For the function ƒ(x) = 5 (x³ – 6), find ƒ−¹(x).
○ ƒ˜¹(x) = (²16) ³
○ f−¹(x) = 2³+6
○ ƒ˜¹(x) = ( ² + 6) ³
○ ƒ−¹(x) = (x+6)³
5
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Answer:

  [-2, 2/5] ∪ [2, ∞)

Step-by-step explanation:

You want the solution to the inequality 7x³ -20x +11 ≥ 2x³ +2x² +3.

The inequality can be rewritten to a comparison with zero by subtracting the right-side expression.

  7x³ -20x +11 -(2x³ +2x² +3) ≥ 0

  5x³ -2x² -20x +8 ≥ 0 . . . . . . . simplify

  x²(5x -2) -4(5x -2) ≥ 0 . . . . . . factor pairs of terms

  (x² -4)(5x -2) ≥ 0 . . . . . . . . . . remove common factor

  (x -2)(5x -2)(x +2) ≥ 0 . . . . . factor difference of squares

The values of x that make this product equal to zero are

  x -2 = 0   ⇒   x = 2

  5x -2 = 0   ⇒   x = 2/5

  x +2 = 0   ⇒   x = -2

These x-intercepts divide the domain into 4 intervals where we need to check the sign.

From left to right:

(-∞, -2)

  Using x = -3, we find the product to be ...

  (-3 -2)(5(-3) -2)(-3 +2) = (-5)(-17)(-1) = -85, less than 0

[-2, 2/5]

  Using x = 0, we find the product to be ...

  (0 -2)(5·0 -2)(0 +2) = (-2)(-2)(2) = 8, part of the solution

(2/5, 2)

  Using x = 1, we find the product to be ...

  (1 -2)(5·1 -2)(1 +2) = (-1)(3)(3) = -9, less than 0

[2, ∞)

  Using x = 3, we find the product to be ...

  (3 -2)(5·3 -2)(3 +2) = (1)(13)(5) = 65, part of the solution

The solution to the inequality is [-2, 2/5] ∪ [2, ∞).

__

Additional comment

The function we're comparing to zero is a cubic with a positive leading coefficient. That means the general shape of its graph is /, negative on the left and positive on the right.

The graph changes sign at each of the zeros, so we already know the curve is positive between the left two x-intercepts, and to the right of the rightmost x-intercept. We just need to define the intervals so the zeros themselves are included in the solution set.

Answer:

square root 75

Step-by-step explanation:

Answer:

(x+6)(x-)

Step-by-step explanation:

The purpose of accounts receivable confirmations is to obtain third-party verification of the account's balance and to determine how frequently misstatements take place.

Here,

Only a small portion of the entire population is often subject to accounts receivable confirmation. The confirmation's goals are to gain external confirmation of the account's balance and to get a sense of how frequently misstatements in the accounts occur.

The majority of errors revealed by discrepancies on the confirmation replies won't be significant; however, discrepancies must be examined individually and collectively to establish their impact on the total balance of accounts receivable.

Even while the discrepancies between individuals may not be significant, they could point to a significant issue with the internal controls over accounts receivable when applied to the entire population.

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Answer:

C. 0.625

Step-by-step explanation:

5 divided by 8 is .625

A.

       .625      

8   5.000

   - 48

        20

       - 16

           40

         - 40

             0

B.

or you can multiply by 8 the answers to see if you get 5

A. 0.375 * 8 = 3

B. 0.40 * 8 = 3.2

C. 0.625 * 8 = 5

D. 0.875 * 8 = 8

C.

if you dont have to you could estimate using the first number after the decimal to see if you get 5

A. 0.375

first number after the decimal is 3

3 * 8 = 24 ≈ 2.4 ≈ 3

B. 0.40

first number after the decimal is 4

4 * 8 = 32 ≈ 3.2 ≈ 3

C. 0.625

first number after the decimal is 6

6 * 8 = 48 ≈ 4.8 ≈ 5

D. 0.875 * 8 = 8

The value of the vector VU is <44, 40>

Vector:

in math vector consist an object that has both a magnitude and a direction.

Given:-

Here we have the vector v and u with the value of v = <11, 5> and the value of u = <4, 8>.

Now, we have to find the value of VU.

