C. If there is no variability (all the scores of the variables have the same value), measures of dispersion will equal zero.
Measures of dispersion are used to describe the spread of data. They include the range, variance, and standard deviation. When all the scores of a variable have the same value, there is no spread or variability in the data. This means that the distance between the minimum and maximum value (range) is zero, and the variance and standard deviation are also zero.
In this case, there is no need to calculate measures of dispersion because they will all equal zero. This is because the data points do not differ from each other in any way, and there is no variation to describe. Therefore, when there is no variability in a set of data, measures of dispersion will always equal zero.
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A savings account balance is compounded annually. If the interest rate is 3% per year and the current balance is $1,530.00, what will the balance be 9 years from now?
The balance of the savings account 9 years from now will be $1,980.58.
To find the balance of the savings account 9 years from now, we can use the formula for compound interest:
[tex]A = P(1 + \dfrac{r}{n})^{(nt)}[/tex]
where A is the ending balance, P is the principal (starting balance), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
Substituting the given values, we get:
A = 1530(1 + 0.03/1)⁹
A = 1530(1.03)⁹
A = 1530(1.295376)
A = 1980.58
Therefore, the balance of the savings account 9 years from now, rounded to the nearest cent, will be $1,980.58.
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in 2000, the population of california was 29,816,591 and increased yearly by 1.28%. what will the population be in the year 2020?
The population of California in the year 2020 using the initial population for the year 2000 will become approximately 38453143.
Population of California in the year 2000 = 29,816,591
Yearly increased rate = 1.28%
use the formula for compound interest,
A = [tex]P\times (1 + r/n)^{(n\times t)}[/tex]
where A is the final amount,
P is the initial amount,
r is the annual interest rate (as a decimal),
n is the number of times the interest is compounded per year,
and t is the number of years.
In this case, P = 29,816,591,
r = 0.0128 (since the annual increase is 1.28%),
n = 1 (since the increase is yearly),
and t = 20 (since we want to know the population in 2020, which is 20 years after 2000).
Substituting these values into the formula, we get,
A = 29,816,591(1 + 0.0128/1)²⁰
A = 29,816,591(1.0128)²⁰
A = 29,816,591 × (1.2897)
A = 38453142.868
Therefore, the population of California in the year 2020 will be approximately 38453143 (rounded to the nearest whole number).
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find two numbers whose difference is 48 and whose product is a minimum. smaller number larger number
In this problem, we are asked to find two numbers whose difference is 48 and whose product is a minimum.
To approach this problem, we can use the fact that the product of two numbers is minimized when the numbers are closest to each other. Therefore, we can let x be the smaller of the two numbers, and then the larger number is x + 48.
The product of these two numbers is:
P = x(x + 48) = x^2 + 48x
To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:
dP/dx = 2x + 48 = 0
Solving for x, we get:
x = -24
Substituting this value of x into the expression for P, we get:
P = (-24)^2 + 48(-24) = 576 - 1152 = -576
Therefore, the two numbers whose difference is 48 and whose product is minimized are -24 and 24. Note that the smaller number, -24, is negative, but this makes sense since the problem did not specify that the numbers had to be positive.
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Latrell has $8 to spend on postcards. He wants to buy one large postcard and some small ones. Write an inequality to determine how many small postcards Latrell can purchase. Postcards Large $2. 00 Medium $1. 50 Small $1. 25
The inequality to determine how many small postcards Latrell can purchase is: 1.25s + 2.00 ≤ 8.00
In the inequality 1.25s + 2.00 ≤ 8.00 s represents the number of small postcards and the left-hand side of the inequality represents the total cost of the postcards, including one large postcard costing $2.00.
To solve for s, we can begin by subtracting 2.00 from both sides of the inequality to isolate the term with s:
1.25s ≤ 6.00
Then, we can divide both sides of the inequality by 1.25 to solve for s:
s ≤ 4.8
Since s represents a whole number, the largest number of small postcards that Latrell can purchase is 4.
In summary, the inequality 1.25s + 2.00 ≤ 8.00 can be used to determine the maximum number of small postcards (s) that Latrell can purchase with $8 while also buying one large postcard. By solving the inequality, we find that s ≤ 4.8, so the largest whole number of small postcards that Latrell can purchase is 4.
