9514 1404 393
Answer:
(4) 750 < p < 1500
Step-by-step explanation:
The total cost for p people is ...
c = 750 +2.25p
The average cost per person is this total divided by the number of people:
c/p = (750 +2.25p)/p
c/p = (750/p) +2.25
Natasha wants this to be between 2.75 and 3.25:
2.75 < c/2 < 3.25
2.75 < 750/p +2.25 < 3.25 . . . . . . use the expression for c/p
0.50 < 750/p < 1.00 . . . . . . . . . . . subtract 2.25
We can split this to two inequalities to find the limits of p.
<u>Left one</u>
0.50 < 750/p
0.50p < 750 . . .multiply by p
p < 1500 . . . . . . multiply by 2
<u>Right one</u>
750/p < 1
750 < p . . . . . . multiply by p
These bounds on p can be summarized as ...
750 < p < 1500 . . . . matches choice (4)
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<em>Additional comment</em>
Once you realize that the fixed costs will be divided by the number of people attending, the maximum cost you want ($1 more than the per-person charge) will set the minimum number of people. To have the $750 fixed cost contribute only $1 to the cost per person, there must be at least 750 people to share that cost. The only answer choice with a 750 person minimum is (4).
This problem can be solved using the Pythagorean Theorem.
<em>Note: the height of the telephone pole is unnecessary information.</em>
Convert the measurement in feet to inches.
The length from the base of the pole to the anchor point on the ground is 
inches. The distance from the base of the pole to the anchor point on the pole is 
inches.
These are the two legs of a right triangle. The length of the stabilizing cable is the hypotenuse of the right triangle.
The Pythagorean Theorem is:
In this formula, 
and 
are the legs and 
is the hypotenuse.
Plug in the known values.
Swap the sides of the equation.
Evaluate the powers.
Simplify using addition.
Take the square root of both sides.
Separate the solutions.
Length and distance cannot be negative, so remove the negative solution.
