Answer:
, 
Step-by-step explanation:
The velocity function of the projectile is obtained by deriving the position function:

Now, the velocities after 3 and 15 seconds are, respectively:




We define the probability of a particular event occurring as:

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are <em>independent</em>, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for <em>each </em>of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.
Now that we've found the number of possible outcomes, we need to find the number of <em>desired</em> outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is <em>at least one 5 rolled</em>. It turns out, there are only 3:
(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5
So, we have

probability of rolling at least one 5.
Answer:
1357, 1359, 1579, 1573, 1375, 1379, 1957, 1953
Step-by-step explanation:
Since this number needs to be less than 2000, the first number has to be 1. You can randomly pick and choose any of the numbers after that.
Answer:
x = 3, y = 6
Step-by-step explanation:
In the figure attached,
If ΔADE and ΔABC are similar triangles, their corresponding sides will be in the same ratio.
By this property,




3x = 2x + 3
3x - 2x = 3
x = 3
Similarly, 

y = 
y = 6
Answer:

Step-by-step explanation:
A fraction can be found be taking the current amount over the total amount:

Since Darlene has only typed 23 pages out of 59, her fraction is 23 over 59. Fractions must always be in simplest form, which means that both the numerator and denominator can no longer be divided by the same factor. Since the numbers 23 and 59 are both prime and have no other factors other than 1 and themselves, the fraction 23/59 is in simplest form.