a) A linear equation for the total remaining oil reserves, R, in terms of t, the number of years since the current year, is 2,090 - 18t.
b) Based on the above linear equation, 15 years from now, the total oil reserves will be 1,820 billion barrels.
c) Using division operation, the world's oil reserves will be completely depleted approximately 116 years from now.
What is a linear equation?A linear equation is a mathematical or algebraic equation written in the form of y = mx + b.
A linear equation consists of a constant and a first-order term, where m is the slope, and variable b, the y-intercept.
The current total world oil reserves, R = 2,090 billion barrels
Average decrease per year = 18 billion barrels
a) Linear equation for R is 2,090 - 18t
b) In 15 years, the total oil reserves = 2,090 - 18(15)
= 2,090 - 270
= 1,820
c) The constant rate of decrease = 18 billion barrels per year
The world's oil reserves will be completely depleted approximately 116 years from now (2,090/18).
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On a coordinate plane, a curved line with minimum values of (negative 1.5, negative 2) and (1.5, 2), and a maximum value of (0, 4), crosses the x-axis at (negative 2, 0), (negative 1, 0), (1, 0), and (2, 0), and crosses the y-axis at (0, 4).
Which is an x-intercept of the graphed function?
(0, 4)
(–1, 0)
(4, 0)
(0, –1
The x-intercepts are (-2, 0), (-1, 0), (1, 0), and (2, 0).
What is meant by the x-intercept?
The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y coordinate equals zero, is the x-intercept for any curve.
The x-intercepts are the points where the graph meets the x-axis.
Which means that the coordinate of y will be zero.
It is given in the question that the graphed function will meet the x-axis at 4 points which are (-2, 0), (-1, 0), (1, 0), and (2, 0)
Therefore the x-intercepts of the function will be: (-2, 0), (-1, 0), (1, 0), and (2, 0).
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Answer: B) (-1,0)
Step-by-step explanation:
Just took the test on edge
Two angles are supplementary angles if the sum of their measures is 180°.
Find two supplementary angles such that the measure of the first angle is 26° less than
three times the measure of the second.
The measure of the first angle is____ft.
The measure of the first angle is 128. 5 degrees
How to determine the angleFrom the information given, we have that;
The two angles are supplementaryThe sum up to 180 degreesThe first angle is 3x - 26Let the second angle be x
We have the representation as;
3x - 26 + x = 180
collect the like terms, we get;
3x + x = 180 + 26
Add or subtract the like terms
4x = 206
Make 'x' the subject of formula by dividing by the coefficient of x, we get;
x = 206/4
divide the values
x = 51.5 degrees
Then, the angle is 128 .5 degrees
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Question 5
A line passes through the point (-1, -1) and has a slope of 6.
Write an equation in point-slope form for this line.
An equation in point-slope form for this line is y=6x+5.
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
Given that;
Point on a line (-1,-1)
Slope of the line 6
Now, substituting the values in the general formula of line
y+1=6(x+1)
y+1=6x+6
y=6x+5
Therefore, the equation with the given slope will be y=6x+5.
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Andrea and Stanley have decided on a $320,000 mortgage value for this new house. They are comparing two mortgage
options from two different lending institutions. They know they want a 30-year term, but they aren't sure which instituti
would be a better fit. Mortgage B institution is closer to their home, and they aren't sure the difference in monthly paym
is worth partnering with someone farther away.
Mortgage A: 4.5% with monthly payments of $1621.39 and a total payback of $583,700.40
Mortgage B: 5% with monthly payments of $1717.83 and a total payback of $618,418.80
How much will Andrea and Stanley save by choosing Mortgage A?
Provide your answer below:
They will save $ by choosing Mortgage A
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In linear equation, $ 618,418.80 will Andrea and Stanley save by choosing Mortgage A .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Total Payback = Instalment Amount * No. of Instalments
Mortgage A:
= $1621.39 * 360
= $ 583,700.40
Mortgage B:
= $1717.83 * 360
=$ 618,418.80
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(2x-5y=4
4x=8+10y
Solve for X and Y
Answer:
Step-by-step explanation:
To solve this system of two equations with two variables (x and y), we'll use the substitution method. Here's how:
Solve one of the equations for either x or y, in terms of the other variable. Let's solve the first equation, 2x - 5y = 4, for x:
x = (4 + 5y)/2
Substitute the expression for x from step 1 into the second equation, 4x = 8 + 10y:
4(4 + 5y)/2 = 8 + 10y
Simplify the equation from step 2:
8 + 10y = 8 + 10y
Solve for y by subtracting 8 from both sides:
10y = 10y
Divide both sides by 10 to find the value of y:
y = y
Now that we have the value of y, we can substitute it back into the expression for x from step 1:
x = (4 + 5 *y)/2
So the solution to the system of equations is (x, y) = ((4 + 5 *y)/2, y=y).
