<em>a</em> = 8 - a train arrives at the station once every 8 minutes, so for any given 8 minute interval, a randomly selected train has uniform probability of arriving at the station at some point in this time.
<em>f(x)</em> = 1/8 - the area under the graph of <em>f(x)</em> must be equal to 1. This area corresponds to a rectangle with length <em>a</em> = 8 and height <em>x</em> such that 8<em>x</em> = 1. Solving for <em>x</em> gives 1/8.
<em>P</em> = 5/8 - this is equal to the area under the graph over the interval [0, 5], which is the area of a rectangle with length 5 and height 1/8.
Two positive integers have gcd (a, b) = 15 and lcm (a, b) = 90. Those two numbers are 15 and 90 or 30 and 45.
Suppose we have 2 positive integers, a and b, then:
gcd (a, b) = the greatest common divisor = common prime factors of a and b
lcm (a, b) = the least common multiple = multiplication of the greatest common prime factors of a and b
In the given problem:
gcd (a, b) = 15
prime factorization of 15:
15 = 3 x 5
Hence,
a = 3 x 5 x ....
b = 3 x 5 x ....
lcm (a, b) = 90
prime factorization of 90:
90 = 3 x 5 x 2 x 3
Therefore the possible pairs of a and b are:
Combination 1:
a = 3 x 5 = 15
b = 3 x 5 x 2 x 3 = 90
Combination 2:
a = 3 x 5 x 2 = 30
b = 3 x 5 x 3 = 35
We can conclude the two integers are 15 and 90 or 30 and 45.
Learn more about gcd here:
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Answer: 504
Step-by-step explanation:
First of all, there are 3 places.
_ _ _
In the first place, any of the 9 horses can be first.
9 _ _
Now, 8 horses are remaining. You can put any of those 8 horses in second place.
9 8 _
Finally, 7 horses are remaining. You can put any of those 7 horses in third place.
9 8 7
We multiply these numbers to find ways horses can be 1st, 2nd or 3rd in race.
= 9 × 8 × 7
= 504
Answer: 16y
Step-by-step explanation: Done this before so easy obviously 16y
Answer:
5182
Step-by-step explanation:
To figure out the mean of a number, you must add all of the numbers together and divide by the amount of numbers you added up.
To find the total sum, we just need to reverse this process.
We are already given the final number so all we have to do is multiply the mean by 100 and we have our answer of 5182.
Hope this helps :D