f(x) = 3x - 4 and g(x) = x2 + 1. Find each of the following and simplify the answers. Show all steps (a) (fog)(x)
(b)(gof)(x)

Where the above conditions exist,

The random variable T = L + C represents the total time it takes Lorelei and Chance to finish a randomly selected 3-layer wedding cake. Since L and C are independent and Normally distributed, T is also Normally distributed with mean:

Mu_T = Mu_L + Mu_C = 37 + 52 = 89

and variance:

Var(T) = Var(L) + Var(C) = 12^2 + 7^2 = 193

So the standard deviation of T is:

Sigma_T = sqrt(Var(T)) = sqrt(193) = 13.89

The shape of T is also Normally distributed, since it is a sum of two independent Normally distributed variables.

To find the probability that Lorelei and Chance finish a randomly selected 3-layer wedding cake in under 90 minutes, we need to calculate the z-score for this value and then find the corresponding probability from the z-table. The z-score is:

z = (90 - 89) / 13.89

= 0.072

From the z-table, we find that the probability of a Z-score less than or equal to 0.072 is 0.5287.

Therefore, the probability that Lorelei and Chance totally finish a randomly selected 3-layer wedding cake in under 90 minutes is 0.5287 or approximately 53%.

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Answer: B.

Step-by-step explanation: (0, 2), (2, 0), and (1, -1) are the correct coordinates of the three vertices of the triangle.

Answer: 4/5

Step-by-step explanation:

Answer:

8 i used a triangular calucator

Step-by-step explanation:

The respective values of x after solving the given equalities are 2.5, -0.5, 9/8 and 1/2.

1. a) -3(x + 2) - 1 = 1 + 2(1 - 2x)

Expanding the left-hand side: -3x - 9 - 1 = 1 + 2 - 4x

Expanding the right-hand side: -3x - 9 - 1 = 1 - 4x

Solving for x: -4x = -10

x = 2.5

b) (3 - 2x)/4 = 1 - 3z

Multiplying both sides by 4: 3 - 2x = 4 - 12z

Adding 2x to both sides: 3 = 2x + 4 - 12z

Adding 12z to both sides: 3 = 2x + 4

Subtracting 4 from both sides: -1 = 2x

Dividing both sides by 2: -0.5 = x

c) (2x -1)/ 5 = (3 - 2x)/3

Cross multiplying: 3(2x - 1) = 5(3 - 2x)

Expanding the left-hand side: 6x - 3 = 15 - 10x

Expanding the right-hand side: 6x - 3 = 15 - 10x

Solving for x: 16x = 18

x = 9/8

d) 3x - 2x = 1 - x

Combining like terms on the left-hand side: x = 1 - x

Solving for x: 2x = 1

x = 1/2

2. a) {1, 2, 3, ...} is set of positive integers

b) {-2, -1, 0, 1, 2, ...} is set of integers

c) {a/b | a, b E Z; b =/ 0} is set of rational numbers.

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Answer: 2x^2-2x+10

Step-by-step explanation:

since f(x) = x^2+2x-1, and you have to find 2 f(x), you would put it as 2(x^2+2x-1)

Solving this would give you 2x^2+4x-2

you do the same thing with g(x) but put -3 un front of the equation. And then you add like terms

I hope this helped :)

Ok, let's find the side HT to help us decide:

Clearing HT:

And, now let's find SW:

And finally let's calculate the angles:

We know that angles T and Q are equal to 90°

M=arccos(30/32)=arccos(0.9375)=20.36

Q=arc cos(44/48)=arccos=23.55

So, finally we have that ΔMTH ~ ΔQWS is similar by SAS.

Answer:

8, 2, 4

Step-by-step explanation:

All the y values of a function are its range and all the x values are its domain

Since the y values of the functions are 8, 2, and -4. the range of this function{(4,8), (9,2), (-3,-4)} will be 8, 2, -4.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

All the y values of a function are its range and all the x values are its domain

All y's potential values are referred to as the function's range. Using the formula y = f(x), one may determine a function's range (x). If there is just one y value for each x value in a relation, then it is merely a function.

The y values of the functions are 8, 2, and -4.

Thus, since the y values of the functions are 8, 2, and -4. the ranges of this function{(4,8), (9,2), (-3,-4)} will be 8, 2, -4.

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Answer:

Step-by-step explanation:

Answer:

C.) f(x) = 2x^2 + 4x + 4

Step-by-step explanation:

The equation of the parabola with vertex (h,k) is y=a(−h+x)^2+k.

