Answers
Recall the binomial theorem.
[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]
1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is
[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]
Observe that
[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]
[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]
When we multiply these by [tex]8-9x[/tex],
• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]
• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]
and the sum of these terms is
[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]
2. The binomial expansion is
[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]
We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :
[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]
Related Questions
A fountains pool is enclosed by a circular plastic tank. The distance from the center of the pool to the wall of the tank is 10 feet. How long is the wall of the tank in feet?
Answers
The length of the wall of the tank in feet is 62.8 feet.
How to solve circumference?Circumference is the perimeter of a circular object. Therefore,
circumference = 2πr
where
r = radiusThe fountains pool is enclosed by a circular plastic tank.
The distance from the centre of the pool to the wall of the tank is 10 feet. This is the radius of the circle
Hence,
length of the tank = 2πr
length of the tank = 2 × 3.14 × 10
length of the tank = 20 × 3.14
length of the tank = 62.8 feet.
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Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table. A 2-column table with 4 rows is shown. The first column is labeled Blood Type with entries O, A, B, AB. The second column is labeled Number of People with entries 22, 20, 6, 2. Use the table to determine the following probabilities. The probability that a randomly chosen person from this group has type B is . The probability that a randomly chosen person from this group has type AB is . The probability that a randomly chosen person from this group has type B or type AB blood is .
Answers
Has type B= 6/50= 3/25 = 12%
Has type AB= 2/50 = 1/25 = 4%
Has type B or type AB = 8/50 = 4/25 = 16%
Hello, I need help with this. Giving brainiliest
9^(a) = (sqrt(3))^(a +2)
Answers
Answer:
2/3
Step-by-step explanation:
Let's solve your equation step-by-step.
9a=(√3)a+2
9a=1.732051a+2
Solve Exponent.
9a=1.732051a+2
log(9a)=log(1.732051a+2)(Take log of both sides)
a*(log(9))=(a+2)*(log(1.732051))
a=(log(1.732051)/log(9))*(a+2)
a=0.25*(a+2)
a=0.25a+0.5(Simplify both sides of the equation)
a−0.25a=0.25a+0.5−0.25a(Subtract 0.25a from both sides)
0.75a=0.5
0.75a/0.75=0.5/0.75
(Divide both sides by 0.75)
a=0.666667
a=2/3
0.666667=2/3
Hope this helps :)
Answer:
2/3
Step-by-step explanation:
9^a = sqrt(3)^a * sqrt(3)^2
9^a = 3^((a/2)+1)
3^(2a) = 3^((a/2)+1)
2a = (a/2)+1
1.5a=1
a=1/(3/2) = 2/3
Look at the equation shown below. 19 - 5 = 3 z - 11 Which of these expressions gives the value of Z
Answers
If the equation is 19-5=3z-11 then the value of z is 15/3.
Given an equation in terms of z is 19-5=3z-11.
We are required to find the value of variable z which exist in equation.
Equation is like a relationship between two or more variables expressed in equal to form. Equations of two or more variables look like ax+by=c. It may be linear equation, quadratic equation,cubic equation,or many more depending on power of the variable.
The value of z can be find as under:
19-5=3z-11
4=3z-11
3z=4+11
3z=15
z=15/3
Hence if the equation is 19-5=3z-11 then the value of variable z is 15/3.
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A bag contains blue, orange and red jelly beans only there are 6x blue jelly beans, 2x-3 orange jelly beans and 15-x red jelly beans there are a total of 54 jelly beans in the bag.
a) how many orange jelly beans are there in the bag?
b) how many blue jelly beans are there in the bag?
Answers
Answer:
a.9
b.36
Step-by-step explanation:
Blue beans + orange beans + red beans = 54
6x + 2x-3 + 15-x = 54
6x+2x-x=54+3-15
7x=42
divide both sides by 7
x=6
a. orange beans = 2x-3
but x=6
2(6)-3
12-3
=9
b.blue beans =6x
6(6)
=36
The graph of the function C(x) = −0.74x2 + 22x + 75 is shown. The function models the production cost, C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands:
graph of a parabola opening down passing through points negative 4 and 57 hundredths comma zero, zero comma 62, 1 and 12 hundredths comma 75, 17 and 65 hundredths comma 167 and 55 hundredths, 34 and 18 hundredths comma 75, and 39 and 87 hundredths comma zero
If the company wants to keep its production costs under $175,000, then which constraint is reasonable for the model?
