The diagram shows a rectangle.
The area of the rectangle is 12b²-30b
Write an expression for
a
b
the length of the rectangle
the perimeter of the rectangle.
6b
A
length
N
Answers
Answer: The diagram shows a rectangle.
The area of the rectangle is 12b²-30b long a+b+a your answer is aStep-by-step explanation:
A rectangle Expression for "a": a = 12b - 30,Expression for "b": b = (12b² - 30b) / (12b - 30),Length of the rectangle: Length = a = 12b - 30,Perimeter of the rectangle: Perimeter = 2 × (13b - 30)
Let's break down the given information step by step:
The area of the rectangle is given as 12b² - 30b.
The expression for "a":
The area of a rectangle is equal to its length (a) multiplied by its width (b). So, set up the following equation:
Area = Length ×Width
12b² - 30b = a × b
To find the expression for "a," divide both sides of the equation by "b":
a = (12b² - 30b) / b
Simplify the expression for "a":
a = 12b - 30
The expression for "b":
From the same equation as above, that:
Area = Length × Width
12b² - 30b = a × b
To find the expression for "b," divide both sides of the equation by "a":
b = (12b² - 30b) / a
Substitute the value of "a" from the previous expression:
b = (12b² - 30b) / (12b - 30)
The length of the rectangle:
The length of the rectangle is represented by "a," so the expression for the length is: a = 12b - 30
The perimeter of the rectangle:
The perimeter of a rectangle is given by the formula: Perimeter = 2 ×(Length + Width)
Since the rectangle has two pairs of equal sides (opposite sides are equal in a rectangle), the expression for the perimeter will be:
Perimeter = 2 × (a + b)
Substitute the value of "a" from the expression we found earlier:
Perimeter = 2 × ((12b - 30) + b)
Simplify the expression for the perimeter:
Perimeter = 2 ×(13b - 30)
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Related Questions
As you increase n (assuming everything else remains the same), the width of the confidence interval increases.
True or False?
Answers
False. As you increase the sample size (n), assuming everything else remains the same, the width of the confidence interval decreases, not increases.
The width of a confidence interval is determined by several factors, including the sample size (n), the variability of the data, and the desired level of confidence. When all other factors remain constant, increasing the sample size (n) leads to a narrower confidence interval.
A larger sample size provides more information and reduces the uncertainty associated with estimating population parameters. This decrease in uncertainty leads to a smaller margin of error, resulting in a narrower confidence interval.
The relationship between the sample size and the width of the confidence interval can be understood by the formula for the margin of error. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the square root of n increases at a slower rate, resulting in a smaller margin of error and narrower confidence interval.
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A pillow that usually costs $18 is marked down 25%. Which expressions can be used to find the new price of the pillow? Check all that apply. 18 – 0.25(18) 18 – 0.75(18) 0.25(18) 0.75(18) 18(0.25) + 18
Answers
Answer:
0.75($18) or $18 – 0.25($18)
Step-by-step explanation:
"A markdown of 25%" can be obtained by multiplying the normal retail price by (1.00 - 0.25), or (0.75). Then the "new price" of the pillow is
0.75($18) or $18 – 0.25($18)
Answer:
0.75($18) and $18 – 0.25($18)
they were both right
hoped this helped (???)
the median of a data set with 179 values would be the average of the 89th and the 90th values when the data values are arranged in ascending order.T/F
Answers
Answer:
False------------------
The median is the middle value of the data set.
If the data set has odd number of values (2n + 1) then the median is the value of the term with the number:
[(2n + 1) - 1]/2 = 2n/2 = nIn our case n would be:
(179 + 1)/2 = 180/2 = 90Hence the given statement is False.
Please help me, I need an explanation as well please, not just the answer
Answers
HELP I need to get my Alex done before 11:59 tonight!!!!!
