Answer:
Unit rate = 0.6
y = 0.6x
x= 24
Step-by-step explanation:
I cannot see the headings to the table, but on examining the questions, the first column contains the values for variable x and the second column the values for variable y
Unit Rate
Unit rate = increase in y for a unit increase in x
We see that the rate is constant for every unit increase in x and is = 0.6
Unit rate = 0.6
Equation
The equation therefore is y = 0.6x
Value of x when y = 14.4
When y = 14.4, plugging into the equation gives:
14.4 = 0.6x
or
0.6x = 14.4 by switching sides - no effect on equation
Divide both sides by 0.6
0.6x/0.6 = 14.4/0.6
x= 24
What’s the answer and what do the transformations look like on the graph?
Transformations on a graph refer to changes made to the graph that affect its appearance or position without changing its underlying structure or properties.
How to explain the transformationSome common transformations on a graph include:
Translation: This involves shifting the entire graph horizontally or vertically without changing its size or shape. For example, if a point on the graph is originally located at (2,3), a translation by (4,-1) would move it to (6,2).
Scaling: This involves enlarging or shrinking the entire graph uniformly in all directions. For example, a scaling factor of 2 would double the distance between all points on the graph, while a scaling factor of 0.5 would halve it.
Reflection: This involves flipping the graph across an axis, such as the x-axis or y-axis. Reflections can also be performed across other lines, such as y = x or y = -x.
An overview on transformation was given as the information is incomplete.
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pls helpp dilation of 1.5 about the origin
F(1, -1), G(0, 2), H(1, 2)
The Coordinates after dilation of 1.5 about the origin is
F'(1.5, -1.5)
G'(0, 3)
H'(1.5, 3)
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. Yet, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
Given:
We have the Coordinates F(1, -1), G(0, 2), H(1, 2).
As, the Dilation Rule for point (x, y) about origin with scale factor h
h(x, y)------>(hx, hy)
Applying the Dilation Rule we get
F(1, -1)-----> 1.5 F'(1, -1)-----> F'(1.5, -1.5)
G(0, 2)-----> 1.5 G'(0, 2)-----> G'(0, 3)
H(1, 2) -----> 1.5 H'(1, 2)-----> H'(1.5, 3)
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Help!!! Will give brain list
Answer:
Elimination , $1.79
Step-by-step explanation:
You were correct with elimination! Good job , now to find the cost of fries we have to put elimination in practice. Elimination is subtracting one equation from the other to get the equation of one variable.
4x + 5y = 24.11
-4x + 3y = 20.53
2y = 3.58
2y/2 = 3.58/2
y = 1.79
Dean set a goal to do more than 900 push-ups this month. So far, he has done 230 push-ups, and there are 20 more days remaining this month. Dean will do the same number of push-ups on each remaining day.
Part A
Create an inequality that represents the number of push-up, p
, Dean must do on each remaining day to reach his goal.
Enter your inequality in the box.
a
Part B
What is the minimum number of push-ups Dean must do on each remaining day to reach his goal?
Enter a number in the box.
The inequality that represents the number of push-up, is p ≥ 33. The minimum number of push-ups Dean must do on each remaining day to reach his goal is 33.
What is solution of inequality in one variable?A mathematical statement describing how one linear expression is either less than or greater than another is known as a linear inequality. A real number that, when used as the variable in a linear inequality, results in a true assertion is the solution. There are either an endless number of solutions to linear inequalities or none at all. If there are an unlimited number of solutions, plot the solution set on a number line or use interval notation to express the solution.
Given that, Dean has done 230 push ups.
The remaining number of push ups to reach his goal is:
R = 900 - 230
R = 670
The number of pushups he needs to do in the next 20 days to reach his goal is:
p = 670/20
p ≥ 33
Hence, the inequality that represents the number of push-up, Dean must do on each remaining day to reach his goal is p ≥ 33.
The minimum number of push-ups Dean must do on each remaining day to reach his goal is 33.
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Find the 7th term of the arithmetic sequence − 3 � + 5 −3x+5, 2 � + 3 2x+3, 7 � + 1 ,. . . 7x+1
The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.