NEED HELP!!!!!!!!!!!
The width of the rectangle is [tex]4x^8y^6[/tex]inches.
Option A is correct.
What is the area of the rectangle?
A rectangle is a four-sided polygon with two pairs of parallel sides, and all four angles are right angles (90 degrees). The area of a rectangle is the amount of two-dimensional space that it occupies and is given by the product of its length and width. In other words, the area A of a rectangle with length l and width w is given by the formula:
A = l x w
To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:
Area = length x width
In this case, we are given the area and the length of the rectangle, so we can rearrange the formula to solve for the width:
width = Area / length
Substituting the given values, we have:
width = [tex]\frac{(32x^{12}y^{9})}{(8x^4y^3)}[/tex]
Simplifying the expression, we get:
width = [tex]4x^{8}y^{6}[/tex]
Therefore, the width of the rectangle is[tex]4x^8y^6[/tex]inches.
Option A is correct.
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Two numbers are in the ratio of 2:3. If 15 is added to both the numbers, then the ratio betwee two numbers becomes 11: 14. Find the greater number.
Answer:
Below
Step-by-step explanation:
(2x+15) / ( 3x+15) = 11/14 cross multiply to get
28x + 210 = 33x + 165
45 = 5x
x = 9 so the larger number is 3 X 9 = 27
(smaller number is 2 x 9 = 18)
Decide whether the following statement is
always, sometimes, or never true. Explain your reasoning.
Any decimal that ends with a digit in the thousandths place can be
written as a fraction with a denominator that is divisible by both 2 and 5.
Yes, the given statement is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.
What is Fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that;
The statement is about the decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.
Now, A fraction is terminating decimal as if the denominator of the fraction contains terms in the form of 2ᵃ, 5ᵇ or 2ᵃ x 5ᵇ.
Then, It is said that, there is a digit in thousandth place.
Hence, the statement given is true that any decimal that ends with a digit in the thousandths place can be written as a fraction with a denominator that is divisible by both 2 and 5.
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Select the items that describe possible effects of incentives for political leaders.
The Possible effects of incentives for political leaders includes options 1, 2, 3, and 4. These options elaborate the incentives of political leaders.
Favor programs with immediate benefits: Political leaders may be incentivized to prioritize policies or programs that provide immediate benefits to their constituents in order to increase their popularity and chances of reelection.
Implement policies that favor a small, powerful group: Incentives for political leaders may also lead them to implement policies or regulations that favor a small, powerful group, such as major donors or influential interest groups, at the expense of the general public.
Provide policies whose costs outweigh the benefits: Political leaders may be incentivized to implement policies that provide short-term benefits but have long-term costs or consequences, such as a large budget deficit or environmental degradation.
Favor programs with immediate costs: Alternatively, incentives may lead political leaders to prioritize programs or policies with immediate costs, such as increased taxes or reduced spending, to address pressing issues and avoid long-term consequences.
Therefore, options 1, 2, 3, and 4 describe possible effects of incentives for political leaders.
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____The given question is incomplete, the complete question is given below:
Select all the items that describe possible effects of incentives for political leaders. 1.favor programs with immediate benefits 2.implement policies that favor a small, powerful group 3.provide policies whose costs outweigh the benefits 4.favor programs with immediate costs
Please help!!!!! Due tomorrow need to understand how to properly do this question :(
The table offers an average rate of change greater than the average rate of change of the function f(x) = x² + 2 · x - 1.
