Answer:
The total cost of the meal is $19.35.
Step-by-step explanation:
As Nicole ordered a $ 15 menu, and on that price she paid a tip of 20% and the town in which she bought it had a sales tax of 9%, the total cost of the meal is determined by performing the following calculation:
1- Menu $ 15
2- Tip $ 3 (15 x 0.2)
3- Sales tax $ 1.35 (15 x 0.09)
Thus, adding the three expenses, the total cost of the food for Nicole is $ 19.35 (15 + 3 + 1.35).
<span>Find the wind speed and the plane's airspeed.
:
Let s = speed of the plane in still air
Let w = speed of the wind
then
(s-w) = plane speed against the wind
and
(s+w) = plane speed with the wind
:
Change 3 3/8 hrs to 3.375 hrs
:
The trips there and back are equal distance, (1890 mi) write two distance equations
dist = time * speed
:
3.375(s-w) = 1890
3.0(s + w) = 1890
:
It is convenient that we can simplify both these equations:
divide the 1st by 3.375
divide the 2nd by 3
resulting in two simple equations that can be used for elimination of w
s - w = 560
s + w = 630
----------------adding eliminates w, find s
2s = 1190
s =
s = 595 mph is the plane speed in still air
Find w
595 + w = 630
w = 630 - 595
w = 35 mph is the wind spee</span>
Answer:
a) -7/9
b) 16 / (n² + 15n + 56)
c) 1
Step-by-step explanation:
When n = 1, there is only one term in the series, so a₁ = s₁.
a₁ = (1 − 8) / (1 + 8)
a₁ = -7/9
The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.
sₙ = sₙ₋₁ + aₙ
(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ
(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ
aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)
If you wish, you can simplify by finding the common denominator.
aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]
aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)
aₙ = 16 / (n² + 15n + 56)
The infinite sum is:
∑₁°° aₙ = lim(n→∞) sₙ
∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)
∑₁°° aₙ = 1
So for 1: You divide 1780 by 36 to get your answer. You will get a remainder but in this situation, we ignore it since you wouldn’t be able to wrap another gift completely
2: Divide 247 by 52. Again, you will get a remainder but in this situation we found up to the nearest whole because to be able to take all the kids, you would need another bus.
3: Divide 98 by 28. You will get a remainder, then you take that and divide it by 28, and simplify it, to get the fraction
