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)
_____
<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).
Answer:
3
Step-by-step explanation:
%25 is 1/4
1/4 of 12 is 3
Answer:
If a triangle has side lengths 3, 4, and 5 units, then its area is 6
Step-by-step explanation:
<em><u>Deductive reasoning </u></em>represents an important form of logical reasoning in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true
we have
If a triangle has side lengths 3, 4, and 5 units, then its area is 6
we know that
1) If triangle has side lengths 3, 4 and 5, then is a right triangle because satisfy the Pythagoras Theorem
2) All right triangles have an area equal to one half the product of the two smaller side lengths
substitute the values
therefore
The statement is valid based on deductive reasoning
Answer:
The answer to your question is 2 rational solutions.
Step-by-step explanation:
Equation
y = x² - 8x + 2
Solve using the general formula
x = [8 ± √(-8)² - 4(1)(2)] / 2(1)
Simplification
x = [8 ± √64 - 8] / 2
x = [8 ± √56] / 2
x = [8 ± 2√14]2
x₁ = 4 + √14 x₂ = 4 - √14
As √14 is positive, we conclude that the equation has two rational solutions.
