Find one value of x that is a solution to the equation:
(x^2+4)^2 – 11(x^2+4) + 24 = 0

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Answer:

Given:

mu = 200 lb, the mean sigma = 25 the standard deviation

For the random variable x = 250 lb, the

z-score is z = (x - mu) / sigma = (250 - 200) / 25 = 2

From standard tables for the normal distribution, obtain

P(x < 250) = 0.977

Answer: 0.977

Answer:

The form for a point-slope equation is y-y1=m(x-x1), where ”m” is the slope and (x1,y1) is a point on the graph. Substituting in the slope and point, the equation is y+7=-4(x-2).

:)

The correct option is:

a. randomly generated from the specified probability distributions

Given,

In the question:

Values for the random variables or uncertain variable inputs to a simulation are:-

a. randomly generated from the specified probability distributions

b. equal to the most likely value

c. selected by the decision maker

d. calculated by fixed mathematical formulas

e. controlled by the decision maker

Choose the correct one.

Now, According to the question:

Let's Know:

How do you generate a random number from a probability distribution?

In general, generating a random number from a probability distribution means transforming random numbers so that the numbers fit the distribution. Perhaps the most generic way to do so is called inverse transform sampling: Generate a uniform random number in [0, 1].

The correct option is:

a. randomly generated from the specified probability distributions

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Answer:

Step-by-step explanation:

Answer:



Step-by-step explanation:

Given: The table of linear function.

x :  -3  , 0 , 3,  6

y :  -6 , -2 , 2,  6

Slope=change in y over change in x



Passing point: (0,-2)

Point slope form:







Slope of the linear function

Linear function is

Hence, The slope of linear function is

The slope of the given linear function which graph represents the data is 3/2.

The slope of a linear function can be calculated by finding the difference between two points on the graph and dividing it by the difference of the corresponding x-values of those points.

In this case, the two points are (2, -2) and (6, 4).

The difference between these y-values = 6,

and the difference between the x-values = 4.

Therefore, the slope of the linear function which graph represents the data = 6/4

= 3/2

This means that the linear function has a slope of 3/2 which summarizes that for every two units that x increases, y increases by three units.

If x increases from 0 to 4, y increases from -5 to 1, which is a difference of 6 units (4 x 3/2 = 6).

The linear function can be written as y = 3/2x -5.

This means that for any given x-value, the corresponding y-value can be calculated by multiplying 3/2 by the x-value and subtracting 5.

If x = 2, the y-value is -2,that is

(2* 3/2)- 5= -2

Therefore, the slope of the linear function which graph represents the data is 3/2.

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Answer:

x+8=10

x−4=22

x÷3=6

7x=28

Step-by-step explanation:

George has cut down a 60ft high oak tree. He now wants to chop it into smaller pieces. He first cuts it into two pieces that are both 30ft. And then he continues on into making ten pieces that all are 6ft long before loading them onto his truck.

picture08

By looking at the different pieces of wood we can see that the following holds true.

60=30+30=6+6+6+6+6+6+6+6+6+6

This is called the reflexive property of equality and tells us that any quantity is equal to itself

a=a

We can also use this example with the pieces of wood to explain the symmetric property of equality. This property states that if quantity a equals quantity b, then b equals a.

ifa=b,thenb=a

Or if we use our example

if60=30+30,then30+30=60

Another property that can be explained by this is the transitive property of equality. It tells us that if a quantity a equals quantity b, and b equals the quantity, c, then a and c are equal as well.

ifa=bandb=c,thena=c

Or in the numbers taken from the oak tree example

if60=30+30

and30+30=6+6+6+6+6+6+6+6+6+6

then60=6+6+6+6+6+6+6+6+6+6

Since we know that 30 + 30 = 20 + 40 and that 30 + 30 = 60 we can substitute 30 + 30 for 20 + 40 and get 60 = 20 + 40. This is called the substitution property of equality.

If a = b, then a can be substituted for b in any expression.George has cut down a 60ft high oak tree. He now wants to chop it into smaller pieces. He first cuts it into two pieces that are both 30ft. And then he continues on into making ten pieces that all are 6ft long before loading them onto his truck.

picture08

By looking at the different pieces of wood we can see that the following holds true.

