Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)

Answer:

x=0, y=4 and z=0.

Explanation:

Given the system of linear equations:

From the third equation:

Substitute z=-4x into the first and second equations.

Solve the two results simultaneously.

Substitute y=4 to solve for x.

Finally, recall that: z=-4x

Therefore x=0, y=4 and z=0.

Inverse table.

- What undoes sine?

writen as:

called: inverse sine

also called: arcsine

- What undoes cosine?

written as

called: inverse cosine

also called: arccosine

- What undoes tangent?

written as

called: inverse tangent

also called: arctangent

Table of sine, cosine, tangent for 30, 45 and 60 degrees.

for 2nd question

for 3rd question,

for 4th question,

Probability of a seal living less than 7.4 years, P(X < 7.4) = 0.023

The distribution is said to be a normal distributuion.

For a normal distribution, you first calculate the z value.

The z value is calculated as:

The probability of a seal living less than 7.4 years can be represented mathematically as:

P ( X < 7.4) Which can be interpreted as P(z < -2)

Checking this is in standard normal table:

P( z < -2) = 0.02275

Approximating to 3 decimal places, P(z < -2) = 0.023

Therefore, P ( X < 7.4) = 0.023

Since there are 52 cards in the standard deck

Since half of them are in black

Then the probability of getting a black card is

Since there are 4 cards of 6, then

The probability of getting 6 is

OR in probability means adding, then

The probability of getting a black card or a 6 is

We can simplify it by dividing up and down by 2

The answer is P(b or 6) = 30/52 OR 15/26

We start by labeling the number of cards of each. The number of cards that Neil has will be "N", and the number of cards that Tom has will be "T".

We are told that Neil has 83 more baseball cards than Tom, this can be represented in an equation:

In this expression, we say that the number of cards that Neil has is equal to the number of cards that Tom has plus 83 more cards.

Since the problem also indicates that Neil has 517 baseball cards:

And we can combine the two equations we have as follows:

With this last equation, we will be able to find the number of baseball cards that Tom has, by solving for T.

To solve for T, we subtract 83 to both sides of the equation:

On the left side +83-83 cancel each other:

And making the subtraction on the right side, we get the value of T:

Tom has 434 baseball cards.

Answer: 434

EXPLANATION

Let's see the facts:

Julian Earns--> $437.00

Worked--> 19 hours

Unit rate=

Ken is building an outdoor walking path

Pavers are sold 10 for $8 or $1 per paver

Ken needs 52 pavers to complete the walking path

if 10 pavers is sold for $8

52 / 10 = 5 remainder 2

This means he is going to buy 50 pavers for

5 x $8 = $40

Remaining two pavers

Since, 1 paver is sold for $1

The 2 pavers will be sold for $2

$40 + $2 = $42

The least amount that 52 pavers will cost is $42

the cost for an adult admission is 22 $

cost for child is 22 - 5 = 17 $

total cost for 12 adults is 12 x 22 = 264

total cost for 15 children is 15 x 17 = 255

so the total cost of admission for 12 adults and 15 children is,

= 264 + 255

= 519 $

so the answer is 519 $

We could write the following proportion and then solve for x:

Therefore, we could expect that 136 students chose CSI as their favorite class in Rydell Middle School.

Use the quadratic formula, given by:

where a, b and c are the coefficients of the equation:

ax² + bx + c = 0

By comparing the given equation 4x² + x - 9 = 0, with the previous general form, you have:

a = 4

b = 1

c = -9

replace the previous values of the parameters into the quadratic formula:

The previous expression contains the solutions to the given quadratic equation.

We are asked to determine the volume of the concrete wall with the given dimensions. To do that we will determine the volume of the exterior prism with dimensions 56ft, 26ft, and 3ft. This volume is given by the product of its dimensions:

Solving the operations we get:

Now, we need to determine the interior volume. That is the prism that is inside the foundation. To determine the dimensions we need to convert 5 inches to feet. To do that we will use the following conversion factor:

Multiplying by the conversion factor we get:

Now we determine the length and width of the inside prism. To do that we use the following:

Therefore, we need to subtract 2 times 5 inches to each of the exterior dimensions to get the inner dimensions, therefore, the interior volume is:

Substituting the inches we get:

Solving the operations:

Now, the volume of the wall is the difference between the exterior volume and the interior volume. Therefore:

Substituting the values we get:

Since we need to express the solution in cubic yards we will use the following conversion factor:

Multiplying by the conversion factor we get:

Therefore, 7.5 cubic yards are needed.

