y = (5/6)x + 5 -7
y = (5/6)x -2
Therefore , the equation of the line is y = (5/6)x -2 .
The given question is incomplete , the complete question is
What is an equation of the line that passes through the point (−6,−7) and is perpendicular to the line 6x+5y=30 ?
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Do adjacency matrices have to be symmetric?
Adjacency matrices have to be symmetric. This is true.
What is an adjacency matrix?An adjacency matrix is a square matrix used to represent a finite graph in graph theory and computer science. The matrix's elements indicate whether or not two vertices in the graph are adjacent. The adjacency matrix of a finite simple graph is an a-matrix with zeros on its diagonal.
An adjacency matrix is a method of representing a graph as a boolean (0 or 1) matrix. Any graph's adjacency matrix is symmetric, for the obvious reason that there is an edge between Pi and Pj if and only if Pj and Pi have an edge (the same one).
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How do I work out this question. Complete 24 : 8 = 3 : ?
The complete ratio is24:8=3:1.
What is ratio?
By comparing two amounts of the same units, the ratio can be used to calculate how much of one item is included in the other. There are two different categories for ratios. The first is a part to part ratio, whereas the second is a part to whole ratio. The relationship between two separate entities or organisations is shown by the part-to-part ratio. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio describes how one group compares to another. For instance, five people enjoy reading books out of every ten persons. Since the ratio of the component to the total is 5:10, 5 out of every 10 persons enjoy reading.
Here the given ratio 24:8=3:?
Let us take missing part as x then,
=> 24:8=3:x
=>24/8=3/x
=>x = 3*8/24
=> x=1
Hence the complete ratio is 24:8=3:1
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The Book Club purchased a bundle of 12 books for $95.40. Calculate the unit rate per book.
Answer: $7.95
Step-by-step explanation:
95.40/12
= $7.95
Answer:
unit rate per book
= $95.40 ÷ 12 books
= $7.95 per book
Lannie has 5 1/2 cups of chocolate chips. She needs 1 3/4 cups to make one batch of chocolate
chip cookies. How many batches of chocolate chip cookies can she make?
Has 5 1/2 cups or 11/2
Needs 1 3/4 or 7/4
Divide how much she has by how much she needs
(11/2) / (7/4)
Is also the same as
(11/2) * (4/7)
Which equals
= 44/14
= 22/7
or 3 1/7
1
Maria buys 12 boxes of mince pies.
There are 6 mince pies in a box.
She is planning an event for 40 people and would like everyone to have 2 pies.
Did she buy enough boxes of mince pies?
Answer:
Step-by-step explanation:
12x6 = 72
So 40x2
72 pies she needs 80
So awnser is no she needs 2 more boxes
2. In an exponential function, f(x)= a(b)^x, it is known that f (5) = 20 and f (9) = 211. Which of the following
is closest to the value of b?
By solving a system of equations, we can see tha the value of b is 3.81
How to get the value of b?We know that we have a exponential function of the form:
f(x)= a*(b)^x
And we know that:
f(5) = 20 and f(9) = 211
Then we can write a system of equations:
20 = a*(b)^5
211 = a*(b)^9
If we take the quotient between the second equation and the first one, we get:
211/20 = (a*(b)^9)/(a*(b)^5)
211/20 = b^(9 - 5)
211 = b^4
(211)^(1/4) = b
3,81 = b
The value of b is 3.81
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√ 4(x+5)² - 130 = 0 , please solve
Answer:
x = 60, -70
Step-by-step explanation:
Let's move the constant (-130) to the right by adding it to both sides.
[tex]\sqrt{x} 4(x+5)^{2} =130[/tex]
Now, we can rewrite the equation as (since the square root and square cancel):
2 × | x + 5 | = 130
To get rid of the 2 multiplication, we can divide both sides by 2:
| x + 5 | = 65
This leaves us with 2 equations:
x + 5 = 65
x + 5 = -65
Simplify.
x1 = 60
x2 = -65
How do you find the margin of error for two samples?
Answer:
Step-by-step explanation:
The margin of error is obtained by multiplying the standard error by t*.
The margin of error can be calculated in two ways, depending on whether you have population parameters or sample statistics:
Margin of error (parameter) = critical value x population standard deviation Margin of error (statistic) = Critical value x Sample standard error
What is a margin of error?A margin of error is a statistical metric that accounts for the difference between actual and projected survey results in a random sample.
