Sixty-five percent of the 8th grade class is selling magazines for the class fundraiser. If 195 students are selling magazines,
1 answer:
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Answer: a) 720, b) c) 336, d) 30240 e) 120.
Step-by-step explanation:
Since we have given that
a) Number of competitors = 6
We need to find the number of ways that 6 competitors can finish a race and there are no ties.
So, Number of ways would be
b) number of people = n
Number of chairs = r (r<n)
so, the number of ways we can sit n people on r<n chairs is given by
c) If there are three awards :
Gold, silver, bronze.
We need to find the number of ways that these medals can be awarded.
Number of ways is given by
d) Number of 5-digit zip codes are possible is given by
e) Number of poeple = 10
Number of people required in committee = 3
Number of different 3 person committee that are selected from 10 people is given by
Hence, a) 720, b) c) 336, d) 30240 e) 120.
Answer:
Step-by-step explanation:
Both expressions are examples of the <em>distributive property</em>, which basically says "if I have <em>this </em>many groups of some size and <em>that</em> many groups of the same size, I've got <em>this </em>+ <em>that</em> groups of that size altogether."
To give an example, if I've got <em>3 groups of 5 </em>and <em>2 groups of 5</em>, I've got 3 + 2 = <em>5 groups of 5 </em>in total. I've attached a visual from Math with Bad Drawings to illustrate this idea.
Mathematically, we'd capture that last example with the equation
. We can also read that in reverse: 3 + 2 groups of 5 is the same as adding together 3 groups of 5 and 2 groups of 5; both directions get us 8 groups of 5. We can use this fact to rewrite the first expression like this:
.
This idea extends to subtraction too: If we have 3 groups of 4 and we take away 1 group of 4, we'd expect to be left with 3 - 1 = 2 groups of 4, or in symbols: . When we start with two numbers like 15 and 10, our first question should be if we can split them up into groups of the same size. Obviously, you could make 15 groups of 1 and 10 groups of 1, but 15 is also the same as <em>3 groups of 5</em> and 10 is the same as <em>2 groups of 5</em>. Using the distributive property, we could write this as
, so we can say that
.
