So for the first one think of it as decimals so it’s easier: 9.20-7.35, subtract and it would be 1.85 so since we use decimals to make it easier it isn’t actually a decimal so it would be 2 hours and 25 minutes. And for the second one you just add 50 minutes to that and you would get 3 hours and 15 minutes.
Answer:
10 black marbles
Step-by-step explanation:
Let black marbles be=2x
Then white marbles=5x
Total marbles=7x which in turn is equal to 35. Hence x=5
Black marbles=2*5=10
H2H
Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Suppose
is the number of possible combinations for a suitcase with a lock consisting of
wheels. If you added one more wheel onto the lock, there would only be 9 allowed possible digits you can use for the new wheel. This means the number of possible combinations for
wheels, or
is given recursively by the formula
starting with
(because you can start the combination with any one of the ten available digits 0 through 9).
For example, if the combination for a 3-wheel lock is 282, then a 4-wheel lock can be any one of 2820, 2821, 2823, ..., 2829 (nine possibilities depending on the second-to-last digit).
By substitution, you have
This means a lock with 55 wheels will have
possible combinations (a number with 53 digits).
