Combinatorial Enumeration. That whole class was a rollercoaster ride of mind-blowing generating functions to prove crazy things. The exam had ridiculous questions like 'count the number of cactus trees with n vertices such that etc etc etc' and you'd do three pages of terrible terrible sums and algebra. Then your final answer would be something beautiful like n/2 and you'd breath a sigh of relief and thank the math gods.
Answer:
y = (-1/2)x + 5
Step-by-step explanation:
As we move from the y-intercept (0, 5) to the x-intercept (10,0), x increases by 10 units while y decreases by 5 units. Thus, the slope of this line is
m = rise / run = -5 / 10 = -1/2.
Since we know both the slope and the y-intercept of this line, let's use the slope-intercept form of the equation of a straight line: y = mx + b.
Substituting -1/2 for m and 5 for b, we get:
y = (-1/2)x + 5
Answer:
y= 4x − 7 or 0=0
Step-by-step explanation:
4x−y+−4x=7+−4x
1/3 of 30 would be 10. So 10 students walk to school.
Answer:
1.8 minutes or 108 seconds
Step-by-step explanation:
The question tells us that the larger belt moves 300 lbs in 2 mins. And this is equal to 150 lb per minute
The question also tells us that a smaller belt moves the same quantity of 300 lbs in 18 mins. And this is equal to an average of 16.667 lb per min.
Both belts will move at a rate of 166.667 lb per min.
So it will take them 300 / 166.667 = 1.8 min or 108 s.
Therefore, the answer is 1.8 min
