Answer:
The speed of the first train is 45 mph and the speed of the second train is 75 mph
Step-by-step explanation:
Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).
The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles
The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles
Since the second train overtakes the first at 6:00 pm, hence:
3x + 90 = 5x
2x = 90
x = 45
Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).
Answer:

Step-by-step explanation:
We have the equation of the position of the object

We need to solve the equation for the variable a

Subtract
and
on both sides of the equality


multiply by 2 on both sides of equality


Divide between
on both sides of the equation

Finally

Answer:
10
Step-by-step explanation:
2+2=4
4+6= 10
A unit rate simply means how many of one type of units you get per 1 other type of unit.
Examples of that:

This is rate of fluid flow of some pump for example. It pumps 300 liters every second.
Other example:

This is example for speed. Somebody is moving at 50 kilometers per hour (every hour he travels 50 kilometers)
Answer:
A. .1070
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they make a purchase, or they do not. The probability of a customer making a purchase is independent from other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.
Forty-four percent of customers who visit a department store make a purchase.
This means that 
What is the probability that in a random sample of 9 customers who will visit this department store, exactly 6 will make a purchase?
This is
when n = 9. So


So the correct answer is:
A. .1070