60=30+30=6+6+6+6+6+6+6+6+6+6

This is called the reflexive property of equality and tells us that any quantity is equal to itself

a=a

We can also use this example with the pieces of wood to explain the symmetric property of equality. This property states that if quantity a equals quantity b, then b equals a.

ifa=b,thenb=a

Or if we use our example

if60=30+30,then30+30=60

Another property that can be explained by this is the transitive property of equality. It tells us that if a quantity a equals quantity b, and b equals the quantity, c, then a and c are equal as well.

ifa=bandb=c,thena=c

Or in the numbers taken from the oak tree example

if60=30+30

and30+30=6+6+6+6+6+6+6+6+6+6

then60=6+6+6+6+6+6+6+6+6+6

Since we know that 30 + 30 = 20 + 40 and that 30 + 30 = 60 we can substitute 30 + 30 for 20 + 40 and get 60 = 20 + 40. This is called the substitution property of equality.

If a = b, then a can be substituted for b in any expression.

Answer:

4 words per minute

Step-by-step explanation:

In 6 minutes Rite typed 24 words, 24 divided by 6 is 4

Based on the theoretical probability from the company, we can expect 5 vehicles out of 5000 to break down.

The answer of the subpart of the question are :-

a. The experimental probability of an N Motors breaking down can be calculated as the ratio of the number of vehicles that have broken down in the sample to the total number of vehicles in the sample:

Experimental probability = Number of vehicles that have broken down / Total number of vehicles in the sample

Plugging in the values given, we get:

Experimental probability = 100 / 5000 = 0.02

Therefore, the experimental probability of an N Motors breaking down is 0.02 or 2%.

b. The number of vehicles from the 5000 samples that can be expected to break down based on the theoretical probability from the company can be calculated as follows:

Expected number of vehicles that will break down = Theoretical probability of a vehicle breaking down * Total number of vehicles in the sample

Plugging in the values given, we get:

Expected number of vehicles that will break down = 0.001 * 5000 = 5

Therefore, based on the theoretical probability from the company, we can expect 5 vehicles out of 5000 to break down.

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Generate categorical variables from continuous data by defining categories and assigning values, but you cannot obtain continuous data from categorical variables due to the loss of precision during the conversion process.

The reason why it is possible to generate categorical variables from continuous data, but not possible to obtain continuous data from categorical variables is due to the inherent nature of each type of variable.
To generate categorical variables from continuous data, you can follow these steps:
1. Define categories or groups based on a specific criterion. For example, dividing people into "short", "medium", and "tall" based on their heights.
2. Assign the continuous data values to the appropriate categories based on the defined criterion. For example, people with height less than 5 feet are considered "short", between 5 and 6 feet as "medium", and above 6 feet as "tall".
However, obtaining continuous data from categorical variables is not possible because categorical data does not have the same level of precision or granularity as continuous data. For instance, if you only know that someone is "tall," you cannot determine their exact height, as the information is lost when converting continuous data to categorical data.

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Answer:

11,214

Step-by-step explanation:

Given that :

Last week sales = 2,346.87

This week sales = 8,867.14

Total sales for bot weeks :

Last week sales + this week sales

2,346.87 + 8,867.14

= 11214.01

= 11,214

The temperature drop is B. 3.968 degrees each hour.

The temperature drop per hour can be computed by dividing the total temperature drop by the number of hours over which the temperature dropped.

The total steady drop in temperature = 24.8 degrees

Total number of hours for the temperature drop = 6¹/₄ hours

6¹/₄ hours = 6.25 hours

Temperature drop per hour = total drop/total hours of drop

= 2(4.8 ÷ 6¹/₄ hours)

= 3.968 degrees

Thus, the temperature drop is B. 3.968 degrees each hour.

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Answer:

A. √(e + 14)

Step-by-step explanation:

\(\frac{dy}{dx} = \frac{e^{x} - 1}{2y}\)

separating the variables, we have

2ydy = (\(e^{x}\) - 1)dx

integrating, we have

∫ydy = ∫(\(e^{x}\) - 1)dx

∫ydy = ∫\(e^{x}\)dx - ∫1dx + C

2y²/2 = \(e^{x}\) - x + C

y² = \(e^{x}\) - x + C

when x = 0, y = 4

So,

y² = \(e^{x}\) - x + C

4² = \(e^{0}\) - 0 + C

16 = 1 + C

16 = 1 + C

C = 16 - 1

C = 15

So,

y² = \(e^{x}\) - x + 15

when x = 1, we find y

y² = \(e^{1}\) - 1 + 15

y² = e + 14

y = √(e + 14)

The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.

