Answer:
.
Step-by-step explanation:
We have been given two sets as A: {71,73,79,83,87} B:{57,59,61,67}. We are asked to find the probability that both numbers are prime, if one number is selected at random from set A, and one number is selected at random from set B.
We can see that in set A, there is only one non-prime number that is 87 as it is divisible by 3.
So there are 4 prime number in set A and total numbers are 5.
We can see that in set B, there is only one non-prime number that is 57 as it is divisible by 3.
So there are 3 prime number in set B and total numbers are 4.
Now, we will multiply both probabilities to find the probability that both numbers are prime. We are multiplying probabilities because both events are independent.
Therefore, the probability that both numbers are prime would be .
Answer:
50m/s
Step-by-step explanation:
We assum the direction the baseball is travelling to the bat is the positive direction at 20 m/s and is hit in the opposite at a faster speed. The change in velocity is the final velocity minus the initial velocity:
The change in velocity is 50m/s
Answer:
See Below.
Step-by-step explanation:
Problem 1)
We want to simplify:
First, let's factor the denominators of each term. For the second term, we can use the difference of two squares. Hence:
Now, create a common denominator. To do this, we can multiply the first term by (<em>a</em> + 1) and the second term by (<em>a</em> + 2). Hence:
Add the fractions:
Factor:
Simplify:
We can expand. Therefore:
Problem 2)
We want to simplify:
Again, let's create a common denominator. First, let's factor out a negative from the second term:
Now to create a common denominator, we can multiply the first term by (<em>a</em> - <em>c</em>) and the second term by (<em>a</em> - <em>b</em>). Hence:
Subtract the fractions:
Distribute and simplify:
Cancel. Hence:
Answer:
The answer is d) 22.4
Step-by-step explanation:
I attached a file below if you want to see the process!
