Factor the function using sum/difference of cubes:
f(x)=x^3-27

Answer:

They would be the same dimensions so the weight should also be the same. For example if you have 3 rectangle boxes dimesions are 4 by 8, let's say the box weighs 32 pounds, then  the other two boxes will weigh the same amount too because it is the same dimensions. This is only true for if the same thing is inside each box of, course if there is a toy in one box, a 50- pound weight in the other box, and a steak in the last box, yeah all the boxes will weigh different.

Step-by-step explanation:

Solution :

Let the three places be 1, 2, 3, 4, 5, 6, 7, 8

a). Number of the cases when a general manager is the next to a vice president is equal to 7 and the these 2 can be arranged in 21 ways. So the total number of ways = 7 x 2

                  = 14

[(1,2)(2,1) (2,3)(3,2) (3,4)(4,3) (4,5)(5,4) (5,6)(6,5) (6,7)(7,8) (8,7)(7,6)]

Therefore the required probability is

  [tex]$=\frac{14}{8!}$[/tex]

 = [tex]$\frac{14}{40320} = 0.000347$[/tex]

b). The probability that the marketing director to be placed in the leftmost position is

   [tex]$=\frac{7!}{8!}$[/tex]

  [tex]$=\frac{1}{8} = 0.125$[/tex]

c). The two events are not independent because

   [tex]$P(A \cap B) \neq P(A) \times P(B)$[/tex]

  [tex]$\frac{12}{8!} \neq \frac{14}{8!} \times \frac{1}{8}$[/tex]

where A is the case a and B is the case b.

(a) The possibility of the general manager is next to the vice president is [tex]\frac{1}{4}[/tex].

(b) The possibility of the marketing director is in the leftmost position is [tex]\frac{1}{8}[/tex].

(c) So, the two events are dependent on each other.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e. how likely they are to happen, using it. The probability of all the events in a sample space adds up to 1.

Total people in company A and company B is [tex]=8[/tex]

Overall ways in which these [tex]8[/tex] people can be lined up[tex]=8![/tex]

                                                                                        [tex]=40320[/tex]

(a) The probability that the general manager is next to the vice president is[tex]=P(A)[/tex]

Now, we can combine the general manager and vice president as one, then the total people in both the company will become [tex]7[/tex].

by arranging these [tex]7[/tex] people in one line [tex]=7![/tex]

                                                                [tex]=5040[/tex]

Again, combine the general manager and vice president in one line[tex]=2![/tex]

                                                                                                                [tex]=2[/tex]

Therefore, [tex]P(A)=\frac{5040\times 2}{40320}[/tex]

                          [tex]=\frac{10080}{40320}[/tex]

[tex]P(A)=\frac{1}{4}[/tex]

(b) The probability that the marketing director is in the leftmost position is[tex]=P(B)[/tex]

Now, fixing the position of marketing director in the leftmost.

arranging the [tex]7[/tex] other people in [tex]7![/tex] ways [tex]=5040[/tex]

Therefore,[tex]P(B)=\frac{5040}{40320}[/tex]

                          [tex]=\frac{1}{8}[/tex]

[tex]P(B)=\frac{1}{8}[/tex]

(c) Assuming event B already occurred which means that the position of marketing director is already fixed in the leftmost position.

Now, trying to find out the probability of the general manager next to the vice president is event A. it comes different because we are not allowed to arrange rest [tex]7[/tex] people, we have to fix the position of one person that causes the repetition of probability.

So, the two events are dependent on each other.

Learn more about the topic of Probability: https://brainly.com/question/26959834

Answer:

1/3

Step-by-step explanation:

6x=2

x= 1/3

Answer:

1 kilo takes 20 minutes

Step-by-step explanation:

6kilo in 2hrs

3kilo in 1 hr

1hr = 60min

3kilo/3 = 1 kilo

60min/ 3 = 20 min

1 kilo * 6 = 6kilo

20min * 6 = 120min ( 2 hours )

Answer:

Step-by-step explanation:

4:7::4x:7x

4x+7x=231

11x=231

x=231/11=21

women=7x=7×21=147

Answer:

The answer to your question is 150 ft

Process

1.- Find the area of the city skate park

2.- Find the equation of the area of the new city skate park.

3.- Find the value of "x",

1.-  Area = length x width

   Area = 100 x 50

            = 5000 ft²

2.-    (100 + x) /50 + x) = 15000

       x² + 150x + 5000 = 15000

       x² + 150x + 5000 - 15000 = 0

       x² + 150x - 10000 = 0

      Factor the equation

      (x + 200)(x - 50) = 0

       x₁ = -200     x₂ = 50       Length can not be negative so the answer is

                                              50.

      New length = 100 + 50 = 150 ft

Answer:

8

Step-by-step explanation:

Hope this is helpful!

Answer:

Not equivalent.

Step-by-step explanation:

The given equations are :

7v-3/2=5 ....(1)

14v-3=15 ....(2)

Taking equation (1) first,

7v-3/2=5

Adding 3/2 to both the sides.

7v-3/2+3/2=5+3/2

7v = 6.5

v = 0.928

Taking equation (2).

14v-3=15

Adding 3 to both sides.

14v-3+3=15+3

14v=18

v = 1.285

So, the values of v in both equations ar not the same. It means two equations are not equivalent.