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Suppose years of schooling, s, is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by: wm = 500 + 100s and wf = 300 + 75s. On average, men have 14 years of schooling and women have 12 years of schooling. (a) What is the male-female wage differential in the labor market? The wage differential can be written as: )75300(100500 fsmsfwmww = 500 + 100(14) – 300 – 75(12) = $700. (b) Using the Oaxaca decomposition, calculate how much of this wage differential is due to discrimination?
Wage differential is due to discrimination = 700 - 700 = 0 .The Oaxaca decomposition is a method used to estimate the portion of the wage differential between two groups (in this case, male and female workers) that can be attributed to discrimination.
The decomposition breaks down the wage differential into two components: the explained component and the unexplained component.The explained component represents the portion of the wage differential that can be attributed to differences in observable characteristics between the two groups, such as years of schooling.
The unexplained component represents the portion of the wage differential that cannot be explained by observable characteristics and is often interpreted as the component related to discrimination or unobserved factors.
To calculate the Oaxaca decomposition, we need to follow these steps:
Step 1: Calculate the average wage of male workers (wm) and female workers (wf) using the given equations:
wm = 500 + 100s, where s = 14 years (average years of schooling for men)
wm = 500 + 100(14) = 1900
wf = 300 + 75s, where s = 12 years (average years of schooling for women)
wf = 300 + 75(12) = 1200
Step 2: Calculate the explained component of the wage differential by estimating the wage differential that can be explained by the differences in observable characteristics (years of schooling) between the two groups.
Explained wage differential = [500 + 100(14)] - [300 + 75(12)] = 700
Step 3: Calculate the unexplained component of the wage differential, which is the portion that cannot be explained by observable characteristics and may be attributed to discrimination or unobserved factors.
Unexplained wage differential = Actual wage differential - Explained wage differential
Unexplained wage differential = 700 - 700 = 0
In this case, the unexplained component of the wage differential is zero, indicating that none of the wage differential can be attributed to discrimination. All of the wage differential can be explained by the differences in observable characteristics (years of schooling) between male and female workers.
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A small sofa has a mass of 6 kilograms. A pillow on the sofa has a mass of 100 grams. How many pillows would it take to equal the mass of the sofa?
Answer:
6000
Step-by-step explanation:
solved
A. y = sin(x - Tt/2)
C. y=sin(x + 1)
Find the equation.
1
NEN
2
k
B. y = sin x
D. y = sin(x +
TT/2)
The requried equation of the graph shown is y = sin (x - π/2).
The curve shown in the graph is of the sine function with some trasformation given as,
The graph of sinx is shifted π/2 units left, so the equation of the graph is given as,
y = sin (x - π/2)
Thus, the requried equation of the graph shown is y = sin (x - π/2).
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please i need help on this
Answer:
b
Step-by-step explanation:
Which expression is equivalent to 12.8-3s+15.5+8s?
A. -2+5s
B. 5s +28.3
C. 33.3s
D. 27.3 +5s
The correct expression which is equivalent to 12.8 - 3s + 15.5 + 8s is,
⇒ 5s + 28.3
We have to given that;
Expression to solve is,
⇒ 12.8 - 3s + 15.5 + 8s
Now, WE can simplify as;
⇒ 12.8 - 3s + 15.5 + 8s
Combine like terms,
⇒ 12.8 + 15.5 - 3s + 8s
⇒ 28.3 + 5s
⇒ 5s + 28.3
Thus, The correct expression is,
⇒ 5s + 28.3
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a motorist travelled from Ibadan to Lagos ,a distance of 142 km,at an average speed of 60km/h. He spent 5/2 hours in Lagos and then returned to Ibadan at an average speed of 80km/h .(a).At what time did the man arrive back in Ibadan? .(b). find his average speed for the total journey.
To solve the given problem, let's break it down into two parts:
(a) At what time did the man arrive back in Ibadan?
We can calculate the time taken for the initial journey from Ibadan to Lagos using the formula:
Time = Distance / Speed
Time = 142 km / 60 km/h
Time = 2.37 hours
The motorist then spent an additional 5/2 hours in Lagos.