Answers
Answer:
y>63
Step-by-step explanation:
the answer for y is 63
Answer:
y>63
-
Step-by-step explanation:
When we are computing a simple linear regression line, there are certain conditions that must be met for this model to be valid. One of these conditions is the equal spread condition. Which of these answers best explains how we check to make sure that this condition is met? a. Make sure there is similar spread around the sample mean of x. b. Make sure there is similar spread around the line at each value of x.
c. Make sure that there is similar spread around the sample mean of y. d. Make sure all outliers are only below the line.
Answers
The answers that best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.
How we check to make sure that this condition is met?The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.
To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.
Therefore the correct option is C.
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The slope of a line that passes through (-2, 5) and (1, -7) in simplest form is
Answers
hope this helps :)
the mean monthly electric bill for 71 residents of the local apartment complex is $62. what is the best point estimate for the mean monthly electric bill for all residents of the local apartment complex?
Answers
If the mean monthly electric bill for 71 residents of the local apartment is $62 , then the best point estimate is $62 .
In the question ,
it is given that ,
the number of residents in the local apartment complex is = 71
the mean electric bill for the 71 residents = $62 ;
we know that the sample mean is itself called as the best point estimate ;
So , best point estimate for mean monthly electric bill for all residents of local apartment complex will be = mean monthly bill for 71 residents of local apartment complex which is given as $62 .
Therefore , the best point estimate is $62 .
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Consider the problem of finding a plane αTx=β (i.e. α1x1+α2x2+α3x3+α4x4=β with α=(0,0,0,0)) that separates the following two sets S1 and S2 of points (some points from S1 and S2 might lie on the plane αTx=β) : S1={(1,2,1,−1),(3,1,−3,0),(2,−1,−2,1),(7,−2,−2,−2)}, S2={(1,−2,3,2),(−2,π,2,0),(4,1,2,−π),(1,1,1,1)}. 1.1 Formulate the problem as a linear optimization problem (LO). 3p 1.2 Find a feasible solution (α,β) for (LO) if it exists, or show that no feasible solution exists. 2p
Answers
All the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.
To formulate the problem as a linear optimization problem (LO), we can introduce slack variables to represent the signed distances of the points from the plane αTx = β. Let's denote the slack variables as y_i for points in S1 and z_i for points in S2.
1.1 Formulation:
The problem can be formulated as follows:
Minimize: 0 (since it is a feasibility problem)
Subject to:
α1x1 + α2x2 + α3x3 + α4x4 - β ≥ 1 for (x1, x2, x3, x4) in S1
α1x1 + α2x2 + α3x3 + α4x4 - β ≤ -1 for (x1, x2, x3, x4) in S2
α1, α2, α3, α4 are unrestricted
β is unrestricted
y_i ≥ 0 for all points in S1
z_i ≥ 0 for all points in S2
The objective function is set to 0 because we are only interested in finding a feasible solution, not optimizing any objective.
1.2 Finding a feasible solution:
To find a feasible solution for this linear optimization problem, we need to check if there exists a plane αTx = β that separates the given sets of points S1 and S2.
Let's set α = (1, 0, 0, 0) and β = 0. We choose α to have a non-zero value for the first component to satisfy α ≠ (0, 0, 0, 0) as required.
For S1:
(1, 2, 1, -1) - 0 = 3 ≥ 1, feasible
(3, 1, -3, 0) - 0 = 4 ≥ 1, feasible
(2, -1, -2, 1) - 0 = 0 ≥ 1, not feasible
(7, -2, -2, -2) - 0 = 3 ≥ 1, feasible
For S2:
(1, -2, 3, 2) - 0 = 4 ≥ 1, feasible
(-2, π, 2, 0) - 0 = -2 ≤ -1, feasible
(4, 1, 2, -π) - 0 = 5 ≥ 1, feasible
(1, 1, 1, 1) - 0 = 4 ≥ 1, feasible
Since all the points in both sets satisfy the constraints, the feasible solution is α = (1, 0, 0, 0) and β = 0. This plane separates the sets S1 and S2.
