if S( 1, 2, 3, 4, 5,6 ) find the probability that a number chosen is more than 4



Answers

Answer 1

[tex]|\Omega|=6\\|A|=2\\\\P(A)=\dfrac{2}{6}=\dfrac{1}{3}[/tex]

Answer 2

Answer:

1/3

Step-by-step explanation:

The list of sample space's elements: {1, 2, 3, 4, 5, 6}

The number of elements in sample space: 6

The list of elements belonged to the event "choosing the number larger than 4": {5, 6}

The number of elements in the event: 2

Hence, the probability of event "choosing a number larger than 4":

P = number of event's elements/number of sample space's elements

  = 2/6

  = 1/3


Related Questions

percent increase formula

Answers

A = old value

B = new value

C = percent change

C = [ (B-A)/A ] * 100%

---------------------

Example:

Lets say we start at A = 10 and increase to B = 15. The percent change would be...

C = [ (B-A)/A ] * 100%

C = [ (15 - 10)/10] * 100%

C = (5/10) * 100%

C = 0.5 * 100%

C = 50%

The positive C value means we have a percent increase. Going from 10 to 15 is a 50% increase.

The lines on a 2-cup liquid measuring cup divide each cup into eighths If you measure 1 3/4 cups of water between which two quantities can you be certain that your exact measurement will be

Answers

Answer:

The line between 1 5/8 and 1 7/8 is exactly 1 3/4.

Step-by-step explanation:

1 3/4 = 1 6/8

Since the lines are every 1/8 of a cup, there are a total of 16 lines indicating 1/8 of a cup for a total of two full cups.

1/8 less than 1 6/8 is 1 5/8.

1/8 more than 1 6/8 is 1 7/8.

The line between 1 5/8 and 1 7/8 is exactly 1 3/4.

Jonas needs a cell phone. He has a choice between two companies with the following monthly billing policies. Each company’s monthly billing policy has an initial operating fee and charge per text message. Sprint charges $29.95 monthly plus .15 cents per text, AT&T charges $4.95 monthly plus .39 cents per text. Create equations for the two cell phone plans.

Answers

Answer:

Since both companies have a different plan, two equations are created to determine which company Jonas should choose with respect to the number of messages sent.

Step-by-step explanation:

- Sprint = $ 29.95 * X (0.15)

- AT & T = $ 4.95 * X (0.39)

One dollar equals 100 cents, so 0.15 cents equals $ 0.0015 dollars.

- Sprint = $ 29.95 * X (0.0015)

- AT & T = $ 4.95 * X (0.0039)

Si Jonas envía 500 mensajes de texto el valor mensual de cada empresa sería de:

- Sprint = $ 29.95 * 500 (0.0015)  = 22.46 dollar per month.

- AT & T = $ 4.95 * 500 (0.0039)  = 9.65 dollar per month.

The company Jonas should choose is AT&T.

AT&T also charges a little more per number of text messages, but since the phone's value is so low it would take thousands of text messages to compare to Sprint's monthly value.

I need help please so if you could help that would be nice. Also i will make brainliest

Answers

No it is not a function. You have to be able to write y=mx+b

In a group of 25 people, only three languages are spoken – English, Spanish and German. If there is at least one person who speaks all the three languages, how many people can interact with each other in English and German? 4 people speak two languages but do not speak Spanish One fifth of the group speaks more than one language.

Answers

Answer:

x + a=5

Step-by-step explanation:

Let

number of people who speak only English = E

the number of people who speak only German = G

the number of people who speak only Spanish = S

the number of people who speak only English & German but not Spanish = x

the number of people who speak only English & Spanish but not German = y

the number of people who speak only German & Spanish but not English = z;

the number of people who speak only German & Spanish & English = a

Find the the value of (x + a).

Statement 1: 4 people speak two languages but do not speak Spanish.

x = 4.

x+a

Value for a is unknown.

(x + a). Insufficient.

Statement 3: One-fifth of the group speaks more than one language.

x + y + z + a

= 25/5

= 5

value of (x + a) unknown

Insufficient.

