Given:
Total number of girls in her class = 16
Total number of boys in her class = 14
To find:
The number of different ways of choosing one girl and one boy.
Solution:
We have,
Total number of girls = 16
Total number of boys = 14
So,
Total number of ways to select one girl from 16 girls = 16
Total number of ways to select one boy from 14 boys = 14
Now, number of different ways of choosing one girl and one boy is
Therefore, the required number of different ways is 224.
The length of SR is 10 inches ⇒ answer B
Step-by-step explanation:
The median of a triangle is the segment drawn from one vertex to
the mid-point of the opposite side to this vertex
In Δ PQR
1. QS is a median
2. RT is a median
We need to find the length of SR
∵ QS is a median in Δ PQR
∵ PR is the opposite side to vertex Q
∴ S is the mid-point PR
∴ PS = SR
∵ PS = 4x - 2
∵ SR = 2x + 4
∴ 4x - 2 = 2x + 4
- Subtract 2x from both sides
∴ 2x - 2 = 4
- Add 2 to both sides
∴ 2x = 6
- Divide both sides by 2
∴ x = 3
Substitute the value of x in the expression of SR
∵ SR = 2x + 4
∵ x = 3
∴ SR = 2(3) + 4
∴ SR = 6 + 4
∴ SR = 10 inches
The length of SR is 10 inches
Learn more:
You can learn more about triangles in brainly.com/question/3358617
#LearnwithBrainly
First, find the LCD (least common denominator) of the two fractions.
List the multiples of each denominator and find the one that is common.
Multiples of 8: 8, 16, 24, 32, 40
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40
40 is your LCD.
Second, what can you divide by to make the denominators of each fraction '40'? Whatever you do to the bottom you must do to the top.
Third, multiply.
Fourth, since the denominators are the same now, we can combine them.
Fifth, subtract '25 - 16' to get 9.
Since
is already in the simplest form, it is your answer.
Answer as fraction:
Answer as decimal:
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:
<u />
<u>1. Name the variables:</u>
- x: number of smaller lifts
- y: number of larger lifts
<u></u>
<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)
<u></u>
<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.