To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:

A = x^2 + 4xh

Solving for h, we get:

h = (A - x^2) / 4x

The volume V of the box is given by:

V = x^2 * h

Substituting the expression for h, we get:

V = x^2 * (A - x^2) / 4x

Simplifying, we get:

V = (Ax^2 - x^4) / 4

The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.

To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).

To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = (2Ax - 4x^3) / 4

Setting this equal to 0 and solving for x, we get:

x = sqrt(A) / sqrt(2)

Plugging this value of x into the formula for V, we get:

V = A^1.5 / (4sqrt(2))

Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).

To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:

V = (10x^2 - x^4) / 4

Simplifying, we get:

V = 2.5x^2 - 0.25x^4

Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.

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Answer:

1- To find the time it takes for the rocket to hit the ground, we need to solve the equation h = 0. Substituting 0 for h and solving for t, we get:

0 = -4.9t^2 + 33.6t + 4.9

-4.9t^2 + 33.6t + 4.9 = 0

Using the quadratic formula, we get:

t = (-33.6 +/- sqrt(33.6^2 - 4(-4.9)(4.9))) / (2(-4.9))

t = (-33.6 +/- sqrt(1124.96)) / -9.8

t = (-33.6 +/- sqrt(1132.56)) / -9.8

t = (-33.6 +/- 33.6) / -9.8

t = (-67.2) / -9.8

t = 6.939

The rocket will hit the ground after approximately 6.939 seconds.

2- Let w be the width of the rectangle and l be the length. We are given that l = 5w - 7 and that the area of the rectangle is 24. We can set up the equation lw = 24 and substitute the expression for l:

(5w - 7)w = 24

5w^2 - 7w = 24

5w^2 - 7w - 24 = 0

Using the quadratic formula, we get:

w = (7 +/- sqrt(49 - 4(5)(-24))) / (2(5))

w = (7 +/- sqrt(49 - -120)) / 10

w = (7 +/- sqrt(169)) / 10

w = (7 +/- 13) / 10

w = 20/10 or w = -6/10

w = 2 or w = -0.6

Since the width cannot be negative, the width of the rectangle is 2 cm. The length is then 5w - 7 = 5(2) - 7 = 3 cm.

3- Jeff can build the wall in 10 - 1 = 9 hours. Kirk can build the wall in 10 hours. The combined time it takes for Jeff and Kirk to build the wall is 9 + 10 = 19 hours. The total time it takes for Kirk to build the wall is 75 / (1/10) = 750 minutes. 750 minutes is equivalent to 750/60 = 12.5 hours. Kirk builds the wall in 12.5 - 10 = 2.5 hours. Kirk builds the wall in 2.5 hours, or 2.5 * 60 = 150 minutes. Kirk will take approximately 150 minutes to build the wall by himself.

4- The student's average score so far is (87 + 85 + 91) / 3 = 263 / 3 = 87.67. To have an average of at least 90, the student needs to score at least 90 * 4 - 263 = 360 - 263 = 97. The student must score at least 97% on the next exam.

The definite integral is \($$\left(r^{\wedge} 3\right) /\left(\text { sqrt }\left(4+r^{\wedge} 2\right)\right) d r$$\) \(=0.116\).

As per given data,

Definite Integral helps to find the area of a curve in a graph. It has limits, which are the start and the endpoints, within which the area under a curve is calculated. The limit points can be taken as [a, b], to find the area of the curve f(x), with respect to the x-axis.

Here,

∫ = Integration symbol

a = Lower limit

b = Upper limit

f(x) = Integrand

dx = Integrating agent

Thus, ∫ab f(x) dx is read as the definite integral of f(x) with respect to dx from a to b.

Indefinite integrals are implemented when the boundaries of the integrand are not specified.

Consider the following integral:

\($$\int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r$$\)

The objective is to evaluate the integral, using substitution method.