Putting (1) and (2) together

x + y + z + a = 5

x = 4 and a=1,

we have only one possible solution from

x + y + z + a = 5

x + a

= 4 + 1

= 5.

Sufficient.

Identify the terms, like terms, coefficients and constants of the following expressions: a) 9 − z + 3 − 2z b) 7 − 5b + 1 terms: _____________ terms: ______________ like terms: ______ like terms: _______ coefficients: _____ coefficients: _____ constants: ______ constants: ______

Answers

Answer:

See below.

Step-by-step explanation:

a) 9 − z + 3 − 2z                             b) 7 − 5b + 1

terms: 9, -z, 3, -2z                          terms: 7, -5b, 1

like terms: 9 & 3; -z & -2z              like terms: 7 & -1

coefficients: -1, -2                           coefficients: -5

constants: 9, 3                                constants: 7, 1

 

What is the length of LM? (Question and answer choices provided in picture.)

Answers

Answer:

24√3

Step-by-step explanation:

cos∅ = adjacent over hypotenuse

Step 1: Use cos∅

cos30° = LM/48

Step 2: Multiply both sides by 48

48cos30° = LM

Step 3: Evaluate

LM = 24√3

Answer:

[tex]\large \boxed{24 \sqrt{3} }[/tex]

Step-by-step explanation:

The triangles are right triangles. We can use trig functions to solve.

cos θ  = adj/hyp

Take the triangle KLM.

cos 30 = LM/KL

cos 30 = LM/48

Multipy both sides by 48

(48) cos 30 = LM/48 (48)

Simplify.

48 cos30 = LM

24√3 = LM

identify the terms of each expression 7 + 5 p + 4r + 6 s ​

Answers

13+5p+4r you add 7+6=13 then you bring down the rest

Find the measure of b.

Answers

Answer:

b = 80°

Step-by-step explanation:

The inscribed angle measuring 100°, is supplementary to the angle opposite it in the inscribed quadrilateral.

Thus, the angle is = 80°

Therefore, b + 80° = 180° (angle on a straight line = 180°).

Thus, b = 180° - 80° = 100°.

The measure of b is 80°.

blake bought two iced coffees at dutch bros. He originally had $13.50 and now has $9 Write and solve an equation to find out how much each iced coffee cost

Answers

Equation: 13.50-2x=9 or 9=13.50-2x

Solve:
13.50-2x=9
-13.50 -13.50
—————————
-2x= -4.50
—— ———
-2. -2

X= $2.25
each coffee costs $2.25

You can check by putting 2.25 into the equation 13.50-2x=9
13.50-2(2.25)=9
13.50-5.50=9
9=9

if he had $13.50 and now he has $9 all you have to do is minus $13.50 by 9 like this 13.50-9=4.50 the ice coffee costs $4.50 simple.

If you still have a question and don't understand this please ask again thank you.

HELP ASAP WILL MARK BRAINLIEST!!!!!! Use the number line​ below, where ​RS=9y+2, ST = 4y+9 and RT = 115. a. What is the value of​ y? b. Find RS and ST. a. What is the value of​ y?

Answers

Answer: y = 7

Step-by-step explanation:


In Exercise 4, find the surface area of the solid
formed by the net.

Answers

Answer:

3. 150.72 in²

4. 535.2cm²

Step-by-step Explanation:

3. The solid formed by the net given in problem 3 is the net of a cylinder.

The cylinder bases are the 2 circles, while the curved surface of the cylinder is the rectangle.

The surface area = Area of the 2 circles + area of the rectangle

Take π as 3.14

radius of circle = ½ of 4 = 2 in

Area of the 2 circles = 2(πr²) = 2*3.14*2²

Area of the 2 circles = 25.12 in²

Area of the rectangle = L*W

width is given as 10 in.

