In your own words, describe how to find the rate of increase if the population of a town changes from 47,230 to 55,112 people. Then calculate the amount of change.

Answer:

Step-by-step explanation:

We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

I = interest at the end of t years

r represents the interest rate.

P represents the principal or initial amount deposited.

t represents the number of years of investment.

From the information given,

P = 1000

R = 2%

T = 5 years

Therefore,

I = (1000 × 2 × 5)/100

I = $100

The total amount in the account after 5 years would be

1000 + 100 = $1100

Yo sup??

The only way to solve this problem is by observing the graph closely and making some approximations.

We have to compare the value of x with the corresponding y value.

at x=4 you will find that the value of y is around 3.8-3.9

Therefore the answer is 3.8

Hope this helps.

Answer:

[tex]f(4) \approx 3.73[/tex]

Step-by-step explanation:

We can see that this function looks like a square root function but only shifted to the right by 1 and up by 2.

A square root function is:

[tex]f(x) = \sqrt{x}[/tex]

Shifting a function up means adding that value to the f(x):

[tex]f(x) = \sqrt{x}+2[/tex]

Shifting a function to the right means replacing a value x with the value (x-the value of shifting a function to the right):

[tex]f(x) = \sqrt{x-1}+2[/tex]

We can check that this really is a graph of a function [tex]f(x) = \sqrt{x-1}+2\\[/tex]:

[tex]f(1) = \sqrt{1-1}+2 = 0+2=2[/tex]

We can see on the graph that this really is the case : f(1)=2

Also,

[tex]f(2) = \sqrt{2-1}+2 = 1+2=3[/tex]

This is also the case if we check the graph.

So, now we have to estimate f(x) at x=4:

[tex]f(4) = \sqrt{4-1}+2 = \sqrt{3}+2[/tex]

where [tex]\sqrt{3} \approx 1.73[/tex] , hence:

[tex]f(4) \approx 1.73+2 = 3.73[/tex]

Answer:

[tex]V=24,501.42\ m^3[/tex]

Step-by-step explanation:

we know that

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

where

r is the radius of the circular base of cylinder

h is the height of the cylinder

we have

[tex]r=34/2=17\ m[/tex] ----> the radius is half the diameter

[tex]h=27\ m\\\pi=3.14[/tex]

substitute the given values in the formula

[tex]V=(3.14)(17)^{2} (27)=24,501.42\ m^3[/tex]

Answer:

Step-by-step explanation

Givens

r is the radius = 17

h is the height of the cylinder = 27

pi = 3.14

Unknowns = Volume

Anwser = 24,501.42 m^3

The sum of -4 and -8 is -12, so the numerical expression for the given phrase is 36 / (-12) and the simplified expression is -3.

To write a numerical expression for the phrase 'The quotient of 36 and the sum of -4 and -8,' we need to divide 36 by the sum of -4 and -8. The sum of -4 and -8 is -12, so the numerical expression is 36 / (-12).

Simplifying this expression, we get -3. Therefore, the simplified expression is -3.

Answer:

C = 1.75M + 3.25

Step-by-step explanation:

Let E represent Economy

Let L represent Luxury

Let M be the number of miles driven

Let C be how much it cost to rent a luxury car than economy

E = -0.70M + 14.95

L = 1.05M + 18.20

C = L - M

C =(1.05M + 18.20) - (-0.70M + 14.95)

C = 1.05M + 18.20 + 0.70M - 14.95

collect like terms

C = 1.05M + 0.70M + 18.20 - 14.95

C = 1.75M + 3.25

The equation representing how much more it costs to rent a luxury car than an economy car, given the number of miles driven, is C = 1.75M + 3.25. This is derived by subtracting the equation for economy car costs from the equation for luxury car costs and simplifying.

The value of C, which is the cost difference between renting a luxury and an economy car, can be found by finding the difference between the charge equations for the two types of cars. To find C in terms of M, subtract the equation for the economy car (E) from the equation for the luxury car (L).

So, C = L - E

Substitute the given equations for L and E into the equation for C:

C = (1.05M + 18.20) - (-0.70M + 14.95)

Simplify the equation by distributing the negative sign on the right side of the equation:  

C = 1.05M + 18.20 + 0.70M - 14.95

Combine like terms:

C = 1.75M + 3.25

This equation represents how much more it costs to rent a luxury car than an economy car based on the number of miles driven.

