What is the gcf for 42n

Suppose that A A is a set containing 13 13 elements. Find the number of different subsets of A.

aivan3 [116]

Answer:

number of subsets of a set with 13 elements are: $2^{13}$

Step-by-step explanation:

In order to solve this intuitively, we can start by a set with lesser elements. This will reveal a pattern that will be used to solve for the subsets of the 13 element set.

If we start with a set B. which contains only 3 elements.

$B = \{1,2,3\}$

how many subsets of B are there? well we can count them. [the set containing {1,2} and {2,1} are the same, arrangement doesn't matter]

$B_{0} = \{\}\\B_{1a}=\{1\}\\B_{1b}=\{2\}\\B_{1c}=\{3\}\\B_{2a}=\{1,2\}\\B_{2b}=\{2,3\}\\B_{2c}=\{3,1\}\\B_{3a}=\{1,2,3\}\\$

there are a total of 9 subsets here.

Similarly, if you try a with a subset with only two elements you'll find that it has a total of 4 subsets.

We can see that combinatorics is at play here.

for the set B. the number of subsets can be written as:

$\text{\# of subsets of B} = ^3C_0+^3C_1+^3C_2+^3C_3\\\text{\# of subsets of B} = 1+3+3+1\\\\text{\# of subsets of B} = 8$

if we try with a 2-element set:

$\text{\# of subsets} = ^2C_0+^2C_1+^2C_2\\\text{\# of subsets} = 1+2+1\\\ \text{\# of subsets} = 4$

We can use the same technique to find the number of subsets of the 13 element set.

But if you recognize a pattern here that this sets of combinations are actually part of the pascal triangle, the sum of each row of the triangle is 2^{the row's number}. hence.

$\text{\# of subsets of B} = 2^3\\\ \text{\# of subsets of B} = 8$

So finally, the subsets of a 13-element set A will be

$\text{\# of subsets of A} = ^{13}C_0+^{13}C_1+^{13}C_2+^{13}C_3\cdots+^{13}C_{12}+^{13}C_{13}\\OR\\\text{\# of subsets of A} = 2^{13}\\\text{\# of subsets of A} = 8192$

6 0

3 years ago

Mark uses 19 gallons of gas while traveling 399

Ket [755]

Answer:

189

Step-by-step explanation:

If mark uses 19 gallons to travel 399 miles, that means he was able to travel 21 miles per gallon.

We get this by taking 399 divided by 19.

So if mark travels on 9 gallons of gas and goes 21 miles per gallon, he will have traveled 189 miles.

We get this by taking 21 times 9

4 0

3 years ago

£1800 is invested at4% compound interest per year.

deff fn [24]

2000=1800(1.04)^t,,log(1.11)/log(1.04)=t use the calculator,,,hope it helps :-)

3 0

3 years ago

A dairy wishes to mix together 1,000 pints of milk that contains 8% butterfat. if the mixture is to be made from milk containing

cricket20 [7]

We can write the question as a mathematical formula as follows:
1000 * 0.08 = m * 0.05 + c * 0.2
1000 = m + c
where m are pints of milk and c are pints of cream
So solving the first equation with m = 1000 - c
1000*0.08 = (1000-c)*0.05 + c*0.2
80 = 50 - 0.05c + 0.2c
80-50 = (0.2-0.05)*c
30 = 0.15*c
c = 30/0.15
c = 200
m = 1000-200 = 800
So the dairy needs 800 pints of milk and 200 pints of cream

8 0

3 years ago

Read 2 more answers

The asking price on a house was $350,000. Because it was on the marked for six months it was finally sold for $297,500. What per

tia_tia [17]

Simply do 297500/350000 and you would get 85%

5 0

3 years ago

What is the gcf for 42n - 27s​

What is the gcf for 42n - 27s