Length (L) = the circumference or perimeter of the circle = πd = 3.14*4 = 12.56 in

Area of rectangle = L*W = 12.56*10 = 125.6 in²

Surface area of net = Area of the 2 circles + area of the rectangle

= 25.12 + 125.6 = 150.72 in²

4. Surface area of the net (S.A) = 2(area of triangle) + 3(area of rectangle)

= [tex] 2(0.5*b*h) + 3(l*w) [/tex]

Where,

b = 8 cm

h = [tex] \sqrt{8^2 - 4^2} = \sqrt{48} = 6.9 cm} (Pythagorean theorem)

w = 8 cm

[tex]S.A = 2(0.5*8*6.9) + 3(20*8)[/tex]

[tex]S.A = 2(27.6) + 3(160)[/tex]

[tex]S.A = 55.2 + 480[/tex]

[tex]S.A = 535.2 cm^2[/tex]

You see Bonnie rock climbing El Capitan. On your telescope is a clinometer. The angle
of elevation is 20 degrees. You know you are standing 950 feet away from El Capitan.
How high up is Bonnie?

Answers

Answer:

≈ 345.8 ft

Step-by-step explanation:

There is a right triangle formed by Bonnie's height (h) the ground and the angle of elevation.

Using the tangent ratio in the right triangle

tan20° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{h}{950}[/tex] ( multiply both sides by 950 )

950 × tan20° = h , thus

h ≈ 345.8 ft ( to 1 dec. place )

Solve 2(x - 5) = 48 - 4(x + 1)​

Answers

2(x - 5) = 48 - 4(x + 1)
2x - 10 = 48 - 4x - 4
6x = 54
x = 9

Answer:

x = 9

Step-by-step explanation:

first remove the brackets

2x - 5 = 48 - 4x + 1

then take numbers to the opposite sides

2x + 4x = 48 + 5 + 1

I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4

now solve

2x + 4x= 6x

48+5+1= 54

6x = 54

now solve for x

divide both sides by 6x

x = 9

LaShawn solved the equation below to the determine the solution.

3 x minus 8 = negative x + 4 (x minus 2)

Answers

Answer:

x = all real numbers.

Step-by-step explanation:

3 x minus 8 = negative x + 4 (x minus 2)

3x - 8 = -x + 4(x - 2)

3x - 8 = -x + 4x - 8

3x - 8 = 3x - 8

3x - 3x = -8 + 8

0 = 0

Since the result is a true statement, but 0 = 0, x is equivalent to all real numbers.

Hope this helps!

Answer:

Step-by-step explanation:

what are the squares from 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20 answer when multiplied by itself​

Answers

Answer:

I hope it helps :)

Step-by-step explanation:

[tex] {1}^{2} = 1 \times 1 = 1\\ {2}^{2} = 2 \times 2 = 4\\ {3}^{2} =3 \times 3 = 9\\ {4}^{2} = 4 \times 4 = 16 \\ [/tex]

[tex]{5}^{2} = 5 \times 5 = 25 \\ {6}^{2} = 6 \times 6 = 36 \\ {7}^{2} = 7 \times 7 = 49\\ {8}^{2} = 8 \times 8 = 64[/tex]

[tex] {9}^{2} = 9 \times 9 = 81 \\ {10}^{2} = 10 \times 10 = 100 \\ {11}^{2} = 11 \times 11 = 121 \\ { {12}^{2} } = 12 \times 12 = 144[/tex]

[tex] {13}^{2} = 13 \times 13 = 169 \\ {14}^{2} = 14 \times 14 = 196 \\ {15}^{2} = 15 \times 15 = 225 \\ {16}^{2} = 16 \times 16 = 256[/tex]

[tex] {17}^{2} = 17 \times 17 = 289 \\ {18}^{2} = 18 \times 18 = 324 \\ {19}^{2} = 19 \times 19 = 361 \\ {20}^{2} = 20 \times 20 = 400[/tex]

Step-by-step explanation:

Is this the answer you want? If nope inform me.i hope you just ignore my handwriting ☺️

Functions f(x) and g(x) are shown: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units

Answers

Answer:

Shift right by 4

Step-by-step explanation:

