MCR3U0 Name: e) Sketch the function 8(x) and state the domain and range of the transformed function g(x). Important: On the same grid, use step-by-step transformations to arrive at the required new function. Use a different colour for each step and include a legend stating the equa tion of each new graph. The transformations should be shown in the following order. 1. Base Graph 2. Vertical reflection/stretch/compression (if any). 3. Horizontal reflection/stretch/compression (if any). st 4 Horizontal and Vertical translations (if any).​

Answer:

Step-by-step explanation:

The total length of the road is 27 miles, and since each cottage is separated from its neighbor by a distance of 1, 2, 3, 4, ..., 25, or 26 miles, the total length of the road occupied by these distances must sum to 27 miles. This is because the road connects the six cottages.

One possible distribution is:

Cottage 1 and 2 are 1 mile apart.

Cottage 3 and 4 are 2 miles apart.

Cottage 5 and 6 are 3 miles apart.

Cottages 1 and 3 are 4 miles apart.

Cottages 2 and 4 are 5 miles apart.

Cottages 3 and 5 are 6 miles apart.

Cottages 4 and 6 are 7 miles apart.

...

Cottages 1 and 6 are 25 miles apart.

Cottages 2 and 5 are 26 miles apart.

A second possible distribution can be obtained by reversing the order of the distances between the cottages. That is:

Cottages 2 and 5 are 26 miles apart.

Cottages 1 and 6 are 25 miles apart.

Cottages 4 and 6 are 7 miles apart.

Cottages 3 and 5 are 6 miles apart.

Cottages 2 and 4 are 5 miles apart.

Cottages 1 and 3 are 4 miles apart.

Cottage 5 and 6 are 3 miles apart.

Cottage 3 and 4 are 2 miles apart.

Cottage 1 and 2 are 1 mile apart.

There may be other possible distributions, but these two demonstrate that there are multiple ways to arrange the distances between the cottages while still satisfying the constraint that the distances must sum to 27 miles.

The surface area of the triangular prism will be 540 square inches. Then the correct option is D.

Let h be the height and b be the base of the triangle. Let L₁, L₂, and L₃ be the length and W be the width of the rectangle. Then the surface area of the triangular prism will be given as,

Surface area = 2 Area of triangle + 3 Area of rectangle

Surface area = (h x b) + (L₁ + L₂ + L₃) x W

The surface area of the triangular prism is given as,

SA = (5 x 12) + (5 + 12 + 13) x 16

SA = 60 + 30 x 16

SA = 60 + 480

SA = 540 square inches

The surface area of the triangular prism will be 540 square inches. Then the correct option is D.

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Based on the slope, which describes a linear equation, the rent payment of Kai in 2016, was $1,073.66.

A linear equation is an algebraic equation written in the form of y=mx+b.

A linear equation involves a constant and a first-order term, where m is the slope and b is the y-intercept.

Kai's rental payment in 2013 = $836

Kai's rental payment in 2022 = $1,549

Slope = Rise/Run

Rise (Difference in rent between the two periods = $713 ($1,549 - $836)

Run = (Difference in the years) = 9 (2022 - 2013)

Slope = $79.22 ($713/9)

Let the number of years between 2013 and the stated year = x

Run = 3 (2016 - 2013)

y = mx + b

Rent in x years = 836 + 79.22x

= 836 + 79.

= $1,073.66 (836 + 79.22(3)

Thus, solving the linear equation, Kai's rental payment in 2016 was $1,073.66.

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Answer:

Below

Step-by-step explanation:

Volume of a cylinder = pi r^2 h

the volume of this FULL pool = 2 x 56.52 = 113.04 ft^3

    the radius is 1/2 of the diameter = 3 ft

V = pi r^2 h     <======re-arrange to

V / (pi r^2) = h

so your equation at the bottom would be

113.04  ÷ 3^2 ÷ 3.14

The probability of getting exactly 1 red is 60/121

Probability theory, a branch of mathematics concerned with the analysis of random phenomena.

There is a bag filled with 5 blue and 6 red marbles.

A marble is taken at random from the bag, the color is noted and then it is replaced. Another marble is taken at random.

