Answer:
1
Step-by-step explanation:
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Answer:
37/3
Step-by-step explanation:
57% of students studied, which decomposes into 52% who both studied and saw an increase in their exam grade 5% who both studied and did Not see an increase in their exam grade The percentages above are relative to the whole population of 100 students, to get the requested probability, recall that: One way to find out the probability of an event is to Take the ratio of the number of times the event happened, over the total number of times the event could have happened. Total number of times the event happened: 52 = 52% of 100 students studied and saw an increase in their exam grade Total number of times the event could have happened: 57 = 57% of 100 students studied
Answer:
- The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.
- Below are all the steps explained in detail.
Explanation:
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<u>1. Name the variables:</u>
- x: number of smaller lifts
- y: number of larger lifts
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<u>2. Build a table to determine the number of hours each lift requires from each department:</u>
<u></u>
Number of hours
small lift large lift total per department
Welding department 1x 3y x + 3y
Packaging department 2x 1y 2x + y
<u></u>
<u>3. Constraints</u>
- 150 hours available in welding: x + 3y ≤ 150
- 120 hours available in packaging: 2x + y ≤ 120
- The variables cannot be negative: x ≥ 0, and y ≥ 0
Then you must:
- draw the lines and regions defined by each constraint
- determine the region of solution that satisfies all the constraints
- determine the vertices of the solution region
- test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)
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<u>4. Graph</u>
See the graph attached.
Here is how you draw it.
- x + 3y ≤ 150
- draw the line x + 3y = 150 (a solid line because it is included in the solution set)
- shade the region below and to the left of the line
- 2x + y ≤ 120
- draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
- shade the region below and to the left of the line
- x ≥ 0 and y ≥ 0: means that only the first quadrant is considered
- the solution region is the intersection of the regions described above.
- take the points that are vertices inside the solutoin region.
<u>5. Test the profit function for each vertex</u>
The profit function is P(x,y) = 25x + 90y
The vertices shown in the graph are:
The profits with the vertices are:
- P(0,0) = 0
- P(0,50) = 25(0) + 90(50) = 4,500
- P(42,36) = 25(42) + 90(36) = 4,290
- P(60,0) = 25(60) + 90(0) = 1,500
Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.
Hi there!
Distributive property are two big words that basically just mean you need to distribute the 3 to the whole parentheses. This means you need to multiply 5 by 3 and also 6 by 3.
3 × 5 = 15
3 × 6 = 18
Now that you've distributed the 3 to the entire parentheses, you just need to add together both answers you got :
15 + 18 = 33
Your answer is: 33
There you go! I really hope this helped, if there's anything just let me know! :)