Answer:
a) The student cannot receive an A in the class.
b) The student must score 119 in the third exams to make an A. This is clearly not possible, since he cannot make 119 in a 100-points exam.
c) The student can make a B but he must score at least 84 in the third exam.
Step-by-step explanation:
To make an A, the student must score 315 (350 x 90%) in both home and the three exams.
The student who scored 35 (7 + 8 + 7 + 5 + 8) in the homework and 161 (81 + 80), getting a total of 196, is short by 119 (315 - 196) scores in making an A.
To make a B, the student must score 280 (350 x 80%) or higher but not reaching 315.
B ≥ 280 and < 315.
Since, the student had scored 196, he needs to score 84 and above to make a B in the last exam.
Answer:
In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.
The full correct process is:
(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15
= 4m - 6m + 9 + 15
= -2m + 24
Answer:
B ∪ C = (-∞, ∞)
B ∩ C = [1, 7)
Step-by-step explanation:
B ∪ C: The union of two sets or intervals is the set of elements which are in <em>either </em>set.
B ∩ C: The intersection of two sets or intervals is the set of elements which are in <em>both </em>sets.
<u>Interval notation symbols</u>
Square brackets [ ]: both endpoints are included in the set.
Round brackets ( ): both endpoints are excluded in the set.
Round, square ( ]: left endpoint is excluded and right endpoint is included in the set.
Square, round [ ): left endpoint is included and right endpoint is excluded in the set.
Given:
- B = {z | z ≥ 1}
- C = {z | z < 7}
Therefore,
B = [1, ∞)
C = (-∞, 7)
Therefore, B ∪ C = (-∞, ∞)
As z is either less than 7, or equal to or more than 1 then the intersection is:
B ∩ C = {z | 1 ≤ z < 7} = [1, 7)
Let us call the rate as velocity. Now the velocities of the plane and of the wind are:
and
:
Now
case 1:
case 2:
from equation 2:
substitute in equation 1:
Which is your velocity in still air (without wind)
Substituting back in:
you get:
which is the wind velocity