It is given that,

cot (x) = 0

To find the smallest non-negative value for x in degrees:

So that,

Hence, the smallest value of x is 90 degrees.

ANSWER

B. 8w - 10 = 174

EXPLANATION

The length of the rectangle is 5 less than 3 times the width.

Let the length be L.

Let the width be w.

This means that:

L = 3 * w - 5

L = 3w - 5

The perimeter of a rectangle is given as:

P = 2(L + w)

The perimeter of the rectangle is 174. This means that:

174 = 2L + 2w

Recall:

L = 3w - 5

=> 174 = 2(3w - 5) + 2w

174 = 6w - 10 + 2w

=> 8w - 10 = 174

That is Option B

Okay, here we have this:

We need to write the following polynomial in factored form as a product of linear factors:

Now, let's solve the following polynomial using the general formula for equations of the second degree:

Finally, we obtain the following polynomial:

EXPLANATION :

From the problem, we have a linear function :

We need 2 points to graph this function.

when x = 0 :

when x = 2

Plot the points (0, -4) and (2, -3)

Since the function is a continuous line, the domain and range are all real numbers.

Domain = (-∞, ∞)

Range = (-∞, ∞)

and since the graph is a line with a defined slope, this is a function

they travelled 15 miles

let the number of miles = m

The total charge per ride= $8 + (amount for each mile × number of miles)

amount for each mile = $1.75

The total charge = $8 + ($1.75 × m)

The total charge per ride = 8 + 1.75m

Last customer paid $34.25

34.25 = 8 + 1.75m

collect like terms:

34.25 - 8 = 1.75m

26.25 = 1.75m

divide both sides by 1.75:

26.25/1.75 = 1.75m/1.75

m = 15

Hence, they travelled 15 miles

We will denote the first spinner as S5 and the second one as S6.

1) Probability spin the same number is both spinners twice

The probability of landing in a given number using S5 is equal to 1/5, while when using the S6 the probability is 1/6.

First, we get the same result twice using S5, this probability is given by:

(An specific number, of the 5 available, twice) Notice that the result we obtain with S5 does not affect what we obtain with S6.

On the other hand, the probability of getting any number twice in a row, using S6, is:

(An specific number, of the 6 available, twice) In case the problem refers to the probability of spinning S5 once, then S6, and obtaining the same number:

First, notice that there are a total of 5 results that satisfy this condition

(1,1),(2,2),(3,3),(4,4),(5,5)

And there is a total of 5*6=30 possible combinations. 30 different pairs (S5,S6).

So, the probability is the number of positive cases divided by the total amount of cases:

This is the probability of getting the same number if you spin S5 and S6 once each.

2) Probability getting two numbers which SUM is equal to 5

Let's suppose that the problem refers to spinning once each one of the spinners and then adding the results.

First, we need to get the pairs that add up to 5

(S5,S6)

(1,4),(4,1)(2,3),(3,2). These are the only pairs that satisfy the condition.

And remember that, when spinning S5 and S6 once each, there are 30 possible combinations. So, the probability we are looking for in part 2 is:

3) Landing on an even number

In the case of S5, there are 2 even numbers:2,4 and 5 numbers on which the spinner can land:1,2,3,4,5.

So, the probability is:

On the other hand, the probability of getting an even number with S6 is:

We can even find the probability of spinning S5 once, then S6, and get an even number. Since the events are independent, that probability is:

d) Get one 2 and one 3.

Once again, there is a total of 2 pairs that satisfy this condition: (2,3) and (3,2), and there is a total of 30 combinations when we spin S5 and S6. So,

And that's the answer to the fourth question

Answer

Explanation

(a) The first step is to arrange the numbers of laps in ascending order:

78, 79, 81, 82, 84, 85, 86, 87, 88, 89.

multiply the expression by 100 to make it into percentage :

Answer : 47.5 %

ANSWER

B

EXPLANATION

The intial balance of the savings account was $676.

Let us check the options A to D to see which of them is going to leave the same amount as the initial amount.

A. A withdrawal of $5 followed by a withdrawal of $45.

A withdrawal means money was taken so, the final balance will be:

$(676 - 45 - 45)

= $586

The final is not the same as the initial.

B. A deposit of $36, followed by a withdrawal of $36.

A deposit means money was added to the account, so the final balance is:

$(676 + 36 - 36)

= $676

The final amount is the same as the initial.

C. A withdrawal of $67, followed by a deposit of $45.

So, the final balance will be:

$(676 - 67 + 45)

= $654

The final amount is not the same as the initial.

D. A deposit of $168, followed by a deposit of $168.

So, the final balance will be:

$(676 + 168 + 168)

= $340

The final amount is not the same as the initial.

So, the correct choice is B because the final amount is the same as the initial amount

ANSWER:

$120

STEP-BY-STEP EXPLANATION:

Jenna is a 40-year-old woman and her policy is for 20 years, so according to the table, for every $1,000, $9.60 per year is deducted.

Now, Jenna's policy is $650,900, therefore, the annual deduction in her case taking into account her rate would be:

Now, this is the annual result, but since the payments are weekly and we know that there are 52 weeks in a year, then:

Which means that in each payment they deduct $120

Answer: (2 · (-4y)) + (2 · 2x) + (2 · (-3))

Step-by-step explanation: Distribute the 2 by multiplying each term in the parentheses by 2.

Given:

Leslie will use more than ½ cup but less than 1 whole cup of flour for a recipe.

Let's find the fraction of a cup Leslie might use.

To find the fraction of a cup Leslie might use, find the fraction that is less than 1 whole and still more than ½.

To find the fraction of a cup Leslie might use, we have the fraction:

This is because the fraction, ¾, is less than 1 whole and it is still more than ½.

¾ is ¼ less than 1 whole and ¼ greater than ½

Therefore, the fraction of a cup Leslie might use is ¾

ANSWER:

This sequence can be represented by the following formula:

an = 3(2n - 5)

n ∈ N

Sides of the pyramid are:

5.6 inches base

Height of the pyramid is:

8.9 inches

Let's recall the formula of the slope:

Slope = Change in y/Change in x

Let x = 8.9 or change in vertical distance

Let y = 2.8 or change in horizontal distance

Slope = 8.9/2.8

Slope = 3.1785

Slope = 3.2 rounding to the next tenth

To answer this question let's remember the definitions of qualitative and quantitative data:

• Qualitative data is data that describes the attributes or properties of what we are studying.

• Quantitative data that describes certain quantity or amount. It is usually express by numbers with some unit associated it with it and it can be discrete or continuous. Discrete data is described by particular numbers in a range and continuos data is described by any number in any range.

With this in mind we conclude that Janelle is measuring qualitative data, since she is measuring the amount of water the student takes, furthermore this is continuous data since each student can drink any amount of water, that is, we can even divide the ounces in any decimal.

En un parallelogramo, los lados opuestos son paralelos. De la misma forma, los angulos opuestos son iguales y los angulos adjacentes suman 180 grados.

Con ello, podemos decir que:

a. Los lados RS y UT son paralelos.

b. Los lados RU y ST son paralelos.

c. El angulo en U es igual al angulo en S pues son opuestos

d. Los angulos en S y T son adjacentes . Esto quiere decir que, su suma es igual a 180 grados.

e. El angulo en R es igual al angulo en T pues son opuestos.

f. De forma similar al caso d, los angulos U y R son adjacentes, su suma es 180 grados.

Given:

3x - y = 10

y = 4x-8

Required:

What is the value of x - y of the solution to the system?

Explanation:

3x - y = 10

y = 4x-8

substitute into one of the equations

Required answer:

C. 14

Answer:

$300 down payment

Step-by-step explanation:

John wants to purchase a boat that costs $1,500. He signs an installment agreement requiring a 20% down payment. How much will john need for the down payment

20% = 0.20

0.20 * 1,500 = $300 down payment