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Darya [45]
3 years ago
9

Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class ta

ken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal.
Let C represent the number of classes a customer takes.
Provide an inequality and the minimum number of classes a customer can take for Rebekah to meet her goal.
Mathematics
2 answers:
Sonja [21]3 years ago
6 0

Answers:

The inequality is 12C+35 \ge 100

The minimum number of classes a customer can take is <u>6 classes</u>

===========================================================

Explanation:

The expression 12C+35 represents how much a customer spends when they take C number of classes. The C is a placeholder for any positive whole number.

For instance, if they take C = 2 classes, then they spend 12*C+35 = 12*2+35 = 59 dollars.

Or if they take C = 3 classes, then they spend 12*C+35 = 12*3+35 = 71 dollars and so on.

We could try various values of C to find when 12C+35 is 100 or larger.

Or we can use algebra as shown in the next section.

---------------

12C+35 \ge 100\\\\12C \ge 100-35\\\\12C \ge 65\\\\C \ge \frac{65}{12}\\\\C \ge 5.4167 \ \text{ (approximate)}\\\\

Because C is a positive whole number, we round up from 5.4167 to 6

We would not round to 5 even though 5.4167 is closer to 5 (hence the phrasing round up, instead of simple rounding).

If the customer took C = 5 classes, then they spend 12*C+35=12*5+35 = 95 dollars which is 5 short of the goal

But if they take C = 6 classes, then we're over the goal because 12*C+35 = 12*6+35 = 107. Larger values of C will result in larger total costs.

So the minimum number of classes a customer can take is 6 classes and this will allow Rebekah to reach her goal of $100 or more.

Maru [420]3 years ago
5 0

Answer:

Inequality: 12c + 35 ≥ 100

Minimum number of classes per customer: 6

Step-by-step explanation:

12c + 35 ≥ 100

      - 35     -35

12c ÷ (12) ≥ 65 ÷ (12)

c ≥ 5.4 (so 6)

Hope this helps good luck!

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Below is a list of city elevations.
Nezavi [6.7K]

Answer:

Oxford, MS, has the highest elevation.

Death Valley, CA, has the lowest elevation.

The elevation of New Orleans, LA, is at sea level.

The elevation of Death Valley, CA, is the furthest from sea level.

Step-by-step explanation:

Given the elevations of few cities as follows:

Elevation of Oxford, MS = 178 feet

Elevation of Death Valley, CA  = -282 feet

Elevation of New Orleans, LA  = 0 feet

Elevation of Palm Beach, FL  = 13 feet

To find:

The true statement of the following:

Oxford, MS, has the highest elevation.

Death Valley, CA, has the lowest elevation.

West Palm Beach, FL, has the lowest elevation.

The elevation of Death Valley, CA, is at sea level.

The elevation of New Orleans, LA, is at sea level.

The elevation of Death Valley, CA, is the furthest from sea level.

The elevation of New Orleans, LA, is the furthest from sea level.

Solution:

First of all, let us put the given elevations in ascending order.

Smallest value is -282 feet, then 0 feet, then 13 feet and then 178 feet.

-282 < 0 < 13 < 178 feet

i.e.

Elevation of Death Valley < Elevation of New Orleans < Elevation of West Palm Beach < Elevation of Oxford

Elevation of 0 feet means that it is at the sea level i.e. New Orleans is at sea level.

Largest value is 178 i.e. the highest elevation is of Oxford.

Minimum value is -282 i.e. the lowest elevation is of Death Valley.

Death valley is furthest from sea level at a distance of 282 feet.

Therefore, the answer is:

Oxford, MS, has the highest elevation.

Death Valley, CA, has the lowest elevation.

The elevation of New Orleans, LA, is at sea level.

The elevation of Death Valley, CA, is the furthest from sea level.

8 0
2 years ago
Find the missing segment in the attached image
uranmaximum [27]

Answer:

25 units

Step-by-step explanation:

This problem can be solved by using concept of Basic proportionality theorem.

This theorem states that if there is line drawn parallel to any side of the triangle, and it intersect the other two sides, then

segment divided on those two sides are in equal proportion.

Let naem this triangle

the side containing 15 and 6 be AB, with A be point on segment having length 15 units

B be  point on segment having length 6 units

c be point on segment having length ? units

DE line parallel to BC

Thus, if apply Basic proportionality theorem. in this then ratio formed will be

15/6 = ?/10

5/2 = ?/10

?= 5/2* 10 = 25

The length of missing segment is 25 units.

6 0
3 years ago
A teacher gave a test with 50 questions, each worth the a a teacher gave a test with 50 questions, each the same number of point
igomit [66]

Answer:

Marci answered 40 out of 50

Marci answered 2 more questions correctly.

Step-by-step explanation:

Donovan got 38 out of 50

Marci got 80% which means 40 out of 50

40-38 = 2

6 0
2 years ago
Find the complex fourth roots \[-\sqrt{3}+\iota \] in polar form.
____ [38]

Let z=-\sqrt3+i. Then

|z|=\sqrt{(-\sqrt3)^2+1^2}=2

z lies in the second quadrant, so

\arg z=\pi+\tan^{-1}\left(-\dfrac1{\sqrt3}\right)=\dfrac{5\pi}6

So we have

z=2e^{i5\pi/6}

and the fourth roots of z are

2^{1/4}e^{i(5\pi/6+k\pi)/4}

where k\in\{0,1,2,3\}. In particular, they are

2^{1/4}e^{i(5\pi/6)/4}=2^{1/4}e^{i5\pi/24}

2^{1/4}e^{i(5\pi/6+2\pi)/4}=2^{1/4}e^{i17\pi/24}

2^{1/4}e^{i(5\pi/6+4\pi)/4}=2^{1/4}e^{i29\pi/24}

2^{1/4}e^{i(5\pi/6+6\pi)/4}=2^{1/4}e^{i41\pi/24}

7 0
3 years ago
Which region represents the solution to the given system of inequalities?<br><br>​
TEA [102]

The first equation shows C and D, and the second shows C and B. The overlap will be at C, so thats the answer.

7 0
3 years ago
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