Consider the following functions.
f(x) = 3/x, g(x) = x/(x + 3)

Find
(f ∘ g)(x).



Find the domain of
(f ∘ g)(x).
(Enter your answer using interval notation.)


Find
(g ∘ f)(x).



Find the domain of
(g ∘ f)(x).
(Enter your answer using interval notation.)


Find
(f ∘ f)(x).



Find the domain of
(f ∘ f)(x).
(Enter your answer using interval notation.)


Find
(g ∘ g)(x).



Find the domain of
(g ∘ g)(x).
(Enter your answer using interval notation.)

Answer:

False

Step-by-step explanation:

When soil is carried away by erosion then most of the minerals present in the soil also gets washed away by that soil erosion.

Hence, very less plants are likely to survive in that soil.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

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The length of the first piece is 5 inches when a 43-inch piece of steel is cut into three pieces.

According to the question,

We have the following information:

A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than five times the length of the first piece.

Now, let's take the length of the first piece to be x inches (as shown in the figure).

Length of second piece = 2x inches

Length of third piece = (3+5x) inches

Now, we have the following expression for addition:

x + 2x + 3 + 5x = 43

8x+3 = 43

8x = 43-3

8x = 40

x = 40/8

x = 5 inches

Hence, the length of the first piece is 5 inches.

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The probability that a truck drives between 150 and 156 miles in a day is 0.0247. Using the standard normal distribution table, the required probability is calculated.

The formula for calculating the probability distribution for a random variable X, Z-score is calculated. I.e.,

Z = (X - μ)/σ

Where X - random variable; μ - mean; σ - standard deviation;

Then the probability is calculated by P(Z < x), using the values from the distribution table.

The given data has the mean μ = 120 and the standard deviation σ = 18

Z- score for X =150:

Z = (150 - 120)/18

   = 1.67

Z - score for X = 156:

Z = (156 - 120)/18

  = 2

So, the probability distribution over these scores is

P(150 < X < 156) = P(1.67 < Z < 2)

⇒ P(Z < 2) - P(Z < 1.67)

From the standard distribution table,

P(Z < 2) = 0.97725 and P(Z < 1.67) = 0.95254

On substituting,

P(150 < X < 156) = 0.97725 - 0.95254 = 0.02471

Rounding off to four decimal places,

P(150 < X < 156) = 0.0247

Thus, the required probability is 0.0247.

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Answer:

12.6 m^2

Step-by-step explanation:

area of sector = 90/360 × 3.14 × 4^2

= 12.56

to the nearest tenth = 12.6 m^2

\(\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} \theta =\stackrel{\textit{in degrees}}{angle}\\ r=radius\\[-0.5em] \hrulefill\\ \theta =270\\ r=4 \end{cases}\implies A=\cfrac{(270)(\stackrel{\pi }{3.14})(4)^2}{360}\implies \underset{\textit{rounded up}}{A\approx 37.7}\)

With the help of probability we can say that, DUM={GG,BB,GB,BG).

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

hence, DUM={GG,BB,GB,BG)

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Answer:

45.5

Step-by-step explanation:

You do the linear length multiplied by the longitudinal length

The distance across the lake is 320 ft.

Given is a scenario of a lake, a survey crew has laid out the concept of similar triangles to find the distance across the lake.

The figure shows the base of the larger triangles is the distance across the lake. [please refer to the figure attached]

The dimensions of the imaginary triangles are 30 ft, 30 ft, 40 ft and 240 ft, 240 ft, x ft.

Here, x is the distance across the lake which we are asked to find.

Using the definition of the similar triangles,

Two triangles are considered similar if their corresponding angles are equal, and the ratios of the lengths of their corresponding sides are equal.

So,

\(\frac{240}{30} = \frac{x}{40}\)

\(x = \frac{240 \times 40}{30}\)

x = 320

Hence the distance across the lake is 320 ft.

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The additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria is

EJ ≅ GJ. Option A

We need to know the properties of a parallelogram, we have;

We know that FJ  ≅ JH, it's given by the marks, now if it were to happen that EJ ≅ GJ, that would mean that the diagonals on that quadrilateral are bisecting each other, and if that's so, then the quadrilateral it's indeed a parallelogram.