Given f(x)=x^2

g(x)= x^2-8x+16

Using

Horizontal Shift theorem dealing with the question

If the graph were to be move to to the right, we must use of graph f (x-L)

Where L= 4 and

NOTE:

POSITIVE L MAKES GRAPH SHIFT RIGHT

2) NEGATIVE MAKES GRAPH SHIFT LEFT

g(x)= x^2-8x+16

If we factorize this we have

(x-4)(x-4)

Since the two terms are the same we have (x-4)^2

Then it can move by factor of 4 to the right since constant 4 can be substracted from the parents function

Answer:

Left by 4

Step-by-step explanation:

graph x^2 and x^2 − 8x + 16 on Desmos . com

you start at f(x) and end at g(x)

Please solve, -7x+8=-4(x+1)​

Answers

Answer: [tex]x=4[/tex]

Simplify both sides of the equation.

[tex]-7x+8=-4(x+1)\\-7x+8=(-4)(x)+(-4)(1)(Distribute)\\-7x+8=-4x+-4[/tex]

Add 4x to both sides

[tex]-7x+8+4x=-4x-4+4x\\-3x+8=-4[/tex]

Subtract 8 from both sides

[tex]-3x+8-8=-4-8\\-3x=-12[/tex]

Divide both sides by -3

[tex]-3x/-3=-12/-3\\x=4[/tex]

Answer:

x=4

Step-by-step explanation:

Let's first simplify the equation.  

-7x+8= -4x-4                    

You get -4x-4 by distributing the -4 into the numbers in the parenthesis because -4 is right outside the parenthesis.

-4 times x= -4x

-4 times 1= -4

-7x+8= -4x-4

Next, move the -4x to where the -7x is because we want to combine like terms.  When a number moves to the opposite side, it changes from positive to negative or negative to positive.  Like here: -4x moves to a different side, so it becomes +4x.  

-7x+4x+8= -4  

Do the same for 8.  Since -4 is on the other side, move 8 to that side.  It turns from +8 to -8.

-7x+4x= -4-8

Combine like terms and solve.  

-7x+4x= -3x

-4-8= -12

So we have this now: -3x= -12

Since 12 divided by 3 is 4, and negative with negative is positive, it becomes positive 4. :)

solve for x 3(x+2) = 12

Answers

Answer:

x=2

Step-by-step explanation:

3(x+2) = 12

Divide by 3

3/3(x+2) = 12/3

x+2 = 4

Subtract 2 from each side

x+2-2 = 4-2

x =2

Answer:

The value of x is equal to 2.

Step-by-step explanation:

3(x + 2) = 12

Distribute 3 to (x + 2)

3x + 6 = 12

Subtract 6 from both sides of the equation.

3x = 6

Divide 3 on both sides of the equation.

x = 2

The value of x is 2

In 2002, the population of a district was 22,800. With a continuous annual growth rate of approximately 5% what will the population be in 2012 according to the exponential growth function?

Answers

Answer:

37,139

Step-by-step explanation:

Given the following :

Population in 2002 = Initial population (P0) = 22,800

Growth rate (r) = 5% = 0.05

Growth in 2012 using the exponential growth function?

Time or period (t) = 2012 - 2002 = 10years

Exponential growth function:

P(t) = P0 * (1 + r) ^t

Where P(t) = population in t years

P(10) = 22800 * (1 + 0.05)^10

P(10) = 22800 * (1.05)^10

P(10) = 22800 * 1.62889

P(10) = 37138.797

P(10) = 37,139 ( to the nearest whole number)

The average life of individual is 70 years. With a standard deviation of 5.5 years. Assume that the lives of these individuals is normally distributed. a. Find the probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years. b. Find the mean data value that separates the top 10% from the rest of the means computed from a random sample of size 5.

Answers

Answer:

The answer is below

Step-by-step explanation:

Given that:

mean (μ) = 70 years, standard deviation (σ)= 5.5 years.

a) The z score measures how many standard deviation a raw score is above or below the mean. It is given as:

[tex]z=\frac{x-\mu}{\sigma}[/tex], for a sample size of n, the z score is: [tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

Given a sample of 5 turtles, we have to calculate the z score for x = 60 and x = 80.