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Answer:

5x - 4

Step-by-step explanation:

2( x + 4 ) + 3( x - 4)

Distribute the 2 into ( x + 4 ) so it comes out to be 2x + 8

now distribute 3 into ( x - 4 ) = 3x - 12

now combine like terms 2x + 8 + 3x - 12

2x and 3x can combine into 5x

-12 and 8 can combine into -4

so it comes out to be 5x - 4

Answer:

The value of the house after adding the garage is $135,700.

Step-by-step explanation:

Given,

value of house before adding garage = $118,200.00

we need to find the value of house after adding two car garage.

Solution,

Since after adding two car garage the value of the house increased by 15%.

So firstly we will find out the 15% of the value of the house after adding garage.

So we can say that;

15% of the value of the house after adding garage is equal to 15 divided by 100 the multiplied with the value of the house before adding garage.

15% of the value of the house after adding garage = [tex]\frac{15}{100}\times118,000=\$17,700[/tex]

Now, The value of the house after adding garage is equal to the sum of value of house before adding garage and 15% of value of house before adding garage.

We can frame it in equation form as;

The value of the house after adding garage = [tex]\$118,000+\$17,000=\$135,700[/tex]

Hence The value of the house after adding the garage is $135,700.

Answer:

  1 1/3 gallons per day

Step-by-step explanation:

To find gallons per day, divide gallons by days. ("per" means "divided by")

  (4 gal)/(3 day) = (4/3) gal/day

Demont used 4/3 = 1 1/3 gallon each day.

To find out how many gallons of gasoline Demonte used each day, divide the total amount used (4 gallons) by the number of days (3), yielding approximately 1.33 gallons per day.

Demonte used 4 gallons of gasoline in three days driving to work and used the same amount of gasoline each day. To calculate the amount of gasoline he used each day, you divide the total gallons of gasoline by the number of days. This can be represented by the following equation:

Gallons per day = Total gallons used ÷ Number of days

Gallons per day = 4 gallons ÷ 3 days

Gallons per day = 1.33 gallons per day (approximately)

Therefore, Demonte used approximately 1.33 gallons of gasoline each day.

Answer:

The number of ways Tony and Maria can both be selected for the committee is 8 ways.

Step-by-step explanation:

i) Tony and Maria have to be on the committee together or not at all.

ii) Let us consider Tony and Maria as combined as one person.

 Therefore now we can say that the number of eligible people for the committee = 9 - 1 = 8.

iii) therefore the number of ways that both Tony and Maria can be selected for the committee are

 = 8C1   =  [tex]\hspace{0.2cm}\binom{8}{1} = \frac{8!}{1! (8-1)!} = \frac{8!}{1!\times 7!} = \frac{8}{1} = \hspace{0.1cm}8 \hspace{0.1cm}ways[/tex]

The number of ways to select exactly one of Tony and Maria is 70.

It is given that,

Explanation:

Excluding Tony and Maria from the 9 people. The number of remaining people is 7.

Exactly one of Tony and Maria be selected for the committee. So, one person is selected from 2 and 3 people are selected from the remaining 7 people.

[tex]\text{Number of ways}=^2C_1\times ^7C_3[/tex]

[tex]\text{Number of ways}=\dfrac{2!}{1!(2-1)!}\times \dfrac{7!}{3!(7-3)!}[/tex]

[tex]\text{Number of ways}=2\times 35[/tex]

[tex]\text{Number of ways}=70[/tex]

Thus, the number of ways to select exactly one of Tony and Maria is 70.

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Answer:

Third option: Definition of Congruent angles.

Step-by-step explanation:

For this exercise it is important to know the definition Congruent angles.

Congruent angles are defined as those angles that have equal measure.

The symbol used for Congruent angles is the following:

≅

Keep the explanation above on mind.

