Solve the equation -128 = 4x for x

Charles should hire 20 workers for each hour.

To determine the optimal number of workers to hire, Charles needs to compare the marginal cost and marginal benefit of each additional worker.

The marginal benefit of each worker is the additional number of drinks they can produce multiplied by the average selling price per drink. The marginal cost is the hourly wage of each worker multiplied by the number of hours they work.

Initially, the marginal benefit of the first worker is 20 drinks * $3/drink = $60.

The marginal cost is $15/worker * 8 hours = $120.

The second worker has a marginal benefit of 18 drinks * $3/drink = $54.

The marginal cost is still $120.

For each additional worker hired, the marginal benefit decreases by 2 drinks * $3/drink = $6, while the marginal cost remains constant at $120.

Charles should hire workers as long as the marginal benefit is greater than the marginal cost.

Once the marginal benefit is equal to or less than the marginal cost, it is no longer profitable to hire more workers.

Therefore, Charles should hire workers until the marginal benefit is equal to the marginal cost, which occurs when the marginal benefit is $120.

To find out how many workers will provide a marginal benefit of $120, we set the marginal benefit equal to $120 and solve for the number of workers:

$6 * n = $120

$n = 20

For more questions on marginal benefit

https://brainly.com/question/8136407

#SPJ4

Then it will take approximately 6.3 hours for the culture to grow to 80,000 bacteria

The given formula for the number of bacteria in a culture after t hours is:y = 5000(3)^tWe are required to find the number of hours it will take the culture to grow to 80,000.

This can be done by setting y equal to 80,000 and then solving for t.5000(3)^t = 80,000

Divide both sides by 5000:3^t = 16Now, we need to solve for t by taking the logarithm of both sides.

However, it is easier to use logarithmic properties to simplify the equation first.3^t = 2^4

Raise both sides to the power of (1/log3):log3(3^t) = log3(2^4)t = 4/log3(2)Using a calculator, log3(2) ≈ 0.631, so:t ≈ 4/0.631 ≈ 6.3.

To learn more about : hours

https://brainly.com/question/14628994

#SPJ8

Answer:

y = - x + 1

Step-by-step explanation:

b = 3 - (-1)(-2) = 3 - 2

b = 1

y = -x +1

You don't give much information but I will give you the definition of "density".

In all simpleness, the definition of density is the compactness of a substance.

Density can be found with the formula; p = m/v

p = density

m = mass

v = volume

Best of Luck!

Answer:

1) 1:2          2) 3

3) 1:8         4) 2:7

5) 1:4         6) 3:7

7) 2:5         8) 3:11

9) 2:7         10) 4:7

11) 8:9        12) 7:11

13) 1:2        14) 3

15) 26:27   16) 1:40

17) 1:10       18) 1:100

19) 1000    20) 10

Step-by-step explanation:

Answer:

5π/4 radians or 225°

Step-by-step explanation:

The perimeter of Todd’s sandbox is found to be 20.8 feet.

As the angles of both triangles are to be kept same.

Applying the similarity of triangles.

Let 'x' and 'y' be the two unknown sides of triangle.

14/ x = 20/8 = 18/y

14/ x = 20/8

x = 14*8 / 20

x = 5.6

20/8 = 18/y

y = 18*8 / 20

y = 7.2

Perimeter of Todd’s sandbox:

= x + y + 8

= 5.6 + 7.2 + 8

= 20.8

Thus,  the perimeter of Todd’s sandbox is found to be 20.8 feet.

To know more about the similarity of triangles, here

https://brainly.com/question/14285697

#SPJ1

Answer:

Domain:\(0 \le t \le 9\)

Range: \(7200 \ge \ d \ge \ 0\)

Step-by-step explanation:

Given

\(d = 7200 - 800t\)

Required

Determine the domain and range

From the attached graph, the values of t (on the horizontal axis) starts from 0 and ends at 9.

Hence, the domain is: \(0 \le t \le 9\)

When t = 0:

\(d = 7200 - 800t = 7200 - 800 * 0 = 7200\)

When t = 9

\(d = 7200 - 800t = 7200 - 800 * 9 = 0\)

Hence, the range is:

\(7200 \ge \ d \ge \ 0\)

Answer:

180+27x=p

Step-by-step explanation:

Answer:

Option A is correct

Step-by-step explanation:

For the box y=mx+c

Hope this helps

Its A.

If you need something more explained go to the other answer.

Answer:

26

Step-by-step explanation:

2 squared equals 4. So 30 - 4 = 26

hope it helps!

Answer:

The probability that one marble drawn at random is not blue is 70%

Answer:

\(\frac{x+7}{3}\) (the second option)

Step-by-step explanation:

Hope this helps!