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The complete question:

What additional information would allow you to prove the quadrilateral is a parallelogram according to the minimum criteria?

A)

ej ≅ gj

B)

ej || gj

C)

fg || eh

D)

ef ≅ hg

Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:

10x + 5y ≥ 500 (minimum 500 units of vitamins)

5x + 10y ≥ 600 (minimum 600 units of minerals)

15x + 15y ≥ 1200 (minimum 1200 calories)

We want to minimize the cost, which is given by:

0.5x + 0.4y

This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:

10x + 5y = 500

5x + 10y = 600

15x + 15y = 1200

Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.

Next, we can calculate the value of the cost function at each corner point of the feasible region:

Corner point A: (20, 40) -> Cost = 20

Corner point B: (40, 25) -> Cost = 25

Corner point C: (60, 0) -> Cost = 30

Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.

Answer:I n no

Step-by-step explanation:

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Answer:

r ≈ 6

Step-by-step explanation:

r=  414.78

     π x 11

≈ 5.99848

Because of this, the answer is rounded up to 6, but the exact answer is about 5.99848

Answer:

this isnt related to the question but i hope ur having a good day

Step-by-step explanation:

Answer:

To find the percent of 125 that 375 is, we need to divide 375 by 125 and then multiply by 100.

375 / 125 = 3

So 375 is 3 times 125. Multiplying 3 by 100, we get:

3 * 100 = 300%

So the correct answer is C) 300%.

Succes!

Answer:

C) 300%

Step-by-step explanation:

Percent of 125 means the value of x/125.

Where x is the value 375.

375/125 = 3

3 * 1 =

3 * 100% = 300%

It can be mistaken as 33.33% since 125 is 33.33% of 375.

^^ This question is asking 125 is what percent of 375.

But remember, the question, 'What percent of 125 is 375?', is asking 375 is what percent of 125, not the other way around.

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

We have,

For Matthew's investment, the continuous compounding formula can be used:

\(A = P \times e^{rt}\)

Where:

A = Final amount

P = Principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = Annual interest rate (in decimal form)

t = Time (in years)

In this case,

Matthew's money has tripled,

So A = 3P.

For Parker's investment, the formula for compound interest compounded annually is used:

\(A = P \times (1 + r)^t\)

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (in decimal form)

t = Time (in years)

We need to find t when Matthew's money has tripled in value.

Let's set up the equation:

\(3P = P \times e^{rt}\)

Dividing both sides by P, we get:

\(3 = e^{rt}\)

Taking the natural logarithm of both sides:

ln(3) = rt

Now we can solve for t

t = ln(3) / r

For Matthew's investment,

r = 3 1/8% = 3.125% = 0.03125 (as a decimal).

For Parker's investment,

r = 2 3/4% = 2.75% = 0.0275 (as a decimal).

Now we can calculate t for Matthew's investment:

t = ln(3) / 0.03125

Using a calculator, we find t ≈ 22.313 years.

Now, we can calculate how much money Parker would have in his account at that time:

\(A = P \times (1 + r)^t\)

\(A = $8,000 \times (1 + 0.0275)^{22.313}\)

Using a calculator, we find A ≈ $13,774.

Therefore,

Parker would have approximately $13,774 in his account when Matthew's money has tripled in value.

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Answer:

20,763

Step-by-step explanation:

I saw the answer after I got it wrong

Answer:

Step-by-step explanation:

Given twice the perimeter of rectangle =160

Let width of the rectangle=X

So length of the rectangle =4x

2(perimeter of rectangle)=160

2[2(length+width)]=160

4(4x+x)=160

5x=160/4

5x=40

X=40/8

X=5cm

So length of the rectangle =4x

=20cm

Width of the rectangle =X

=5cm.

Length = 4*5 = 20 cm

Width. = 4 cm.

Answer:

960cm³

Step-by-step explanation:

Find the base of the triangle (use phytagoras theorem)

c²= a²+b²

20²= 16²+b²

400=256+b²

b²=400-256

b²= 144

b=

\( \sqrt{144} \)

base= 12

Volume: (1/2×b×h)×l

= (1/2×12×16)×10

=(6×16)×10

=96×10

=960cm³

The ratio table in this problem is completed as follows:

The ratio table in this problem is completed applying the correct proportion for the number of boys and the number of girls.