It is required to find the probability of getting exactly one red marble.

Now, the red marble can occur on the first draw or the second draw.

The probability of getting exactly 1 red marble from the first draw will be,

P(1) = 6/11 x 5/11

p(1) = 30/121

The probability of getting exactly 1 red marble from the second draw will be,

P(2) = 6/11 x 5/11

p(2) = 30/121

So, the total probability of the event will be,

P = P(1) + P(2)

P =  30/121 +  30/121

P = 60/121

hence, the probability of getting exactly 1 red is 60/121

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Answer:

<FAB

Step-by-step explanation:

Supplemental angles add to 180. They make a straight line.

Supplementary angles add up to 180°. Using this knowledge, write an equation with the given information:

x°+45°=180°

Subtract 45° from both sides:

x°=135°

We now know that we're looking for an angle in the figure that equals 135°. Notice that ∠BAF accomplishes this, therefore ∠BAF is supplementary to ∠FAE.

The commission amount is $15250.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the selling price of the house is $305000. The value of the commission will be calculated as:-

Commission = ( $305000 x 5% ) / 100

Commission = $15250

Therefore, the commission amount is $15250.

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In mathematical terms, the equation e^-2.5 = h states that the exponential value of -2.5 (e^-2.5) is equal to the variable h. To convert this equation into its logarithmic form, we can take the natural logarithm of both sides of the equation. The natural logarithm, represented by the function ln, returns the power to which e must be raised to obtain a given number.

So, taking the natural logarithm of both sides of the equation, we have:

ln(e^-2.5) = ln(h)

Since ln(e^x) = x, we can simplify the left side of the equation:

ln(h) = -2.5

Thus, the logarithmic equivalent of the equation e^-2.5 = h is ln(h) = -2.5.

The logarithmic equation ln(h) = -2.5 can be interpreted as follows: the natural logarithm of h is equal to -2.5. In other words, h is the result of raising e to the power of -2.5. To find the value of h, we can use the exponential function:

h = e^-2.5

Therefore, the original equation e^-2.5 = h and the logarithmic equation ln(h) = -2.5 are mathematically equivalent and can be used interchangeably.

It is worth mentioning that logarithms are used in many areas of mathematics and science, including engineering, finance, and physics. They allow us to simplify complex calculations and to solve problems that are otherwise difficult or impossible to solve.

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Answer: f(x) = (x+8)^(1/2) - 9 / 12

Step-by-step explanation:

To find f(x), we need to apply the steps given in the problem in the order they are presented.

First, we add 8 to the input value x. This step is represented by the term x+8.

Next, we take the square root of the result from step 2. This step is represented by the exponent (1/2) on the term x+8.

Next, we subtract 9 from the result of step 3. This step is represented by the term -9.

Finally, we divide the result of step 4 by 12. This step is represented by the division operator '/' and the denominator 12.

So f(x) is a function that takes the input x, adds 8, takes the square root, subtracts 9, and divides by 12.

Answer:

f(x) = [√(x + 8) - 9]/12

Step-by-step explanation:
The expression f(x) begins with ->

Step 1: x + 8
Step 2: √(x + 8)
Step 3: √(x + 8) - 9
Step 4: [√(x + 8) - 9]/12

The equation is now:
f(x) = [√(x + 8) - 9]/12

Option • 12 is the answer .The number of treatments in the experiment is 12.

The understudy is directing a trial to comprehend the connection between microwave power and time on the quantity of unpopped bits in a pack of popcorn. There are three degrees of microwave power: low, medium, and high. Each sack of popcorn can be popped for either 3 minutes or 4 minutes, which provides us with a sum of double cross variables. To cover every one of the potential mixes of time and power, the understudy runs 12 distinct medicines (3 degrees of force x 2 degrees of time). Every treatment addresses one sack of popcorn that is popped for a particular time frame and with a particular power setting. The quantity of unpopped parts is recorded for every treatment, and the outcomes are utilized to make determinations about the impacts of microwave power and time on the quantity of unpopped pieces.