For x = 60:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{60-70}{5.5/\sqrt{5} } =-4.07[/tex]

For x = 80:

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{80-70}{5.5/\sqrt{5} } =4.07[/tex]

The probability that a mean life of a random sample of 5 such turtles falls between 60 and 80 years = P(60 < x < 80) = P(-4.07 < z < 4.07) = P(z < 4.07) - P(z < -4.07) = 1 - 0 = 1 = 100%

b) The z score that corresponds to top 10% is -1.28.

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\-1.28=\frac{x-70}{5.5/\sqrt{5} }\\ x-70=-3\\x=70-3\\x=67\ years[/tex]

¿Cuál es el área de un rectángulo, sabiendo que su perímetro mide 24 cm y que su base es el triple de su altura?

Answers

Answer:

El área del rectángulo es:

27 cm²

Step-by-step explanation:

Consideración:

La formula del perímetro de un rectángulo es:

p = 2(altura + base)

Planteamiento:

24 = 2(a+b)

b = 3a

a = longitud de la altura del rectángulo

b = longitud de la base del rectángulo

Desarrollo:

sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:

24 = 2(a + 3a)

24/2 = 4a

12 = 4a

a = 12/4

a = 3 cm

de la segunda ecuación del planteamiento:

b = 3a

b = 3*3

b = 9 cm

Comprobación:

de la primer ecuación del planteamiento:

24 = 2(3+9)

24 = 2*12

Respuesta:

la formula del área de un rectángulo es:

A = base * altura

A = 9cn * 3cm

A = 27cm²

The Area of rectangle is 27 unit².

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter = 24 cm

let the height of rectangle be x.

then the base= 3x

Now, Perimeter of rectangle= 2 ( l + w)

24 = 2( x+ 3x)

12 = 4x

x= 12/4

x= 3 units

So, length= 9 units and width= 3 units

Thus, Area of Rectangle= l x w

                                       = 9 x 3

                                       = 27 unit²

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The translated Question is:

What is the area of a rectangle, knowing that its perimeter measures 24 cm and that its base is three times its height?

A geometric sequence has a common ratio of 22 and the 12th12th term is −12,288.−12,288.

What is the explicit rule that describes this sequence?

Answers

Answer:

Tₙ = -3(2)ⁿ

Step-by-step explanation:

The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;

a is the first term of the geometric sequence

r is the common ratio

n is the number of terms

If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;

T₁₂ = ar¹²⁻¹

T₁₂ = ar¹¹

Given T₁₂ = -12,288 and r = 2, we can calculate the first term a

-12,288 = a2¹¹

a = -12,288/2¹¹

a =  -12,288/2048

a = -6

Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;

Tₙ = -6(2)ⁿ⁻¹

Tₙ = -6 * 2ⁿ * 2⁻¹

Tₙ = -6 * 2ⁿ * 1/2

Tₙ = -3(2)ⁿ

Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ

If f(x) = 3x^2 + 2 and g(x) = x^2- 9, find (f-g)(x).
O A. 4x2 - 7
O B. 2x2 +11
O c. 2x2 - 7
O D. 4x2 +11

Answers

Answer:

[tex] \boxed{\sf B. \ 2x^{2} + 11} [/tex]

Given:

f(x) = 3x² + 2

g(x) = x² - 9

To Find:

(f - g)(x)

Step-by-step explanation:

[tex]\sf (f -g)(x) = f(x) - g(x) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} + 2) - (x^{2} - 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} + 2 - x^{2} + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3x^{2} - x^{2} + 2 + 9 \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =(3x^{2} - x^{2}) + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + (2 + 9) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =2x^{2} + 11 [/tex]

In how many ways can we put five identical fruits into three bowls? Note that the bowls may be empty.