In this case, you know that [tex]\angle ABC[/tex] measures 90 degrees (This is also known as "Rigth angle"):

[tex]\angle ABC=90\°[/tex]

And you can observe in the table attached that the measure of [tex]\angle ABD[/tex] is also 90 degrres:

[tex]\angle ABD=90\°[/tex]

Therefore, since they have exactly the same measure, these angles are congruent. Then:

[tex]\angle ABC[/tex] ≅ [tex]\angle ABD[/tex]

Based on this, you can identify that the missing reason number 8 is: Definition of Congruent angles.

Answer:

12

Step-by-step explanation:

Given: Diagonal of square= [tex]3\sqrt{2}[/tex]

To find the perimeter of square, we need to find the length of sides of square.

∴ Using the formula of diagonal to find side of square.

Formula; [tex]Diagonal= s\sqrt{2}[/tex]

Where, s is side of square.

⇒ [tex]3\sqrt{2} = s\sqrt{2}[/tex]

Dividing both side by √2

⇒[tex]s= \frac{3\sqrt{2} }{\sqrt{2} }[/tex]

∴[tex]s= 3[/tex]

Hence, Length of side of square is 3.

Now, finding the perimeter of square.

Formula; [tex]Perimeter= 4s[/tex]

⇒[tex]Perimeter= 4\times 3[/tex]

∴ [tex]Perimeter= 12[/tex]

Hence, Perimeter of square is 12.

The perimeter of a square with a diagonal of 3 square root 2 units is 12 units.

To find the perimeter of a square with a diagonal of 3√2, we can use the fact that the diagonal of a square divides it into two congruent right triangles. The length of each leg of the triangle is equal to one side of the square. We can use the Pythagorean theorem to find the length of the side of the square. Let's assume that the length of the side of the square is s.

Using the Pythagorean theorem, we have s2 + s2 = (3√2)2. Simplifying, we get 2s2 = 18. Dividing by 2, we have s2 = 9. Taking the square root of both sides, we get s = 3.

The perimeter of the square is equal to 4 times the length of one side, so the perimeter is 4 * s = 4 * 3 = 12 units.

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Answer: Charlotte finished the word search in 16 minutes.

Step-by-step explanation:

Frank finished the word search in 32 minutes.

Terrence finished a word search in 3/4 the time it took Frank. This means that the time it took Terrence to finish the word search would be

3/4 × 32 = 24 minutes.

Charlotte finished the word search in 2/3 the time it took Terrence. This means that the time it took Charlotte to finish the word search would be

2/3 × 24 = 16 minutes

Final answer:

To find the difference in time, subtract the bike time from the bus time by finding a common denominator and subtracting the fractions.

Explanation:

To compare the time it took Josh to bike to work with the time it took him to take the bus, we need to subtract the bike time from the bus time.

The time it took Josh to bike to work is given as 2/5 of an hour. We can represent this as a fraction, 2/5.

The time it took Josh to take the bus is given as 5/8 of an hour. This can also be represented as a fraction, 5/8.

To find the difference, we subtract the bike time from the bus time: 5/8 - 2/5. To do this, we need a common denominator, which in this case is 40.

Multiplying the numerator and denominator of 5/8 by 5, we get 25/40. Multiplying the numerator and denominator of 2/5 by 8, we get 16/40.

Now we can subtract the fractions: 25/40 - 16/40 = 9/40.

Therefore, it took the bus 9/40 of an hour longer than it took Josh to bike to work.

The average net force on the man as he is brought to rest is: F = -1143.9N

Therefore, P.E = K.E

When the man comes to rest, the final velocity becomes, 0.

As, such, acceleration which is the rate of change of velocity becomes;

The force on the man; F = mass × acceleration.

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The average net force on the diver as he is brought to rest is approximately 689.56 N.

First, we can find the velocity of the man just before he reaches the water using the kinematic equation:

d = vt + 1/2at²

Now, let's calculate the velocity of the man just before he reaches the water using the equation:

vf​=0+(−9.8m/s2)×0.782s≈−7.664m/s

Since the velocity is negative, it means the man is moving downward.

After entering the water, the man comes to rest in 0.55 seconds. During this time, he decelerates due to the force of gravity, but this time in the opposite direction to his motion. We can use the equation:

Finally, we can determine the average net force using Newton's second law:

Given that the mass m of the man is 82 kg, we find:

F net = 82 kg × 14.025 m/s 2 ≈ 1147.35 N

Therefore, the average net force on the diver as he is brought to rest is approximately 1147.35 N.