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Triangles KLM and NLM are said to be congruent are they are identical with the same measurement of angles and edges.

A congruent triangle is the triangle that equal sides and angles when measured. That is to say the two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

The side are equal= KM = MN; KL = NL

The angles are equal= < LKM = <LNM

Therefore, from the diagram given above concerning the triangles, they are both congruent.

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The factor which the function grows is 16.

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is g(x)=[tex]4^x[/tex]

Now to find the factor of the interval 14 to 16 then,

put x=14 into g(x) then

=> g(14) = [tex]4^{14}[/tex]

put x=16 into g(x) then

=> g(16) = [tex]4^{16}[/tex]

Now the factor which function grows is,

=> [tex]\frac{g(16)}{g(14)}[/tex]

=> [tex]\frac{4^{16}}{4^{14}}[/tex]

=> [tex]4^2[/tex]

=> 16.

Hence the factor which the function grows is 16.

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Answer:

i believe the answer is 18 3/10

Step-by-step explanation:

Answer:Vowels

The letters a, e, i, o, u, are vowels and other letters are considered consonants.

The value of the product is 378

To find 14 x 27 using the area model and the distributive property

We can find the partial products and then add them up to find the final product.

First, we use the distributive property to expand the expression:

14 x 27 = (10 + 4) x 27 = 10 x 27 + 4 x 27

Next, we find the partial products:

10 x 27 = 270

4 x 27 = 108

Finally, we add the partial products to find the final product:

270 + 108 = 378

So, 14 x 27 = 378.

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In order for Lashonda to achieve a final average of 80, she must receive a score of 86 on her last exam.

Score is a numerical value or result that is used to indicate the performance or achievement of an individual or team in a particular activity or game. A high score indicates excellence or success while a low score indicates the opposite. Score is often used to track progress and can be used to compare individuals or teams against each other. Score can also be used as a measure of progress or improvement.

To calculate her score, we add up all of her previous exam scores (95 + 82 + 89 + 70 + 76) and divide them by 6 (the number of exams taken). This gives an average of 81. We then subtract the current average (81) from her desired average (80) to arrive at the score she must receive on her last exam (86).

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The highest integer that the student can possibly score is given as follows:

92.

If the student does not study, the grade that he should expect is of:

56.

The exponential function for this problem is defined as follows:

P(t) = 36(1 - e^(-0.24t)) + 56.

In which:

The highest grade is for large values of t, meaning that e^(-0.24t) = 0, and thus:

P(t) = 36 + 56

P(t) = 92.

If the student does not study, we have that t = 0, hence the grade is given as follows:

P(0) = 36(1 - e^(-0.24 x 0)) + 56

P(0) = 0 + 56

P(0) = 56.

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Let's call the number of strawberry cupcakes "s".

So the number of chocolate cupcakes is 4s and the number of vanilla cupcakes is 3s.

Altogether, Hannah made s + 4s + 3s = 8s cupcakes.

We know that Hannah made 152 cupcakes, so 8s = 152

Therefore, s = 19

So Hannah made 19 strawberry cupcakes, 4 * 19 = 76 chocolate cupcakes, and 3 * 19 = 57 vanilla cupcakes.

Nathan can cut 3 one-acre lawns with a full tank of gas

What is Cross multiplying fractions?

Cross multiply fractions by multiplying one fraction's denominator by the second fraction's numerator and then comparing the two values. The larger fraction is the one with the higher value.

Since Nathan's lawnmower uses one tank of gas to cut three one-acre lawns, it means that he can cut one one-acre lawn with 1/3 of a tank of gas. So, if he has a full tank of gas, he can cut one-acre lawns equal to the number of times 1/3 fits into a full tank. In other words, he can cut a full tank of gas divided by 1/3 of a tank of gas.

The number of one-acre lawns Nathan can cut with a full tank of gas is:

1 tank / (1/3 tank) = 3 one-acre lawns.

So, Nathan can cut three one-acre lawns with a full tank of gas.