To calculate the total time taken for the return journey from Lagos to Ibadan, we use the formula:
Time = Distance / Speed
Time = 142 km / 80 km/h
Time = 1.775 hours
Adding the time spent in Lagos to the return journey time:
Total time = 2.37 hours + 5/2 hours + 1.775 hours
Total time = 6.145 hours
Therefore, the man arrived back in Ibadan approximately 6.145 hours after he left.
(b) To find the average speed for the total journey, we use the formula:
Average Speed = Total Distance / Total Time
The total distance covered in the round trip is 2 times the distance between Ibadan and Lagos, which is:
Total Distance = 2 x 142 km
Total Distance = 284 km
Average Speed = 284 km / 6.145 hours
Average Speed = 46.22 km/h
Therefore, the average speed for the total journey is approximately 46.22 km/h.
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The radius of Circle A is 8 cm. The radius of Circle B is 2 cm greater than the radius of Circle A. The radius of Circle C is 4 cm greater than the radius of Circle B. The radius of
Circle D is 3 cm less than the radius of Circle C. What is the area of each circle? How many times greater than the area of Circle A is the area of Circle D?
A quadratic function f(x) is hidden from view. You must find all
intervals where f(x) is negative. Choose the form of the quadratic
function f(x) that you would like to see in order to answer the
question most efficiently.
Form: Standard Form, Factored form, or vertex form
To answer the question most efficiently , the standard form of the quadratic equation is the most suitable.
What is a quadrilateral function?A quadratic function is one of the form f(x) = ax² + bx + c, where a, b, and c are numbers with a not equal to zero.
The highest power of a quadratic function is 2.
To solve a quadratic function efficiently, we need to put the function in standard form. i.e We arrange the power in descending order.
For example, a quadratic functionf(x)= 5x-2 +x² is not in standard form. To solve this we need to put it in a form of f(x) = x²+5x -2.
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eliminate the parameter t for both parametrizations and write down the equation of the ellipse in terms of x and y only.
The differential equation of the ellipse in terms of x and y only: (x/2) ^2 + (y/3)^2 = 1. To eliminate the parameter t for a parametric equation of an ellipse, we can solve for t in terms of x or y and substitute it into the other equation.
Consider the parametrization of an ellipse given by x = 2cos(t) and y = 3sin(t).
We can eliminate t by solving for cos(t) and sin(t) in terms of x and y, respectively. From the first equation, we have cos(t) = x/2, so t = Arcos(x/2). Substituting this expression for t into the second equation, we get y = 3sin(arccos (x/2)) = 3sqrt(1-(x/2)^2). This gives us the equation of the ellipse in terms of x and y only:
(x/2)^2 + (y/3)^2 = 1.
This is the standard form equation of an ellipse with center at the origin and semi-axes of length 2 and 3 in the x and y directions, respectively.
In general, to eliminate the parameter t for a parametrization of an ellipse, we can use trigonometric identities to express cos(t) and sin(t) in terms of x and y, respectively. Substituting these expressions for cos(t) and sin(t) into the parametric equations and simplifying should give us the equation of the ellipse in terms of x and y only.
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if r is the ring of integers, let u be the ideal consisting of all multiples of 17. prove that if v is an ideal of r and r ⊃ v ⊃ u then either v = r or v = u. generalize!
(a) is a prime ideal of R, and since v is contained in (a), we have either v = (a) or v = R. Therefore, The only ideals of R containing u are u and R itself.
To prove that if v is an ideal of r and r ⊃ v ⊃ u, then either v = r or v = u, we need to use the fact that the only ideals of r are the trivial ones (0 and r) and the maximal ones (prime ideals). Since u is not a prime ideal (since it contains multiples of 17), the only possibilities for v are u and r. To see this, suppose that v is a proper ideal of r containing u. Then there exists some non-zero element a in v that is not in u. Since a is not a multiple of 17, it must have a prime factor p that is not 17 (otherwise, it would be a multiple of 17). But then (a) is a prime ideal of r (since r is a UFD), and since v is contained in (a), we have either v = (a) or v = r. Therefore, we have shown that if v is an ideal of r and r ⊃ v ⊃ u, then either v = r or v = u. We can generalize this result to any ring R and any proper ideal u of R by using the same argument. If v is a proper ideal of R containing u, then there exists some non-zero element a in v that is not in u. But then (a) is a prime ideal of R, and since v is contained in (a), we have either v = (a) or v = R. Therefore, the only ideals of R containing u are u and R itself.