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To Determine:

So, here is the complete proof of the Pythagorean theorem.

Given: Δ ABC is a right triangle, with

a right angle at ∠C

Prove: A²+B² =C²

Answer:

Note: All the answers for the questions marks are filled with in bold text.

Statement

1. ΔABC is a right triangle, with a right angle at ∠C

2. Draw an altitude from point C to line AB

3. ∠CDB and ∠CDA are right angles.

4. ∠BCA ≅ ∠BDC

5. ∠B ≅ ∠B

6. AA Similarity Postulate          

7.   [tex]\frac{a}{x}\:=\:\frac{c}{a}[/tex]

8. a² = cx

9. ∠CDA ≅ ∠BCA

10. ∠A ≅ ∠A

11. ΔCBA ~ ΔDBA      

12.  [tex]\frac{b}{y}\:=\:\frac{c}{b}[/tex]

13. b² = cy

14. a² + b² = cx + cy

15. [tex]\left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)[/tex]

16. x + y = c

17. a² + b² = c²

Reason

1. Given

2. From a point not on a line, exactly one perpendicular can be drawn through the point to the line.

3. Definition of altitude

4. All right angles are congruent.

5. Reflexive Property

6. AA Similarity Postulate

7. Polygon Similarity Postulate

8. Cross Multiply and Simplify

9. All right angles are Congruent

10. Reflexive Property

11. AA similarity Postulate

12. Polygon Similarity Postulate

13. Cross Multiply and Simplify

14. Addition Property of Equality

15. Distributive Property

16. Segment Addition Postulate

17. Substitution Property

Keywords: statement, reason

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Answer:

1. 1/2-2/5

2. 3/4-2/5

3. 1/2-3/4

Step-by-step explanation:

For you to be able to create such fractions you must make sure that the numerator is divisible by 20.

Clearly the number 2,4 and 5 can divide 20.so therefore any fraction formed with them will give the denominator 20

Answer:

[tex]a.\ 12[/tex]

Step-by-step explanation:

[tex]\frac{5}{6}y-8=2\\\\Add\ 8\ both\ sides\\\\\frac{5}{6}y-8+=2+8\\\\\frac{5}{6}y=10\\\\Multiply\ by\ 6\ both\ the\ sides\\\\\frac{5}{6}y\times 6=10\times 6\\\\5y=60\\\\divide\ by\ 5\ both\ the\ sides\\\\\frac{5y}{5}=\frac{60}{5}\\\\y=12[/tex]

Answer:

Option C) z = 3                                  

Step-by-step explanation:

We are given the following in the question:

IQ scores are normally distributed.

An IQ score is three standard deviations above the mean. Let x be the IQ score. Then, we can write,

[tex]x = \mu + 3\sigma[/tex]

Formula:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

[tex]z = \dfrac{\mu + 3\sigma-\mu}{\sigma} = \dfrac{3\sigma}{\sigma} = 3[/tex]

Thus, the z-score is 3.

Thus, the correct answer is

Option C) z = 3

The z-score for a student with an IQ three standard deviations above the mean would be z = 3.

If a very bright student is described as having an IQ that is three standard deviations above the mean, and if this student's IQ is reported as a z-score, the z-score would be z = 3. This is because a z-score is a measure of how many standard deviations an observation is above or below the mean. When we say an observation is three standard deviations above the mean, we are describing a z-score of 3. Thus, the correct answer is c. z = 3.

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The area of the purple band is [tex]A = 4 - x^2[/tex]

Since both the shape contains the square so here the area square should be applied,

A  = Total purple area - Total green area

[tex]A = (2)^2 - (x)^2\\\\A = 4 - x^2[/tex]

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Final answer:

The area of the purple band around the green square is calculated by finding the difference between the area of the larger purple square and the green square. It is determined by subtracting the green square's area (x²) from the total area of the larger square ((x + 4)²), resulting in an area of 8x + 16 square inches for the purple band.