In order to find the value of VU, we have to perform the multiplication operation on the given vector,

In order to perform the multiplication on it, we have to arrange them in the following order,

=> VU = <11, 5> x <4,8>

Now, we have to combine the values like the following,

=> <(11 x 4) , (5 x 8)>

Now, do the multiplication then we get,

=> <44, 40>

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Answer:

C≈31.9

Step-by-step explanation:

The equation that can be solve to know the amount of tights needed is c = 20p.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the teacher orders 20 tights for the dance class and she buys as many as p tights as there are students.

The equation will be illustrated thus:

Let total amount be c

c = 20 × p

c = 20p

The equation is c = 20p.

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Complete question

A teacher orders 20 tights for the dance class. She buys as many as p tights as there are students. What equation can solve the amount of tights needed?

The score that Alaina would have to get to tie the winning team's score is of:

4.4 meters.

The combined score of the winning team is given as follows:

25.6 m.

The scores of Alaina's teammates are given as follows:

5.46 m, 4.84 m, 4.92 m, 5.98 m.

Considering Alaina's score, the scores of her team are given as follows:

5.46 m, 4.84 m, 4.92 m, 5.98 m, x m.

In which x is the unknown Alaina's score.

Then their combined scores are given as follows:

5.46 + 4.84 + 4.92 + 5.98 + x = 21.2 + x.

The scores will be tied when they are equal, that is:

21.2 + x = 25.6.

Then the score that Alaina needs is obtained as the subtraction of 25.6 and 21.2, as follows:

x = 25.6 - 21.2

x = 4.4 meters.

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The answer of the given expression as a common fraction in lowest terms is  437/495  .

In the question ,

it is given that ,

the expression is 0.4overline 8 + overline 0.37 ,

that can be written as [tex]0.4\overline{8}[/tex] + [tex]0.\overline{37}[/tex]

On further simplifying the above expression further ,

we get ,

= (48 - 4)/90 + 37/99

= 44/90 + 37/99

taking the LCM of 90 and 99 as 990 and solving further ,

we get ,

= 484/990 + 390/990

= ( 484 + 390 )/990

= 874/990

in lowest form it is = 437/495 .

Therefore , the answer to the expression is  437/495  .

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Jo's sum is easy   = (100)(101)/2  =  50 * 101   =  5050

Given,

In the question:

Jo adds up all the positive integers from 1 to 100. Kate does a similar thing with the first 100 positive integers.

She first rounds every integer to its nearest multiple of 10 (rounding 5s up) and then adds the 100 values.

To find the what is the positive difference between jo's sum and Kate's sum?

Now, According to the question:

Kate  would first start with 5  [ since 1 - 4 ]  are rounded to 0

Starting with 5 thru 14  she will have ten 10s

15 - 24   she will have  ten 20s

25 - 34 she will have  ten 30s

.

.

.

.

.

85 - 94 she will have ten 90s

95 - 100   she will have six 100s

So.....her sum is

10  [10  + 20 + 30 + 40 + 50 + 60 + 70 + 80 + 90]  + 6 [100]

10  [ (10) (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) ] + 6[100]  

10 (10)  [  sum of the first nine positive integers ] + 6 [ 100]

100  [  (9)(10) / 2 ]  + 6[100]  

100 [ 45]  + 6[100]

100 [ 45 + 6 ]  

100 [ 51 ]

5100

Hence, The positive difference is 5100 - 5050  =  50

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Answer:

36.9 gallons were used in one month.

Step-by-step explanation:

In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other:

3 ÷ 5 = 0.6

Then, we can set up this equation to figure out how much gallons of gasoline was used:

0.6 x 61.5 = 36.9

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Answer: 36.9 gallons were used in one month.

Step-by-step explanation:

In order to find this out, we first take 3/5 and convert it into a decimal by dividing each other: 3 ÷ 5 = 0.6

Then, we can set up this equation to figure out how much gallons of gasoline was used: 0.6 x 61.5 = 36.9

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Answer:

$14.45

Step-by-step explanation:

To make the equation easier you would have to make the percent decimal and to do that move it twice to the left. So it would be 0.17 x 85 which is 14.45 and add that dollar sign there. :)

Answer:

x = 1, p = 32

Step-by-step explanation:

4(4x+4) = 2(x+2x+13)

16x+16 = 6x+26

10x+16=26

10x=10

x=1

4(4(1)+4) = 4(4+4) = 4(8) = 32

Technically, it would be impossible to truly know without "computing" at all, but once you add 2 and 3, you would be able to know that the sum of all three numbers of positive without accounting for the -2, because 6 is a greater absolute value than -1.

Some examples:
12 + - 4
7 + - 3
18 + -10

All will be positive because those positive numbers (12, 7, 18) are greater than the others (4, 3, 10).