Let \($u=4+r^2 \rightarrow r^2=u-4$\)

\($$\begin{aligned}& d u=2 r d r \\& r d r=\frac{d u}{2}\end{aligned}$$\)

when \($r=0$\), then \($u=4$\)

When \(r =1\), then \(u=5\)

Use the above details to evaluate the integral.

\(& =\frac{1}{2}\left[\frac{2 u^{\frac{3}{2}}}{3}-8 \sqrt{u}\right]_4^5 \\& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right]\)

\($$& \int_0^1 \frac{r^3}{\sqrt{4+r^2}} d r=\int_0^1 \frac{r^2}{\sqrt{4+r^2}}(r d r) \\& =\int_4^5 \frac{(u-4)}{\sqrt{u}}\left(\frac{d u}{2}\right) \\& =\frac{1}{2} \int_4^5 \frac{(u-4)}{\sqrt{u}} d u \\& =\frac{1}{2} \int_4^5\left(\sqrt{u}-\frac{4}{\sqrt{u}}\right)^{d u} \\\)

\(& =\left[\frac{u^{\frac{3}{2}}}{3}-4 \sqrt{u}\right]_4^5 \\& =0.116 \\& =\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}-\frac{4^{\frac{3}{2}}}{3}+8 \\& =0.11585 \\& \left.=\left[\frac{5^{\frac{3}{2}}}{3}-4 \sqrt{5}\right]^{-}\left(\frac{4^{\frac{3}{2}}}{3}-4 \sqrt{4}\right)\right]\)

Therefore, the evaluated integral is 0.116.

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The height of the steeple is 12.66 feet.

To find the height of the steeple, we will use the concept of angle of elevation. Angle of elevation is the angle between the horizontal line and the line of sight when we look up at an object.

Let's denote the height of the church as h1 and the height of the steeple as h2. Then, the total height of the church and the steeple is h1 + h2.

Using the concept of angle of elevation, we can write the following equations:

tan(35°) = h1/50 tan(47°40') = (h1 + h2)/50

Solving the first equation for h1, we get:

h1 = 50 * tan(35°) = 35.08 feet

Substituting the value of h1 into the second equation and solving for h2, we get:

50 * tan(47°40') = 35.08 + h2

h2 = 50 * tan(47°40') - 35.08

= 47.74 - 35.08 = 12.66 feet

Therefore, the height of the steeple is 12.66 feet.

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An Edgeworth box is used to represent the initial allocation of goods between David and Wilson based on their endowments of onion rings and chips.

An Edgeworth box is a graphical representation used to analyze the allocation of goods between two individuals.

In this case, we consider David and Wilson's initial endowments of onion rings and chips.

To draw the Edgeworth box, we create a rectangular box where the horizontal axis represents the quantity of onion rings (q1) and the vertical axis represents the quantity of chips (q2). The box is divided into four quadrants, representing the allocation of goods to each individual.

Based on their initial endowments, David has 35 onion rings and 10 chips, while Wilson has 5 onion rings and 20 chips.

We label the initial allocation of goods as point "e" within the Edgeworth box, indicating the quantities of onion rings and chips for each person.

By visually representing the initial allocation in the Edgeworth box, we can analyze the potential for trade and the possibility of mutually beneficial exchanges between David and Wilson based on their preferences and utility functions.

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Answer:

C) 3

Step-by-step explanation:

To find the slope given a table with points, use the formula:
\(\frac{y_2-y_1}{x_2-x_1}\)

Use the points:

(-2,-2) and (-1,1)

\(\frac{1+2}{-1+2}\)

simplify

3/1

=3

So, the slope is 3.

Hope this helps! :)

The annual premium of Susie's insurance company apply as a result of accident is $255 for an year. This is because the monthly insurance payment has been increased by $21.25.

What is Health insurance?

Health insurance or the medical insurance is an insurance which covers the whole or a part of the risk of a person which is incurring the medical expenses. Depending upon the health insurance plan, the risk is shared among many individuals.

Main body:

The increase in monthly insurance payment = $21.25

So, the annual increase in the premium amount paid by Susie will be:

Monthly increase in insurance payment × 12

(As there are 12 months in an year)

Annual increase in premium amount = $21.25 × 12

Annual increase in premium amount = $255

Therefore, the annual increase in the amount of premium paid by Susie for health insurance is $225.

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Answer:

13824 is the answer

Step-by-step explanation:

8*12*2*6*12

The value of x when f(x) of 8 according to the graph is; 4.