Explanation:

To calculate the area of the purple band on the rug, we must first determine the dimensions of both the inner green square and the larger purple square that includes the band. The side length of the green square is given as x inches, and we know the width of the purple band surrounding it is 2 inches. To find the side length of the larger purple square, we add twice the width of the purple band (2 inches on each side) to the side length of the green square, giving us x + 2 + 2 or x + 4 inches.

The area of the larger purple square is therefore (x + 4)² square inches. The area of the inner green square is x² square inches. To find the area of just the purple band, we subtract the area of the green square from the area of the larger purple square.

So, the area of the purple band is (x + 4)² - x² square inches. Expanding this expression, we get x² + 8x + 16 - x² which simplifies to 8x + 16 square inches. Therefore, the area of the purple band around the green square is 8x + 16 in²

Answer:

72 = 2h

Step-by-step explanation:

6 dozens = 6×12 = 72

72 = 2h

Each hen lays eggs, so h hens will lay 2×h eggs

The equation you've made implies every hen lays 36 eggs

72 = 2h is the equation,

Which simplifies to

h = 36

Answer:

Step-by-step explanation:

x+x+(x+12)=180

3x=180-12=168

x=56

third angle=56+12=68

so angles are 56°,56°,68°

The larger angle is x + 12 i.e. 56 + 12 = 68⁰.

A triangle is a closed shape with 3 angles, 3 sides, and 3 vertices.

Let the first angle be x.

then second angle is equal to first i.e. x

and third angle = x + 12

we know that,

Sum of all angles of a triangle is 180⁰.

Now,

x + x + x + 12 = 180

3x = 180 -12

3x = 168

x = 168/3

x = 56

Thus, the larger angle is x + 12 i.e. 56 + 12 = 68⁰.

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Answer:

a) Positively skewed

b) Median

Step-by-step explanation:

We are given the following in the question:

For a particular data, mean levels of attraction are much higher than the median and the mode for these data.

[tex]\text{Mean} > \text{Median}\\\text{Mean} > \text{Mode}[/tex]

a) Shape of data

Since the mean of data is greater than the median and mode of the data, thus, is a skewed data.

For a positively skewed data:

[tex]\text{Mean} > \text{Median} > \text{Mode}[/tex]

Thus, the given data is positively skewed data.

b) Measure of central tendency

Since it is a positively skewed data, median is a better measurement of central of tendency.

Advantage of median:

Final answer:

The data likely has a right-skewed distribution, making the median the most suitable measure of central tendency due to the impact of outliers.

Explanation:

a. What is the shape of the distribution for the data in this study?
The data distribution is likely skewed to the right, as the mean is much higher than the median and mode, indicating a long tail to the right.

b. What measure of central tendency is most appropriate for describing these data? Why?
In this case, the median is the most appropriate measure of central tendency because it is less affected by extreme values compared to the mean. Since the mean is much higher than the median and mode, it suggests outliers are pulling the mean upwards.

Answer:

A. The economy switches to producing less of one product without increasing the production of the other product

Step-by-step explanation:

PPC is the graphical representation of product combinations that an economy can produce, given resources & technology. It is downward sloping because given resources & technology, production of a good can be increased  by decreasing production of other good.

It is based on assumption that resources are efficiently utilised. Points on PPC show resources efficient utilisation, Points under PPC show under utilisation, Points outside PPC are beyond country's productive capacity.

If country produces less of a good without increasing production of other goods, implying wasted resources & production below PPC. This case doesn't satisfy productive efficiency

Other cases : Producing more of a good & less of other is just re allocative movement on the PPC itself. Production point at PPF intersection with either axis implies economy is producing only the good on that axis.

In all the cases except A. satisfy the 'productive efficiency'

Answer:

Step-by-step explanation:

On pet day 18 children brought a pet to school.

2/3 of the pets were dogs. This means that the number of pets that were dogs would be

2/3 × 18 = 12 dogs

1/9 of the pets were cats. This means that the number of pets that were cats would be

1/9 × 18 = 2 dogs

Total number of dogs and cats is

12 + 2 = 14

The number of animals that were neither dogs nor cats is

18 - 14 = 4

Final answer:

There were 12 dogs, 2 cats, and 4 animals that were neither dogs nor cats among the 18 pets that children brought to school on pet day.