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Answer:

To find the time it takes for a car to stop from a velocity of 35 m/s using a braking force of 4000 N, we can use the following formula:

vf = vi + at

where

vf = final velocity (0 m/s in this case, since the car is stopping)

vi = initial velocity (35 m/s)

a = acceleration, which can be calculated as a = F/m, where F is the braking force (4000 N) and m is the mass of the car (2000 kg)

t = time

Rearranging the formula:

t = (vf - vi)/a = (0 - 35) / (4000 / 2000) = (35) / (2) = 17.5 s

Answer:

It takes the car 17.5 seconds to stop from a velocity of 35 m/s with a braking force of 4000 N.

Answer:

Pour calculer la moyenne, nous devons multiplier chaque valeur par sa fréquence, additionner tous les produits, puis diviser par la fréquence totale.

Le calcul ressemblerait à ceci :

(7 * 7) + (8 * 1) + (9 * 1) + (10 * 1) + (11 * 1) + (12 * 3) + (13 * 2) + (14 * 1) + (15 * 1) + (16 * 1) + (18 * 1)

= 49 + 8 + 9 + 10 + 11 + 36 + 26 + 14 + 15 + 16 + 18

= 238

Fréquence totale = 7 + 1 + 1 + 1 + 1 + 3 + 2 + 1 + 1 + 1 + 1 = 21

Moyenne = 238/21 = 11,333

La moyenne de la série est de 11,3333.

The statement given is true. When the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles.

In the attached picture of ΔABC, we can see that AD is the bisector of ∠A that meets BC in D, so that BD = DC.

Now, we need to prove that AB = AC.

As construction, produce AD to E so that AD = DE, and then join CE.

So, in ΔABD and ΔECD, we have:

BD = CD

AD = ED

and ∠ADB = ∠EDC because those are vertically opposite angles.

Consequently, based on SAS congruence criterion, ΔABD ≅ ΔECD.

Thus, AB = EC and ∠BAD = ∠CED. And also, ∠BAD = ∠CAD.

For that reason, it means ∠CAD = ∠CED, and AC = EC.

Hence, AB = AC. It is proved that the triangle is isosceles.

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(a) The sum a + (a + 1) + (a + 2) + ... + (a + n - 1) is Sn = n/2 * (a + n)

It can be represented as the sum of an arithmetic series. The nth term of the series is (a + n - 1) and the first term is a.

The common difference between consecutive terms is 1. The formula to calculate the sum of an arithmetic series is:

[tex]Sn = n/2 * (2a + (n - 1)d)[/tex]

Where n stands for the number of terms, a will be the first term, and d is a common difference. By substituting the values for n, a, and d, we'll get:

Sn = n/2 * (2a + (n - 1) * 1)

Sn = n/2 * (2a + n - 1)

Sn = n/2 * (a + n)

(b) The pairs of positive integers (a,n) that will fulfill the conditions are (10,10), (15,8), and (20,6).

To find all pairs of positive integers (a,n) such that n is greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100, we can rearrange the formula from the above problem part (a) to solve for a:

Sn = n/2 * (a + n) = 100

a = 2 * (100/n) - n

Since a must be a positive integer, we can use trial & error to find all possible values of n that make a positive integer. Here are some of the solutions:

For n = 10, a = 10.

For n = 8, a = 15.

For n = 6, a = 20.

So the pairs of positive integers (a,n) that satisfy the conditions are (10,10), (15,8), and (20,6).

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The populations of states in order of greatest to least value would be:

To find the populations of the state and compare them accurately, you need to convert the populations from scientific notations to standard form.

Population of Florida :

= 1. 98 x 10 ⁷

= 19, 800, 000 people

Washington :
= 7. 06 x 10 6

= 7, 060, 000 people

California:

= 3.88 x 10 ⁷

= 38, 800, 000 people

Massachusetts :

= 6. 74 x 10 ⁶

= 6, 740, 000 people

This shows that the order of the most populous states is California, Florida, New York, Washington, Massachusetts and then Arizona.

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According to the information, the frequency table would look like this: 0 - 9 = 1, 10 - 19 = 4, 20 - 29 = 3, 30 - 39 = 5, 40 - 49 = 0, 50 - 59 = 3.

