Find the last three digit-numbers of: \(E=2^{2017}\)
Find the last two digit-numbers of: \(D=1978^{1986^8}\)
Find the last two digit-numbers of: \(C=29^{9^{2012}}\)
Find the last two digit-numbers of: \(B=7^{9^{7^9}}\)
Find the last two digit-numbers of: \(A=2016^{2017}\)
Given \(A=n^{n-1}+n^{n-2}+...+n^2+n+1\). Prove that: \(A⋮n-1\) with n\(\in N\)
Prove that: \(\left(2^{2^{4n+1}}+7\right)⋮11\) with \(n\in\) N*
Prove that: \(\left(2^{2^{2n}}+5\right)⋮7\) with n \(\in\) N
Prove that: \(1924^{2003^{2004^n}}+120⋮124\) with n \(\in\) N*.
The mean score of the students who took a mathematics test was 6. Exactly 60% of the students passed the test. The mean score of the students who passed the test was 8. What was the mean score of the students who failed the test?
In a group of kangaroos, the two lightest kangaroos weigh 25% of the total weight of the group. The three heaviest kangaroos weigh 60% of the total weight. How many kangaroos are there in the group?
Circles of radius and touch each other externally, and they touch a common tangent at points and respectively, where lies between and . Prove that
Let denote the mean, median, range and standard deviation of a set, respectively. Let . Describe a set that maximises .
Given and , prove that . Does anyone have an elegant proof for this? My proof was super bashy and horrible. Then, generalize this to such that and , express this as such that .
Triangle ABC has side lengths AB = 9, BC = 10, and AC = 13. If D is the midpoint of BC, what is the length of AD?
Suppose and are polynomials, and that . Find the degree of given that the degree of is and the degree of is .
Suppose a function has domain and range . If we define a new function bythen what is the range of ? Express your answer in interval notation.
Yu has coins, consisting of pennies, nickels and dimes. He tosses them all in the air. What is the probability that the total value of the coins that land heads-up is exactly cents?
How many ordered quintuples have coordinates of value or and satisfy Could you somehow approach this using stars and bars or something?
What is the value of tan given tan