There are 5 blue balls out of a total of 15 balls, so the fraction is 5/15, which simplifies to 1/3.

The total number of balls is 10 + 5 = 15. The ratio of red balls to total balls is 10:15, which simplifies to 2:3.

There are 10 balls in total (5 + 3 + 2). The fraction of blue balls is 3 out of 10, which is 3/10.

The combined rate is 1/4 + 1/6 = 5/12, so together they complete the task in 12/5 hours, which is 2.4 hours.

At 3:15, the hour hand is at 97.5 degrees (3*30 + 15*0.5) and the minute hand is at 90 degrees (15*6). The angle between them is 97.5 - 90 = 7.5 degrees.

If 3 are registered, then 10 - 3 = 7 participants can still be added.

Let x be the number of members in the smaller team. Then the larger team has x + 3 members. The equation is x + (x + 3) = 15, which simplifies to 2x + 3 = 15. Solving gives x = 6, so the teams have 6 and 9 members.

Let the number of members in the smaller team be x. Then the larger team has x + 3 members. The equation is x + (x + 3) = 11, which simplifies to 2x + 3 = 11. Solving gives x = 4, so the teams have 4 and 7 members.

Let the smaller team have x members. Then the larger team has x + 3 members. The equation is x + (x + 3) = 11, which simplifies to 2x + 3 = 11. Solving gives x = 4, so the teams have 4 and 7 members.

The number of combinations is calculated using the binomial coefficient C(5,3) = 10.

If A is taller than B and B is taller than C, then A must be taller than C.

A is to the left of B, and C is to the right of B, so A is to the left of C.

The idiom 'barking up the wrong tree' means to make a mistake in judgment or to pursue a mistaken or misguided course of action.

'Under the weather' is an idiom that means feeling sick.

If 3 out of 8 slices are eaten, then 5 slices remain, which is 5/8 of the pizza.

The train travels for 2 hours at 60 miles per hour, so it will cover 2 * 60 = 120 miles.

The train travels for 2 hours (from 3 PM to 5 PM) at 60 miles per hour, so it will travel 60 * 2 = 120 miles.

Since some animals are not pets, it follows that some cats, being animals, may also not be pets.

Since some mammals are not dogs and all cats are mammals, it follows that some cats must not be dogs.

Since some flowers are red, it is possible that some roses, being flowers, are also red.

Since some flowers fade quickly and all roses are flowers, it is possible that some roses fade quickly.

The statement allows for the possibility that some flowers are not roses, but does not specify anything about roses.

The number of selections is given by C(4,2) = 6.

The students are the youngest as the teacher is older than them.

Since X is older than Y and younger than Z, Y is the youngest.

P is heavier than Q is a direct statement from the given information.

S is to the left of T.

Lifting constraints typically leads to increased freedom and opportunities.

If X is constrained by Y, it means that Y limits or restricts X.

Y is the shortest as X is taller than Y and Y is shorter than Z.