How to determine the average rate of change of a function
In this problem we need to determine two average rates of change, one from an equation and another from a table. Graphically speaking, average rate of change is the slope of a line secant to a curve and it can be computed by secant line formula:
m = [f(2) - f(- 2)] / [2 - (- 2)]
First, we proceed to determine the average rate of change for the function f(x) = x² + 2 · x - 1:
f(- 2) = (- 2)² + 2 · (- 2) - 1
f(- 2) = 4 - 4 - 1
f(- 2) = - 1
f(2) = 2² + 2 · 2 + 1
f(2) = 9
m = [9 - (- 1)] / [2 - (- 2)]
m = 10 / 4
m = 5 / 2
m = 2.5
And the average rate of change of the table:
m = (6.25 - 0.16) / [2 - (- 2)]
m = 0.09 / 4
m = 609 / 400
m = 1.523
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Current assets are assets that are expected to be converted to cash, sold or consumed in the next
12 months. They include cash, accounts receivable, notes receivable, inventory and prepaid
expenses. Step 8 explains each one in detail.
1. You are the owner of an appliance store. Choose four categories from above and explain how
that asset may fit into your business. For example, if I owned a company that installed furnaces,
my inventory would include different types of furnaces and air conditioners as well as controls
to operate them. Accounts receivable would include the installations we did but have not been
paid for yet.
How these current asset may fit into your business, like mine, is explained as follows:
Cash: Cash is a crucial asset for any business, as it is needed to pay for expenses such as salaries, rent, and other operating costs.Accounts Receivable: It represents the amount of money owed to the business by its customers and is a key part of the business's revenue stream. Inventory: Inventory represents the value of the goods that are available for sale and can include raw materials, work-in-progress, and finished products.Prepaid Expenses: Prepaid expenses can be a helpful asset for businesses that make regular payments for services or goods, such as insurance or rent. Explanation on items of the Current assets:Cash: Cash refers to physical currency or money that is readily available to a business or individual. It includes cash on hand, in bank accounts, or other forms of liquid assets that can be easily converted to cash.Accounts Receivable: Accounts receivable refers to the amount of money owed to a business by its customers or clients for goods or services that have been sold but not yet paid for. It represents the short-term credit that a business has extended to its customers.Notes Receivable: Notes receivable are similar to accounts receivable but involve more formal written agreements. They are written promises by a borrower to pay a specific sum of money at a future date to a creditor, with interest.Inventory: Inventory refers to the goods that a business holds for sale to customers or for use in its operations. It includes raw materials, work-in-progress, and finished goods that have not yet been sold.Prepaid Expenses: Prepaid expenses refer to payments made by a business for goods or services that have not yet been used or consumed. They are considered assets because they represent future economic benefits that will be realized by the business. Examples include prepaid rent, insurance premiums, and other prepayments.Read more about Current assets
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Upon enlisting in the Marine Corps. I was given the
)
opportunity to create a College Sovings fund for every
$1.00 I deposited the government would deposit
an additional $2.00 with a max of $100.00/month.
If I deposited the max each month how much money did I have
at the end of 5 years if I started with $100.00
Answer:
Step-by-step explanation:
Here's a step-by-step explanation of the solution:
Calculate the government deposit: For every $1.00 you deposit, the government deposits $2.00. So if you deposit the maximum of $100.00 each month, the government deposit would be $100.00 * $2.00 = $200.00.
Calculate the total deposit each month: The total deposit each month is the sum of your deposit and the government deposit, so it would be $100.00 + $200.00 = $300.00.
Calculate the number of months: You started with $100.00 and made the maximum deposit of $100.00 each month for 5 years. Five years is 5 * 12 = 60 months.
Calculate the total deposit over 5 years: Over 5 years, you made 60 deposits of $300.00 each, so the total deposit over 5 years would be 60 * $300.00 = $18,000.00.
Calculate the final balance: Adding the initial deposit of $100.00 to the total deposit over 5 years, the final balance in your account after 5 years would be $18,000.00 + $100.00 = $18,100.00.
So, at the end of 5 years, if you deposited the maximum of $100.00 each month into the College Savings fund, you would have $18,100.00 in your account.
Find the slope of the line on the graph. Reduce all fractional answers to lowest terms.
-4
-1
-2
The slope of the line on the graph will be a negative one. Then the correct option is A.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the graph, the two points are (-2, 2) and (2, -2). Then the slope is given as,
m = (- 2 - 2) / (2 + 2)
m = - 4 / 4
m = - 1
The slope of the line on the graph will be a negative one. Then the correct option is A.
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The complete question is attached below.
Find the difference between the simple interest
and compound interest on 16000 at 5%
per annum at the end of one and a half year
if the interest is compounded half yearly.
