Free 2 Asset Portfolio Calculator - Given a portfolio with 2 assets, this determines the expected return (mean), variance, and volatility (standard deviation) of the portfolio.

A set has a cardinality of 9. How many proper subsets does the set have? The set has 2^9 = [B]512 proper subsets[/B]

A U ? = A Let x ? [I]S[/I], where [I]S[/I] is the universal set. First we show that if A ? Ø ? A. Let x ? A ? Ø. Then x ? A or x ? Ø. by definition of the empty set, x cannot be an element in Ø. So by assumption, x ? A ? Ø, x must be in A. So A ? Ø ? A. Next, we show that A ? A ? Ø. This is true because the set resulting from the union of two sets contains both of the sets forms the union Since A ? Ø ? A and A ? A ? Ø, we have that A ? Ø = A.

Aryion has 3 sets of hair ties. Each set contains 2 hair ties. How many hair ties does Aryion have? Total hair ties = Sets of hair ties * number of hair ties per set Total hair ties = 3 * 2 Total hair ties = [B]6[/B]

Ava set her watch 2 seconds behind, every day it sets back 1 second. How many days has it been since she last set her watch if it is 41 seconds behind? Right now: Watch is 2 seconds behind [U]Let d be the day after right now[/U] (1)d + 2 = 41 d + 2 = 41 [U]Subtract 2 from each side[/U] [B]d = 39[/B]

Find the subset of {a,b,c,d,e} Using our power set calculator, we find [URL='https://www.mathcelebrity.com/powerset.php?num=a%2Cb%2Cc%2Cd%2Ce&pl=Show+Power+Set+and+Partitions']all the 32 subsets of {a,b,c,d,e}[/URL]

Five sets of ear buds cost $53.15. How much will 9 sets of ear buds cost? Set up a proportion of earbuds to cost where c is the cost of 9 ear buds: 5/53.15 = 9/c To solve this proportion for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=9&den1=53.15&den2=c&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get: c = [B]95.67[/B]

Free Grand Mean Calculator - Calculates the grand mean of a set of number sets.

Omar's classroom has 2 closets. Each closet has 3 shelves. There are 5 backpacks on each shelf. 2 closets * 3 shelves per closet * 5 backpacks per shelf = [B]30 backpacks[/B]

Free Permutations and Combinations Calculator - Calculates the following:
Number of permutation(s) of n items arranged in r ways = _nP_r
Number of combination(s) of n items arranged in r unique ways = _nC_r including subsets of sets

Free Portfolio Rate of Return Calculator - Given a portfolio of individual assets with returns and weights, this calculates the total portfolio rate of return.

power set for S= {b,c,f} The [I]power set[/I] P is the set of all subsets of S including S and the empty set ?. Since S contains 3 terms, our Power Set should contain 2^3 = 8 items [URL='https://www.mathcelebrity.com/powerset.php?num=b%2Cc%2Cf&pl=Show+Power+Set+and+Partitions']Link to power set for this problem[/URL] P = [B]{{}, {b}, {c}, {f}, {b,c}, {b,f}, {c,f}, {b,c,f}}[/B]

Free Power Sets and Set Partitions Calculator - Given a set S, this calculator will determine the power set for S and all the partitions of a set.

Free Set Notation Calculator - Given two number sets A and B, this determines the following:
* Union of A and B, denoted A U B
* Intersection of A and B, denoted A ∩ B
* Elements in A not in B, denoted A - B
* Elements in B not in A, denoted B - A
* Symmetric Difference A Δ B
* The Concatenation A · B
* The Cartesian Product A x B
* Cardinality of A = |A|
* Cardinality of B = |B|
* Jaccard Index J(A,B)
* Jaccard Distance J_σ(A,B)
* Dice's Coefficient
* If A is a subset of B
* If B is a subset of A

Free Sets Calculator - This lesson walks you through what a set is, how to write a set, elements of a set, types of sets, cardinality of a set, complement of a set.

Free Sharpe Ratio Calculator - Calculates the Sharpe ratio given return on assets, risk free rate, and standard deviation

The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ? Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is: 36 Now, the mean (average) or 19 and N is found by adding them together an dividing by 2: (19 + N)/2 Since both number sets have equal means, we set (19 + N)/2 equal to 36: (19 + N)/2 = 36 Cross multiply: 19 + N = 36 * 2 19 + n = 72 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]53[/B]

Free Truth Tables Calculator - Sets up a truth table based on a logical statement of 1, 2 or 3 letters with statements such as propositions, equivalence, conjunction, disjunction, negation. Includes modus ponens.

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stop on an odd number or a number less than 4. We want P(odd number) or P(n<4). [LIST] [*]Odd numbers are {1, 3, 5, 7, 9} [*]n < 4 is {1, 2, 3} [/LIST] We want the union of these 2 sets: {1, 2, 3, 5, 7, 9} We have 6 possible pointers in a set of 10. [B]6/10 = 3/5 = 0.6 or 60%[/B]