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).
Answer:
- sin(X) = 6/7.5
- XY = 4.5
- cos(X) = 4.5/7.5
- tan(X) = 6/4.5
Step-by-step explanation:
It is convenient to use the Pythagorean theorem to find XY to start with. That theorem tells you ...
XZ² = YZ² + XY²
Solving for XY, you find ...
XY² = XZ² - YZ²
XY = √(XZ² - YZ²) = √(7.5² -6²) = √(56.25 -36) = √20.25
XY = 4.5
The mnemonic SOH CAH TOA is very helpful here. It reminds you that ...
Sin = Opposite/Hypotenuse
sin(X) = 6/7.5
Cos = Adjacent/Hypotenuse
cos(X) = 4.5/7.5
Tan = Opposite/Adjacent
tan(X) = 6/4.5
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<em>Comment on the triangle and ratios</em>
The side lengths of this triangle are in the ratios ...
XY : YZ : XZ = 3 : 4 : 5
If you recognize that the given sides are in the ratio 4 : 5, this tells you that you have a "3-4-5" right triangle with a scale factor of 1.5. At least, you can find XY = 1.5·3 = 4.5 with no further trouble.
The trig ratios could be reduced to sin(X) = 4/5; cos(X) = 3/5; tan(X) = 4/3, but the wording "don't simplify" suggests you want the numbers shown on the diagram, not their reduced ratios.
Answer:
Step-by-step explanation:
She has 36 yards of material.
She needs 1 1/3 + 1/6 for each place setting
1/3 + 1/6 = 1/2
She needs 1 1/2 yards of material for each setting
1 1/2 = 1.5
She has to divide 36 by 1.5. If there is anything left over, it becomes scrap to be used for her next project.
You can use the following formula
- # settings = Total material/setting length
- # settings = 36/1.5 = 24
She can make 24 settings with nothing left over.
Answer:
about 4.9x10^5
Step-by-step explanation:
(4.9x10^5-5.8x10^4)= 4899999.9994