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A square has a diagonal length of 10 meters. How long is the side of the square?
Answers
Answer:
50
Step-by-step explanation:
I did the work on a time for learning
A square has a diagonal length of 10 meters. Then the side of the square will be √50 meters.
What is a Pythagoras theorem?The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
A square has a diagonal length of 10 meters. Then the length of the side of the square will be given as,
(10)² = a² + a²
100 = 2a²
a² = 50
a = √50 meters
Thus, the side of the square will be √50 meters.
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In one afternoon's shopping Seedevi spent half as much money as Georgia, but $6 more than Amy. If the three of them spent a total of $258, how much did Seedevi spend?
Answers
The amount spent by Seedevi is $66
How to determine the amount spent by Seedevi?From the question, the given parameters are:
Seedevi = half as much money as Georgia,
Seedevi = $6 more than Amy
The three of them = $258
To solve this question, we use the following representations
x = Seedevi
y = Georgia
z = Amy
So, we have the following equations
x = 0.5y
x = 6 + z
x + y + z = 258
Make y and z the subjects
y = 2x
z = x - 6
Substitute y = 2x and z = x - 6 in x + y + z = 258
x + 2x + x - 6 = 258
Evaluate the like terms
4x = 264
Divide by 4
x = 66
Hence, the amount spent by Seedevi is $66
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two dice are rolled at the same time and the numbers on the face up are read what is the probability of the numbers facing up and add up to 8
Answers
The probability of rolling two dice and getting a sum of 8 is 5/36.
There are a total of 36 possible outcomes when two dice are rolled at the same time. Each die has 6 possible outcomes (1, 2, 3, 4, 5, or 6). To calculate the probability of getting a sum of 8, we need to count the number of ways that the dice can add up to 8.
There are five possible combinations that add up to 8: (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2). Each of these combinations has a probability of 1/36 (since there is only one way to roll each of these combinations).
Therefore, the probability of rolling two dice and getting a sum of 8 is the sum of the probabilities of each of these five outcomes, which is:
1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 5/36
So the probability of the numbers facing up and adding up to 8 is 5/36.
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Estimate this by rounding each number to 1 significant figure
a. 326 X 4.89
Answers
Step 2: 1594.1400
Step 3: 2000
Answer: 2000
10. The distance of the point (a, b) from the origin is twice its
distance from the point (-1, -2). Find the relation between a
and b.
Answers
Answer:
b = 2a
Step-by-step explanation:
in a certain amount of time, a plane traveling at a constant $250$ miles per hour traveled $20,\!000$ feet. in this same amount of time, how many feet would a plane traveling at a constant $400$ miles per hour travel?
Answers
At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.
The speed of an object is the ratio of distance and time it takes for the object to travel that distance.
Mathematically,
S = D/T
where
S is velocity
D is the distance traveled or distance traveled
T is the time it takes to travel that distance
Velocity is considered a scalar quantity. A scalar size only has a size. It does not provide information about the direction of object movement.
If an object moves at a constant speed, it means that the object moves the same distance in the same time interval.
Acceleration of an object is the ratio of velocity and time. vector size. Vector quantities have both magnitude and direction.
Mathematics,
a = v/t
When an object is in motion, its acceleration is never zero.
When an object moves, it moves a constant distance over time. Therefore, body positions cannot be the same from the same coordinate system.
Given in the question:
First the plane was travelling at a constant rate of 250 miles per hour.
Initial height was 20000 feet
Now,
As the speed increases and travels at a constant rate of 400 miles per hour.
Now,
(400 /250 ) × 20000
= 1.6 × 20000
= 32000 feet
Thus, At a constant rate of 400 miles per hour travel, the plane would be travelling from 32000 feet above the land.
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Use the binomial series to find a Taylor polynomial of degree 3 for 1 1+ 2.5x T3() = X + 22+ 23
Answers
To find the Taylor polynomial of degree 3 for the function f(x) = 1/(1+2.5x), we can use the binomial series expansion.