In order to determine a point's coordinates in a coordinate system, you must do the opposite. Start at the point and move in a vertical line in either an upwards or downwards direction to the x-axis. Here is the x-coordinate for you. Next, repeat the process while following a horizontal line to determine the y-coordinate.

According to the graph;

To determine the value of x when f(x) = 8.

We must plot a line of the equation; y = 8.

This y = 8 line produces a horizontal line.

The point at which the horizontal line, y = 8 intersects the given graph has an x coordinate.

Ultimately, this point has x coordinates of 4, making 4 the value of x when f(x) = 8.

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The required values of x in the collinear points A, B and C are -3, 1, -12 and 12

Points that lie on the same line are called collinear points.

Given that, Points A, B, and C are collinear point B is between A and C.

We will use here segment addition postulate, to solve each part.

The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.

1) AB = x+15, BC = x+13 and AC = 22

x+15+x+13 = 22

2x = 22-28

2x = -6

x = -3

2) BC = 2x-2, AC = 3x-3 and AB = 4

3x-3-(2x-2) = 4

3x-3-2x+2 = 4

5x = 5

x = 1

3) BC = x+28, AB = 2x+28 and AC = 12

x+20+2x+28 = 12

3x+48 = 12

3x = -36

x = -12

4) BC = x-8, AB = 9 and AC = 2x-11

x-8+9 = 2x-11

x+1 = 2x-11

x = 12

Hence, the values of x are -3, 1, -12 and 12

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Answer:

C

Step-by-step explanation:

domain is the numbers for x.

In this case x could be any number

Answer:

0.6

Explanation: 60 over 100 would be 60/100, so when converting this into a decimal, the 60 would be in the hundreths place. Therefore, the decimal would be 0.6.

Hope this Helps!

The third side is between 33.33 and 132.83 yards long.

In Euclidean geometry, the triangle inequality is the theorem that states that the sum of any two sides of a triangle is greater than or equal to the third side. The theorem basically states that the shortest distance between two points is defined by a straight line.

The triangle inequality has a counterpart in other metric spaces, or spaces with a way to measure distances.

Given that the two sides of the triangle are 99-100 yards (say 99.5) and 33.33 yards, there is a triangle here. The third side's length must be determined using triangle inequality because it is not a right triangle.

The longer side, which is 99.5 yards long, must be shorter than the other two sides taken together. If c is on the second side, then

99.5 < 33.33 + c.

The side c must be longer than 33.33

The side c must be shorter than the sum of the other two sides:

c < 99.5 + 33.33.

c < 132.83

Combining both we will get that

33.33  <  c  <  132.83.

All possible lengths for the third side of the triangle are provided by this interval (33.33, 132.83).

Therefore, the length of the third side varies from 33.33 to 132.83.

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The number of trips max would have to make in order to deliver 12 cords of wood is 16 trips.

We will use unitary method to solve this problem.

Pick up truck carry ( 3/4 ) cord of firewood in trip = 1

Pick up truck will carry 1 cord of firewood in the trips =  ( 1/(3/4) ) trips                                                                                                                

                                                                                        = ( 4/3 ) trips

Truck will carry 12 cords of firewood in the trips = 12 × ( 4/3 )

                                                                                = 16 trips.

Therefore, the number of trips max would have to make in order to deliver 12 cords of wood is 16 trips.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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9514 1404 393

Answer:

  13

Step-by-step explanation:

Let n represent that number.

  (2 +n)/(5 +n) = 5/6 . . . . . . . . n is added to numerator and denominator

  6(2 +n) = 5(5 +n) . . . . . . . . . multiply by 5(5+n)

  12 +6n = 25 +5n . . . . . . . . . eliminate parentheses

  n = 13 . . . . . . . . . . . subtract 5n+12

Adding 13 to each term will give 5/6.

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Check

  (2 +13)/(5 +13) = 15/18 = (3·5)/(3·6) = 5/6

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Alternate solution

The difference of denominator and numerator in 2/5 is 5-2 = 3. The difference of denominator and numerator in 5/6 is 6-5 = 1. In order to make the latter difference 3, we must have (3/3)(5/6) = 15/18. We can get 15/18 from 2/5 by adding 13 to numerator and denominator.