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Proofs
Proof means sufficient evidence to establish the truth of something. It is obtained from deductive reasoning, rather than from empirical arguments. Proof must show that a statement is true in all cases, without a single exception.
1,294 Questions
What is the definition of a numerical equation?
A numerical equation is an equation expressed purely in numbers and unknown variables. For example x2+2x+3=0 and x+y=4 are both numerical equations where x and y are variables, but an equation such as 2x2+ax-5=0 is not a numerical equation because one of the constants is not known and is represented here by an a.
Chapter circles from Ncert class 9?
Abcd is a cyclic quadrilateral whose diagonals intersect ata point E.If <dbc=70 and <bac=30. Find <bcd further ab=bc, find <ecd
Determine which postulate or theorem can be used to prove that REM DME?
i got AAS for apex on this question...
How to determine number of isomorphic group of order 121?
Since 121 is the square of a prime, there are only two distinct isomorphic groups.
How do you calculate the mean and variance of a poisson distribution as a function of time t?
Divide the total number of incidents by the total time. The result, representing the average number of incidents per unit of time, is the mean as well as the variance of the Poisson distribution.
How can a statement be a postulate?
A statement which appears to be true but has not been proven to be so, is a postulate.
Every subgroup of a cyclic group is cyclic?
Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
Define the 4 scales of measurements?
The first is Nominal. It is data that iscategorized and can't be arranged in an order from low to high; e.g. answer a question yes or no, colors of cars in a parking lot, race and gender. The second is Ordinal. It is data that is categorized and can be arranged in an order from low to high, but differences can not be determined, or are meaningless; e.g. grades A, B, C, D, E or grade levels 9th, 10th, 11th, 12th, or survey type questions such as do not like, somewhat like, like, love; or another is movie ratings. The third is Interval. It is the ordinal scale, but with the additional property that the difference is meaningful between the data, but does not have a natural zero starting point; e.g. the years (2009, 2000, 1610, etc), the temperature scale (50, 68, 90, oF etc). The fourth is Ratio. It is the interval scale, but with the additional property that it does have a natural zero starting point. Money and weight are examples; 0 money means you have none, and $4.00 is 2 X $2. Likewise with weight; no weight means there is none and 4 pounds is 2 x 2 pounds; the same analogy applies with height.
Kevin runs 2 miles in 10 minutes if Kevin runs at the same rate how far can he run in 45 minutes?
Kevin runs 2 miles in 10 minutes, that is, he takes 10 minutes to run 2 miles. [That may sound a trivial step, but will help solve similar examples where the numbers give complicated answers]. So he takes 5 minutes to run 1 mile. He has 45 minutes, or 9 times the number of minutes. So he runs 9 times the distance, that is, 9*1 = 9 miles.
Prove that the intersection of any two subgroups of a group ia s again a subgroup?
Let H and I be subgroups of G. A group B is a subgroup of a group A if and only if every member of B is a member of A. Thus, every member of H is a member of G, and every member of I is a member of G.
The intersection of two groups A and B is the set of things that are members of both A and B. Hence, if a group C is equivalent to the intersection of A and B, then everything that is a member of both A and B is a member of C, and everything that is a member of C is a member of both A and B.
Hence, everything that is a member of the intersection of H and I is a member of H. We established above that every member of H is a member of G. Thus, everything that is a member of the intersection of H and I is a member of G.
Recall that A group B is a subgroup of a group A if and only if every member of B is a member of A. Hence, if everything that is a member of the intersection of H and I is a member of G, then the intersection of H and I is a subgroup of G, and so the intersection of H and I is indeed a subgroup of G.
Find the equation of the line tangent to when x equals 8?
The question is suppose to read:
Find the equation of the line tangent to y=(x²+3x)²(2x-2)³, when x=8
If we call the weight of the cat x, then the weight of the dog is 2x. We're told that the sum of the weights is 27, so 2x + x = 27. This is the same as saying that 3x = 27, so x must be 9. So the cat weights 9, the dog weighs 18.
A dog and a cat together weigh 27 pounds if the dog's weight is an odd number and if he weighs twice as much as shedoes how much does each weigh?
I know it isn't proper English but the cat is male (he) and the dog is female (she). So the cat weighs the 18 pounds and the dog weighs the 9 pounds so the dog has an odd number for it's weight.
You do not need an iterative formula: just some logical thinking.
If N is a natural number that is no greater than 1, then N can only be 1.
There is only one real solution to x^5 = 1 and that is x = 1.
How do you verify the identity of cos θ tan θ equals sin θ?
To show that (cos tan = sin) ???
Remember that tan = (sin/cos)
When you substitute it for tan, cos tan = cos (sin/cos) = sin
QED
