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).​

Answers

Answer 1

Answer:

The function 8(x) is a parabola that opens downward and is centered at (0,0). The domain of 8(x) is x∈R and the range of 8(x) is y∈[0,∞).

To arrive at the new function g(x), follow these steps:

Base Graph: The base graph of 8(x) is shown below.

Vertical Reflection: To reflect the parabola about the x-axis, multiply the function by -1. The new function is g(x) = -8(x).

Horizontal Reflection: To reflect the parabola about the y-axis, multiply the function by -1. The new function is now g(x) = 8(-x).

Horizontal and Vertical Translations: To translate the parabola 4 units to the left and 2 units up, add 4 to the x-coordinates and subtract 2 from the y-coordinates. The new function is g(x) = 8(x-4)-2.

The resulting graph is shown below. The domain of g(x) is x∈R and the range of g(x) is y∈[-2,∞).

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Related Questions

Please help me with this question.

Answers

The commission amount is $15250.

What is the percentage?

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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The ages of the students in an art class at the community center are listed below. 9, 11, 14, 14, 16, 21, 24, 26, 32, 33, 37, 38, 38, 52, 53, 55 Complete the frequency table

Answers

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.

How to identify the frequency of student ages?

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.

0 - 9 = 110 - 19 = 420 - 29 = 330 - 39 = 540 - 49 = 050 - 59 = 3

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Question 12: Hannah baked some chocolate, strawberry and vanilla cupcakes.
She baked four times as many chocolate as strawberry cupcakes.
She baked three times as many chocolate as vanilla cupcakes.
Altogether Hannah made 152 cupcakes.
How many cupcakes of each flavour did Hannah make?

Answers

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.

Chocolate cupcake be x=16
Strawberry cupcake be x/4=16/4=4
Vanilla cupcake be x/3=16/3=5.3=5

Explanation:-

Let the chocolate box be x
Therefore the strawberry be x/4
The vanilla be x/3
Now
x+x/4+x/3=152
12x+3x+4x/12=152
19x=152 x 12
x=152 x 2/19=16

Now Chocolate cupcake be x=16
Strawberry cupcake be x/4=16/4=4
Vanilla cupcake be x/3=16/3=5.3=5

36 9/10 − 18 6/10
Please help
Thanks :)

Answers

Answer:

i believe the answer is 18 3/10

Step-by-step explanation:

The answer is 183/10 or 18 3/10 or 18.3

A triangular prism and two nets are shown:

Which is the correct net of the prism and what is the surface area of the prism? (1 point)

A. Net B with 184 square inches
B. Net B with 248 square inches
C. Net A with 268 square inches
D. Net A with 540 square inches

Answers

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

What is the surface area of a triangular prism?

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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Let P(t)=36(1−e^(−kt))+56

represent the expected score for a student who studies t

hours for a test. Suppose k=0.24

and test scores must be integers.

Answers

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.

What is the exponential function?

The exponential function for this problem is defined as follows:

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

In which:

t is the number of hours studied for the test.P(t) is the expected grade.

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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Rewrite e^-2.5 =h as an equivalent logarithmic equation. Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c*ln(h).

Answers

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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WILL GIVE 30 POINTS
Suppose f is a function that takes a real number x and performs the following steps in the order given:
(1) add 8
(2) take the square root
(3) subtract 9
(4) divide into 12
f(x)=?

Answers

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

pls help
Which angle is supplementary to
∠FAE?

Answers

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.

There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 red?
helppp

Answers

The probability of getting exactly 1 red is 60/121

What is probability?

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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Nathan's lawnmower uses of a tank of gas to cut three one-acre
lawns. How many one-acre lawns can he cut with a full tank of
gas? Explain.

Answers

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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If the bisector of an angle of a triangle bisects the opposite side, the is the triangle isosceles. If true then enter 1 else if False enter 0

Answers

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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At Aaron's Automobile's, Bob sold $150,000 worth of cars last month. If Bob earns a 5% commission on his sales, how much did he make in
commission last month?
Bob's commission was

Answers

Answer: 7,500

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

a student runs an experiment to test how microwave power and temperature affect popping. each bag of popcorn can be popped for 3 minutes or 4 minutes. the microwave power can be set to low, medium, and high. each combination of time and power is tested on one bag of popcorn and the number of unpopped kernels is recorded. The number of treatments in this experiment are:
• 12
• 6
• 4

Answers

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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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 ________ .

Answers

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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Find the sum a + (a + 1) + (a + 2) + ... + (a + n - 1) in terms of a and n.
Part (b): Find all pairs of positive integers (a,n) such that n greater than 2 and a + (a + 1) + (a + 2) + ... + (a + n - 1) = 100.

Answers

(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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Use the area model and the distributive property to find 14×27 find each partial product and then find the product

Answers

The value of the product is 378

How to determine the product

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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Calculer la moyenne de la série suivante :

Valeurs 7 8 9 10 11 12 13 14 15 16 18
Effectifs 7 1 1 1 1 3 2 1 1 1 1


On donnera la réponse sous la forme d'un entier relatif ou d'un nombre décimal.

Answers

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.

Will reward please help

Answers

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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How long does it take a 2000-Kg car to stop from a velocity of 35 m/s if a braking force of 4000 Newtons is used?

Answers

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.

Do you have enough information to show that AKIM = ANLM? If so, explain why they are congruent. If not, what information do you need?

Answers

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

What is a congruent triangle?

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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in 2013, kai renters a 2-bedroom apartment for $836. last year, 2022, kai renewed her lease and the rent had increased to $1549. if the rise in rent for kai’s apartment was liner how much was her rent payment in 2016

Answers

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

What is a linear equation?

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)

Linear Equation:

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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A pile is a post-like support made of timber, steel, or concrete used in foundations that are driven deep into the ground to support structures such as piers. While the tide is out, a pile at Old Pier in Naples Florida, casts a shadow that is 31 inches long. At the same time, a person standing on the shore who is 6 feet 4 inches tall casts a shadow that is 45 inches long. How much of the pile is above the water? Round your answer to the nearest feet and inches.

Answers

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

What are ratio and proportion?

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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A 12-ounce soda can has a height of 4.875 inches. What is its average diameter in
inches?
8 ounces = 1 cup, 16 cups = 1 gallon,
7.48 gallons = 1 ft3, 1 foot = 12 inches.

Answers

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

What is the volume?

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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I added a screenshot.

Answers

The solution is Option C.

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

What is union and intersection of sets?

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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PLEASE HELPP!!’
The population of six different states as shown below drag and drop the populations from the source to the target in order of greatest to least value

Answers

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

CaliforniaFlorida New YorkWashington Massachusetts Arizona

What is the population in order ?

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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6.The letters a, e, i, o, u are called__________________

Answers

Answer:Vowels

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

Vowels
A, e, I, o, u are called vowels and sometimes the letter y is a vowel

A country road is 27 miles long and goes all the way around a lake, connecting the six cottages that
are next to the lake. Two of the cottages are 1 mile apart (along the road). Two cottages are 2 miles
apart, two are 3 miles apart, two are 4 miles apart..... two are 25 miles apart, and two are 26 miles
apart. How are the cottages distributed along the road? Find a second way to distribute
them. Explain your thinking.

Answers

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.

PLSSSS HELPPPP ME TY

Answers

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

Lashonda has received scores of 95, 82, 89, 70, and 76 on her first five exams. Her goal is to achieve a final average of 80. What score must she receive on the last exam to realize her goal?


Possible answers
1. 86
2. 75
3. 68
4. 80

Answers

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

What is score?

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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