A starting principal of $3,000 is invested at 7% compounded annually for 6 years. The compound amount (or future value) is: $___
1 answer:
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The triangles ABD, ADC and ABC are similar (AA stands for "angle, angle" and means that the triangles have two of their angles equal).
If two triangles have two of their angles equal, the triangles are similar.
Therefore the sides of triangles are in proportion.
cross multiply
Use the Pythagorean theorem for calculate x:
Answer:
Step-by-step explanation:
<em>Given:</em>
The set A = {5, 13, 17, 20}
<em>Question: </em>
Find the number of subsets of A
Find the number of proper subsets of A
<em>Simple solution by counting:</em>
Subset of A that has 0 element:
{∅} - 1 set
Subset of A that has 1 element:
{5}, {13}, {17}, {20} - 4 sets
Subset of A that has 2 elements:
{5, 13}, {5, 17}, {5, 20}, {13, 17}, {13, 20}, {17, 20} - 6 sets
Subset of A that has 3 elements:
{5, 13, 17}, {5, 13, 20}, {5, 17, 20}, {13, 17, 20} - 4 sets
Subset of A that has 4 elements:
{5, 13, 17, 20} - 1 set
In total, the number of subsets of A: N = 1 + 4 + 6 + 4 + 1 = 16
The number of proper subsets (all of subsets, except subset which is equal to original set A): N = 16 - 1 = 15
<u><em>Key-point:</em></u>
The counting method might be used for finding the number of subsets when the original set contains few elements.
The question is that, for a set that contains many elements, how to find out the number of subsets?
The answer is that: there is a fix formula to calculate the total number () of subsets of a set containing
elements: N =
With original set A = {5, 13, 17, 20}, there are 4 elements belonged to A.
=> Number of subsets of A: N =
(same result as using counting method)
<em>Brief proof of formula: N = </em><em />
Each element of original set is considered in 2 status: existed or not.
If existed => fill that element in.
If not => leave empty.
For i.e.: empty subset means that all elements are selected as not existed, subset with 1 element means that all elements are selected as not existed, except 1 element, ... and so on.
=> From the point of view of a permutation problem, for each element in original set, there are 2 ways to select: existed or not. There are elements in total. => There are
ways to select, or in other words, there are
subsets.
Hope this helps!
:)