Word problem.. i need help. Due at midnight
1 answer:
The Brady family received 1 letter on July 28.
Step-by-step explanation:
Step 1:
Assume a = the number of letters, b = the number of bills, c = the number of ads, and d = the number of magazines.
From the question, they got 15 pieces of mail that day so
They got 5 more magazines than bills so
The got the same number of letters as ads so
They got 3 more bills than ads so
Step 2:
As we have only one equation to solve the values, we need to make every term in terms of a single term.
We make everything in terms of c.
So
Substituting all this in the equation, we get
Step 3:
Substituting c = 1 in other terms, we get
and
As a = 1, they received 1 letter that day.
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28.65 Degrees
Answers:
- a) 2048
- b) 2047
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Explanation:
If a set has n elements inside it, then it has 2^n different subsets.
Consider a set like {a,b,c}. It has n = 3 elements.
It has 2^n = 2^3 = 8 subsets
Those 8 subsets are...
- {a,b,c} ..... any set is a subset of itself
- {a,b}
- {a,c}
- {b,c}
- {a}
- {b}
- {c}
- { } .... the empty set
As you can see, each subset consists of items that are selected from the original set {a,b,c}. We can't have any repeat letters.
In that list, items 2 through 4 represent subsets with exactly two things inside it. Items 5 through 7 are known as singletons as they only have one item inside each set. The empty set can be written with the symbol or you could have a pair of braces with nothing inside them. The empty set is a subset of any set.
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Note how I included {a,b,c} as a subset. Any set is a subset of itself.
A proper subset will ignore the original set and only look at smaller subsets. If we say B is a proper subset of A, then set B will have fewer items compared to set A. Without the "proper" in there, it's possible that A = B.
So all we've done really is kick out one set which drops 2^n to (2^n)-1 when counting the number of proper subsets. I'm using parenthesis to indicate the "-1" is not part of the exponent. If you wrote this on your paper, then you would likely write
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For this problem, n = 11
This means there are 2^n = 2^11 = 2048 subsets and (2^n)-1 = 2048-1 = 2047 proper subsets.