Answers
If the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands. This can be obtained by using the given graph of the function.
Which constraint is reasonable for the model:A constraint is a condition of an optimization problem that should be satisfied the condition.
From the we have the function,
⇒ C(x) = −0.74x² + 22x + 75
the production cost C, in thousands of dollars for a tech company to manufacture a calculator, x is the number of calculators produced, in thousands.
In the graph the dotted line is the line where C(x) is $175,000. Above this line every the value is greater than $175,000.
The points where this line, that is C(x) = y = 175, intersect the graph of the given function C(x) = −0.74x² + 22x + 75 is (5.6, 175) and (24.13, 175).
This means that above the point (5.6, 175) the graph has the value greater than 175000 and below the point the graph has the value below 175000.Similarly, below the point (24.13, 175) the graph has the value greater than $175,000 and above the point the graph has the value below $175,000.Therefore, x ≥ 5.6 and x ≤ 24.13
⇒ 5.6 ≤ x ≤ 24.13
Hence if the company wants to keep its production costs under $175,000, then 5.6 ≤ x ≤ 24.13 constraint is reasonable for the model given that the function C(x) = −0.74x² + 22x + 75 ,the production cost C, in thousands of dollars for a tech company to manufacture a calculator, where x is the number of calculators produced, in thousands.
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Answer:
0 ≤ x < 5.6 and 24.13 < x ≤ 32.82
Step-by-step explanation:
the length of the sides of a triangle are in the ratio 3:4:5. find the lengths of the sides of the triangle if its perimeter is 96cm
Answers
Answer:
let the angles be 3x,4x&5x
Now,
perimeter (p)=sum of all sides
or, 96=3x+4x+5x
or, 96=12x
or,96/12=x
or,8=x
or,x=8
Then,
3x=3*8
=24
4x=4*8
=32
5x=5*8
=45
A rectangle is 5 inches long and 2x inches wide. The value of the perimeter
(in inches) is equal to the value of the area (in square inches). Find x.
Answers
Answer:
Area=length× berngth
A=5×2x
A=10x square
List the sides in order from the smallest to the largest 83 56 41
Answers
the order from smallest to largest is:
41, 56, 83.
How to list from smallest to largest?
Here we have 3 values, that are:
{83, 56, 41}
To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.
Then the middle number. Which is 56, that is larger than 41 and smaller than 83.
Finally, the largest number, which is 83.
Then the order is:
41, 56, 83.
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If the circumference
of a circle is
62.8 feet, what is the radius of the
circle?
Use 3.14 for I.
Hint: C = 2Tr
radius-12] foot
Please explain how you got the answer for future problems
Answers
Answer:
Hope you like my answer
Answer:
radius = 10 feet
Step-by-step explanation:
C represents the circumference.
C = 2πr ,where r is the radius.
We are given C = 62.8 ft
Equating the two expressions of C :
2πr = 62.8
Then
2 × 3.14 × r = 62.8
Then
6.28 × r = 62.8
Then
[tex]r = \frac{62.8}{6.28} = 10[/tex]
Here are the steps Tyler took to solve the equation.
Please answer these two questions! Thank youuu
Answers
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. Thus the steps taken by Tyler are correct if x = 22.
ii. Tyler made no mistake.
Algebraic expressions include both alphabet and number so that the value of the alphabet is to be determined. The value of the alphabet in the expression would be determined by applying mathematical operations appropriately.
To solve the question given to Tyler, we have:
[tex]\sqrt{x + 3}[/tex] = -5
square both sides of the equation to have;
(x + 3) = [tex](-5)^{2}[/tex]
x + 3 = 25
collect like terms to get;
x = 25 - 3
= 22
x = 22
1. Thus the equation is true if x = 22.
2. Tyler did not make any mistake in solving for x.
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A circle with center O. Two tangents to the circle from the point C meet the circle at points A, and B. Two lines O B, and O C forms an exterior angle of 250 degrees. Two lines B D, and A D are drawn from a point D on the circle.
In this figure, m∠BDA =
° and m∠BCA =
°.
Answers
Based on the calculations, the measure of m∠BDA and m∠BCA are 55° and 70° respectively.
What is a tangent?In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.
