Find the volume of the figure.
1 answer:
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Answer:
(a) There are 113,400 ways
(b) There are 138,600 ways
Step-by-step explanation:
The number of ways to from k groups of n1, n2, ... and nk elements from a group of n elements is calculated using the following equation:
Where n is equal to:
n=n1+n2+...+nk
If each team has two students, we can form 5 groups with 2 students each one. Then, k is equal to 5, n is equal to 10 and n1, n2, n3, n4 and n5 are equal to 2. So the number of ways to form teams are:
For part b, we can form 5 groups with 2 students or 2 groups with 2 students and 2 groups with 3 students. We already know that for the first case there are 113,400 ways to form group, so we need to calculate the number of ways for the second case as:
Replacing k by 4, n by 10, n1 and n2 by 2 and n3 and n4 by 3, we get:
So, If each team has either two or three students, The number of ways form teams are:
113,400 + 25,200 = 138,600
Answer:
- 914.4 mm
- 0.0479594 km
Step-by-step explanation:
For units conversion, use a conversion factor ratio with the units you do want in the numerator and the units you don't want in the denominator. The numbers in the numerator and denominator give the ratio a value of 1: the numerator is equal to the denominator--just in different units.
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1. For feet to mm, you need a couple of additional conversion factors besides the ones shown:
1 foot = 12 in
1 cm = 10 mm
So, the conversion is ...
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2. The additional factor you need for this problem is ...
1 mile = 5280 feet
So, the conversion is ...
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<em>Additional comment</em>
You can use Google to do units conversion by typing "3 feet to mm" or "157 feet to km". However, the conversion factor for the latter will be more exact than the one given in this problem. Hence the Google answer to the second question will not be applicable here.