Thus, the equation of the parabola is y=a(x+1)^2+2.

To find a, use the fact that the parabola passes through the point (2,20): 20=9a+2.

Solving this equation, we get that a=2.

Thus, the equation of the parabola is y=2(x+1)^2+2.

TO STANDARD FORM

= 2*(x^2+2x+1)+2  

=(2x^2+4x+2)+2  

= 2x^2+4x+2+2  

= 2x^2+4x+4

A ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

So, e are informed that the volume is halved, and the pressure increases by a factor of 2.5.

We shall therefore have:

PVγ = 2.5P(0.5V)γ

We'll condense this to:

(1/0.5)γ = 2.5

γ = In2.5/In2

γ = 1.32

The volume temperature relation is written as follows if the volume expands in an adiabatic process:

T1V1∧γ-1 = T2V2∧γ-1

T1V1∧1.32-1 = T2(0.5V1)∧1.32-1

Condensing this results in:

T₁ = 1.24T₂

Therefore, a ratio in mathematics displays how often one number occurs in another and the given situation's specific heat ratio is 1.24.

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Answer:

true

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

A pE x

Answer:

(4,1)

Step-by-step explanation:

hope that can help!!

Answer:

60 sq m

Step-by-step explanation:

Area of the figure

= Area of top rectangle + Are of the bottom rectangle

= 5*3 + 5*(3+3+3)

= 15 + 5*9

= 15 + 45

= 60 sq m

Answer:

60 m²

Step-by-step explanation:

Area of the figure

= Top rectangle vertical + Bottom rectangle horizontal

= 3 x 5 + 5 x 9

= 15 + 45

= 60 m²

Brand A: Price = $18.75

Brand B: Price = $15

Brand C: Price = $21.25

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

original price = $25.00.

Brand A:

Discount = 25%

So, Price after discount = 25 - 25% of 25

                                       = 25 - 0.25 x 25

                                       = $18.75

Brand B:

Discount = 40%

So, Price after discount = 25- 40% of 25

                                       = 25 - 0.40x 25

                                       = $15

Brand C:

Discount = 15%

So, Price after discount = 25 - 15% of 25

                                       = 25 - 0.15 x 25

                                       = $21.25

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The completed relationship is:

0.001 grams = 0.0000000551 µg

To complete the relationship, we need to convert the units of the left-hand side and simplify the right-hand side.

Starting with the left-hand side:

1 mg = 1 milligram = 0.001 grams

Now, we can substitute this into the relationship:

For the right-hand side:

1100 in binary is equal to\(12^3 + 12^2 + 02^1 + 02^0 = 8 + 4 = 12\)

10001000 in binary is equal to \(12^7 + 02^6 + 02^5 + 02^4 + 12^3 + 02^2 + 02^1 + 02^0 = 128 + 8 = 136\)

100 in binary is equal to \(12^2 + 02^1 + 0*2^0 = 4\)

Now, we can substitute these values into the relationship:

0.001 grams = 12 µg / 136 / 4

Simplifying the right-hand side:

12 µg / 136 / 4 = 12 * (1/1000000) * (1/136) * (1/4) = 0.00000005514706...

Rounding this to a reasonable number of significant digits, we get:

0.0000000551

Therefore, the completed relationship is:

0.001 grams = 0.0000000551 µg

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Answer:

c

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

One number is 3 times another

x and 3x

difference between the numbers is 14,

3x - x = 14

simplify

2x = 14

Divide both sides by 2

x = 7

3x = 21

Answer:

The larger number is 21.

Step-by-step explanation:

let, the smaller number be x.

the larger number be 3*x =3x.

Now,

3x-x=14

or, 2x=14

or, x=14/2

x=7

here,

3x=3*x=3*7=21

The overall relapse rate from this study would be =58.3%.

To calculate the relapse rate , the the proportion of all the individuals that have a relapse should be converted to a percentage as follows:

The total number of individuals that has relapse= 28

The total number of individuals under study = 48

The percentage = 28/48 × 100/1

= 58.3%

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The expression for the total floor-space area which is square of the room would be total_area = side_length * side_length

The total floor-space area of the room can be calculated by multiplying the length of one side of the room by itself (since it's a square).

Assuming the length of one side of the room is stored in the variable "side_length", the expression for the total floor-space area of the room would be:

total_area = side_length * side_length

However, based on the information provided, it seems like the dimensions of the room are determined by the lengths of the smaller and larger pieces of sheetrock (stored in the variables "small" and "large"). If we assume that the room is a rectangle, with the smaller piece of sheetrock determining the length of one side and the larger piece determining the length of the other side, the expression for the total floor-space area of the room would be:

total_area = small * large

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After printing the long pdf Document of 47 pages , the remained balance in Fathi's printing account is -$4.90 ..

