The length of each bar is given as follows:
3.5 inches.
As a mixed number, the length of each bar is given as follows:
3 and 1/2 inches.
How to obtain the length of each bar?The length of each bar is obtained applying the proportions in the context of this problem.
The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:
7/2 = 3.5 inches.
The fraction equivalent to a decimal of 0.5 is given as follows:
1/2.
(which is used to construct the mixed number).
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the sum of 6 and the square of 12
the quotient of 30 and the sum of 5 and 7
the difference of 4 cubed and 25
5 more than the product of 12 and 8
The solutions are 150, 2.5, 39 and 101. The solutions have been obtained using the arithmetic operations.
What are arithmetic operations?
In all, there are four basic mathematical operations which are applicable for all the real number. The operations are as follows:
1.Addition(‘+’) operation which gives the sum of the numbers.
2.Subtraction(‘-’) operation which gives the difference of the numbers.
3.Multiplication(‘×’) operation which gives the product of the numbers.
4.Division(‘÷’) operation which gives the quotient of the numbers.
1. The sum of 6 and the square of 12
The square of 12 = 12*12 = 144
Sum of 6 and 144 = 6 + 144 = 150
2. The quotient of 30 and the sum of 5 and 7
The sum of 5 and 7 = 5 + 7 = 12
The quotient of 30 and 12 = 30 ÷ 12 = 2.5
3. The difference of 4 cubed and 25
The cube of 4 = 4*4*4 = 64
The difference of 64 and 25 = 64 - 25 = 39
4. 5 more than the product of 12 and 8
The product of 12 and 8 = 12*8 = 96
5 more than 96 = 5 + 96 = 101
Hence, the solutions are 150, 2.5, 39 and 101.
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Rewrite the fractions using the least common denominator (LCD) you found in part C
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
What is the least common denominator about?The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.
When two or more fractions are given, the least common denominator is the smallest number among all the common multiples of the denominators.
The denominators of the given fractions are 6 and 4 and the least common multiple of 6 and 4 = 12
To rewrite 1/6 with denominator 12, we need to multiply 2 to the numerator and the denominator, we get:
1/6 =(1 × 2)/(2 × 6)
= 2/12
Also 1/4 = 3/12
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Complete question
Describe how you would rewrite the fractions 1/6 and 1/4 with their least common denominator
Answer:
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
Step-by-step explanation:
Suppose a college bookstore buys a textbook from a publishing company and then marks up the price they paid for the book 30% and sells it to a student at the marked-up price. If the student pays $145 for the textbook, what did the bookstore pay for it? Round your answer to the nearest cent.
The amount paid by the store is given as follows:
$111.54.
How to obtain the amount paid by the store?The amount paid by the store is obtained applying the proportions in the context of the problem.
The original price is symbolized as follows:
x.
The markup price was of 30%, hence the decimal multiplier is given as follows:
130% = 1.3.
The selling price is of $145, hence the original price is obtained as follows:
1.3x = 145
x = 145/1.3
x = $111.54.
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Determine the number of classes in the frequency table below.
Class | Frequency
23-24 , 7
25-26 , 2
27-28 , 6
29-30 , 4
31-32 , 1
The number of classes in the frequency table given below is; 5 classes
How to Interpret a Frequency Table?We are given the classes of the frequency table as;
23 - 24
25 - 26
27 - 28
29 - 30
31 - 32
Now, we see from the class intervals that there are a total of five classes because each class interval has a frequency of occurrence as seen in the given frequency table.
The frequencies for each class interval is as follows;
7, 2, 6, 4, 1
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find the inverse of 8x^5+7
The inverse of a function is another function that "undoes" the original function. In other words, the composition of a function and its inverse results in the identity function.
To find the inverse of a function, you can follow these steps:
Replace the function with "y"
Switch the x and y variables
Solve for y (or in this case x)
So in this case, we can find the inverse of 8x^5+7 by replacing y with 8x^5+7, switching the x and y variables, and solving for x:
y = 8x^5+7
x = 8y^5+7
This is not an invertible function because it's not a one-to-one function, it's not a function of x.