Answer:

5.2

Step-by-step explanation:

I took the Quiz.

If An architect is reading a plan that is drawn on a scale of 0.65 inches to 1.25 ft. If the plan says that a room is 10 feet high, then the roof is 8.13 high in the drawing.

A fraction represents a part of a whole or, more generally, any number of equal parts.

Based on the given conditions formulate 1.25÷10=1+x

If the fraction is defined, the denominator cannot equal 0,x≠0

Append the inequality as the domain x≠0

Multiply both sides by the common denominator:

1.25×10x/10=10x/x

Reduce the fractions: 5x/4=10

5x=40

x=8

It is approximately near to 8.13 inches.

Hence, 8.13 inches high is the roof in the drawing.

To learn more on fractions click:

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#SPJ2

Answer: C

Step-by-step explanation:

The slope is

[tex]\frac{2-6}{6-0}=-\frac{2}{3}[/tex]

This eliminates all the options except for C.

Answer:

B

Step-by-step explanation:

the truck owner saves 7$ from every tires by buying at the selling price.

Answer:

11/36

Step-by-step explanation:

We have 36 possible outcomes when rolling a pair of dice.

Only 1 outcome gets both 3's. (3 3)

For the sum to be greater than 8, there are 10 outcomes.

(3 6) (4 5) (4 6) (5 4) (5 5) (5 6) (6 3) (6 4) (6 5) (6 6)

The probability is therefore (1+10)/36=11/36.

Answer:

5609604 OR 11219200

Step-by-step explanation:

i dont know if its 6 plus 6 dollars like 12 or just 6 so yeah

Answer:

The median would be $700.00 dollars

The mean would be $685.71 dollars

The mode would be $580.00 dollars

Step-by-step explanation:

    May I have brainiest please I'm trying to level up!

                    </3 PureBeauty

Answer:

/Its $700.000

Step-by-step explanation:

its the middle number

Answer: domain: {-2, -1, 0, 1}

range: {0, 1, 2, 3}

Answer: 4

Step-by-step explanation: Good luck! :D

Answer:

4

Step-by-step explanation:

Answer:

34^23 (that is 34 to the 23 power)

Step-by-step explanation:

Do 3.4x10^23=34^23

Answer:

20:60 12:36 2:6

Step-by-step explanation:

The second number is going to be 3 times as big as the first ine

Answer:

15 (A)

A is the legit answer.

Answer:

10

Step-by-step explanation:

5×10= 50

6×10=60

8×10=80

so its going by ×10

Answer:

C/10

Step-by-step explanation:

k=y/x

10=50/5

Answer:

k = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

5k + (-7) = 13

Step 2: Solve for k

Step 3: Check

Plug in k into the original equation to verify it's a solution.

Here we see that 13 does indeed equal 13.

∴ k = 4 is the solution to the equation.

Answer:

Step-by-step explanation:

Here you go mate

PEMDAS

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction

Step 1

5k+(-7)=13  Equation/Question

Step 2

5k+(-7)=13  Remove parenthesis

5k=20

Step 3

5k=20  Divide 5 from the sides             Check (5)(4)=20

answer

4

Answer:

$3562.50

Step-by-step explanation:

If the cost ratio is ...

 labor : parts = 3/5 : 1 = 3 : 5

then the ratio of labor to the whole cost is ...

 labor : total = 3 : (3+5) = 3 : 8

The amount saved by not paying for labor is ...

 (3/8) × $9500 = $3562.50 . . . labor charge

Answer:

X=3 Y=-7

Step-by-step explanation:

You can solve a system of equations a number of ways. Substitution makes the most sense in this case. Take the top equation and set it equal to y making it: y=17-8x

Then substitute y in the bottom equation for the y solved in the top. So,

5x + 5(17-8x) = -20

Then solve for x

x=3

Now that we know x, plug it back into the equation for y

y = 17 - 8(3)

y = -7

So your solution is (3, -7)

Answer:

Step-by-step explanation:

40x + 5y = 85

-5x - 5y = 20

35x = 105

x= 3

15 + 5y = -20

5y = -35

y = -7

(3, -7)

9514 1404 393

Answer:

  (x, y) = (1, 8)

Step-by-step explanation:

A graphing calculator quickly tells you the point of intersection.

__

You can equate the y-values and solve for x.

  3x +5 = -2x +10

  5x = 5 . . . . . . . . . add 2x-5

  x = 1 . . . . . . . divide by 5

  3·1 +5 = y = 8 . . . . substitute for x in the first equation

The point of intersection is (x, y) = (1, 8).

Answer:

Does Anyone Know how to do this?

Step-by-step explanation:

Hello!

[tex]\large\boxed{\frac{\pi }{4} < x < \frac{5\pi }{4}}[/tex]

To begin, we can solve the inequality:

sin(x) > cos(x)

Divide both sides by cos(x):

sin(x) / cos(x) > 1

tan(x) > 1

x > π/4

However, we can also solve it the other way to produce the end to the interval:

sin(x) > cos(x)

1 > cot(x)

x < 5π/4

Therefore, sin(x) > cos(x) on the interval π/4 < x < 5π/4.

Answer:

π/4 < x < 5π/4.