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Which group of voters has the greatest percentage of student voters?
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred twenty and two hundred forty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has one hundred fifty and two hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has two hundred and four hundred fifty.
A table with two columns and one row. The title of the first column is Student Voters. The title of the second column is Total Voters. The row has three hundred fifty and nine hundred.
11 of 20 Questions
thomas believes that a group is cohesive when it is marked by strong positive bonds between members of a group. thomas considers cohesion to be
Thomas considers cohesion to be the presence of strong positive bonds between members of a group. In his perspective, cohesion represents a sense of unity, attachment, and solidarity among individuals within the group.
Cohesion, according to Thomas, goes beyond mere cooperation or coordination of activities. It encompasses the emotional and social aspects of group dynamics, emphasizing the quality and strength of the relationships between members. The existence of strong positive bonds implies that individuals feel connected, trust each other, and have a shared sense of identity and purpose.
Thomas likely believes that cohesive groups are characterized by mutual support, collaboration, and a sense of belonging. Members are more likely to work together effectively, communicate openly, and have a higher level of commitment to group goals. Cohesion may also contribute to increased satisfaction, motivation, and overall well-being within the group.
Thomas's perspective aligns with the socio-emotional aspect of group cohesion, emphasizing the interpersonal connections and social dynamics that contribute to the cohesiveness of a group.
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Find the value of x.
Answer:
x = 46
Step-by-step explanation:
These 2 angles would add up to 180 degrees.
So 41 + (3x+1) = 180
Let's solve for x.
41 + 3x + 1 = 180
Combine like terms.
42 + 3x = 180
subtract 42 from both sides
3x = 180-42
3x = 138
divide both sides by 3
x = 46
Which graph shows the line of best fit for the data ?
Answer:
Bottom left
Step-by-step explanation:
It covers the most points
what is the probability that at least 30 of the women in the sample will not meet the age requirement
To calculate the probability that at least 30 of the women in the sample will not meet the age requirement, we need to use the binomial distribution formula:
P(X >= 30) = 1 - P(X < 30)
where X is the number of women who do not meet the age requirement, and P(X < 30) is the cumulative probability of X being less than 30.
The probability of a woman not meeting the age requirement is given as 0.2, so the probability of a woman meeting the age requirement is 0.8. We are sampling 200 women, so the number of women who do not meet the age requirement follows a binomial distribution with n = 200 and p = 0.2.
Using a binomial calculator or software, we can find that P(X < 30) = 0.1656. Therefore, the probability of at least 30 women not meeting the age requirement is:
P(X >= 30) = 1 - P(X < 30) = 1 - 0.1656 = 0.8344
Therefore, the probability that at least 30 of the women in the sample will not meet the age requirement is 0.8344, or approximately 83.44%.
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the me
appropriat
metric unit of measurement from the word bank below. Write the answer on the
line. Each word will be used only once.
1. The most appropriate metric unit to measure the:
a. distance from Florida to Texas is
b. length of a car is
c. thickness of a cell phone is
d. height of a coffee mug is
e. mass of a cookie is
f. mass of a large watermelon is
g. mass of small feather is
h. capacity of a large bottle of lemonade is
i. capacity of a small food coloring bottle is
j. capacity of a swimming pool is
milliliters
liters
kiloliters
Word Bank
milligrams
grams
kilograms
millimeters
centimeters
meters
The measurement units for each is described below.
The metric system is a measurement system. It is utilized in calculations and research all over the world. Here are some instances of how we use the metric system to measure things:
a. distance from Florida to Texas is: Kilometers (km)
b. length of a car is : Meters (m)
c. thickness of a cell phone is: Millimeters (mm)
d. height of a coffee mug is: Centimeters (cm)
e. mass of a cookie is: Grams (g)
f. mass of a large watermelon is: Kilograms (kg)
g. mass of small feather is: Milligrams (mg)
h. capacity of a large bottle of lemonade is : Liters (L)
i. capacity of a small food coloring bottle is : i. Milliliters (mL)
j. capacity of a swimming pool is: Cubic meters (m³)
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If nominal wages and prices are not flexible which of the following must be true when the economy has a severe recessionary gap? (A The aggregate demand curve is vertical (B The aggregate demand curve is horizontal (CThe short run aggregate supply curve is vertical DThe short run aggregate supply curve is upward sloping (E) The short run aggregate supply curve is hotizontal
If nominal wages and prices are not flexible, then the short-run aggregate supply curve is vertical.
