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grigory [225]
2 years ago
6

The function, f(x)=70n-400, models the profit of the instructor of a guitar class per month, where n is the number of students e

nrolled in the class.
How many students must be enrolled in the class for the instructor to make a profit?


How many students must be enrolled in the class if the instructor needs to make 1,000.00 profit per month?

Mathematics
1 answer:
zimovet [89]2 years ago
4 0

profit=f(x)

so solve for f(x)=1000

1000=70n-400

add 400 to both sides

1400=70n

divide both sides by 70

20=n

20 students need to be enrolled to make a profit of 1000.00

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3 years ago
Can someone please teach me how to do this? You can please do like 2 questions and please explain exactly how you got the answer
spayn [35]

All of these questions require one thing: trigonometric functions.

There are 3 main trigonometric functions, which can only be used on right triangles: sine, cosine, and tangent.

Sine = opposite / hypotenuse

Cosine = adjacent / hypotenuse

Tangent = opposite / adjacent

When trying to figure out what function to use, we always start by looking from the angle. Take problem a, for example. Looking from angle E, of which the value is not given, we have the side opposite and the side adjacent. Therefore, we should use the tangent function.

---The hypotenuse is always the longest side of the triangle. It is never considered the opposite or adjacent side.

Let's set up our function with the given information from problem a.

tan(x) = 9.7 / 5.2

---The tangent of an unknown angle is equal to the quotient of the opposite side and the adjacent side.

Now, solving for the value of x will require a calculator. We'll need to use what's called an inverse trigonometric function. Most calculators have these directly above the regular trigonometric functions, and the inverse functions are accessed using a "second" key.

---Ensure that your calculator is in degrees, not radians!

x = tan^-1(9.7 / 5.2)

x = 61.805 = 62 degrees

Next, let's take a look at problem b. This time, we're solving for a side length instead of an angle. But, we're still going to start by looking from our angle.


Looking from the 38 degree angle, we are given the adjacent side and an unknown hypotenuse. Therefore, we should use the cosine function.

cosine(38) = 53.1 / r

---The cosine of a 38 degree angle is equal to the quotient of 53.1 and an unknown hypotenuse, r.

Use your algebra skills to isolate the variable r.

r * cosine(38) = 53.1

r = 53.1 / cosine(38)

---From here, all you need to do is plug this into your calculator. Since we are solving for a side length (and given an angle), we are just using the regular trigonometric function buttons on the calculator.

r = 67.385 = 67.4 units

Hope this helps!

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2 years ago
1. On Tuesday, 12 Kittens at the shelter were adopted and 4 dogs also found new homes. What percentage of the newly adopted pets
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3 years ago
The following data was collected from the manufacturing of an auto component. It represents the diameter (in mm) of that compone
kari74 [83]

Answer:

14.6

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(1). Row one = (10 + 12 + 12 + 14 ) = 48/4 = 12.

(2). Row Two: (12 + 11 + 13 + 16 ) = 52/4 = 13.

(3). Row three : (11 + 13 + 14 + 14)/4 = 13.

(4). Row four: (11 + 10 + 7 + 8)/4 = 36/4 = 9.

(5). Row five: (13 +12 + 14 + 13)/4 = 52/4 = 13.

(B). STEP TWO:

- determine the maximum and minimum value for each row.

- for each row, maximum - minimum.

Maximum values for each row:

Row one = 14, row two= 16, row three = 14, row four = 11 and row five = 14.

Minimum value for each row:

Row one = 10, row two = 11, row three = 11, row four =7 and row five = 12.

DIFFERENCES in each row :

row one = 14 - 10 = 4, row two = 16 - 11 = 5, row three = 14 - 11 = 3, row four = 11 - 7 = 4 and row five = 14 -12 = 2.

(C). STEP THREE: Calculate the mean of all the rows = 60/5 = 12.

(D). STEP FOUR : Calculate the Average Range = 18/5 = 3.6.

(E). STEP FIVE : Calculate the UCL.

A = Average rage × 0.729 = 3.6 × 0.729.

B = overall mean = 12.

UCL = A + B = 14.6.

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