The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer
also has fixed costs each month of $8,000.
a. Find the cost function C when "x" energy drinks are manufactured. C(x) =
Write your answer in slope-intercept form.
b. Find the revenue function R when "x" drinks are sold. R(x) =
Write your answer in slope-intercept form.
c. Graph both your Revenue and Cost functions on the graph below that shows the break-even point.

The puck travelled a distance of 53.8 meters when the puck is 120 centimeters before the opponent's goal and puck travelled a distance of 56.2 meters when the puck is 120 centimeters after the opponent's goal.

Given that the distance to the opponent's goal from the player's current position is 55 meters. And after the shot, the puck is 120 centimeters from his opponent's goal.

We need to find out how many meters the puck travelled.

Also given there are 100 centimeters in 1 meter.

So, 55 meters = 55 × 100 centimeters

⇒ 55 metets = 5500 centimeters

Now, we are given that the puck is 120 centimeters from the opponent’s goal. It is not clear whether the puck landed before or after the goal post. So, considering both cases.

Case 1: the puck is 120 centimeters beyond the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters + 120 centimeters = 5620 centimeters

Divide 5620 by 100 to convert centimeters to meters.

The puck travelled a distance of 5620 cm or 56.2 meters.

Case 2: the puck is 120 centimeters before the opponent's goal.

So, the distance travelled by the puck is

5500 centimeters - 120 centimeters = 5380 centimeters

Divide 5380 by 100 to convert centimeters to meters.

The puck travelled a distance of 5,380 cm or 53.8 meters.

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Taking into account the definition of a system of linear equations, the cost of each shirt is 12 and the cost of each pair of slacks is 18.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be found and they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You buy 3 shirts and 2 pairs of slacks on sale at a clothing store for 72. The next day, a friend buys 2 shirts and 4 pairs of slacks for 96.

So, the system of equations to be solved is

[tex]\left \{ {{3S + 2PS=72} \atop {2S + 4PS=96}} \right.[/tex]

To solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

Isolating the variable S from the first equation, you obtain:

3S= 72 - 2PS

S= (72 - 2PS)÷3

S= 72÷3 - 2PS÷3

S=24- 2/3PS

Replacing this expression in the second equation:

2(24 - 2/3PS) + 4PS= 96

Solving:

2×24 - 2×2/3PS+ 4PS= 96

48 - 4/3PS + 4PS= 96

48 + 8/3PS= 96

8/3PS= 96 - 48

8/3PS= 48

PS= 48÷ 8/3

PS= 18

Replacing this value in the expression S=24- 2/3PS, you obtain:

S= 24 -2/3×18

S= 24 - 12

S= 12

Finally, the cost of each shirt is 12 and the cost of each pair of slacks is 18.

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Final answer:

I would play the game because we could win with probability 17/27.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.

According to the First Law of Probability, the outcomes of one chance event have no bearing on those of succeeding chances occurrences. Consequently, the chance of getting heads the second time you flip it remains at 1 in 2. The chances of getting heads on the sixth flip, even if you got five consecutive heads, stay at 12.

Everyday existence heavily relies on probability. Weather predictions, sports and gaming tactics, insurance purchases or sales, internet shopping, and online gaming.

Explanation:

If both of your dice, or at least one of them, match at least one of the other player's dice, you win. This provides us five scenarios where we win. Let's use the letters A, B, C, and D to represent the results of the dice, with your dice being A and B and the other player's being C and D. The five possibilities are:

1) [tex]A = B[/tex]

2) [tex]A = C[/tex]

3) [tex]A = D[/tex]

4) [tex]B = C[/tex]

5) [tex]B = D[/tex]

A B C D

1) [tex]6 * 1 * 6 * 6[/tex] A can be anything, B has 1 option, C and D can be anything.

2) [tex]6 * 5 * 1 * 6[/tex] A can be anything, C has 1 option, A != B so B has 5 options.

3) [tex]6 * 5 * 5 * 1[/tex] A can be anything, D has 1 option, A !=B and A != C so B and C have 5 options.

4) [tex]5 * 6 * 1 * 5[/tex] B can be anything, C has 1 option, A != B and A != D so B and D have 5 options.

5) [tex]5 * 6 * 4 * 1[/tex] B can be anything, D has 1 option, A != B so A has 5 options, C != A and C != B so it has 4 options.