This means that the economy is operating at full employment, and any increase in aggregate demand will not result in an increase in output but rather lead to higher prices.
In other words, the economy is supply-constrained, and there is no excess capacity to produce more output in response to an increase in demand.
In a severe recessionary gap, the economy is operating below its potential output, and there is excess capacity in the economy. However, if nominal wages and prices are not flexible, firms cannot adjust their prices downwards,
and wages cannot be reduced, leading to a situation where the short-run aggregate supply curve is vertical.
This results in a situation where any increase in aggregate demand will not lead to an increase in output, and the economy remains stuck in a recessionary gap with high unemployment and low output.
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(-2 3/4)^2
what does this equal?
Answer:
The answer is 121/16 or 7.5625
Step-by-step explanation:
(-2¾)²
(-11/4)²
=121/16 or 7.5625
find the exact length of the curve. x = 6 6t2, y = 5 4t3, 0 ≤ t ≤ 1
To find the length of the curve given by x=6t^2 and y=5t^3, the exact length of the curve x=6t^2 and y=5t^3 for 0≤t≤1 is approximately 7.697 units long.
To find the length of the curve given by x=6t^2 and y=5t^3, we need to use the arc length formula, which is:
L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 dt
Here, a=0 and b=1 since 0≤t≤1. Also, dx/dt = 12t and dy/dt = 15t^2. Substituting these values in the above formula, we get:
L = ∫[0,1] √(12t)^2 + (15t^2)^2 dt
Simplifying, we get:
L = ∫[0,1] √(144t^2 + 225t^4) dt
Taking out the common factor of t^2 inside the square root, we get:
L = ∫[0,1] t√(144 + 225t^2) dt
To evaluate this integral, we need to make a substitution u = 144 + 225t^2, which gives du/dt = 450t. Substituting these values, we get:
L = (1/450) ∫[144,369] √u du
Now, we can evaluate the integral using the power rule of integration:
L = (1/450) * [(2/3) u^(3/2)]_144^369
Simplifying, we get:
L = (1/450) * [(2/3) * (369^(3/2) - 144^(3/2))]
L = 7.697
Therefore, the exact length of the curve x=6t^2 and y=5t^3 for 0≤t≤1 is approximately 7.697 units long.
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Apples are $1.79 per lb at Food Lion. If I purchase 3.8 lbs, how much sure I expect to pay?
Answer:
$6.80
Step-by-step explanation:
1.79 x 3.8 = 6.802
So $6.80
what is the depth at node 23 and 70 respectively? a. Depth at node 23 is 2. Depth at node 70 is 0. b. Depth at node 23 is 1. Depth at node 70 is 0. c. Depth at node 23 is 2. Depth at node 70 is 2. d. Depth at node 23 is 2. Depth at node 70 is 3.
Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).
Explanation:
To determine the depth at a particular node in a tree, we count the number of edges from the root to that node.
Without more information about the tree, it is impossible to determine the depths of nodes 23 and 70. However, if we assume that the root of the tree is at depth 0, and that the tree is binary (each node has at most two children), then we can make an educated guess.
Based on the given options, we can eliminate choices B and C, as they contradict each other.
Option A suggests that node 23 is two levels below the root, while node 70 is at the root level. This is possible if node 70 is the root of the tree, and node 23 is its child.
Option D suggests that node 23 is two levels below the root, while node 70 is three levels below the root. This is possible if node 70 is a grandchild of node 23.
Therefore, Without more information, it is impossible to determine the depths of nodes 23 and 70. Based on the given options, either node 70 is the root and node 23 is its child (Option A), or node 70 is a grandchild of node 23 (Option D).
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What is the slope from (−7, 5) to (−3, 4)?
Answer:
m = -1/4
Step-by-step explanation:
Slope = rise/run (y2 - y1) / (x2 - x1)
Points (−7, 5) (−3, 4)
We see the y decrease by 1, and the x increase 4, so the slope is
m = -1/4
The formula A=Pe^{rt} can be used to find the dollar value of an investment of $7500 after t years when the interest is compounded continuously at a rate of r percent. Find the value of the investment after 4 years if the interest rate is 6.8%.