In layman's terms, the margin of error measures the degree of unpredictability in data and research results. The margin of error formula is calculated by multiplying a critical factor. The result is then divided by the square root of the sample's number of observations.
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Given the equation of the ellipse in general conic form, convert to standard form.
4x² + y² + 72x+10y + 285 = 0
.
O.
(x-6)²
16
(x+5)²
16
(x+9)²
16
(x+9)²
64
+ (y+8)²
64
+
+
+
(y-9)²
64
(y+5)²
64
(y+5)²
16
= 1
1
= 1
= 1
The equation of ellipse in standard form is:
[(2x + 18)² /8²] + [(y + 5)² /8²] = 1
The equation of the ellipse in general conic form is,
4x² + y² + 72x+10y + 285 = 0
comparing given equation with Ax^2+Bxy+Cy^2+Dx+Ey+F=0 we get,
A = 4, B = 0, C = 1, D = 72, E = 10, F = 285
Consider given equation of conic,
4x² + y² + 72x+10y + 285 = 0
4x² +72x + y² + 10y = - 285
4x² +72x + 324 + y² + 10y = - 285 + 324
(2x + 18)² + y² + 10y + 25 = - 285 + 324 + 25
(2x + 18)² + (y + 5)² = 64
(2x + 18)² + (y + 5)² = 8²
(2x + 18)² /8² + (y + 5)² /8² = 1
Therefore, the equation of ellipse in standard form is:
[(2x + 18)² /8²] + [(y + 5)² /8²] = 1
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Morris’s family is selling their house. They want to have
$150,000 after paying 6% commission to the realtor. What
should be the sale price of the house?
Sale price of the house should be $141509
Amount = $150000
Commission% = 6 %
By formula
Selling price x commission rate = commission paid
SP × 6% = commission paid
(6·SP)/100 = commission paid …. (1)
Again by formula
Selling price – commission paid = net amount to seller
SP - (6·SP)/100 = 150000 (from equation 1)
SP ( 1 - 0.06) = 150000
SP = 141509.43 ≈ 141509
$141509 should be the sale price of the house.
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Graphing and Solving Inequalities
m-1<-3
————————➡️
-4y <-20
————————➡️
5+b>1
————————➡️
-18
————————/➡️
There are two arrows on each side. And little marks on the body of the graph. Could not paste graph. Thank you.
The Solutions for given inequalities are -2, 5, and -4
Inequalities:Inequalities are algebraic expressions in which both sides are not equal to each other. In inequality, we compare two values with signs like less than (<) (or less than or equal to), greater than (>) (or greater than or equal to), or not equal to sign(≠), etc.
Here we have three inequalities
m -1 < -3, - 4y < - 20, and 5 + b > 1
We can solve each equation and can give a graph as given below
m -1 < -3
Add 1 on both sides
=> m - 1 + 1 < -3 + 1
=> m < -2
- 4y < - 20
Divide both sides with - 4 on both sides
=> - 4y/4 < - 20/4
=> -y < - 5
Multiply with -1 on both sides
=> -1(-y) < -5(-1)
=> y < 5
5 + b > 1
Subtract - 5 on both sides
=> 5 + b - 5 > 1 - 5
=> b > -4
Therefore,
The Solutions for given inequalities are -2, 5, and -4
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Q10
What is the value of angle a?
a
25°
105°
Answer:
Assuming this is a triangle, angles would equal up to 180 degrees
Step-by-step explanation:
105 + 25 = 135
180 - 135 = a, a = 45 degrees
Kayla is a basketball player who makes 50 of her 2 point shots and 20 of her 3 point shots find Kayla expected value for a 2 point shot
Kayla's expected value for a 2- point shot is 1 point.
What is expected value?
The expected value, also known as expectation, expectancy, arithmetical expectation, mean, average, first or moment, is a generalization of the weighted average in the field of probability theory. Informally, the estimation is the arithmetic mean of a significant number of values of a random variable that were independently chosen. A weighted average of all potential outcomes constitutes the expected value of the a random variable with such a finite number of outcomes. When there is a continuum of potential outcomes, integration defines the expectation. The expectation is provided by Lebesgue integration in the measure theory-based axiomatic foundation for probability.