Answer: The simple interest on 16000 at 5% per annum for 1.5 years is calculated as:
I = P * r * t
I = 16000 * 0.05 * 1.5
I = 1200
The compound interest on 16000 at 5% per annum compounded half yearly for 1.5 years is calculated as:
A = P * (1 + r/n)^(nt)
A = 16000 * (1 + 0.05/2)^(2 * 1.5)
A = 16000 * (1.0253)^3
A = 16000 * 1.07897
A = 17253.576
The difference between the compound interest and simple interest is:
17253.576 - 1200 = 16053.576
So the difference between the simple interest and compound interest is 16053.576.
Step-by-step explanation:
The Nutty Professor sells cashews for $7.70 per pound and Brazil nuts for $5.00 per pound. How much of each type should be used to make a 30 pound mixture that sells for $6.08 per pound?
Round answers to the nearest pound.
The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.
What is Mixture?A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.
According to question:Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.
We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.
The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.
The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.
The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:
$7.70x + ($150 - $5.00x) = $182.40
Expanding and simplifying the equation:
$2.70x = $32.40
Dividing both sides by 2.70:
$x = 12
So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.
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Convert 40 fluid ounces to pints.
Answer:The answer is 2.5 pints.
-4x+7x=4(x+2)-(x+8)
The best way to figure out if there is a solution to the equation:
--> solve this whole thing algebraically
Let's solve:
[tex]-4x+7x=4(x+2)-(x+8)\\3x=4x+8-x-8\\3x=3x[/tex]
If we get this kind of circumstance:
--> where the left/right part of the equation are equal and cannot be
solved further
---> the solution is all real numbers
Answer: solution is all real numbers
The longer leg of a right triangle is nine less than three times the shorter leg. The
hypotenuse is two more than the longer leg. What is the length of the hypotenuse if the
perimeter is 24?
Answer: 71/7
Step-by-step explanation:
I like this problem a lot!
Let the shorter leg length be x:
then the longer leg length is 3x - 9
the hypotenuse length is (3x - 9) + 2 = 3x - 7
Perimeter of Triangle = Sum of all 3 sides of a triangle
24 = x + (3x - 9) + (3x - 7)
24 = 7x - 16
40 = 7x
.: x = 40/7
.: hypotenuse = 3x - 7 = (120/7) - 7 = 71/7
Done!
Which rules define the function graphed below? y=2x+3, y=-1/3x+3
piecewise function defines the function graphed between y=2x+3 and y=-1/3x+3.
How to compare linear equations?
The comparison method, a procedure for solving systems of independent equations, starts by rewriting each equation with the same variable as the subject. Any of the variables may be chosen as the first variable to isolate. Each equation is now an isolated-subject equation, and equation where one variable is isolated.
Given:
y = 2x+3
y = -1/3x+3
The left portion of the blue curve is y = 2x+3 but it is only graphed when x < 0 (we could argue that but I'll set that aside for the other portion).
The right portion is the line y = -1/3x + 3 and it's only graphed when
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are
y = 2x + 3; y = -1/3 x + 3e could have this piecewise function
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Given the equations below, what is the value of x?
2y - 4x = 8
3(x + 4) - 2y = 5
By using the substitution method, the value of x is equal to -1.
How to solve this system of equations?In order to solve the given system of equations, we would apply the substitution method. From the information provided in the image attached above, we have the following system of equations:
2y - 4x = 8 .......equation 1.
3(x + 4) - 2y = 5 .......equation 2.
From equation 1, we have:
y = 2x + 4 .......equation 3.
By using the substitution method to substitute equation 3 into equation 2, we have the following:
3(x + 4) - 2(2x + 4) = 5
3x + 12 - 4x - 8 = 5
-x + 4 = 5
x = 4 - 5
x = -1.
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Algebra 1, slope of coordinate plane on table
The y-intercept of the line passing through the given points is -26 and the slope is -13/17
What is y-intercept?The y-intercept is the point where the graph intersects the y-axis.
Given that, the pair of coordinates of some points, we need to find the y-intercept,
To find the same, we will firstly find the equation of the line passing through these points,
We know that, the equation of a line passing through two points is given by,
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Considering the points, (34, -52) and (51, -65)
The equation will be,
y+52 = -65+52 / 51-34 (x-34)
y+52 = -13/17(x-34)
y+52 = -13x/17+26
y = -13x/17-26
Hence, the y-intercept of the line passing through the given points is -26.
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Winston planned to spend no more than $150 on a helmet and goggles for skiing. After
spending $90.50 on a helmet, he bought a pair of goggles that put him over his budget.