Therefore, it becomes [tex](6^3 + 6^2*5 + 2*6*5^2 + 6*5*4) / 6^4[/tex]

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Answer: A=30 degrees, B=60 degrees, C=90 degrees

Step-by-step explanation:

B=2A

C=3A

A+B+C=180

A+2A+3A=180

6A=180

A=30 degrees

B=2A

B=2(30)

B=60 degrees

C=3(30)

C=90 degrees

Answer:

Angle A = 30°

Angle B = 60°

Angle C = 90°

Step-by-step explanation:

Let x represent the measure of A. Using this information, we can figure out the measure of B and C in terms of x.

Since B is twice the measure of A, then it would be 2x. Similarly, C is three times the measure of A, thus it would b 3x.

We also know that the sum of the angles is 180 degrees. We can use this information to set up an equation.

We know that:

Angle A + Angle B + Angle C = 180

Substituting the values we gave for A, B, and C, we find:

x + 2x + 3x = 180

Now, we solve the equation for x.

Start by combining like terms:

6x = 180

Now, divide both sides by 6:

x = 30

Since we know the value of x, we can find the values of the angles.

A = x = 30°

B = 2x = 60°

C = 3x = 90°

Answer:

y=-3x-7/3

Step-by-step explanation:

You just subtract 18x from both sides and then divide by 6 on both sides to get it, lmk if that was what your asking for :)

The given vector can be expressed as B = B (cos θ  x ^ + sin θ  y ^)

The strength of the field and its angle with respect to a particular coordinate axis must be known in order to express the magnetic field B using unit vectors. Trigonometry can be applied after this information is known.

Let's utilize trigonometry if the angle we have is with respect to the x-positive axis's side.

          cos θ = Bₓ / B

            sin θ = B / B

            Bx = By cos θ

            B_{y} = B sin θ

so the resulting vector is

            B = Bₓ i ^ + B_{y} j ^

unit vectors

            x ^ = i ^

            y ^ = j ^

B = B (cos θ  x ^ + sin θ  y ^)

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Answer:

third one for me same thing.

Answer: -100/27

Step-by-step explanation:

[tex]x^3 - 4[/tex]=

[tex](\frac{2}{3} )^3 - 4[/tex]=

[tex](\frac{2^3}{3^3} ) - 4[/tex]=

[tex]\frac{8}{27} - 4[/tex]=

([tex]\frac{8}{27} - 4[/tex])*27/27=        ==> multiply by 27 to get rid of denominator

(8-4*27)/27=

(8-108)/27=-100/27

The number of days took by Rita to travel the distance of 1,875 miles is 4.5 days.

We will learn how to calculate the value of such a unit from value of a multiple and thus the value of a multiple from value of a unit using the unitary method.

Now, as per the given question;

The total day taken by Rita to cover 1,250 miles is 3.

Thus,  1250 miles ----> 3 days

Let number of days taken by Rita to cover 1875 miles is 'x'.

So, 1875 miles ----> x

Then, the total distance will be

1875×(3) = 1250x

x = (1875×3)/1250

x = 4.5 days

Therefore, the total time taken by Rita to finish the distance of 1,875 miles is 4.5 days.

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[tex]f( - 4) = - 122[/tex]

And

[tex]g(5) = - 21[/tex]

Step-by-step explanation:

Greetings !

For the first expression

[tex]f(x) = 2x {}^{3} + 6[/tex]

plug in -4 at the variable x and solve the expression.

[tex]f( - 4) = 2( - 4) {}^{3} + 6[/tex]

Follow the PEMDAS order of operations

calculate the exponents

[tex]( - 4) {}^{3} = - 64[/tex]

Apply exponent rule

[tex]( - a) {}^{n} = - a {}^{n} . \: if \: n \: is \: odd[/tex]

Thus,

[tex]( - 4) {}^{3} = - 4 {}^{3} = - 64[/tex]

Multiply and divide (left to right )

[tex]2( - 64) = - 128[/tex]

[tex] = - 128 + 6 \\ = - 122[/tex]

Fairly follow the same. process for the second function

Hope it helps !!

Answer:

Contract

Step-by-step explanation:

The location of the orca relative to the surface of the water is 13.36 below the surface

The given parameters are

Initial = 0 feet i.e  surface of the water

Dives below = 25.5 feet.