Sol- The expected value is calcuated using the formula:
EV= x.P(x)
where x is the weight/value of the event, and P(x) is the probability of the event occurring.
For a 2-point shot, we have:
X=2
P(x) = 50/100 = 0.5
There for the expected value will be -
EV = 2×0.5 = 1
Thus,
The expected value will be 1 point.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
The angles are equal because the angles are corresponding and the value of x is 7.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
Two parallel lines are intersected by a transversal.
The angles shown in the picture is called corresponding angles.
The angles are equal to each other
75 = 11x - 2
11x = 77
x = 7
Thus, the angles are equal because the angles are corresponding and the value of x is 7.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer: 1: Congruent angles
2: Corresponding Angles
3: 7
Step-by-step explanation:
I'm not entirely sure if I got all of these correct due to the fact I'm not the best when it comes to math, but when I searched the word bank options and looked at the images, I made sure they looks the most similar.
Solve #19 and show explanation
The next equation will be 6²-4²=2×10.
Here, we have given three equations and we have to find out the next equation.
The first three equations are like this
1. 3²-1²=2×4
2. 4²-2²=2×6
3. 5²-3²=2×8
Now,
As from the equation
On the L.H.S. we can see that every time it is creating a sequence
Like, every time it is subtracting square value of the one’s from the another number’s square
Which is the value we got from adding 2 in first value.
And on the R.H.S.
We can say that every time 2 multiplies with the next even number than the previous one
So,
The last equation was 5²-3²=2×8
Therefore,
The next equation will be
6²-4²=2×10
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3 4 5
Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48
minutes. How many minutes does Hannah travel? Select the model that represents the
problem and complete the equation to solve.
A
B
12
Hannah m
Raoul m
Hannah
Raoul
xm = 48
Hannah travels
E
m
m
E
E
E
minutes to work.
m
m
Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.
Define equation.In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given,
Let Raoul travel in minutes be x
So, Hannah travel in minutes will be 5x
Together, they travel for 48 minutes.
Equation:
x + 5x = 48
6x = 48
x = 8
Hannah travel in minutes will be 5x.
Total travel by Hannah:
5(8)
40
Hannah travel for 40 minutes when Hannah travels 5 times as many minutes to work as Raoul does. Together, they travel for 48 minutes.
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I need to know the z-score to percentile of 1
The z-score to percentile of 1 = -2.326
In this question, we need to find the z-score to percentile of 1
We know that a Z-scores is a normalized score that used to compare values relative to their population. z-score represents a specific location in the normal distribution, so that there is a certain area that is to the left of that z-score. The percentile associated to a z-score is nothing but the area to the left of that z-score.
the z-score to percentile of 1 = -2.326
Therefore, the z-score to percentile of 1 = -2.326
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2x + y = 4
x - y = 2
Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.
Define equation.A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.
Given,
Equation:
2x + y = 4
x - y = 2
From equation 2,
x = 2 + y
Equating in equation 1,
Using substitution method,
2(2+ y) + y = 4
4 + 2y + y = 4
3y = 0
y = 0
x = 2 + y
x = 2+ 0
x = 2
Value of x is 2 and y is 0 of the equations 2x + y = 4 and x - y = 2.
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Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
Write an equation relating N to M. Then use this equation to find the number of novels Kevin needs to read in 19 months.
The equation relating N to M be N = 3M and
Kevin needs to read 57 Novels in 19 months.
Given, Kevin needs to read 3 novels each month.
Let N be the number of novels Kevin needs to read in M months.
According to question,
1 month = 3 novels
M months = 3M novels
Now, as he needs to read a total of N novels.
So, N = 3M.
Also, the number of novels he needs to read in 19 months be,
N = 3×19
N = 57 novels.
Hence, the equation relating N to M be N = 3M and the number of novels Kevin needs to read in 19 months be 57.
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If you are buying some food for a party. My food costs $130 but there is a 12% discount. If there is a 13% tax. Find the sale price I will pay?
Answer:
$129.27 Sale price Including tax
Step-by-step explanation:
Original Price - Discount = Sale Price
130 - 130(0.12) = 114.40
114.40 + 114.40(0.13) = 129.27 Include sale tax