Let x represent the cost of the goggles. Which inequality describes the problem?
90.50 + x>
150
90.50 + x <
150
Solve the inequality. Then, complete the sentence to describe the solution.
The goggles cost more than $
Submit
Answer:
(a) 90.50 +x > 150The goggles cost more than $59.50Step-by-step explanation:
You want an inequality and its solution for finding the cost of goggles that put Winston over his $150 budget when combined with the purchase of a $90.50 helmet.
Total costIf x represents the cost of the goggles, then Winston's total spending is ...
90.50 + x
If that is over is $150 budget, the relation is described by ...
90.50 +x > 150
SolutionSubtracting 90.50 from both sides gives ...
x > 59.50
This tells us the goggles cost more than $59.50.
<95141404393>
I ALSO NEED HELP WITH THIS TOO
Answer:
Step-by-step explanation:
Two angles are said to be supplementary when their sum is equal to 180°.
Given angle 1 and 50° are supplementary.So, angle1+50°= 1880°
angle1 =180°-50°
angle 1=130°
Given 50° and angle 3 are supplementary
So,50°+ angle 3=18=0°
angle 3=130°
So angle 1 equals to angle
7 5/6 / 2 2/3
Leave as a mixed number
Answer:
2.9375
Step-by-step explanation:
7 5/6 / 2 2/3 = 47/16 = 2 15/16 = 2.9375
Hello I need help please
Answer:
(-9)×(-7/3)=9×7/3=3×7=21
Answer:
21
Step-by-step explanation:
-9 is equal to -9/1
the negative sign on the -7/3 can be put on the top or bottom
-9 -7 63
--- x --- = ---
1 3 3
63 divided by 3 equals 21 and is therefore in the simplest form
Which expression is a factor of -2x2 - 11x - 20
A-(x - 10)
B-(2x - 5)
C-No real Factors
D-(2x + 10)
Answer:
C. No real factors
Step-by-step explanation:
Not factorable
What is the average speed of a car that traveled 300 miles in 5.5 hours? Round answer to the nearest hundredths
place.
O 150 mph
O 54.54 mph
Answer: 54.54 mph
Step-by-step explanation: To calculate the average speed of a car that traveled 300 miles in 5.5 hours, you can divide the total distance traveled by the total time taken: Average speed = Total distance / Total time-average speed = 300 miles / 5.5 hours = 54.55 miles per hour (mph)So, the average speed of the car is 54.55 mph.
2. 34 is 34% of what number?
Look at the photo please
The equations that explains the process to find the number of square yards of fabric she will use and the number of square yards of fabric she will have left, using the addition of fractions are;
(3/8) + (2/8) = 5/8 square yards of fabric will be used
1 - 5/8 = 3/8 square yard of fabric will be left
What are fractions?A fraction is a representation of a part of a whole, consisting of a number in the numerator divided by another number in the denominator expressed as a quotient.
The amount of fabric Diana has = 1 square yard
Amount of fabric to make one pillow = 3/8 square yard
Amount of fabric required to make the other pillow = 2/8 square yard
Therefore, the amount of fabric Diana will use can be found by adding the fractions of the areas of the fabric she uses for each pillow as follows;
3/8 + 2/8 = ((3 × 1) + (2 × 1))/8 = (3 + 2)/8 = 5/8 square yard of fabric will be usedThe number of square yard of fabric Diana will have left can be found from the difference between the initial number of square yards of fabric Diana has and the amount of square yards of fabric she will use.
Initial number of square yards of fabric = 1
Number of square yards of fabric she will use = 5/8
Therefore;
Number of square yard of fabric Diana has left = (Initial number of square yards of fabric) - (Number of square yards of fabric she will use)
Number of square yard of fabric Diana has left = 1 - 5/8 = (8 - 5)/8 = 3/8
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Angela fully charged her laptop, then unplugged it and tracked the battery level at certain times under constant use. The table below shows her findings. The equation for the line of best
fit is below. Use the equation to estimate the battery level after two hours of constant use unplugged. Round to the nearest percent. (2:00 is an x-value of 0)
The battery level after two hours of constant use unplugged is found replacing the instance of x on the line of best fit by 2.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The variables for this problem are given as follows:
Variable x: time in hours.Variable y: battery percentage.Hence after a time of two hours the battery level is found as the numeric value at x = 2.
Missing InformationThe problem is incomplete, hence the general procedure to solve the problem is presented.
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