From the first row of the table, we have that:

For two boys, there are 15 girls.

The ratio is given as follows:

15/2 = 7.5.

The interpretation of the ratio is given as follows:

For each boy, there are 7.5 girls.

Hence, to obtain the number of boys, we divide the number of girls by 7.5 in each case as follows:

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Answer:

(-2, 3) , 2nd has no answer

Step-by-step explanation:

5x + 6y = 8   and   2x + 3y = 5

Multiply the second x 2 so they both have 6y

5x + 6y = 8

4x + 6y = 10     Now subtract

x = -2      Put -2 in for x:

2(-2) + 3y = 5

-4 + 3y = 5

3y = 9

y = 3

Second problem:

4y = 12x + 3     and y = 3x + 1

Substitute the second equation into the first

4(3x + 1) = 12x + 3

12x + 4 = 12 x + 3

4 = 3

There is no answer

Parallelogram have two pairs of opposite sides that are parallel and congruent.

In a parallelogram, two pairs of opposite sides are parallel and congruent. A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. Therefore, any pair of opposite sides in a parallelogram satisfies the criteria of being both parallel and congruent.

For example, let's consider a parallelogram ABCD:

These two pairs of opposite sides, AB and CD, and AD and BC, are parallel (they never intersect) and congruent (they have the same length).

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Angie decorates 8 cupcakes after putting 4 sugar flowers on each cupcake.

To find the number of cupcakes c Angie decorates, we can use the equation:4c = 32where 'c' is the number of cupcakes Angie decorates.

4 represents the number of sugar flowers Angie puts on each cupcake, and 32 is the total number of sugar flowers Angie puts on the cupcakes.

To solve this equation for c, we need to isolate c on one side of the equation. We can do this by dividing both sides of the equation by 4. This gives us:c = 8

Therefore, Angie decorates 8 cupcakes.Here's how we get to this answer:4c = 32Divide both sides by 4 to isolate c:c/4 = 32/4c = 8

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According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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The following excel commands would give you the critical value is T.INV(0.95,25)

What is excel commands?

The following describe the commands in Excel: They carry out tasks the same way users do. They can change Excel settings, open, close, and edit documents, start recalculations, and other actions that users may perform (within the bounds of the interface being utilized). Excel's command menu interface is called the Ribbon. It logically and visually groups together frequently used actions. These make up the Ribbon's principal components. Related groupings of commands are grouped together by tabs.

Population sd is not available so we have to use t test.

0.95 is for upper bound and 25 is df of t test.

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Graph and its translation

We first graph y = x

We know y = |x|, is just as the previous graph but the negative values of y are positive, then on those part it gets reflected

The graphic of y = -|x| is just like the previous graph but since all the values have opposite signed it gets totally reflected:

We know that if we add a number to x if will be translated to the left and if we subtract a number it will be translated to the right. Then y = -|x+5| has the same graphic as y = -|x| but it is translated to the left 5 places

Answer:

\(d \approx 10.2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra II

Step-by-step explanation:

Step 1: Define

Point A (3, -8)

Point B (1, 2)

Step 2: Find distance d

Answer:

10.2

Step-by-step explanation:

Answer:

okay i'll keep this in mind

Step-by-step explanation:

Answer:

25% were knives

Step-by-step explanation:

Answer:$2050.

Step-by-step explanation:

To find out how much a person will pay for renting a car for one day and driving it 100 miles using the given equation, you can substitute x = 100 into the equation y = 50 + 20x and solve for y:

y = 50 + 20x

y = 50 + 20(100)

y = 50 + 2000

y = 2050

Therefore, a person who rents a car for one day and drives it 100 miles will pay $2050.

See the attached truth tables.

• A ∧ B is true only when both A and B are true

• A ⇒ B is true only when both A and B are true, or A is false. This logically equivalent to ¬A ∨ B

• ¬A is true only when A is false

• A ⇔ B is true only when both A ⇒ B and B ⇒ A are true. Equivalently, (¬A ∨ B) ∧ (¬B ∨ A)