Explain when it would be more useful to use the Counting Principle than a tree diagram to count possible outcomes of an event.
1 answer:
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Answer:
Part 1: 31.4 feet
Part 2: 61 feet
Part 3: 99,000 stalks of corn
Step-by-step explanation:
<u>Part 1:</u>
Diagram attached.
You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.
The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.
Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2
Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:
Hence Bethany has to walk 31.4 feet
<u>Part 2:</u>
See 2nd diagram attached.
The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.
We use Pythagorean Theorem twice on the two triangles and add up the results.
<u>Left Triangle:</u>
If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:
<u>RightSide triangle:</u>
two legs are 25 and 15 respectively, so we use the pythagorean theorem again:
Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)
<u>Part 3:</u>
The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].
Area of Maze:
100 * 100 = 10,000 sq. yd.
Area of Path = 1.5 * 3000 = 4,500 sq. yd.
Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.
Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:
18 * 5,500 = 99,000 stalks of corn
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