Ben is a pool technician who is preparing a client's pool for the winter by draining the water. For each hour that he drains the pool, the volume of the water in the pool decreases by approximately how many gallons?

1. F(x) represents the total cost function for renting a Popcorn machine.

2. The 40 in the equation represents the Fixed Cost per day of the rental.

3. The 0.15 represents the variable cost per hour.

4. The x represents the number of hours the machine is rented.

A function is a mathematical expression, rule, or law defining the mathematical relationship between the independent variable and the dependent variable.

Mathematical functions are used to define the mathematical relationships that show how the dependent variable can be determined, given an independent variable.  They are written with the equal sign (=).

Thus, we can conclude that the rental cost function ƒ (x) = 40 + .15x shows the total amount that a customer would be charged each day for renting a Popcorn machine.

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Answer:

$9.50

Step-by-step explanation:

      9.5

7  66.5

   63

      35

       35

        0

Hopes this helps please mark brainliest

Answer: 9.50

Step-by-step explanation:

I calculated and estimated a solution to this problem.

Its 9.50

figure it out ig thats how I did it.

Alexander the Great, also referred to as Alexander III of Macedon, was a ruler of the Macedonian kingdom in ancient Greece. At the age of 20, he succeeded his father Philip II to the throne in 336 BC, and throughout the majority of his reign, he waged a protracted military campaign across Western Asia and Egypt.

Alexander the Great, who ruled ancient Macedonia for fewer than 13 years, altered the course of history. He built a massive empire that spanned from Greece to part of India and from Macedonia to Egypt, making him one of history's greatest military leaders.

Aristotle taught Alexander until he was 16 years old. He campaigned in the Balkans in 335 BC, not long after assuming the throne of Macedon, and reasserted control over Thrace and Illyria before marching on the city of Thebes, which was subsequently slain in combat.

Then, Alexander served as the League of Corinth's head and utilized his position of power to undertake the pan-Hellenic project that his father had envisioned, taking charge of all Greeks in their conquest of Persia.

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The vertices of parallelogram MNOP after a rotation of 180° are: M' (-1, -7), N' (-8, -5), O' (-4, -2), and P' (3, -4).

A counterclockwise rotation of 270° to triangle GHI would produce an image with this vertices: G' (-2, 0), H' (-6, -7), and I' (-8, -3).

In this exercise, you are required to rotate parallelogram MNOP by 180° and triangle GHI by 270° in a counterclockwise direction. In Geometry, the rotation of parallelogram MNOP 180° about the origin in a clockwise or counterclockwise direction would produce a point that has the vertices (-x, -y):

(x, y)                           →               (-x, -y)

Point M' = (1, 7)        →    Point M' = (-(1), -(7)) = (-1, -7).

Point N' = (8, 5)       →    Point N' = (-(8), -(5)) = (-8, -5).

Point O' = (4, 2)       →    Point O' = (-(4), -(2)) = (-4, -2).

Point P' = (-3, 4)       →   Point P' = (-(-3), -(4)) = (3, -4).

In Geometry, the rotation of triangle GHI by 270° about the origin in a counterclockwise direction would produce a point that has the vertices (y, -x):

(x, y)                           →               (y, -x)

Points at G = (0, -2)   →  Points at G' = (-2, 0)

Points at H = (7, -6)   →  Points at H' = (-6, -(7)) = (-6, -7).

Points at I = (3, -8)   →  Points at I' = (-8, -(3)) = (-8, -3).

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"not more" means "less than or equal to". We just have to use the inequality sign "less than or equal to" which means 5 is less than or equal to x.

Having said that, we can express the statement as follows

Answer: 2 complex solutions; the discriminant is less than zero

Step-by-step explanation:

When the D<0 there are no real solutions because the quadratic does not intercept the x-axis on the graph.

Answer

Santa visits 5,882,353 kids per hour

Explanation

The mathematical expression to get the number of kids visited per hour is

Total number of kids = 200,000,000 kids

Total number of hours available = 34 hours

Hope this Helps!!!

Answer:

it grew 6 inches. 3x2=6.

Every animal in the world needs these things to survive:

A living organism can be defined as an organism which possesses an organized structure, cells, and equally show the characteristics of life.

Basically, some of the characteristics of a living organism include the following:

In this context, we can reasonably and logically deduce that all living organisms in the world such as animals, human beings, etc., all require food, water and oxygen in order to survive.

On the other hand (conversely), living organisms such as plants only require water, carbon dioxide, and sunlight in order to survive.

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Okay, here we have this:

Considering the provided sentences, we are going to apply the law of syllogism, so we obtain the following:

Let us remember that the law of Syllogism says that:

(1) If p , then q . And (2) If q , then r .

Then we can derive that: (3) If p , then r .

Applying:

(1) If the dog jumps in the lake, then it gets wet. (R->S)

(2) If the dog gets wet, then it can't come in the house. (S->T)

We can derive that:

(3) If the dog jumps in the lake, then it can't come in the house. (R -> T)

Answer:

the 2nd one

Step-by-step explanation:

Answer:

[tex]x=3[/tex]

Step-by-step explanation:

Since on one side of the triangle, both of the side halves are equal, then 5x-4 and 3x+2 are equal.

[tex]5x-4=3x+2[/tex]

We can just use simple algebra to find x.

[tex]5x-4=3x+2\\5x=3x+6\\2x=6\\x=3[/tex]

Answer:

f=12

Step-by-step explanation:

F(4) = 4^(2) + 6(4) + 8

Answer:

what kind of math question Is this?

Answer:

14

Step-by-step explanation:

becaus3 9+5=14......

