Answer:
The slope is 1/2.
The y-intercept is 1.
Step-by-step explanation:
We have:
Let’s divide both sides by 2. This gives us:
Simplify:
Add 3 to both sides:
Flip:
This is in the slope-intercept form:
Where m is the slope and b is the y-intercept.
Hence, our slope m is 1/2 and our y-intercept b is 1.
Answer:
45 ways
Step-by-step explanation:
We are given;
there are 3 different math courses, 3 different science courses, and 5 different history courses.
Thus;
Number ways to take math course = 3
The number of ways to take science course = 3
The number of ways to take history course = 5
Now, if a student must take one of each course, the different ways it can be done is;
possible ways = 3 x 3 x 5 = 45 ways.
Thus, number of different ways in which a student must take one of each subject is 45 ways.
Answer:
30^
Step-by-step explanation:
Answer:
$180000
Step-by-step explanation:
Let's c be the number of chair and d be the number of desks.
The constraint functions:
- Unit of wood available 4d + 3c <= 2000 or d <= 500 - 0.75c
- Number of chairs being at least twice of desks c >= 2d or d <= 0.5c
c >= 0
d >= 0
The objective function is to maximize the profit function
P (c,d) = 400d + 250c
We draw the 2 constraint functions (500 - 0.75c and 0.5c) on a c-d coordinates (witch c being the horizontal axis and d being the vertical axis) and find the intersection point 0.5c = 500 - 0.75c
1.25c = 500
c = 400 and d = 0.5c = 200 so P(400, 200) = $250*400 + $400*200 = $180,000
The 500 - 0.75c intersect with c-axis at d = 0 and c = 500 / 0.75 = 666 and P(666,0) = 666*250 = $166,500
So based on the available zones in the chart we can conclude that the maximum profit we can get is $180000
So we need to find a number that has the same ratio to 64 as 3 has to four. We do this by diving 64 into 4:(this is 16): so the two ratios are different by 16. To find the remaining number we multiply 3 by 16: this is 48. So 48 has the same ratio to 64 as 3 has to 4.
And 48 is the answer!