The binomial series expansion for (1+x)^n, where n is a positive integer, is given by:
\((1+x)^n = 1 + nx + (n(n-1)/2!)x^2 + (n(n-1)(n-2)/3!)x^3 + ...\)
In this case, we have f(x) = 1/(1+2.5x), which can be written as f(x) = (1+2.5x)^(-1).
Using the binomial series expansion, we can express f(x) as:
\(f(x) = 1/(1+2.5x) = 1 - (2.5x) + (2.5x)^2 - (2.5x)^3 + ...\)
Now, let's find the Taylor polynomial of degree 3 for f(x) by keeping terms up to x^3:
\(T3(x) = 1 - (2.5x) + (2.5x)^2 - (2.5x)^3\)
Simplifying:
\(T3(x) = 1 - 2.5x + 6.25x^2 - 15.625x^3\)
Therefore, the Taylor polynomial of degree 3 for the function f(x) =
\(1/(1+2.5x) is T3(x) = 1 - 2.5x + 6.25x^2 - 15.625x^3.\)
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Write an equation for the line, in point-slope form, that passes through
the following point and has the following slope:
Slope: 3
Point: (-7, -6)
Answers
Answer:
The answer is \(y + 6 = 3(x + 7)\)
-
Step-by-step explanation:
☆The point-slope form looks like:
\(y - y_1 = m(x - x_1)\)
☆All you simply need to do is plug in according to the formula!
☆\(y + 6 = 3(x + 7)\)
Please help 25p- it’s urgent
Answers
Answer:
p = 20, q = 20, r = 30
Step-by-step explanation:
The triangle to the left of OA is isosceles ( 2 equal radii ), then the base angles are congruent, so
p = 20
The 3 angles in this triangle sum to 180°, then the angle at O is
180 - (20 + 20) = 180 - 40 = 140°
AB is a straight line so angle in triangle containing q is 180 - 140 = 40
The triangle containing q is also isosceles ( 2 equal radii ) then base angles are congruent, then
q = \(\frac{180-140}{2}\) = \(\frac{40}{2}\) = 20
The triangle to the right of OA is also isosceles ( 2 equal radii ) then the base angles are congruent, so
r = 30
Then p = 20, q = 20, r = 30
HELP QUICK PLEASE
What is the slope of the line that passes through the points (-10, 9)(−10,9) and (-12, 7) ?(−12,7)?
Write your answer in simplest form.
Answers
Answer:
1
Step-by-step explanation:
(7-9)/(12-10)= 1
The sum of three numbers is 107. The second number is 7 less than the first. The third number is 3 times the second. What are the numbers?
Answers
Answer:
27, 20, 60
Step-by-step explanation:
We use the equation
(x) + (x - 7) + (3 * (x - 7)) = 107
= x + x - 7 + 3 * (x - 7) = 107
= 2x - 7 + 3(x - 7) = 107
Add 7 on both sides
= 2x + 3(x - 7) = 114
Expand the 3
= 2x + 3x - 21 = 114
= 5x - 21 = 114
Add 21 on both sides
= 5x = 135
Divide 5 on both sides
= 5x/5 = 135/5
= x = 27
Plug the functions in
(27) + (27 - 7) + (3 * (27-7)) = 107
You would get
27 + 20 + 60 = 107, therefore the numbers are 27, 20, 60
Please solve this for me and show me the steps. I will give the Brainliest.
Answers
area = 1/2 * diagonal 1 * diagonal 2
but since we are given the base
area = base * height
= 12 * 8
=96units2
Answer:
Am I finding perimeter or area
Step-by-step explanation:
The negation of the product of five times a number divided by two is ten?