What is a circle?A circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Also, a circle simply refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
First of all, we would determine angle BOA:
∠BOA + ∠BOA = 360° (Angles at a point)
∠BOA + 250° = 360°
∠BOA = 360° - 250°
∠BOA = 110°
Next, we would determine angle BDA:
2 × m∠BDA = ∠BOA (Angle inscribed at the center is twice the angle at the circumference)
2 × m∠BDA = 110°
m∠BDA = 110°/2
m∠BDA = 55°.
What is the theorem of intersecting secants?The theorem of intersecting secants states that when two (2) lines intersect outside a circle, the measure of the angle formed by these lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.
By applying the theorem of intersecting secants, angle BCA will be given by this formula:
m∠BCA = ½ × (m<AO - m<BO)
Substituting the given parameters into the formula, we have;
m∠BCA = ½ × (250 - 110)
m∠BCA = ½ × 140
m∠BCA = 70°.
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Answer:
70
Step-by-step explanation:
A video game shop is analyzing its sales performance using matrices. matrix a contains the unit sales data for each product category (horizontally) per week (vertically). matrix b contains the unit sales data for weekends for each category (horizontally) per week (vertically). to find the number of games in each product category that were sold each week only on weekdays, which matrix operation must be performed? a. add matrix a to the inverse of matrix b. b. more data is needed to calculate the sales during weekdays. c. subtract matrix b from matrix a. d. add matrix b to matrix a.
Answers
Answer:
Matrix B should be subtracted from Matrix A.
Step-by-step explanation:
Kent has two similar cylindrical pipes, pipe a and pipe b. the radius of pipe a is 6 cm, and the radius of pipe b is 2 cm. what is the ratio of the volume of pipe a to the volume of pipe b?
Answers
The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
What is cylinder?A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder.
Given that,
Radius of pipe a is 6 cm, and the radius of pipe b is 2 cm.
We know that the volume of cylinder is :- [tex]\pi r^{2}h[/tex]
where r is radius and h is height of the cylinder.
If two figures are similar then ratio of volume is equal to the cube of any dimension.
The ratio of the volume of Pipe a to the volume of Pipe b :-
[tex]\frac{V(a)}{V(b)}=\frac{6^{3} }{2^{3} }[/tex]
= [tex]\frac{27}{1}[/tex]
Hence, The ratio of the volume of pipe a to the volume of pipe b is 27:1 .
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Which characteristic is necessary to create a table that compares two functions?
Answers
The characteristic that is necessary to create a table that compares two functions is D. Choose the same values for each functions .
What is the usefulness of table?The Mathematical tables can be regarded as the lists of numbers which is used in showing the results of a calculation and these can have varying arguments.
It should be noted that when necessary to creating a table that compares two functions it is important to Choose the same values for each functions .
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Which of the following values would complete the ordered pair if the point is on the graph of f(x) = -3x + 2?
(-1, )
0-1
05
01
0-5
Answers
The y-coordinate that completes the point exists 5.
What is an ordered pair?An ordered pair (x, y) denotes the x-and-y coordinates of a general point, where x exists the input value of a function and y exists the output value of a function.
The output value exists y = f(x) and must be found using the rule (function) to the given input value.
In this case the rule exists f(x) = - 3x + 2, and the input value, x, exists - 1 (the first value of the ordered pair).
This exists the mathematical procedure:
x = - 1
f(x) = f (-1)
Then substitute the value x = -1 then
f(-1) = -3 (-1) + 2 = 3 + 2 = 5.
Therefore, the correct answer is option b) 5.
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The length of the base of the plot is 12 feet, and the length of one side is 5 feet, as shown in the diagram. Tammy makes a scale drawing of
the plot using a scale of 1 inch to 2 feet. The area of the plot in the scale drawing is
square inches
Answers
Answer:
15
Step-by-step explanation:
12 / 2 = 6
5 / 2 = 2.5
6 x 2.5 = 15
15 inches²
Select the correct answer. which expression shows the factors of 5x2 17x 6? a. (5x 1)(x 6) b. (5x 2)(x 3) c. (5x 3)(x 2) d. (5x 6)(x 1)
Answers
Answer:
B. (5x + 2)(x + 3)
Step-by-step explanation:
5x times x = 5x^2
5x times 3 = 15x
2 times x = 2x
2 times 3 = 6
15x + 2x = 17x
5x^2 + 17x + 6
P.S. next time please word your question better. Took me a while you meant "5x^2 plus 17x plus 6", since your equation reads "5 times 2 BLANK 17 times 6".