What is the 7th term of the arithmetic sequence?To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:
(2x+3) - (-3x+5) = 5x - 2
This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:
aₙ = a₁ + (n - 1)d
Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:
a₇ = (-3x+5) + (7 - 1)(5x - 2)
Simplifying the equation:
a₇ = -3x + 5 + 30x - 12
a₇ = 27x - 7
Therefore, the 7th term of the arithmetic sequence is 27x - 7.
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Parker just started a running plan where he runs 16 miles the first week and then
increases the number of miles he runs by 5% each week. If he keeps up this plan for 5
weeks, how many total miles would Parker have run, to the nearest whole number?
The total number of miles that Parker would have to run is given as follows:
88.41 miles.
What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
As the number of miles increases by 5% each week, the common ratio is obtained as follows:
100% + 5% = 105% = 1.05.
Hence the number of miles each week is given as follows:
16 miles.16 x 1.05 = 16.8 miles.16.8 x 1.05 = 17.64 miles.17.64 x 1.05 = 18.52 miles.18.52 x 1.05 = 19.45 miles.Then the total number of miles is given as follows:
16 + 16.8 + 17.64 + 18.52 + 19.45 = 88.41 miles.
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5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14
The algebraic expression of the statement is 5 + 3y ≤ z + 14
How to determine the algebraic expressionFrom the question, we have the following parameters that can be used in our computation:
5 more than the product of 3 and a number y is less than or equal to the sum of another number z and 14
When represented as expression, we have
5 + 3y is less than or equal to z + 14
As an inequality, we have
5 + 3y ≤ z + 14
hence, the expresion si 5 + 3y ≤ z + 14
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39.5 Degrees Celsius to Fahrenheit
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.
Temperatures, across the worlequal td, are measured either in Fahrenheit(the US temperature scale) or Celsius(the metric scale), two of the most popular and widely used scales.Temperature Conversion – Degrees Celsius into Degrees Fahrenheit.
Celsius to Fahrenheit conversion formula is all about converting the temperature denoting in Celsius to Fahrenheit. As mentioned earlier, the temperature of boiling (hot) water in Celsius is 0 degrees and in Fahrenheit is 21 degrees, the formula to convert C to F is
F = C x (9/5) + 32To convert 39.5 degrees Celsius to Fahrenheit, you can use the formula:
°F = (°C × 9/5) + 32
Substituting 39.5 for °C, we get:
°F = (39.5 × 9/5) + 32
°F = (71.1) + 32
°F = 103.1
Therefore, 39.5 degrees Celsius is equal to 103.1 degrees Fahrenheit.
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In triangle ABC, AB is unequal to BC. Show that there does not exist a point P on altitude BD that is equidistant from A and C
There cannot be a point P on altitude BD that is equidistant from A and C, as this would mean that the two smaller triangles are congruent. This is because the altitude BD divides the triangle into two smaller triangles, ABD and CBD. If AB is unequal to BC, then these two smaller triangles cannot be congruent.
To prove this, let's assume that there is a point P on altitude BD that is equidistant from A and C. This would mean that AP = CP. However, since AB is unequal to BC, we know that AD is not equal to DC. Therefore, the triangles ABD and CBD are not congruent, and there cannot be a point P on altitude BD that is equidistant from A and C.
In conclusion, if AB is unequal to BC, then there does not exist a point P on altitude BD that is equidistant from A and C. This is because the altitude BD divides the triangle into two smaller triangles that cannot be congruent if AB is unequal to BC.
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(D^3+1)y=(e^x+1)^2 solve this differential equation
The solution to the differential equation is:
[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]
What is a differential equation?
Any equation involving the derivatives of one dependent variable with respect to another independent variable is referred to as a differential equation. Differential equations are widely used in mathematics, but they also play an important role in the sciences of medicine, chemistry, physics, and engineering.
To solve this differential equation, we need to find a function y(x) that satisfies the equation. Here's how to do it:
First, we can divide both sides of the equation by D³ + 1 to get:
y = (eˣ+1)² / (D³+1)
Next, we can take the derivative of both sides with respect to x:
dy/dx = d/dx[(eˣ+1)² / (D³+1)]
Using the quotient rule of differentiation, we get:
dy/dx = [(D³+1)(2eˣ)(eˣ+1) - (eˣ+1)²(3D²)] / (D³+1)²
Simplifying the numerator, we get:
[tex]dy/dx = [2e^{(2x)} + 2e^x - 3D^{2}(e^x+1)^2] / (D^3+1)^2[/tex]
Therefore, the solution to the differential equation is:
[tex]y = \int\limits [(2e^(2x) + 2e^x - 3D^2(e^x+1)^2) / (D^3+1)^2] dx + C[/tex]
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let r be the region bounded by the following curves. find the volume of the solid generated when r is revolved about the y-axis.