The value of the investment after 4 years is equal to $9844.40.
How to determine the value of the investment after 4 years?In Mathematics and Financial accounting, continuous compounding interest can be determined or calculated by using this mathematical equation (formula):
[tex]A(t) = P_{0}e^{rt}[/tex]
Where:
A(t) represents the future value.P₀ represents the principal.r represents the interest rate.t represents the time measured in years.When time, t = 4 years, the future value can be calculated as follows:
[tex]A(t) = 7500e^{0.068 \times 4}\\\\A(t) = 7500e^{0.272}[/tex]
A(t) = 7500(1.31258700131)
A(t) = 9844.4025 ≈ $9844.40.
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Find a Cartesian equation for the curve and identify it.r = 4sin(θ) + 4cos(θ)
To convert the polar equation r = 4sin(θ) + 4cos(θ) into a Cartesian equation, we can use the identities:
x = r cos(θ)
y = r sin(θ)
Substituting r = 4sin(θ) + 4cos(θ) into these identities, we get:
x = (4sin(θ) + 4cos(θ))cos(θ) = 4sin(θ)cos(θ) + 4cos²(θ)
y = (4sin(θ) + 4cos(θ))sin(θ) = 4sin²(θ) + 4sin(θ)cos(θ)
Simplifying these expressions using the trigonometric identity sin²(θ) + cos²(θ) = 1, we obtain:
x = 4cos(θ) + 4cos²(θ)
y = 4sin(θ) + 4sin(θ)cos(θ) = 4sin(θ) + 4cos(θ)sin(θ)
Therefore, the Cartesian equation for the curve is:
(x - 4)² + y² = 16
This equation represents a circle with center (4, 0) and radius 4. The original polar equation r = 4sin(θ) + 4cos(θ) can be interpreted as the distance from the origin to a point on the circle, measured along a line that makes an angle of θ with the positive x-axis.
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for the following factored polynomial, find all of the zeros and their multiplicities. f(x)=(x−5)5(x 1)7
the question is that the zeros of the polynomial f(x)=(x−5)5(x+1)7 are x=5 and x=-1, and their multiplicities are 5 and 7, respectively.
the zeros and their multiplicities is as follows:
To find the zeros of the polynomial, we set each factor equal to zero and solve for x.
For the factor (x−5)5, we get x=5 as the only zero.
For the factor (x+1)7, we get x=-1 as the only zero.
To determine the multiplicities of the zeros, we count the number of times each zero appears as a factor.
Since (x−5)5 is a factor of the polynomial, the zero x=5 has a multiplicity of 5.
Similarly, since (x+1)7 is a factor of the polynomial, the zero x=-1 has a multiplicity of 7.
the zeros of the polynomial f(x)=(x−5)5(x+1)7 are x=5 and x=-1, and their multiplicities are 5 and 7, respectively.
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a camper lights an oil lantern at noon and lets it burn continuously. once the lantern is lit, the lantern burns oil at a constant rate each hour. at p.m., the amount of oil left in the lantern is ounces. at p.m., the amount of oil left in the lantern is ounces. based on the average rate of oil burning per hour, how much oil, in ounces, was in the lantern at noon?
There were 16 ounces of oil in the lantern at noon.
Let's start by defining the variables we know. We'll call the amount of oil in the lantern at noon "x," the rate at which the oil burns "r," and the time elapsed from noon to 2 pm "t." We know that the amount of oil in the lantern at 2 pm is 12 ounces, and at 4 pm, it's 8 ounces.
We can use the rate of oil burning to create an equation relating the amount of oil in the lantern to the time elapsed. The equation is:
x - rt = y
where "y" is the amount of oil in the lantern at any given time after noon. We can solve for "x" by plugging in the values we know at 2 pm:
x - 2r = 12
And at 4 pm:
x - 4r = 8
Now we have two equations with two variables. We can solve for "r" by subtracting the second equation from the first:
2r = 4
r = 2
Now we can plug in "r" to one of the equations to solve for "x." Let's use the first equation:
x - 2(2) = 12
x - 4 = 12
x = 16
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