Answer:
120
Step-by-step explanation:
If order doesn't matter, there are 10 ways to chose the first ride, 9 ways to choose the second, and 8 ways to choose the third. This product (720) has you riding the same 3 coasters in 6 different orders. Dividing by 6 gives ...
720/6 = 120 different combinations of roller coasters
_____
This number might be written as 10C3 (choose 3 from 10). The meaning of that notation is ...
nCk = n!/(k!(n-k)!)
10C3 = 10!/(3!·7!) = 10·9·8/(3·2·1) = 120
<h2>Answer: A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm </h2>
The parallelogram in the figure has an area of 
, according to the following formula, which works for all rectangles and parallelograms:
(1)
Where 
is the base and 
is the height
The<u> area of a triangle</u> is given by the following formula:
(2)
So, for option A:
Now, the <u>area of a trapezoid </u>is:
(3)
For option B:
For option C:
>>>>This is the correct option!
For option D:
<h2>Therefore the correct option is C</h2>
The problem is asking how much each person will need to pay. Simplifying the problem into an equation with variables (an algorithm) will greatly help you solve it:
S = Sales Tax = $ 7.18 per any purchase
A = Admission Ticket = $ 22.50 entry price for one person (no tax applied)
F = Food = $ 35.50 purchases for two people
We know the cost for one person was: (22.50) + [(35.50/2) + 7.18] =
$ 47.43 per person. Now we can check each method and see which one is the correct algorithm:
Method A)
[2A + (F + 2S)] / 2 = [ (2)(22.50) + [35.50 + (2)(7.18)] ]/ 2 = $47.43
Method A is the correct answer
Method B)
[(2A + (1/2)F + 2S) /2 = [(2)(22.50) + 35.50(1/2) + (2)7.18] / 2 = $38.55
Wrong answer. This method is incorrect because the tax for both tickets bought are not being used in the equation.
Method C)
[(A + F) / 2 ]+ S = [(22.50 + 35.50) / 2 ] + 7.18 = $35.93
Wrong answer. Incorrect Method. The food cost is being reduced to the cost of one person but admission price is set for two people.
Answer:
d. converges, -25
Step-by-step explanation:
An infinite geometric series converges if the absolute value of the common ratio is less than 1.
Here, the common ratio is 4/5:
| 4/5 | = 4/5 < 1
So the series converges. The sum of an infinite geometric series is:
S = a₁ / (1 − r)
where a₁ is the first term and r is the common ratio.
Here, a₁ = -5 and r = 4/5:
S = -5 / (1 − 4/5)
S = -25
Multiply the equation:
The solution set is the same, because multiplying both sides of an equation by a non-zero number doesn't change the solution set. In fact, if you rewrite the equation as
Multiplying this by 3 (or whatever number, for all it matters) gives
Now, a product is zero if and only if at least one of the factor is zero. So, either 
or
Since the first is clearly impossible, the second one must be true, which is the original equation.