Swims up = 12.14 feet.

The location of the orca relative to the surface of the water is calculated as

Location = Initial - Dives below + Swims up

This gives

Location = 0 - 25.5 + 12.14

Evaluate

Location = -13.36

Hence, the location of the orca relative to the surface of the water is 13.36 below the surface

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The parametric equations for this line :

x=11+5s , y=4s , z=2+6s

The value of t that creates the point (11,0,2)

Substitute 11 for x:

11

10

t=1

check that t=1 works for the y and z values:

15−1=0

15+1=2

These check, t=1

Tangent vector:

dxdt=5√t

dydt=5t4−1

dzdt=5t4+1

The tangent vector for all points, ¯v(t), is:

¯v(t)={5√t}ˆi+{5t4−1}ˆj+{5t4+1}ˆk

The tangent vector at the indicated position is the object of our interest:

¯v(1)=5ˆi+4ˆj+6ˆk

The vector equation of the tangent line :

(x,y,z)=(11,0,2)+s(5ˆi+4ˆj+6ˆk)

Parametric equations can be used to describe all types of curves that can be represented on a plane but are most often used in situations where curves on a Cartesian plane cannot be described by functions (e.g., when a curve crosses itself).

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Answer:

2x(x + 3)

Step-by-step explanation:

2x² + 6x ← factor out 2x from each term

= 2x(x + 3)

The parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Also, the point (17,–30,31) does not lie on the line.

for given question,

We need to find the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1)

Let [tex]\vec r_0= < 5,2,7 >[/tex]

and

[tex]\vec v= < 8-5,-6-2,1-7 > \\\\\vec v= < 3,-8,-6 >[/tex]

where vector v is the direction vector.

So, the equation of the line would be,

[tex]\vec r=\vec r_0+\lambda \vec v\\\\\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Now we need to determine whether the point (17, -30, 31) is on the line.

Let [tex]< 17,-30,31 > = < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

For first component,

⇒ 17 = 5 + 3λ

⇒ 3λ = 12

⇒ λ = 4

For the second component,

⇒ -30 = 2 - 8λ

⇒ -8λ = -32

⇒ λ = 4

For third component,

⇒ 31 = 7 - 6λ

⇒ -6λ = 24

⇒ λ = -4

since the values of the λ are not consistent, the point (17,–30,31) does not lie on the line.

Therefore, the parametric equation of the line that passes through the points (5,2,7) and (8,–6,1) is [tex]\vec r= < 5,2,7 > +\lambda < 3,-8,-6 >[/tex]

Also, the point (17,–30,31) does not lie on the line.

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Sash's elevation is -8/3 miles with respect to the sea level, by basic algebra.

Now,

Given:

To find: Sasha's elevation in miles?

Finding:

=> She will be down by 4 (2/3) = 8/3

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The unit segments from 3 to 7 are infinite.

The number from 3 to 7 is given.

We have to find out the no. of segments between the two numbers.

What is algebra ?

Algebra is the branch that deals with various symbols and the arithmetic operations such as addition , division , etc.

As per the question ;

Consider any number x such that 3 < x < 6

Then ;

The segment from x to x+1 is a unit segment and, by definition, it will lie within the interval to 7.

As, there are infinitely many possible choices for x, then there are infinitely many unit segments.

i.e.,

from 3 to 4

from 3.1 to 4.1

from 3.01 to 4.01

from 3.00002 to 4.00001

and you can keep adding decimal digits forever.

Thus , there are infinite unit segments from 3 to 7.

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The number of boxes containing both pens and pencils is 2.

What is set?

A set is defined as a well-defined collection of distinct objects. It is denoted by the capital letters of the English alphabet. Its value remains the same for every individual.

Calculation for the number of boxes containing both pens and pencils

Total number of boxes is given by the union of two sets A and B; i.e. A∪B= 20

Boxes having pencils is given by the set A = 13

Boxes having pens is given by the set B = 9

Boxes having neither pens nor pencils, A'∩B' = 3

Boxes containing both pens and pencils are given by the intersection of the sets, A∩B

A∩B = A + B - A∪B

= 13 + 9 - 20

= 2

Hence, the number of boxes containing both pens and pencils is 2.