Answer:

12, 14

Step-by-step explanation:

Let x = smaller positive even integer.

Then x + 2 is the next greater even integer.

Add the squares of the numbers.

x² + (x + 2)²

Set the sum equal to 340.

x² + (x + 2)² = 340

x² + x² + 4x + 4 = 340

2x² + 4x - 336 = 0

x² + 2x - 168 = 0

We need to factor the left side. We need 2 factors of -168 that add to 2.

168 = 2³ × 3 × 7

2² × 3 = 12

2 × 7 = 14

14 × (-12) = -168

14 + (-12) = 2

The factors are 14 and -12.

x² + 2x - 168 = 0

(x - 12)(x + 14) = 0

x - 12 = 0  or  x + 14 = 0

x = 12  or  x = -14

x = 12

x + 2 = 12 + 2 = 14

Answer: 12, 14

After rotating a point C 90° counterclockwise about the origin the coordinates of C' would be (-2, 1)

In this question, we have been given a triangle ABC.

A point C is at (1, 2)

The triangle is rotated counter clockwise 90° about the origin.

We need to find the coordinates of C' which is image of vertex C  after rotation.

We know that, if we rotate a point 90° counterclockwise about the origin a point (x, y) becomes (-y, x).

Here C(1, 2) is rotated 90 degrees counterclockwise about the origin.

So, the coordinates of C' would be,

C' = (-2, 1)

Therefore, after rotating a point C 90° counterclockwise about the origin the coordinates of C' are (-2, 1)

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The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A) =

To solve this problem we will use Baye's theorem which states

P(B1 |A) = P(A/B1)P(B1) / P(A|B1)P(B1) + P(A|B2)P(B2) + P(A|B3)P(B3)       (1)

where P(A|B) is the probability of event A occurring given that event B has already taken place.

Probability of hospital 1 having the case = P(B1) = 50

Probability of hospital 2 having the case = P(B2) = 30

Probability of hospital 3 having the case = P(B3) = 20

Probability of case resulting in malpractice in hospital 1= P(A/B1) =0.001

Probability of case resulting in malpractice in hospital 2= P(A/B2) =0.005

Probability of case resulting in malpractice in hospital 3= P(A/B3) =0.008

The probability that if a malpractice suit is filed, it originated in hospital 1 = P(B1|A)

Using equation (1)

P(B1|A) = (0.001)(50) / (0.001)(50) + (0.005)(30) + (0.008)(20)

          = 0.05 / ( 0.05 + 0.15 + 0.16 )

          = 0.05 / 0.36

          = 0.138

Problem based on Bayes's theorem

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Answer:

Both the line right before the 2 and the line right before the one

Step-by-step explanation:

8400000cm

84 kilometer is 8400000 centimeter.

Here given 84 km ,

We know that 1 km = 1000 meter

               so 84 km  = 84 x 1000 meter

                                 = 84000 meter

 and 1 meter = 100 cm

 so here 84000 meter = 84000 x 100 cm

                                       = 8,400,000 Centimeters

∴ 84 km = 8400000cm

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Step-by-step explanation:

[tex]110 \times 10^{-1}[/tex]

[tex]= 11[/tex]

Answer:

Given the answer is 11, we can round that down to 10.5

Hope this helps!

Answer:

[tex]-n^3+7n+3[/tex]

Step-by-step explanation:

[tex](f-g)(n)=f(n)-g(n) \\ \\ =4n+3-n^3+3n \\ \\ =-n^3+7n+3[/tex]

The name of the line equation that runs parallel to the line x-2y=6 and goes through the point (-6,-8). The equation standard form is x - 2y = 10.

Given that,

We have to find what is the name of the line equation that runs parallel to the line x-2y=6 and goes through the point (-6,-8).

This slope is m for a line equation in slope-intercept form (y=mx+b).

When a line in Standard Form (Ax+By=C) is transformed into slope-intercept form, the slope is (-A/B).

The question gives the equation x-2y=6.  The parallel line has the equation in Standard Form, or x-2y=C.  Use the point to find C:

x-2y = C

(-6)-2(-8) = C

10 = C

Therefore, The parallel line has the following "an equation" in Standard Form: x - 2y = 10.

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Answer: y = 3x -2

Step-by-step explanation:

1) slope formula

y2 - y1 / x2 - x1

2) find the y's and x's

y2 = 10

y1 = -2

x2 = 4

x1 = 0

3) plug them into the equation

10 - (-2) / 4 -0

10+2/4

12/4

4) simplify

slope = 3

5) write out equation

y = 3x + b

6) plug in coordinates

(0,2)

-2 = 3(0) + b

7) find the y intercept

-2 = b

8) plug in y intercept

y = 3x -2

a) Initial Value = 5575

Decay factor = 0.35

The given expression is:

a) What is the initial value

The initial value of Y will take place when t = 0

Substituting t = 0 into the given equation:

b) What is the decay factor

The value of a substance due to an exponential decay is given by the general expression:

Where A = original/Initial value, and r = decay rate

Comparing the above equation with the given equation shown below:

It is clear from the comparison of both equations that A = 5575 and :

The integer -5 represents Kyle’s location relative to Nadim’s location on the game board.

It is given in the question that Kyle and Nadim are on the same space on a board game they are playing. Kyle moves back 2 spaces in one turn and moves back 3 more spaces in his second turn while Nadim remained in the same place.

We have to find the integer that represents Kyle’s location relative to Nadim’s location on the game board.

We usually denote going ahead by the positive sign and the going back by the negative sign.

Hence, Kyle moving back 2 spaces and then again moving back 3 spaces is equal to moving back 5 spaces which will be represented by the integer -5.

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