Answer:

X = 97.45 - 42

Step-by-step explanation:

If 42 + X = 97.45, X needs to be 97.45 - 42

you can do the same thing with smaller numbers, for example:

5 + X = 7

7 - 5= 2 and you can check for sure that this is the answer by adding them together 5 + 2= 7 so it's definitely the right answer

so for this question, 97.45- 42 = 55.45 so that's X

you can check that by 55.45 + 42 and if the answer is 97.45 that's the right answer!

I hope that makes sense

The key features of the given quadratic functions are listed below.

In Mathematics and Geometry, the graph of any quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0) i.e 3 > 0.

For the quadratic function y = 3x² - 5, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, -5).

Domain: [-∞, ∞]

Range: [-5, ∞]

For the quadratic function y = -2x² + 12x - 15, the key features are as follows;

Axis of symmetry: x = 3.

Vertex: (3, 3).

Domain: [-∞, ∞]

Range: [-∞, 3]

For the quadratic function y = -x² + 1, the key features are as follows;

Axis of symmetry: x = 0.

Vertex: (0, 1).

Domain: [-∞, ∞]

Range: [-∞, 1]

For the quadratic function y = 2x² - 16x + 30, the key features are as follows;

Axis of symmetry: x = 4.

Vertex: (4, -2).

Domain: [-∞, ∞]

Range: [-2, ∞]

Read more on quadratic functions here: brainly.com/question/24020644

#SPJ1

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

Learn more on Pythagorean theorem here;

https://brainly.com/question/343682

#SPJ1

The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

Read more about area at

https://brainly.com/question/24487155

#SPJ1

The mean of the distribution is 3

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

According to the first graph,

Given the bar of observations as :

0, 5, 6, 3, 1, 1, 3, 6, 4, 1

Here the Sum of Observations = 30

And the total number of observations = 10

The mean of the distribution = 30/10

The mean of the distribution = 3

According to the second graph,

Given the bar of observations as :

0, 1, 3, 3, 9, 0, 9, 4, 4, 1

Here the Sum of Observations = 34

And the total number of observations = 10

The mean of the distribution = 34/10

The mean of the distribution = 3.4

The mean of the distribution = 4 (closest)

Learn more about Arithmetic means here:

brainly.com/question/13000783

#SPJ1

Answer:

hihihihihihihiihihihihihi

Step-by-step explanation:

this figure can be divided into three parts one is rectangle other one is semicircle and the third one is one fourth of the circle .so let's find the area of each figure one by one. For the rectangle 12×8 =96

for semicircle that is on the top it has the radius 6 which is a half of 12

so area of the semicircle is

\( \frac{1}{2} \pi \: r {}^{2} \\ \frac{1}{2} \times 3.14 \times 6 {}^{2} \\ 3.14 \times 18 \\ 56.52\)

no that's fine. 80 of the 1/4 of the other Circle

\( \frac{1}{4} \pi {}^{2} \\ \frac{1}{4} 3.14 \times 8 {}^{2} \\ 3.14 \times 16 \\ 50.24\)

add all these areas

96+56.52+50.24 =202.76

Answer:

Step-by-step explanation:

110

Answer:

I dont really know

Step-by-step explanation:

The goal to proving identities is to transform one side into the other. We can only pick one side to transform while the other side stays the same the entire time. The general rule of thumb is to transform the more complicated side (though there may be exceptions to this guideline).

So I'll take the left hand side and try to turn it into \(\csc^2( B )\)

One way we can do that is through the following steps:

\(\frac{\tan(B) + \cot(B)}{\tan(B)} = \csc^2(B)\\\\\frac{\tan(B)}{\tan(B)} + \frac{\cot(B)}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\frac{1}{\tan(B)} = \csc^2(B)\\\\1 + \cot(B)*\cot(B) = \csc^2(B)\\\\1 + \cot^2(B) = \csc^2(B)\\\\1 + \frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)}{\sin^2(B)}+\frac{cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{sin^2(B)+cos^2(B)}{\sin^2(B)} = \csc^2(B)\\\\\frac{1}{\sin^2(B)} = \csc^2(B)\\\\\csc^2(B)=\csc^2(B) \ \ {\Large \checkmark}\\\\\)

Since we've shown that the left hand side transforms into the right hand side, this verifies the equation is an identity.

Answer:

Step-by-step explanation:

a) (x-1)(2x-5)

b) x=-1 x=-2.5      x+1=0 x=-1        2x-5=0      2x=5     x=2.5

c) The degree is even so the ends of the graph will point in the same direction, the leading coefficient is positive so both ends will point up

d) First plot the x intercepts, then plug f(0) into the equation to get the y intercept. Plot the y intercept and then connect the points

e)