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According to the question, the line is through the points [tex](0,5)[/tex] and [tex](-2,11)[/tex]

To calculate the slope using standard formula that is :

[tex]m = \frac{(y(2)-y(1))}{(x(2)-x(1))} = \frac{(11-5)}{(-2-0)} =\frac{6}{-2} = -3[/tex]

Now the slope equation will be: [tex]m(x(2)-x(1)) = (y(2)-y(1))[/tex]

[tex]y-5 =(-3)(x-0) = y = -3(x)+5[/tex]

The slope-intercept form is:[tex]y = -3x+5[/tex]

What is the equation of the line?

To represent the set of points in an algebraic form is known as the equation of line. The set of points represent lines in the coordinate system. The parameters can be calculated and those parameters are slope and y-intercept.

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answer:

3/8 is the slope, also stated as .4 (from 3.75)

the segment length is 8.5 (using the pythagorean theorem)

Answer:

the answer is -2, substitution took place tht is why w turned to -w

Step-by-step explanation:

-W=9 - 7

-W= 2.

W=-2

Answer:

scale factor = 3

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, copy to original , so

scale factor = [tex]\frac{12}{4}[/tex] = [tex]\frac{9}{3}[/tex] = 3

Answer:

Step-by-step explanation:

Answer is 4250 students attend the college

4250 x .56 = 2,380

x ≤ 7 days is the maximum number of days Faith can afford to rent while staying within her budget.

When you take a single number and multiply it by several, you are multiplying. There are a number distinct indications of amplification that people utilize. The "x" sign represents the most typical, however, other symbols like the "*" sign are also occasionally used.

Information that is given

Renting a car from a rental car agency costs $62.12 per day plus $0.05 for every mile traveled.

Considering that she will be traveling 500 miles,

She can only spend up to $440.

Assume that the number of days will be x

cost per day will be 62.16 × x

Miles per day will be 0.05 × 500

The inequality used will be

62.16x + 0.05 × 500 ≤ 500

62.16x ≤ 500 - 25

62.16x ≤ 475

x ≤ 475 ÷ 62.16

x ≤ 7.64 days

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Answer: I hope this helps you.

Step-by-step explanation:

The number of groups of 3/4 that are in 11/4 will be 3 2/3.

The number of 3/4 that are in 6 1/2 will be 8 2/3.

It should be noted that from the diagram given, you want to get solutions to the numbers circled and this will be solved accordingly.

The number of groups of 3/4 that are in 11/4 will be:

= 11/4 ÷ 3/4

= 11/4 × 4/3

= 11/3

= 3 2/3

Also, the number of 3/4 that are in 6 1/2 will be:

= 6 1/2 ÷ 3/4

= 13/2 ÷ 3/4

= 13/2 × 4/3

= 26/3

= 8 2/3

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Answer:

5 ornaments

Step-by-step explanation:

2 ornaments is 6 hours = 2/6 ornaments/hour = 1/3 ornaments/hour

1/3 ornaments/hour × 15 hours = 5 ornaments

In the Second order decomposition, 2.0008 m are needed after 78.3 s, the concentration of the remaining HI is 3.56 m.

Second-Order Reaction:

A second-order reaction system with a single reactant species will have a squared dependence of the reaction rate on this reactant's molarity value. Therefore, the rate will show an exponential decrease over time as the reactant is consumed.

The integrated rate law for a second-order reaction is

1/[A]t = 1/[A]0 + kt

where

[A]t = the concentration of A at time t

[A]0 = the concentration of A at time 0 (i.e., at the beginning of the reaction)

k = the rate constant for the reaction

Given,

The second-order decomposition of hi has a rate constant of 2.80 x 10⁻³ m⁻¹s⁻¹.

Time = 78.3 s

Initial Concentration = 3.56 m

Here we need to find the second order decomposition.

Apply the values on the formula,

Then we get,

=> 1/[A]t = 1/(3.56 m) + 2.80 × 10⁻³ m⁻¹s⁻¹ x 78.3 s

=> 1/[A]t = 0.28 m⁻¹ + 0.2192 m⁻¹

=> 1/[A]t = 0.4992 m⁻¹

=> 1/[A]t = 1/0.4992 m

=> 1/[A]t = 2.0008 m

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Answer: let's see... the coefficient of a number is Placed in front of a variable like 2y. so it's 2y

Step-by-step explanation: your welcome

Answer:

Could you show how the graph looks like?

Step-by-step explanation: