Answer:
look at the pictures
Step-by-step explanation:
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1 answer:
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Answer:
Step-by-step explanation:
We are asked to find the length of the third side in a triangle, given the other 2 sides.
Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.
In this theorem, <em>a</em> and <em>b</em> are the legs of the triangle and <em>c</em> is the hypotenuse.
We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.
- b= 5
- c= 10
Substitute the values into the formula.
Solve the exponents.
- (5)²= 5*5 = 25
- (10)²= 10*10= 100
We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.
a is being squared. The inverse of a square is the square root, so we take the square root of both sides.
Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 up to a 7 in the tenth place.
The length of the third side is approximately <u>8.7</u>
Answer:
a) 1,440 ways
b) 59,280 or 64,000
Step-by-step explanation:
a) Aircraft boarding.
8 people, 2 in first class, boarding first, then 8 economy class.
The 2 people in first class board first, but they can board as AB or BA... so 2 ways here.
For the 6 economy class passengers, we have a permutation of 6 out of 6, so 720, as follows:
Since the two are independent, we multiply them to have a global number of ways: 2 * 720 = 1,440 different ways for the 8 passengers to board that plane.
b) combination lock.
Here we do have a little problem... the question doesn't specify if the 3 numbers are different numbers of not. So, we'll calculate both:
Numbers go from 1 to 40 inclusively... so 40 possibilities.
Normally, in a combination lock, the numbers are different, so let's start with that one:
First number: 40 options available
Second number: 39 options available (cannot take the first one again)
Third number: 38 different options (can't take First or Second number again)
Overall, we then have 40 * 39 * 38 = 59,280 different lock combinations.
If we can pick pick the same number twice:
First number: 40 options available
Second number: 40 options available
Third number: 40 options available
Overall 40 * 40 * 40 = 64,000 different lock combinations