To identify the frequency of the ages of the students we must analyze the information on the age of each student. Once we have this information we must classify each student in a range. Later we must count how many students we have in each range to identify the frequency.

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Answer: 7,500

Step-by-step explanation: 5% of 150,000 is 7,500.

The height of the pile above the water is 4 feet 4 inches.

A ratio is a comparison between two similar quantities in simplest form.

Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.

In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.

We know 1 foot is equal to 12 inches.

6 feet 4 inches = 6×12 = 4 = 76 inches.

let, The height of the pole above the sea is 'x' inches.

Therefore,

x : 31 : : 76 : 45.

x/31 = 76/45.

x = 31×1.68.

x = 52. 35 inches.

or 4 feet 4 inches.

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The solution is Option C.

The value of the set n ( A' ∪ B' ) = n ( A ∩ B )' = 15

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

From the Venn diagram , we get

n ( A ) = { 3 , 1 }

n ( B ) = { 7 , 1 }

And , n ( A ∩ B ) = { 1 }

And , the universal set n ( U ) = { 5 , 3 , 1 , 7 }

From the set theory , we get

Now , the value of n ( A' ∪ B' ) = n ( A ∩ B )'

n ( A ∩ B )' = n ( U ) - n ( A ∩ B )

n ( A ∩ B )' = { 5 , 3 , 1 , 7 } - { 1 }

So , n ( A ∩ B )' = { 3 , 7 , 5 }

And , n ( A ∩ B )' = 3 + 7 + 5 = 15

Hence , the set n ( A ∩ B )' is 15

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The average diameter of a can in inches is 2.4 inches.

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, a 12-ounce soda can has a height of 4.875 inches.

We know that, 1 ounce = 1.805 cubic inches

Here, 12 ounce = 21.6563 cubic inches

As we know, volume of cylinder is πr²h.

Now, 21.6563 = 3.14×r²×4.875

21.6563 =r²×15.3075

r²=21.6563/15.3075

r²=1.414

r=1.2 inches

Then, diameter = 2.4 inches

Therefore, the average diameter of a can in inches is 2.4 inches.

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The equation representing the amount spend on salad and pizza is       E = 5S + 2P , P in terms of E and S is P = (1/2)(E - 5S) and the completion of table is given by:

Budget        Bowls of salad    Slice of pizza

$40.00              0                         20

$40.00              4                         10

$40.00             8                         0

Let 'E' represents the dollars spends on salad and pizza.

'S' represents the bowls of salad, 'P' represents the slice of pizza

Cost of bowl of salad = $5.00

Cost of slice of pizza = $2.00

Equation represents dollars spends on salad and pizza is :

E = 5S + 2P

Equation representing P in terms of E and S is:

P = (1/2)(E - 5S)

If E = $40.00

Then to make equation true value of S and P for the table is:

E = $40.00

S = 0

40 = 5(0) + 2P

⇒P = 20

E = $40.00

S = 4

40.00 = 5(4) + 2P

⇒P = 10

E = $40.00

P = 0

40.00 = 5S + 2(0)

⇒S = 8

In table form:

Budget        Bowls of salad    Slice of pizza

$40.00              0                         20

$40.00              4                          10

$40.00              8                          0

Therefore, the equation representing total amount of money spend is

E = 5S + 2P , representation of P in terms of E and S is P = (1/2)(E - 5S) and complete table is equal to :

Budget        Bowls of salad    Slice of pizza

$40.00              0                         20

$40.00              4                          10

$40.00              8                          0

Paolo is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $5.00, and slice of costs $2.00.Let E be the amount in dollars that Paolo spends on salad and pizza. If Paolo buys S bowls of salad and P slices of pizza, then the total amount of money he spends E can be represented by the equation _____.Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation _____.Suppose Paolo has $40.00 to spend on salad and pizza; that is E = $40.00Complete the following table with values of S or P that make the equation true. To complete the first row, determine the number of pizza slices Paolo can purchase with $40.00, when the number of salad bowls he purchases is 0.Budget (Dollars) Salad (Bowls) Pizza (Slice)40.00 0 _____40.00 4 _____40.00 _____ 0

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