The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Volume of Solid:
The volume of a solid is a measure of the space occupied by an object. This article explains how to calculate the volume of solids and the volume of regular and irregular solids.
According to the Question:
We know that:
A ( y ) = π × (f₁ (y)² - f₂ (y)²)
where,
f₁ (y) is the function further away from y axis
f₂ (y) is the function closer to y axis
f₁ (y) = 2
f₂ (y) = 2y²
A ( y ) = π × [2² - (2y)²]
A (y) = π × (4 - 4y²)
A (y) = 4π (1 - y²)
Now,
Computing V (y)
[tex]V =\int\limits^1_0 {A(y)} \, dy[/tex]
[tex]V = 4\pi \int\limits^1_0 {(1-y^2)} \, dx[/tex]
V = 4π (1 - 0.2)
V = 3.2π
Therefore, The volume of the solid generated when r is revolved about the y-axis is 3.2π.
Complete Question:
Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis. y= square root of (x/2) , y=0 , x=2
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Please help me
five subtracted from the product of 6 and a number is less than or equal to 29. Write as an inequality
Answer:
6x-5 ≤ 29
Step-by-step explanation:
Let translate each part of the sentence into an equation or expression.
1. "five subtracted from the product of 6 and a number"
Lets say the "number" is x. The product of 6 and a number would be: 6x'five subtracted from" would be -5So the "five subtracted from the product of 6 and a number" would be 6x-5.2. "is less than or equal to 29"
using just math symbols, this would be ≤ 293. Assemble the two expression into an equation
Combine parts 1 and 2 into an equation.
6x-5 ≤ 29
=============
Extra
6x-5 ≤ 29 can be simplified:
6x ≤ 29+5
6x ≤ 36
x ≤ 6
Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Step-by-step explanation:
Principal (P)=$7869
Rate (R)= 13%
Time (T)= 5 years
Compound Interest (CI)=?
We know that,
CI = P { (1+R/100)^T -1}
= $7869 {(1+13/100)^5 -1}
= $7869 {(113/100)^5 -1}
= $7869 {(1.13)^5 -1}
= $7869 {1.84-1}
= $7869 × 0.84
= $6609.96
Compound Amount= CI+p
= $6609.96+7869
= $14478.96
Therefore, he will have $14478.96 after 5 years.
Faith is going to use a computer at an internet cafe. The cafe charges $0. 80 for every minute using a computer on top of an initial charge of $3. Make a table of values and then write an equation for C,C, in terms of t,t, representing the total cost of using a computer for tt minutes at the internet cafe. Number of Minutes Total Cost to Use Computer
00 3\hspace{3px}\color{green}{\checkmark}3✓3
11 3. 80\hspace{3px}\color{green}{\checkmark}3. 80✓3. 80
22 4. 60\hspace{3px}\color{green}{\checkmark}4. 60✓4. 60
33 5. 40\hspace{3px}\color{green}{\checkmark}5. 40✓5. 40
Answer: C=C=
The equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3
The cost of using a computer at the internet cafe can be represented by a linear equation, where C is the total cost and t is the number of minutes used. The equation can be written as C = 0.80t + 3, where 0.80 is the cost per minute and 3 is the initial charge.
To make a table of values, we can plug in different values of t into the equation and solve for C
Number of Minutes (t) Total Cost to Use Computer (C)
0 C = 0.80(0) + 3 = 3
1 C = 0.80(1) + 3 = 3.80
2 C = 0.80(2) + 3 = 4.60
3 C = 0.80(3) + 3 = 5.40
So the equation for the total cost of using a computer for t minutes at the internet cafe is C = 0.80t + 3.
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how to convert 151 cm in feet?
On converting the length , 151 centimeter is equivalent to 4.954 feet .
The Units of measuring the length are used to measure the distance between two points of an object. There are several units of measuring length , which are : meter , centimeter , kilometer , feet .
We have to convert 151 cm to feet,
So , we use the conversion factor of 0.03281 feet per centimeter , which means that there are approximately 0.03281 feet in 1 centimeter.
So , to convert 151 cm to feet, we multiply the number of centimeters by this conversion factor ;
Using this method, we get ;
⇒ 151 cm × 0.03281 feet/cm = 4.954 feet ;
Therefore, 151 cm is equal to approximately 4.954 feet.
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Rob has $7,869 in an account that earns 13% interest compounded annually.To the nearest cent, how much will he have in 5 years?
Answer:
$14,498.1
Step-by-step explanation:
To find the amount Rob will have in 5 years with compound interest, we can use the formula:
A = P (1 + r/n)^(nt)
where:
A = the future value of the investment
P = the principal amount invested
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case, we have:
P = $7,869 (the principal amount)
r = 13% or 0.13 (the annual interest rate)
n = 1 (the interest is compounded annually)
t = 5 (the number of years)
Substituting these values into the formula, we get:
A = $7,869 (1 + 0.13/1)^(1*5)
A = $7,869 (1.13)^5
A = $14,964.92
Therefore, to the nearest cent, Rob will have $14,964.92 in 5 years.
Due nowww please help mee
Answer:
Step-by-step explanation:
I cant see
what is the area of these shapes . step by step pls beed today before school
The value where the histogram balances when supported at that point is called ____.
The value where the histogram balances when supported at that point is called the mode of the distribution.
The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.
For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.
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i need help on this equation
Answer:
c
Step-by-step explanation:
DO THE MATH!!!!!!!PLEASE
Greg is building birdhouses in shop class. The amount of wood he has on hand determines how many birdhouses he can build. w = the amount of wood Greg has on hand b = the number of birdhouses Greg can build Which of the variables is independent and which is dependent?
Answer:
Step-by-step explanation:
w is the independent
b is the dependent
Think of it this way: the number of birdhouses depends on the amount of wood available.
Express 4 + ln 2 - ln 4 as a single natural logarithm.a. ln 2b. ln 4 c. ln 64
The single natural logarithm for the expression 4 + ln 2 - ln 4 is ln(2). So, correct option is A.
To express 4 + ln 2 - ln 4 as a single natural logarithm, we can use the properties of logarithms to combine the terms.
First, we can use the rule that ln(a) - ln(b) = ln(a/b) to simplify ln 2 - ln 4:
ln 2 - ln 4 = ln(2/4) = ln(1/2)
Now, we can rewrite the expression as:
4 + ln(1/2)
We can use another logarithmic property, ln(a) + ln(b) = ln(ab), to write this as:
4 + ln(2^(-1))
Simplifying further:
4 - ln(2)
Therefore, 4 + ln 2 - ln 4 can be expressed as a single natural logarithm of:
ln(2^2 / 2) = ln(2)
So, the answer is (a) ln 2.
In general, when simplifying expressions involving logarithms, it's helpful to remember the logarithmic properties and rules, such as the product, quotient, and power rules, as well as the fact that ln(e) = 1. By applying these rules systematically, we can simplify complex expressions into simpler forms that are easier to work with.
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What is the result 3 x 6 ?
Answer:
Step-by-step explanation:
3*6=18
(1 point) Let A be a matrix with linearly independent columns_ Which one of these statements must be true? You have only three attempts at this problem_ OA The equation Ax b has a solution for all b precisely when it has more columns than rows B. The equation Ax =b always has a solution for all b_ C. There is no easy way to tell if Ax = b has a solution for all b D: The equation Ax b has a solution for all b precisely when it has more rows than columns_ E: The equation Ax = b has a solution for all b precisely when it is a square matrix: F The equation Ax b never has a solution for all b_ none of the above
The statement that must be true is option (f) "The equation Ax = b has a solution for all b precisely when it has more columns than rows".
A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.
This is because if the matrix has more columns than rows, then the system of equations cannot be underdetermined, meaning that there is a unique solution for the equation.
On the other hand, if the matrix has more rows than columns, then it is possible that the equation Ax = b could have no solutions, which would mean that it is an overdetermined system.
Furthermore, if the matrix is a square matrix, then it will have the same number of rows and columns, and it is possible that the equation Ax = b could have either one solution or no solutions.
Therefore, the statement "The equation Ax = b has a solution for all b precisely when it has more columns than rows" is the only one out of the six given that must be true
Hence the option (f) is correct.
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how much is 140 lbs in kg
On converting the weight of 140 lbs to Kilogram , we get that 140 lbs is equivalent to 63.49 Kg .
The Conversion Factors is used to convert the weight between pounds and kilograms. that means : To convert 1 pound to kilograms , We multiply the number of pounds by 0.4535 .
In this case , we have to convert 140 pounds to kilograms ;
So , we multiply the given weight in pounds with 0.4535 .
On multiplying ,
We get ;
⇒ 140 pounds = 140 × 0.4535 Kg ;
⇒ 140 pounds = 63.49 Kg .
Therefore , 140 lbs is approximately equal to 63.49 Kg .
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Solve the system by substitution.
y=-7x-3
5x+4y= -35
Answer: (x,y)=(1,-10)
Step-by-step explanation:
y=-7x-3
5x+4y=-35
substitute the value of y
5x+4(-7x-3)=-35
solve the equation
x=1
substitute the value of x
y=-7 x 1-3
solve the equation
y=-10
A possible solution is
(x,y)=(1,-10)
Check the solution
-10=-7 x 1-3
5 x 1+4 x (-10)=-35
simplify
-10=-10
-35=-35
The ordered pair is a solution
(x,y)=(1,-10)
A ballet company has sold 540 tickets for the next performance. Tickets for the center section are $56 while tickets for the left and right sections are $38. They have sold $24,120 in tickets. How many $56 and $38 tickets were sold?
The number of $56 dollar tickets to center section was 200 and the number of tickets costing $38 to the left and right sections were 200.
Let us consider the number of tickets to the center section be x and right and left sections be y.
Here the total number of tickets sold are 540.
So, x+ y = 540 ---------> i
The cost of tickets cost $56 will be 56x
The cost of tickets cost $38 will be 38y.
The total cost was given as $24120
So, 56x+ 38y = 24120 -----------> ii
Multiplying equation i with 56,
56x + 56y = 30240 ------------> iii
Subtracting equation ii from equation iii
56x+ 56y = 30240
- 56x + 38y = 24120
So 18y = 6120
y = 6120/18 = 340
Since x+ y = 540
x+ 340 = 540
x = 540- 340 = 200
So the number of $56 ticket sold is 200 and the number of $38 ticket sold is 340.
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Solve ( x + 6 ) ^2 = 64
A . X = 8 or x = -8
B . X = 2 or x = -2
C . X = 2 or x = -14
D . X = 4 or x = -16
The required solutions to the equation are x = 2 or x = -14.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Starting with the equation:
(x + 6)² = 64
Taking the square root of both sides, we get:
x + 6 = ±8
Solving for x, we have two cases:
Case 1:
x + 6 = 8
x = 8 - 6
x = 2
Case 2:
x + 6 = -8
x = -8 - 6
x = -14
Therefore, the solutions to the equation are x = 2 or x = -14.
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Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side TQ.
Round your answer to the nearest tenth. Figures are not drawn to scale.
HELPPPP
Quadrilateral MNOP is similar to quadrilateral QRST. The measure of side RS is approximately 39.2 units.
If two quadrilaterals are similar, their corresponding sides are in proportion. Therefore, we can set up a proportion between the corresponding sides of quadrilaterals MNOP and QRST as follows:
MN / QR = NO / ST = OP / RS
We are given the lengths of MN, NO, and OP, but we need to find the length of RS. We can solve for RS by rearranging the proportion as follows:
OP / RS = MN / QR
RS = OP / (MN / QR)
We can substitute the given values to get:
RS = 58 / (19 / 13)
Simplifying this expression gives:
RS = 58 * (13 / 19) = 39.241 ≈ 39.2
Therefore, the measure of side RS is approximately 39.2 units.
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____The given question is incomplete, the complete question is given below:
Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale. QT =58, PM= 19 ON=13.
What whole number is equal to the fraction 1 over 1?
Answer:
Anything.
Step-by-step explanation:
The reason why I say " anything " is because the fraction, [tex]\frac{1}{1}[/tex] is bascially representing the number 1, nothing else so you can put whatever you want, tens, hundreds, thousands, millions, and so on.
So whatever number you want to put it will always equal, [tex]\frac{1}{1}[/tex], But just remember to always put the number that you choose on top or the numerator such as the following:
[tex]\frac{4}{1}[/tex].
Thus, you answer is, anything.