The probability that:

A student has a cat and they do not have a dog = 1/8 or 0.125.

Use the concept of probability defined as:

Probability is the ratio of:

The number of favorable outcomes to the total number of outcomes for an event's taking place.

Given that,

The number of students in the class = 25

[tex]5[/tex] students have a cat.

[tex]9[/tex] students have a dog.

[tex]3[/tex] students have both a cat and a dog.

The objective is to find the probability that given that they don't have a dog, a student has a cat.

To find the probability that one of the pupils has a cat because there isn't a dog in the class:

First, determine the total number of pupils without a dog..

Since there are 25 students in total and 9 have a dog,

Now, 25 - 9 = 16

So the number of students who do not have a dog = 16

Now, determine the number of students who have both a cat and a dog.

According to the question:

There are 3 students who have both,

Subtract this from the percentage of students who own cats.

Therefore,

5 - 3 = 2

So, there are 2 students who have a cat but not a dog.

[tex]Probability = \frac{\text{(Number of students with only a cat)}}{\text{ (Number of students who do not have a dog)}}[/tex]

Probability = 2 / 16

Probability = 1 / 8

Hence,

The required probability that a student has a cat given that they do not have a dog = 1/8 or 0.125.

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The probability that a car chosen to random will need:

A) no repairs: 72%

B) No more than one repairs: 89%

C) some repairs: 11%

The total amount of cars that will need some type of repair is 28%; 17% will need to be repaired once + 7% will need to be repaired twice + 4% will need to be repaired more than two times.

The amount of cars that wouldn´t need any type of repairs is the total amount of cars minus the percentage that need some type of repair:                

                                   100% - 28% = 72%.

The amount of cars that will need no repairs or only one repair is the total amount of cars minus the percentage that need more than one of repair:

                             100% - (7% + 4%) = 89%.

The amount of cars that need some repairs is the sum of those cars that need two repairs plus those that need three or more repairs:

                                  7% + 4% = 11%

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The factors by applying distributive property out the greatest common factor is 20(3 - 2y).

For the stated equation;

= 60 − 40 y

Do the prime factorization of the both numbers-

60 = 2×2×3×5

40 = 2×2×2×5

Thus, the greatest common factor from both numbers is-

2×2×5 = 20

Taking 20 common from both terms in equation-

Using distribute property;

= 20(3 - 2y)

Thus, factors by applying distributive property out the greatest common factor is 20(3 - 2y).

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It belongs to isometric sampling or systematic sampling in every fifth adult entering an airport is checked for extra security screening.

What is systematic sampling?

Systematic sampling is a type of probability sampling method in which sample members from a larger population are selected according to a random starting point but with a fixed, periodic interval. This interval, called the sampling interval.

Security workers at an airport randomly choose one of the first 50 people to pass through a checkpoint for extra security screening.

After that person, they choose every 50th person who passes through for extra screening as well

By the topic

The sampling interval is 50, which is periodic.

It belongs to isometric sampling or systematic sampling.

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Answer:

78 in²   (Choice B)

Step-by-step explanation:

Since they have exploded the 3-D cuboid into 2-D, it is easier to compute

Looking at the 2-D version you can see 4 rectangles each 3" x 5"

At the bottom on each side are 2 squares each 3" x 3"

Area of a rectangle = l x w

In this case, area of each rectangle = 3 x 5 = 15

Since there are 4 rectangles, total area of these four = 4 x 15 = 60 in²

Each square is area 3" x 3" = 9"

Since there are 2 such squares, total area of these two = 9 x 2 = 18in²

Total area of the 2-D blowup which is the same as the Surface Area of the prism = 60 in² +  18in² = 78 in²

With any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

So, considering that n is 40:

n = 40 as a positive integer

Probability of not choosing any of the six ideal numbers in a lottery:

C(34 , 6)/C(40 , 6)

The likelihood of choosing none of the six correct integers in a lottery:

1344904/3838380

Probability of not winning a lottery with any of the six correct integers:

0.35

Therefore, with any of the six correct integers, there is a 0.35 percent probability of not winning the lottery.

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Correct question:
Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)

a) 0.40

b) 0.48

c) 0.56

d) 0.64

e) 0.35

By identifying all possible outcomes and the probability of each outcome the negotiation used here is Game theory.

The study of mathematical models of strategic interactions between rational beings is known as game theory and it has uses in computer science, logic, systems science, and all branches of social science.