Answer:
Hey there! The inverse of 8x^5+7 doesn't exist because it's not a function. Think about it like this, a function is like a machine that takes an input and gives you a unique output. But in this case, the machine isn't working correctly and it doesn't give you a unique output for a given input. So, in simple terms, it doesn't have an inverse.
________________________________________________________
How do you determine if an equation has an inverse?To determine if an equation has an inverse, we need to check if it is a one-to-one function. A one-to-one function is a function in which every unique input corresponds to a unique output. If an equation is one-to-one function, then it has an inverse. If it's not one-to-one function, then it doesn't have an inverse.
How do you find the inverse of a linear equation?To find the inverse of a linear equation, we can follow these steps:
1. Switch the x and y variables
2. Solve for y (or x)
3. Replace y (or x) with f^-1 (x) (or f^-1 (y))
For example, if we have the equation y = 2x+1, we can follow these steps:
1. x = 2y+1
2. x-1 = 2y
3. f^-1(x) = (x-1)/2
So, the inverse of the equation y = 2x+1 is f^-1(x) = (x-1)/2
What is the Product?
The product meaning in maths is a number that we get to by multiplying two or more other numbers together.
What is Product?
In mathematics, a product is the outcome of multiplying two or more numbers together.
Let us consider the scenario. A person had to buy 4 cupcakes. Each cupcake costs $5.
To calculate the total amount he needs to pay at the checkout counter, add the cost of each cupcake 4 times (as he needs to buy 4 cupcakes).
So, the answer will be -
5 + 5 + 5 + 5 = 20
If he needed 10 cupcakes, he would have to add the cost 10 times.
This is where the concept of multiplication and product can help him.
He can find the cost as -
4 times 5 or 4 × 5,
He can skip count by 5, four times and get the answer as 20.
Therefore, product is repetition for the sum of numbers.
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How many solutions can be found for the system of linear equations represented on the graph?
A infinitely many solutions
B no solution
C two solutions
D one solution
8, find two additional roots of a polynomial function pp(xx) with rational coefficients given below where pp(xx)
The two additional roots of a polynomial function P(x) = 0 with rational coefficients are -i and 7-8i.
We have to find the determine the two additional roots of a polynomial function P(x) = 0.
The answers to any given polynomial for which we must ascertain the value of the unknowable variable are known as the roots of polynomials. We can evaluate a polynomial's value to zero if we know its roots.
The given roots of P(x) = 0 is i and 7+8i.
So there conjugate are also the roots of P(x).
So the two additional roots of P(x) = 0 should be -i and 7-8i.
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The complete question is:
Find two additional roots of a polynomial function P(x) = 0 with rational coefficients given below where additional roots of P(x) = 0, i and 7+8i.
I need help with this equation nowww
The new coordinate of Q after a rotation of 90° is (10, -5)
How to determine the new coordinate of Q after a rotation of 90°?Rotation simply means turning
In order to answer this question, you need to know the rotation rule for 90° about the origin.
If a point P, whose position vector is (x,y), is rotated 90° counterclockwise rotation about the origin, the position of the image P' is (-y, x).
From the graph, the initial coordinate of Q is (-5, -10).
Thus, the new coordinate of Q will be (10, -5)
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What is the percent change from 36 to 99?
Answer:
To calculate the percent change from 36 to 99, you can use the formula:
((New Value - Original Value) / Original Value) x 100
((99 - 36) / 36) x 100 = 175%
So the percent change from 36 to 99 is 175%.
The percentage change from 36 to 99 will be 175% .
Given,
Number changes from 36 to 99 .
Here,
To calculate the percent change from 36 to 99, you can use the formula:
=((New Value - Original Value) / Original Value) x 100
=((99 - 36) / 36) x 100
= 175%
So the percent change from 36 to 99 is 175%.
