A standard 52-card deck of playing cards includes four aces. What is the probability that two cards selected randomly, without replacement, will both be aces? Express your answer as a common fraction.

What is the first year after 2018 that is a palindrome?

How many diagonals are in a convex heptagon? 

What is the value of 5 − 5 × 5 + 5 ÷ 5?

Based on the last problem, what fraction of Ansel’s total travel time was spent traveling upstream? Express your answer as a common fraction.

Ansel left the dock in his motorboat, traveled 10 miles, and then returned to the dock along the same route. On the return trip, Ansel was traveling against the current of the river, and his average speed relative to the water was 20 mi/h. If the round-trip took Ansel 64 minutes, what is the speed of the river’s current?

(#1000: 1000 best IQ question in history)

Two mathematician met each other in a flight to Moscow.

You have 3 children, don't you. How old are they now? - Ivan asked.

Their ages product is 36 and their ages sum is exactly the date of today! The other mathematician said.

After thinking for a while, Ivan said: Sorry but I need more info.

"Oh, I forgot. The biggest child has a red hair."

"Now I know." Can you guess what their age is?

Given \(\overline{ab}=b^2\) and \(\overline{acbc}=\left(\overline{ba}\right)^2\). Find the value of \(\overline{abc}\)

Given the number \(\overline{\left(a+1\right)a\left(a+2\right)\left(a+3\right)}\) is a square number. Find a.

Find the numbers a,b,c,d such that: a,ad,cd,abcd are all square numbers.

Notice: a,ad,cd,abcd are numbers, not equations. (Sorry I don't know how to do that)

Prove that: \(2^m+3^n⋮23\left(\forall m,n\in N\right)̸\)

There are some users breaking the rules at present time and in the past. So here are the rules that some users should get on:

RULES IN MATHULIKE (FOR NEW AND OLD MEMBERS):

- No A\(^4\) (Auto Ask Auto Answer)

- No Self-tick: https://e-learning.codienhanoi.edu.vn/users/fccontra123 -> \(\approx450\) faults, this user must not be in Mathulike, I suggest Mathulike delete this user

- No bad words, harassing

- Do not copy questions, answers

IN MY QUESTION: When no one answers the question, after 2-5 days I'll give the answer.

Jana begins jogging along a path and, 5 minutes later, Zhao begins riding his bicycle along the same path, which has a length of 2 miles. Zhao rides his bicycle at a speed of 10 mi/h, and Jana’s jogging speed is 6 mi/h. If they both begin at one end of the path and end at the other, how many minutes after Zhao reaches the end of the path will Jana reach the end of the path?

Based on the last problem, how many miles does Alysha travel to get from home to the market? 

Alysha’s average speed when walking from home to the market is 5 mi/h, and it takes her 21 minutes longer than when she drives to the market. If Alysha drives to the market, along the same route, at an average speed that is eight times her average walking speed, how many minutes does it take her to drive from home to the market?

When Jack and Jill meet, as described in the previous problem, how many yards will they be from the bottom of the hill? 

At 2:20 p.m., Jack is at the top of the hill and starts walking down at the exact same time that Jill, who is at the bottom of the hill, starts walking up. If they maintain the same uphill and downhill speeds from the previous problem, and the distance from the bottom to the top of the hill is 1.5 miles, at what time will Jack and Jill meet? 

Jack and Jill travel up a hill at a speed of 2 mi/h. They travel back down the hill at a speed of 4 mi/h. What is their average speed for the entire trip? Express your answer as a mixed number.

The degree measures of the interior angles of a quadrilateral form a geometric sequence whose terms have integer values and are all integer multiples of the first term. What is the largest possible degree measure of an angle in this quadrilateral?

Let f(x) = 2x + 3 and f\(^2\)(x) = f(f(x)) = f(2x + 3) = 2(2x + 3) + 3 = 4x + 9. If f\(^5\)(x) = ax + b, what is the value of a + b?