Answers
The algebraic expression that can be represented by the statement is -5x/2 = 10
How to make a algebraic expression that can be represented by the statement?From the question, we have the following statement that can be used in our computation:
The negation of the product of five times a number divided by two is ten
Represent the variable with y
So, we have the following representation
The negation of the product of five times x divided by two is ten
Express the product as an actual product
So, we have the following representation
The negation of 5x divided by two is ten
Express the quotient as an actual quotient
So, we have the following representation
The negation of the 5x/2 is ten
Lastly, we have
-5x/2 = 10
Hence, the expression is -5x/2 = 10
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Evaluate the following expressions: plz help me
0.65 x 10^2
1.1 X 10^3
0.56 x 10^3
Answers
Answer:
first answer is 65
second answer is 1,100
third answer is 560
Step-by-step explanation:
hope this helps!!!
Andrea attends the county fair the fair charges for admission and for each ride
A. Use the pattern in the table to find the cost for Andrea to ride 5 rides or 8 rides. Then write an equation for the pattern
Answers
The cost of admission to the fair (A) $18 (B) 2.50x +18 (C) Coefficient of x-term represents the cost for each ride ticket and constant term represents the cost of admission to the fair.
How to find the cost of admission?Note that the county fair charges $2.50 per ticket for the rides and Henry bought 15 tickets for the rides.
So, the total cost of the 15 tickets will be: (2.5* 15)r = $37.50
He spent total $55.50 on ride tickets and fair admission.
So, the cost of admission to the fair will be:
(B) If x represents the number of ride tickets and represents the total cost, then the cost for number of ride tickets is 2.50x +18
So, the linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission will be:
(C) In the above linear equation, coefficient of x-term is 2.50, which represents the cost for each ride ticket.
And the constant term is 18, which represents the cost of admission to the fair.
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complete question
The county fair charges $2.50 per ticket for the rides. Henry bought 15 tickets for the rides and spent a total of $55.50 at the fair. Henry spent his money only on ride tickets and far admission. The price of the fair admission is the same for everyone. Use x to represent the number of tide tickets and y to represent the total cost.
(A) Find the cost of admission to the fair. Explain how you found the cost of admission.
(B) Write a linear equation that can be used to determine the cost for anyone who pays for ride tickets and fair admission.
(C) Explain what the coefficient on x and the constant of your linear equation represent.
a circular cake is split into four quarters. if the diameter of the cake is 25 cm, how long is the perimeter of each piece?
Answers
Answer:
(6.25\(\pi\) + 25)cm is the exact answer
44.625 cm is an approximation
Step-by-step explanation:
c = circumference (perimeter)
d = diameter
C = \(\frac{\pi d}{4}\)
C = \(\frac{25\pi }{4}\) = 6.25\(\pi\) This is the exact answer
That would be the curved part of the pi. Then we need to add the 2 sides which would be \(\frac{25}{2}\) + \(\frac{25}{2}\) = \(\frac{50}{2}\) = 25 The sides are the length of the radius which is half of the diameter.
(6.25\(\pi\) + 25)cm is the exact answer
If we use 3.14 for \(\pi\) The approximate answer would be:
6.25(3.14) + 25
19.625 + 25
44.625 cm is an approximation
What is the slope of the line?
Answers
Answer:
3
Step-by-step explanation:
slope is 3/1 which is just 3
I have a late assignment Please help!!