Answers

So u have 5 fruits and 3 bowls

Divide 5 into 3 that would equal how many grams you would put in one bowl then measure that and then complete it by adding that amount into each bowl

Xia Paul pale dye all’s shh eke eve when’s

10 points :) Graph this for me :P

Answers

Answer:

-2≤x≤2   f(x)=[x+3]

first  the sign is ≤ it means the point is solid point and the interval is x+3

what is a coterminal angles

Answers

Answer: Coterminal Angles are angles who share the same initial side and terminal sides. Finding coterminal angles is as simple as adding or subtracting 360° or 2π to each angle, depending on whether the given angle is in degrees or radians.

A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price

Answers

Answer:

162.5 Cedis

Step-by-step explanation:

Cost Price= 125

Profit % = 30%

Selling price=?

Selling price= Cost price+ profit

Profit = ?

[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]

[tex]30 \% = \frac{x}{125} \times 100[/tex]

[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]

[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]

Profit = 37.5 gh Cedis

Selling price= 125+37.5

Selling price= 162.5 gh Cedis

The selling price of a bag is 162.5Cedis.

It is required to find the selling price.

What is profit?

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.

Given that :

Let the profit be x.

Cost Price= 125

Profit % = 30%

profit%=profit/cp*100

30=profit/125*100

3750=100x

x=37.5

profit=37.5

Selling price= Cost price+ profit

Selling price=125+37.5

Selling price=162.5ghcedis

So, the selling price of a bag is 162.5Cedis.

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Find the distance across the lake. Assume the triangles are similar.
80 m
х
у
20 m
60 m

Answers

Answer:

a

Step-by-step explanation:

Answer:

A.   L = 240 m

Step-by-step explanation:

use similar triangle

L / 60 = 80 / 20

L = (80 * 60) / 20

L = 240 m

SOMEONE PLZ HELP ME!!!! I WILL GIVE BRAINLIEST!!!

Answers

Answer:

Step-by-step explanation:

Let the quadratic equation of the function by the points in the given equation is,

f(x) = ax² + bx + c

If the points lying on the graph are (-3, -10), (-4, -8) and (0, 8),

For (0, 8),

f(0) = a(0)² + b(0) + c

8 = c

For a point (-3, -10),

f(-3) = a(-3)² + b(-3) + 8

-10 = 9a - 3b + 8

9a - 3b = -18

3a - b = -6 --------(1)

For (-4, -8),

f(-4) = a(-4)² + b(-4) + 8

-8 = 16a - 4b + 8

-16 = 16a - 4b

4a - b = -4 ------(2)

Subtract equation (1) from equation (2)

(4a - b) - (3a - b) = -4 + 6

a = 2

From equation (1),

6 - b = -6

b = 12

Function will be,

f(x) = 2x² + 12x + 8

     = 2(x² + 6x) + 8

     = 2(x² + 6x + 9 - 9) + 8

     = 2(x² + 6x + 9) - 18 + 8

     = 2(x + 3)² - 10

By comparing this function with the vertex form of the function,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the function 'f' will be (-3, -10)

And axis of symmetry will be,

x = -3

From the given graph, axis of the symmetry of the function 'g' is; x = -3

Therefore, both the functions will have the same axis of symmetry.

y-intercept of the function 'f' → y = 8 Or (0, 8)

y-intercept of the function 'g' → y = -2 Or (0, -2)

Therefore, y-intercept of 'f' is greater than 'g'

Average rate of change of function 'f' = [tex]\frac{f(b)-f(a)}{b-a}[/tex] in the interval [a, b]

                                                               = [tex]\frac{f(-3)-f(-6)}{-3+6}[/tex]

                                                               = [tex]\frac{-10-8}{3}[/tex]

                                                               = -6

Average rate of change of function 'g' = [tex]\frac{g(b)-g(a)}{b-a}[/tex]

                                                                = [tex]\frac{g(-3)-g(-6)}{-3+6}[/tex]

                                                                = [tex]\frac{7+2}{-3+6}[/tex]

                                                                = 3

Therefore, Average rate of change of function 'f' is less than 'g'.

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