The most well-known application of game theory is The Prisoner's Dilemma for instance take two offenders who were detained following an arrest as an example. The prosecution lacks concrete proof to prove their guilt. Officials, however, take the inmates out of their isolation cells and question each one separately in order to extract a confession.

The area of mathematics known as "game theory" is concerned with the analysis of such games. Classical game theory and combinatorial game theory are the two primary subfields of game theory. Traditional game theory examines games where participants can move, wager, or strategize all at once.

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Answer:

[tex]\textsf{D)} \quad 27x^3+33x^2-x -8[/tex]

Step-by-step explanation:

Given expression:

[tex](9x+8)(3x^2+x-1)[/tex]

Distribute the parentheses:

[tex]\implies 9x \cdot 3x^2+9x \cdot x+ 9x \cdot (-1) + 8 \cdot 3x^2 + 8 \cdot x +8 \cdot(-1)[/tex]

Simplify:

[tex]\implies 27x^3+9x^2-9x + 24x^2 + 8x -8[/tex]

Collect like terms:

[tex]\implies 27x^3+9x^2+ 24x^2-9x + 8x -8[/tex]

Combine like terms:

[tex]\implies 27x^3+33x^2-x -8[/tex]

hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

Odd integer + even integer

 = 2k + 1 + 2k

= 4k + 1

 = 2(2k) + 1

Let 2k = t, where t is integer

  = 2t + 1

 = Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd

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Answer:

12x^2.y^2 + 2xy - 2

Step-by-step explanation:

I put the dot so you don't get confused thinking it is 2y. Tell me if I misinterpreted the question

In Coralbank $ 1,359,468.19 and In Bank of Munich $ 1,240,088.97

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as a yearly percentage of the loan amount. The interest rate on the loan is known as this percentage.

Given:

Coralbank is providing him an interest rate of 3% on the first $500,000 he invests with them and 1% on whatever else he invests beyond that point.

So, After 15 years

First, convert R as a percent to r as a decimal

r = R/100

r = 3/100

r = 0.03 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00[tex](1 + 0.03/1)^{(1)(15)[/tex]

A = 500,000.00[tex](1 + 0.03)^{(15)[/tex]

A = $778,983.71

and, for Another $500,000

A = P[tex](1 + r/n)^{nt[/tex]

A = 500,000.00 [tex](1 + 0.00/1)^{(1)(15)[/tex]

A = 500,000.00 [tex](1 + 0.01/1)^{(1)(15)[/tex]

A = $580,484.48

Total he Invests= $ 1,359,468.19

and, Bank of Munich is willing to pay him an interest rate of 2% on up to $250,000 of his money, and 1.25% on everything beyond that point.

Then solve the equation for A

r = R/100

r = 2/100

r = 0.02 rate per year,

Then solve the equation for A

A = P[tex](1 + r/n)^{nt[/tex]

A = 250,000.00[tex](1 + 0.02/1)^{(1)(15)[/tex]

A = 250,000.00 [tex](1 + 0.02)^{(15)[/tex]

A = $336,467.08

and, for Another $750,000 .

A = P[tex](1 + r/n)^{nt[/tex]

A = 750,000.00[tex](1 + 0.0125/1)^{(1)(15)[/tex]

A = 750,000.00 [tex](1 + 0.0125)^{(15)[/tex]

A = $903,621.89

Total he Invests= $ 1,240,088.97

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In 609638400 ways eight men and five women can stand in a line so that no two women stand next to each other.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. The permutation of the set A=1,6 is 2, for instance, 1,6, and 6,1. There is no alternative way to organize the components of set A, as you can see.

In contrast to combination, where the order of the parts is irrelevant, permutation calls for a specific arrangement of the elements in many ways.

We genuinely wonder how the timetables of trains, buses, and airlines are set up in accordance with the convenience of the general population. Of course, the permutation is quite useful in planning the departure and arrival timetables for these.

How to solve?

For 8 men in a line: 8! = 40320  

In order to separate 2 women, we have to choose 5 out of 9

C(9,5) = 9! / 5!4! = 126

Random place 5 women in the 5 chosen places: 5! = 120

Total ways= 40320 * 126 * 120 = 609638400

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The equation of the line in point slope form is y = -1/4x + 17/2.

The slope of the equation of the line is given as;

slope m = -1/4

Passing point = (-2,9)

Equation of the line;

y - y1 = m(x - x1)

y - 9 = -1/4(x + 2)

y = -1/4x -1/2 + 9

y = -1/4x + 17/2

Thus, the equation of the line in point slope form is y = -1/4x + 17/2.

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