Explanation:

On pet day, 18 children brought a pet to school. To find out how many dogs were there, we calculate two-thirds of 18, and for the cats, we calculate one-ninth of 18.

Dogs: ⅓ × 18 = 12 dogs

Cats: ⅙ × 18 = 2 cats

To determine how many animals were neither dogs nor cats, we subtract the number of dogs and cats from the total number of pets: 18 - (12 + 2) = 4 animals neither dogs nor cats.

So, there were 12 dogs, 2 cats, and 4 animals that were neither dogs nor cats.

Answer:

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle,

DE represents the hypotenuse of the right angle triangle.

With m∠E as the reference angle,

EF represents the adjacent side of the right angle triangle.

DF represents the opposite side of the right angle triangle.

To determine m∠E, we would apply

the Tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan E = 8/5 = 1.6

E = Tan^-1(1.6)

W = 58.0° to the nearest tenth.

Answer:

Vanilla milkshake = 1/3 and Chocolate milkshake = 2/3

Step-by-step explanation:

Given data:

Total ounce of milkshake = 12 ounce

Vanilla milkshake = 4

Chocolate is the rest which can be interpreted as 12 - 4= 8 ounce

Representing as fractions

Vanilla milkshake = 4/12 (Reducing to lowest terms that is diving numerator and denominator by common factor in this case 4)

Vanilla milkshake = 1/3

Chocolate milkshake = 8/12 (Reducing to lowest terms that is diving numerator and denominator by common factor in this case 4)

Chocolate milkshake = 2/3

Answer: the ratio that represents Cos C = a/b

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AC represents the hypotenuse of the right angle triangle.

With m∠C as the reference angle,

BC represents the adjacent side of the right angle triangle.

AB represents the opposite side of the right angle triangle.

To determine m∠C, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos C = a/b

Model A's optimal price is $5, with a $3 increase, and Model B's optimal price is $6, with a $4 increase.

Let's walk through the step-by-step calculations for both Model A and Model B.

Model A:

Given Function:

f(x) = -12.5x^2 + 75x + 200

Completing the Square to Find Vertex:

f(x) = -12.5(x^2 - 6x - 16)

f(x)/(-12.5) = (x^2 - 6x - 16)

f(x)/(-12.5) + 16 + 9 = (x-3)^2

f(x)/(-12.5) + 25 = (x-3)^2 - 25

f(x) = (-12.5)[(x-3)^2 + 312.5]

Vertex Form:

f(x) = (-12.5)(x-3)^2 + 312.5

The vertex is at (3, 312.5).

Optimal Price Calculation:

The x-coordinate of the vertex indicates the optimal increase, which is $3. So, the optimal price is 3 + 2 = $5.

Y-intercept:

f(x) = -12.5(9) + 312.5 = 200

The y-intercept is $200.

X-intercepts:

Factorizing the original equation, we get x = 8 and x = -2.

Model B:

Symmetry Axis Calculation:

Midpoint between x-intercepts x = (-2 + 10)/2 = 4.

Optimal Price Calculation:

The optimal increase is $4, resulting in a price of 4 + 2 = $6.

Y-intercept:

The y-intercept is graphically determined to be between $180 and $210.

In summary, Model A's optimal price is $5, achieved with a $3 increase, while Model B's optimal price is $6, attained with a $4 increase.

Answer:

pictured and shown and solved

Answer:

The answer to your question is  [tex]\frac{3b}{a}[/tex] , check your options, maybe you forgot one.

Step-by-step explanation:

Original operation

                                [tex]\frac{6a^{2}}{5b^{2}} \frac{45b^{3}}{18a^{3}}[/tex]

Process

1.- Simplify 6 and 18 and 45 and 5

   [tex]\frac{6}{18} = \frac{3}{9} = \frac{1}{3}[/tex]

  [tex]\frac{45}{5} = \frac{9}{1} = 9[/tex]

 Result

  [tex]\frac{9}{3} = \frac{3}{1} = 3[/tex]

2.- Simplify a² and a³

    [tex]\frac{a^{2}}{a^{3}} = \frac{1}{a}[/tex]

3.- Simplify b³ and b²

     [tex]\frac{b^{3}}{b^{2}} = b[/tex]

4.- Join the results [tex]\frac{3b}{a}[/tex]