In mathematics, a basic algebraic operation is any of the common arithmetic operations, including addition, subtraction, multiplication, division, raising integers to powers, and taking square roots.

We have given that,

Total or initial balance of fathi's printing account

= $1.10

Each sheet of paper reduce his balance by $0.25..

Total number of pages in pdf document

= 47

He wants to print this pdf document.

When he print both sides of paper then it reduce the counts of paper used for printing the pdf.

That's if he print only one side then he will print 47 pages but now, he print on both sides .

so, total pages used to print pdf Document= 47/2

= 23 both sided printed + 1 one side printed = 24 pages

Using all provided details, we get

After Fathi print, the balance in his printing account = Initial balance - 24 × balance reduce by each page print

= $1.10 - 24 × $0.25 = $1.10 - $ 6

= - $4.90

Hence, - $4.90 balance in his printing account.

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Answer: y ≥ \(\frac{3}{2}\)x + 3

Step-by-step explanation:

       Since the shaded area is above the line, we will use either > or ≥ for our inequality.

       Next, since this is a solid line we will use the ≥ symbol for our inequality. This means the answer is the first option.

The solution to the equation in the given interval is 2.365

From the question, we have the following parameters that can be used in our computation:

3sin(2x - 4) = 2

Divide both sides of the equation by 3

So, we have the following representation

sin(2x - 4) = 2/3

Take the arcsin of both sides

This gives

2x - 4 = 0.73

Evaluate the like terms

2x = 4.73

Divide by 2

x = 2.365

Hence, the value of x is 2.365

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Step-by-step explanation:

p=2l+2w

p-2w=2l

p-2w = l

2

The superposition is the imposing of one wave on the other and resulting in the change of the amplitude of the final wave.

When two or more waves travel through the same space in superposition, their combined amplitudes equal the amplitudes they would have produced individually. For instance, two waves moving in the same direction will pass through each other without causing any distortion on the other side.

The pattern you see when shining light through two slits, the sounds you hear in acoustically sound rooms and music halls, the interference radios receive when moved close to other electronic devices, and any tone produced by a musical instrument are all examples of the superposition principle in action.

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Answer: 58

Step-by-step explanation:

180-114= 66

66+56=122

180-122= 58

Given data:

In a rectangle the opposite sides are always parallel and equal.

The number of 8 adults will supervise 48 children, 66 children will be supervised by 11 adults and 15 adults will supervise 90 children.

According to the question,

We have the following information:

1 adult supervises 6 children.

Now, for the first one, we have to find number of children to be supervised by 8 adults.

1 adult = 6 children

8 adults = 8*6 children

8 adults = 48 children

Now, for the second one, we have to find the number of adults for 66 children:

1 children = 1/6 adult

66 children = 66/6 adults

66 children = 11 adults

Now, for the third one, we have to find number of children for 15 adults:

15 adults = 15*6 children

15 adults = 90 children

Hence, the number of 8 adults will supervise 48 children, 66 children will be supervised by 11 adults and 15 adults will supervise 90 children.

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Answer: First is 48 Second is 11 Third is 90

Step-by-step explanation: I did it on Khan ✔

Answer:

f(y - 3) = y - 2

Step-by-step explanation:

to find f(y - 3) , substitute x = y - 3 into f(x) , that is

f(y - 3) = y - 3 + 1 = y - 2

The volume will be 1004.5 ft³.

It should be noted that the volume is calculated as:

= Length × Width × Height

= 12.25 × 10 × 8.2

= 1004.5 ft³

Therefore, the volume will be 1004.5 ft³.

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Answer: 132 square units

Step-by-step explanation:

Area of a trapezoid:

a = top base; b = bottom base; h = height

\(A=\frac{a+b}{2}+h\)

Find the bases and the height:

b: 21 (given)

h: 8 (given)

a: find from the bottom

need to find the only not given value by subtracting the values we know. (this might be a little confusing but I think it'll be easier if you look at the original picture)

21 - 9 - 3 = 9

add the new number with the given length of the top base

9 + 3 = 12

Substitute the values into the equation:

\(A=\frac{a+b}{2}+h\\\)

\(A=\frac{12+21}{2}+8\)

(I used a calculator to find it out)

Area = 132 square units