16. On your own paper, graph the following system of equations. Describe the graphs (perhaps give a few points on each line) and give the solution to the system of equations.
-2x - 5y = 20
y=4/5x+2
Answers
Answer:
(-5, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]
Both equations are linear equations.
Equation 1Rearrange Equation 1 to make y the subject:
[tex]\implies -2x-5y=20[/tex]
[tex]\implies -5y=2x+20[/tex]
[tex]\implies y=-\dfrac{2}{5}x-4[/tex]
Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]
[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]
Plot the found points and draw a straight line through them.
Equation 2The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).
Find two points on the line by substituting two values of x into the equation:
[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]
[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]
Plot the found points and draw a straight line through them.
SolutionThe solution(s) to a system of equations is the point(s) of intersection.
From inspection of the graph, the point of intersection is (-5, -2).
To verify the solution, substitute the second equation into the first and solve for x:
[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]
[tex]\implies \dfrac{6}{5}x=-6[/tex]
[tex]\implies 6x=-30[/tex]
[tex]\implies x=-5[/tex]
Substitute the found value of x into one of the equations and solve for y:
[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]
Hence verifying that (-5, -2) is the solution to the given system of equations.
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First simplify first one
-2x-5y=205y=-2x-20y=-2/5x-4Another one is
y=4/5x+2On first line
at x=0
y=-4At x=5
y=-2-4=-6On second line
At x=0
y=2At x=5
y=20+2=22Graph attached
Solution is (-5,-2)
A honeybee leaves its hive and travels 100 m due west, 200 m due south, and then returns to a position 5 m north of its hive. what is its total displacement?
Answers
The total displacement of the honeybee as it travels west, south and north is 219.2 m.
Total displacement of the honeybeeThe total displacement of the honeybee is calculated as follows;
total horizontal displacement, x = 100 m due west
total vertical displacement, y = 200 m - 5 m = 195 m
total displacement, d = √x² + y²
d = √(100² + 195²)
d = 219.2 m
Thus, the total displacement of the honeybee as it travels west, south and north is 219.2 m.
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Determine what type of model best fits the given situation: principal p is invested at an annual interest of rate r, compounded k times a year for t years.
Answers
The most appropriate model for a given situation is exponential.
What is compound interest?The interest you earn on interest is known as compound interest.Compound interest is a use of exponential functions. A specific sum is added to the account balance each time money is invested (or lent out). Interest is the amount of money that is added to the balance. The sum will continue to accrue interest after that interest has been added during the subsequent compounding period.In the settings of investments and savings, compound interest is used. A = P(1 + RT) is the formula for simple interest. The next section contains a definition of the variables. This indicates that the account value is the sum of the initial investment amount multiplied by one and the rate multiplied by the time.The most appropriate model for a given situation is exponential.
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13. In A ABC, if m
BF is an angle bisector, find
m
Answers
If in the triangle ABC , BF is an angle bisector and ∠ABF=41° then angle m∠BCE=8°.
Given that m∠ABF=41° and BF is an angle bisector.
We are required to find the angle m∠BCE if BF is an angle bisector.
Angle bisector basically divides an angle into two parts.
If BF is an angle bisector then ∠ABF=∠FBC by assuming that the angle is divided into two parts.
In this way ∠ABC=2*∠ABF
∠ABC=2*41
=82°
In ΔECB we got that ∠CEB=90° and ∠ABC=82° and we have to find ∠BCE.
∠BCE+∠CEB+EBC=180 (Sum of all the angles in a triangle is 180°)
∠BCE+90+82=180
∠BCE=180-172
∠BCE=8°
Hence if BF is an angle bisector then angle m∠BCE=8°.
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2 plus 0.5x if x is equal to 5
Answers
Answer: 4.5
Step-by-step explanation:
2 + 0.5x
x = 5
2 + 0.5 ( 5 )
2 + 2.5
2 + 2.5 = 4.5
Hope this helps!
Systems requests do not deal with factors involved in improving service.
a. true
b. false
Answers
How many lattice points (points with integer coordinates) are on the line segment whose endpoints are $(3,17)$ and $(48,281)
Answers
Any line through the points [tex](a,b)[/tex] and [tex](c,d)[/tex] has
[tex]\gcd(c-a,d-b)+1[/tex]
lattice points. In this case, the count is GCD(45, 264) + 1.