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whats the standard deviation for the following set of data 6, 2, 3 ,5 .9, 12, 15
Answer: √29.5= 5.43139
In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. He uses four times as much solution a solution as solution b. Solution A is 18% alcohol and solution b is 50% alcohol. How many milliliters of solution b does he use, if the resulting mixture has 261 mL of pure alcohol?
If In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. The many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
How to find the milliliters of solution b?Let x be the amount of solution B he used in milliliters.
We know that the amount of solution A used = 4× x, and that the resulting mixture has 261 mL of pure alcohol.
Percentage of alcohol in solution A is 18% and in solution B is 50%.
Set up the proportion:
(0.18 × 4x + 0.50x) = 261
Simplifying,
0.72x + 0.50x = 261
1.22x = 261
x = 261 / 1.22
x = 213.93 mL (Solution b)
Trey used 213.93 mL of solution B and 3( 213.93mL) = 855.72 mL of Solution A.
Therefore the many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
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A study showed that vitamin A oil reduces pain levels in patients with Lyme disease. During each session, the oil was injected into the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether vitamin A oil also reduces pain in patients suffering from pinched nerves in the cervical region of the back. Two hundred patients aged 20–40 years are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (5 points)
Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, would you change the study design? If so, how would you modify your design? If not, why not? (5 points)
Part C: Suppose the data in the following table was collected at the end of the study you described in part A.
Vitamin A Oil Placebo
Reported Pain Reduction 37 21
Total Treated 100 100
Construct 90% confidence intervals for the proportion of pain reduction for each treatment group. Show all work. (5 points)
Part D: What can you conclude about the use of vitamin A oil for patients with pinched nerves in the cervical region of the back? (5 points)
The appropriate design for the study includes; Treatment used; Chamomile oil treatment
How to find the appropriate design for the new study?Appropriate Design!” asks about the identity of design.
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the Appropriate Design!” asks about the identity of design can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
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What is the percent of decrease from 100 to 60?
Answer:
40% decrease
Step-by-step explanation:
since it is 100 it is easy to convert to a percentage. 100-60=40 so you have a 40% decrease
How do I do this problem I do not get it do I add when I found the volume of both
Answer: 149 cm^3
To find the volume for a cube, the formula is V = a^3, where a = length of one side.
Smaller cube:
a = 3
(3)^3, or 3 x 3 x 3
= 27 cm^3
Larger cube:
a = 5
(5)^3, or 5 x 5 x 5
= 125 cm^3
To find the volume of the entire sculpture, add the volumes of each of the cubes.
27 + 125
= 149 cm^3
Which of the following is most likely the next step in the series?
Answer:
Choice C. is the answer
Step-by-step explanation:
greetings !!
just following the series the
First starts with simple square which have four sides.The second have five sides which is a Pentagon.The third one will have a hexagon or six side shape.Then, finally it will be preceded by a heptagon which is a seven sided have in regard to the series.If any questions and unclear ideas tag on comment box.
Hope it helps!!!
Anything would be awesome!
The composition with rotation to map ΔABC to ΔA'B'C' is;
Reflection across the y-axis and 270 degrees counterclockise rotation about the origin
How to interpret Rotation transformation?
A rotation is defined as a type of transformation that takes each point in a figure and rotates it to a specific number of degrees around a given point.
Now, the coordinates of triangle ABC from the graph are;
A(-8, -2)
B(-6, 3)
C(-5, -1)
The coordinates of triangle A'B'C' from the graph are;
A(-2, -8)
B(3, -6)
C(-1, -5)
Now, the transformation rule for reflection across the y -axis is (x, y) → (-x, y) .
Finally rotation 270 degrees counterclockwise will produce;
(-x, y) → (y, x)
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sum is not divisible by 2 and not divisible by 5.
Round your answers to two decimal places.
(a) P(A) = 11.1
(b) P (B) =
The probability of each of the following events are given below:
What is Probability?
Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 representing no chance of the event occurring, and 1 representing a certainty that the event will occur. Probability is widely used in mathematics, statistics, and science to calculate the probability of a given event occurring. It is also used to assess risk and uncertainty in decision-making.
Event A: 0.306 or 30.6%
Event B: 0.44 or 44%.
Event A: The sum is greater than 9.
We have already computed this, the probability of getting a sum greater than 9 is 11/36, which can be simplified as 0.306 or 30.6%
Event B: The sum is not divisible by 2 and not divisible by 5.
To find the probability of this event, we need to find the number of outcomes that have a sum that is not divisible by 2 or 5.
We can calculate this by listing out all the possible outcomes and counting the number that have a sum that is not divisible by 2 or 5: (1,3), (1,4), (1,6), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (6,1), (6,3), (6,4) and (6,6)
There are 16 outcomes that have a sum that is not divisible by 2 or 5, so the probability of getting a sum that is not divisible by 2 or 5 is 16/36, which can be simplified as 0.44 or 44%.
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MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 pounds of soil
and a box with 13 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
What is mixed fraction?To create a mixed fraction, a suitable fraction and a whole number must be combined. Usually, it denotes a value between 0 and 1. A mixed fraction is one that contains both a whole number and a fraction. One example of a mixed fraction is 1(1/3), where 1 is a whole number and 1/3 is a fraction.
Denise need 4 pounds of soil
By adding the mixed fraction we will know if its enough or not
[tex]$=1\frac{3}{4} + 2 \frac{1}{8}[/tex]
[tex]$=\frac{7}{4} + \frac{17}{8}[/tex]
[tex]$=\frac{14}{8} + \frac{17}{8}[/tex]
[tex]$=\frac{14+17}{8}[/tex]
[tex]= \dfrac{31}{8}[/tex]
[tex]=3 \dfrac{7}{8}[/tex]
Thus, As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
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Principal 1,565.89 1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
The annual percentage rate for this credit card account is 15.75%.
How is the annual percentage rate determined?The annual percentage rate (APR) is the actual annual cost of borrowing money.
Before applying the APR on the account balance, we determine the monthly percentage rate (MPR) by dividing the APR by 12.
Given the interest in dollars and the principal or account balance, the APR can be computed by dividing the interest by the account balance and multiplying it by 12.
Principal $1,565.89 $1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
Interest rate (MPR) = 1.31235% ($20.55/$1,565.89 x 100)
Annual percentage rate = 15.75% (1.31235% x 12)
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Question Completion:What is the annual percentage rate?
Three partners share a business. Max owns 3 8 , Sherry owns 2 5 , and Duane owns the rest. If the profits this year are $350,000, how much does each partner receive (in $)?
answer:
Max =$131,250
Sherry=$140,000
Duane=$78,750
Step-by-step explanation:
Max will receive 3/8 ×$350,000=$131,250
Sherry will receive 2/5 × $350,000=$140,000
Duane will receive $350,000-$(131,250+140,000)
$350,000-$271,250=$78,750.
the factored form of n^3+27/125
Answer:(n+3)(n^2-3n+9)/125
Step-by-step explanation:
Answer:
(n+3)(n^2-3n+9)/125
Step-by-step explanation:
We can figure out the factored form of n^3+27/125 by adding all the brackets in the correct places. (I forgot what my math teacher called this process ;-;)
After adding the brackets it becomes:
(n + 3) (n² - 3n + 9) ÷ 125
(Our answer would be 125)
Use properties to find a product of 4×9×25
Answer:900
Step-by-step explanation:
A restaurant server believes the distribution of their tips has a model that is slightly skewed to the left, with a mean of $10.70 and a standard deviation of $6.70. They
usually wait on about 60 parties over a weekend of work.
a) Estimate the probability that they will earn at least $800 in tips.
b) How much do they earn on the best 10% of such weekends?
Answer:
a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))
We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.
P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)
b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)
We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.
Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)
Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.
You are standing 143 feet away from the base of a building and your clinometer measures 17° when it’s looking at the top of the building. (This angle is the one between the ground and the top of the building). Please calculate the height of the building.
Answer:
43.7 ft
Step-by-step explanation:
h= height of the building
tan(17) = h/143
h = tan(17) x 143 = 43.7 ft
What number after being increased by 22% results in a value of 305 round your answer to the nearest hundredth if necessary
According to the given information in the question answer is 250.
What does "rounding to the nearest hundredth" actually mean?Any decimal number is rounded down to the closest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, increasing 2.167 to the closest tenth yields 2.17.
To the closest hundredth, what is 10.2719?In this exercise, we must round the supplied number up to the nearest hundred, making it 10.2719. We must add two more decimal places to this number in order to round it to the nearest hundreds. Additionally, we saw that all of the numbers following the second decimal place are fewer than five, therefore they can be ignored and the result is 10.27.
Using the following formula, you can determine this:
x = (100 * 305) / 122
Where x is the original number and 122 is 100 + 22 (the 100 representing the original value and 22 representing the increase of 22%).
x = (100 * 305) / 122 = 250
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On the curve y=x/3 , point P has coordinates (2, 0.667). What is the slope of the curve at point P?
A. 0.033
B. 0.067
C. 0.333
D. 0.667
The correct option regarding the slope of the linear function at point P is given as follows:
C. 0.333.
How to obtain the slope of the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the value of y when x = 0.The line in this problem is defined as follows:
y = x/3.
Meaning that:
The slope is of 1/3.The intercept is of 0.The slope is the same for each point on the curve, hence the correct option is given by option C.
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the distance around a standard tennis court is 228 feet. if the length of the court is 30 feet more than twice the width, find the dimensions of the tennis court
The dimensions of the tennis court are 42 feet by 114 feet.
Let the width of the tennis court be x feet.
We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.
2(2x + 30) + 2x = 228
4x + 60 = 228
4x = 168
x = 42
The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.
The dimensions of the tennis court are 42 feet by 114 feet.
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The picture shows six equal squares. The total is 54ft2. What is the perimeter?
Answer:
72ft
Step-by-step explanation:
Area of one square = 54ft^2/6 = 9ft^2
The side of the square is the square root of the area, so the side length of one square is
√9ft^2 = 3ft.
each square has a perimeter of
4*3ft = 12ft.
So the perimeter of all six squares is
12ft * 6 = 72ft
Oil is leaking from an oil tanker at the rate of 3000 liters per hour. 8 liters of oil spread out over 10 square meters of ocean surface.
a) The radius of the area of the oil leakage is described by R = √(112.345 · t).
b) The time related to a radius 1 kilometers is approximately 8901.153 hours.
How to analyze an oil leakage from oil tanker
In this problem an oil tanker has a leakage on ocean surface, the consequence of such event is a contaminated area of circular form, whose formula is described below:
A = π · R²
Where:
A - Area, in square meters. R - Radius, in meters.And the area density (σ), in liters per square meter, is defined by following formula:
V = σ · A
Where V is the volume leaked, in liters, whose formula is described:
V = V' · t
Where:
V' - Leaking rate, in liters per hour.t - Time, in hour.Part A - The resulting expression in terms of time is shown below:
V = σ · A
V' · t = σ · π · R²
R = √[(V' · t) / (σ · π)]
(V' = 3000 L / h, σ = 4 / 5 L / m²)
R = √[(3000 · t) / (8.5π)]
R = √(112.345 · t)
Part B - If we know that R = 1000 m, then the time needed is:
1000 = √(112.345 · t)
t = 8901.153 h
Remark
Statement is incomplete. Complete form is shown below:
Oil is leaking from an oil tanker at the tanker of 3000 liters per hour. 8 liters of oil spread out over 10 square meter of ocean surface. A circular oil slick forms.
a) Express the radius R of the oil slick as a function of the time t (in hours) the tank has been leaking.
b) After how many hours will the oil slick have radius 1 kilometer?
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