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sesenic [268]
3 years ago
14

Write a linear cost function for the situation. Identify all variables used. A parking garage charges 4 dollars plus 65 cents pe

r half-hour. A linear cost function for the situation is C(x)=L (Use integers or decimals for any numbers in the expression)
Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0

Answer:

The linear cost function is C(x)=1.3x+4 dollar.

Step-by-step explanation:

Given : A parking garage charges 4 dollars plus 65 cents per half-hour. A linear cost function for the situation is C(x)=L.

To find : Write a linear cost function for the situation ?

Solution :

Cost function is defined as sum of marginal cost and fixed cost.

Let x be the number of hours i.e. time for which parking cost.

A parking garage charges 4 dollars plus 65 cents per half-hour.

The fixed price is $4.

Marginal cost is 65 cents per half-hour.

Converting cents into dollar,

1 cent = 0.01 dollar

65 cent = 0.65 dollar

The cost of \frac{1}{2} hour = $0.65

The cost of x hours = 0.65\times 2x

So, marginal cost is $1.3x.

Cost function is defined as

C(x)=MC+FC

C(x)=1.3x+4

C(x)=1.3x+4 dollar.

Therefore, The linear cost function is C(x)=1.3x+4 dollar where x is the number of hours.

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2 years ago
Solve each problem. NO LINKS!!!!!​
Sauron [17]
<h3>Answers:</h3>
  • Problem 10) There are 220 combinations
  • Problem 11) There are 126 combinations
  • Problem 12) There are 154,440 permutations
  • Problem 13) There are 300 different ways

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

Explanations:

Problem 10

The order of the toppings doesn't matter. All that matter is the group itself. We'll use the combination formula nCr = (n!)/(r!*(n-r)!) where n = 12 and r = 3 in this case.

So,

nCr = (n!)/(r!*(n-r)!)

12C3 = (12!)/(3!*(12-3)!)

12C3 = (12!)/(3!*9!)

12C3 = (12*11*10*9!)/(3!*9!)

12C3 = (12*11*10)/(3*2*1)

12C3 = 1320/6

12C3 = 220

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

Problem 11

Like with problem 10, the order doesn't matter. This is assuming that each member on any given team has the same rank as any other member.

If you used the nCr combination formula, with n = 9 and r = 5, you should get the answer 126

Here's another way to get that answer.

There are 9*8*7*6*5 = 15120 different permutations. If order mattered, then we'd go for this value instead of 126

Within any group of five people, there are 5! = 120 different ways to arrange them. So we must divide that 15120 figure by 120 to get the correct value of 126 combinations

15120/120 = 126

Note the connection between nCr and nPr, namely,

nCr = (nPr)/(r!)

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

Problem 12

Now this is where order matters, because the positions in basketball are different (eg: a point guard differs from a center).

We have 13 choices for the first position, 12 for the second, and so on until we reach 13-r+1 = 13-5+1 = 9 as the number of choices for that last slot.

So we'll have 13*12*11*10*9 = 154,440 different permutations

Now if the condition that "each player can play any position" isn't the case, then the answer would very likely be different. This is because for the center position, for instance, we wouldn't have 13 choices but rather however many choices we have at center. To make the problem simpler however, your teacher is stating that any player can play at any slot. Realistically, the answer would be far less than 154,440

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

Problem 13

We have 6 applications for the 2 math positions. Order doesn't matter. That means we'll have 6C2 = 15 different ways to pick the math people. Use the nCr formula mentioned in problem 10. Since we'll use this value later, let's make x = 15.

There are 2 people applying for the chemistry teaching position, meaning there are 2 ways to fill this slot. We could compute 2C1 = 2, but that's a bit overkill in my opinion. Let y = 2 so we can use it later.

Similarly, there are 10 applicants for the Spanish teacher position, leading to 10 ways to get this position filled. You could compute 10C1 = 10 if you wanted to. Let z = 10 so we can use it later.

Once we figured out those x,y,z values, we multiply them together to get our final answer: x*y*z = 15*2*10 = 30*10 = 300

There are 300 different ways to select 2 math teachers, a chemistry teacher, and a Spanish teacher from a pool of 6 math applicants, 2 chemistry applicants, and 10 Spanish teacher applicants.

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