Answers
The interquartile range for the data set are
Andre
Interquartile Range: = 2
For Lin
Interquartile Range = 8
For Noah
Interquartile Range = 8
How to fill the tableFor Andre
Min: 25 the minimum number
Q1: 27 (the third position)
Median: 28 (the sixth position)
Q3: 29 (the 9th position)
Max: 30 (the maximum number)
Interquartile Range: Q3 - Q1 = 29 - 27 = 2
For Lin
Min: 20 the minimum number
Q1: 21 (the third position)
Median: 28 (the sixth position)
Q3: 29 (the 9th position)
Max: 32 (the maximum number)
Interquartile Range: Q3 - Q1 = 29 - 21 = 8
For Noah
Min: 13 the minimum number
Q1: 15 (the third position)
Median: 20 (the sixth position)
Q3: 23 (the 9th position)
Max: 25 (the maximum number)
Interquartile Range: Q3 - Q1 = 23 - 15 = 8
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Homework: Lab 3 (Chapter 5) HW Score: 74.83%, 34.33 of 48 Question 14, 5.3 Study Exercise 14 (Algo) Part 4 of points Points: 0.44 of 4 Save Consider the market for milk in Saskatchewan. If p is the price of milk (cents per le) and is the quantity of milk (milions of the per month suppose that demand and supply curves for milk are given by the following Demand Supply p=220-200 p* 10+300 a Assuming there is no government intervention in this market, what is the equilibrium price and quantity? eText The equilibrium quantity is 42 millions of litres. (Round your response to one decimal place) The price is 136 cents per tre (Round your response to the nearest cent. The monthly revenue for milk producers without government intervention is $5.7 million(s) of dollars. (Round your response to one decimal place) Resources b. Now suppose the government guarantees milk producers a price of $2.06 per litre (that is, 206 conts per litre) and promises to buy any amount of milk that the producers cannot sell. What is the quantity demanded and the quantity supplied at this guaranteed price? The quantity demanded at the guaranteed price is mition(s) of Itres (Round your response to one decimal place) Check anwer Etext pages Get more help- Help me solve this Home ments lan Clear all elp
Answers
a. The equilibrium price and quantity are 0.42 million litres and 136 cents per litre respectively. The monthly revenue for milk producers without government intervention is $5.712 million.
b. The quantity supplied and the quantity demanded at the guaranteed price are 0 million litres and 1.0897 million litres respectively.
a. To find the equilibrium price and quantity in the market for milk in Saskatchewan, we need to equate the demand and supply equations:
Demand: p = 220 - 200q
Supply: p* = 10 + 300q
Setting p equal to p*, we have:
220 - 200q = 10 + 300q
Combining like terms:
500q = 210
Dividing both sides by 500:
q = 0.42 (rounded to two decimal places)
So the equilibrium quantity is 0.42 million litres.
Substituting this value back into either the demand or supply equation, we can find the equilibrium price:
p = 220 - 200(0.42)
p = 136 (rounded to the nearest cent)
Therefore, the equilibrium price is 136 cents per litre.
To calculate the monthly revenue for milk producers without government intervention, we multiply the equilibrium quantity by the equilibrium price:
Revenue = 0.42 million litres * 136 cents per litre
Revenue = $5.712 million (rounded to one decimal place)
So the monthly revenue for milk producers without government intervention is $5.712 million.
b. If the government guarantees a price of $2.06 per litre, we can set this price equal to the supply equation and solve for the quantity supplied:
2.06 = 10 + 300q
Subtracting 10 from both sides:
300q = 2.06 - 10
300q = -7.94
Dividing both sides by 300:
q = -0.0265 (rounded to four decimal places)
Since quantity cannot be negative, the quantity supplied at the guaranteed price is 0 million litres.
To find the quantity demanded, we can substitute the guaranteed price into the demand equation:
p = 220 - 200q
2.06 = 220 - 200q
Subtracting 220 from both sides:
-217.94 = -200q
Dividing both sides by -200:
q = 1.0897 (rounded to four decimal places)
So the quantity demanded at the guaranteed price is 1.0897 million litres.
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Running at 5 miles an hour how long will it take you to go 12 miles
Answers
Answer:
2 hours and 24 minutes.
Jack ran a total of 30 miles over the course of 15 track practices. How many track practices would it take for Jack to run 44 miles? Solve using unit rates.
My brain isn’t functioning and i need this done before December 21.
Answers
Answer:
22
Step-by-step explanation:
Use a proportion.
30/15 = 44/x
30x = 15 × 44
2x = 44
x = 22
Answer:
22
Step-by-step explanation:
30 miles/ 15 sessions of tract practice
Per practice Jack is running a total of 2 miles.
So 44 miles/2 miles
22 sessions of track practice