Answer:
0.3333 = 33.33% probability that the employee will arrive between 8:15 a.m. and 8:25 a.m.
Step-by-step explanation:
A distribution is called uniform if each outcome has the same probability of happening.
The uniform distributon has two bounds, a and b, and the probability of finding a value between c and d is given by:
A particular employee arrives at work sometime between 8:00 a.m. and 8:30 a.m.
We can consider 8 am = 0, and 8:30 am = 30, so 
Find the probability that the employee will arrive between 8:15 a.m. and 8:25 a.m.
Between 15 and 25, so:
0.3333 = 33.33% probability that the employee will arrive between 8:15 a.m. and 8:25 a.m.
Answer:
You should graph the lines (0, 0) to (2, 120), (2, 120) to (2.5, 120), and (2.5, 120) to (3.5, 150).
Step-by-step explanation:
If we see, for the first part, she drive 60 miles an hour and drives for 2 hours. This means that after 2 hours, she has driven 60 * 2 = 120 miles in 2 hours. Then she spends 30 minutes, or half an hour, no moving forward as she changes the tire. Finally, she drives at 30 miles an hour for an hour. This means she has driven 120 + 30 = 150 miles in total after 3 and a half hours.
Our first line goes from (0, 0) to (2, 120), as thats how far we drove in 2 hours. The next line goes from (2, 120) to (2.5, 120), as she was changing a tire and made no progress. Finally, the last line goes from (2.5, 120) to (3.5, 150), as she drives for another hour at 30 miles an hour.
Answer:
x = 28 m
y = 14 m
A(max) = 392 m²
Step-by-step explanation:
Rectangular garden A (r ) = x * y
Let´s call x the side of the rectangle to be constructed with a rock wall, then only one x side of the rectangle will be fencing with wire.
the perimeter of the rectangle is p = 2*x + 2*y ( but in this particular case only one side x will be fencing with wire
56 = x + 2*y 56 - 2*y = x
A(r) = ( 56 - 2*y ) * y
A(y ) = 56*y - 2*y²
Tacking derivatives on both sides of the equation we get:
A´(y ) = 56 - 4 * y A´(y) = 0 56 - 4*y = 0 4*y = 56
y = 14 m
and x = 56 - 2*y = 56 - 28 = 28 m
Then dimensions of the garden:
x = 28 m
y = 14 m
A(max) = 392 m²
How do we know that the area we found is a local maximum??
We find the second derivative
A´´(y) = - 4 A´´(y) < 0 then the function A(y) has a local maximum at y = 14 m
Answer:
Table of values
<em>See attachment for graph</em>
Step-by-step explanation:
Given
Solving (a): Make a table
Considering the values of x from 0 to 5, we have:
When 
When 
When 
When 
When 
When 
So, we have:
Solving (b): The graph
See attachment