Using Euclid's algorithm, we have
264 = 5•45 + 39
45 = 1•39 + 6
39 = 6•6 + 3
6 = 2•3 + 0
so that GCD(45, 264) = 3. Then there are 3 + 1 = 4 lattice points.
during the drive from the church to the graveyard , you cover 16,4 km in 1,5 hours . calculate your average speed
Answers
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Avg. speed = 11 km/h[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Average speed (v) :
[tex]\qquad❖ \: \sf \:v = \cfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} [/tex]
[tex]\qquad❖ \: \sf \:v = \dfrac{16.4}{1.5} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:v = 11 \: \: kmph[/tex]
Drag each length to the correct location on the image. Each length can be used more than once, but not all lengths will be used.
What are the missing segment lengths shown in the image?
Answers
By applying Pythagoras theorem, the missing segment lengths of this triangles include:
CD = 10√2AC = 10√2BC = 10AB = 10How to find the missing segment lengths?Since triangle ACD is a right-angle triangle, we would use Pythagoras theorem to find the missing segment lengths of this triangles as follows:
c² = a² + b² ≡ AD² = CD² + AC²
Next, we would use cos trigonometric ratio to find side CD,
cos45 = adjacent/hypotenuse
cos 45 = CD/20
1/√2 = CD/20
CD = 1/√2 × 20
CD = (20√2)/2
CD = 10√2
For side AC, we have:
AD² = CD² + AC²
AC² = AD² - CD²
AC² = 20² - (10√2)²
AC² = 400 - 100(2)
AC = √200
AC = 10√2
From triangle ABC, we have:
cos45 = BC/10√2
BC = 10√2 × cos45
BC = 10√2 × 1/√2
BC = (10√2)/√2
BC = 10
For side AB, we have:
AB² = (10√2)² - 10²
AB² = 200 - 100
AB² = 100
AB = 10.
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A sample consists of every 25th student from a group of 1000 students. the sampling technique used is:
Answers
A sample consists of only the 25th student in a group of 1,000 students, called Systematic sampling.
What is meant by systematic sampling?Systematic sampling is a probability sampling technique in which researchers periodically choose people from the population.Comparatively speaking, systematic sampling is easier and clearer than a random sample. Additionally, it might make it easier to cover a large study region. Systematic sampling, however, puts certain arbitrary parameters into the data. This may result in some patterns being overrepresented or underrepresented.Imagine that a statistician randomly chooses 100 individuals from a population of 10,000 as an example of systematic sampling. For example, selecting a fresh sample to draw from every 12 hours is one way to make the sampling intervals systematically.A sample consists of only the 25th student in a group of 1,000 students, called Systematic sampling.
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A local smallholder is putting animals in different fields. She put them in different ratios. 50 POINTS AND BRAINLIEST!!
She spilt the 54 pigs in the ratio 1:2:3. How many are in each field as a ratio? __:__:__
She split the 154 chikens in the ratio 2:3:6. How many are in each field? __:__:__
Answers
Answer:
Part 1: 9:18:27
Part 2: 28:42:84
Step-by-step explanation:
Part 1:
54 pigs are split into the ratio 1:2:3. Treating a "1" ratio as x, we have x:2x:3x is 54 pigs. We can add up all parts of the ratio to become the whole. x+2x+3x=54. Solving, x=9. Substituting, our ratio is 9:18:27.
Part 2:
Similar to part 1, we treat a "1" ratio as y. Our ratio is 2y:3y:6y for a total of 154 chickens. Adding all the parts, we have 2y+3y+6y=154, so y=14. Substituting, our ratio is 28:42:84.
A coach shows the following ratio table to a team. The table shows the average amount of calories burned for a certain number of minutes of running.
Practice
Minutes of running
Calories burned
4
20
8
40
?
100
Based on the table, how many minutes does a person need to run to burn 100 calories?
12
20
28
68
Answers
Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes
How many minutes does a person have to run?Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.
The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.
Ratio = minutes run / calories burned
8 / 40 = 1/5
Now, multiply this ratio by 100
1/5 x 100 = 20 minutes
To learn more about ratios, please check: brainly.com/question/25927869
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