Math Is Fun Forum

Hi, could you please help me solve this question? Thank you!

If x and y are positive, which of the following must be greater than  1/sqrt(x+y)   ?

1)  (sqrt(x+y))/(2x)

2)  (sqrt(x)+sqrt(y))/(x+y)

2)  (sqrt(x)-sqrt(y))/(x+y)

Could you tell me the most effective way to quickly solve this question? Thank you.

In the xy plane, does the line with equation y=3x+2 contain the point (r,s)?

1) (3r+2-s)(4r+9-s)=0

2) (4r-6-s)(3r+2-s)=0

A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient
C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient

I'm sorry, I do not seem to get a hold of this problem:

A certain basket contains 10 apples, 7 of which are red and 3 are green. If 3 apples are selected at random fron the basket, what is the probability that 2 of the apples will be red and 1 green?

I went this way:

(7/10)(6/9)(3/8)=7/40

the answer is posted as 21/40, could you explain what am I doing wrong and correct it so I won't make the same mistake?

If y>=0 , what is the value of x?

1) |x-3|>=y

2) |x-3|<=-y

A) Statement 1) alone is sufficient
B) Statement 2) alone is sufficient
C) Statements 1) and 2) together are sufficient
D) Each statement alone is sufficient
E) Statement 1) and 2) together are not sufficient

the excercise book I'm using gives B) as correct answer, could you explain the reasoning behind it?
thank you

hi, could you please help me explaining the correct mathematical approach to this question? It's quite intuitive the reslt is 13, but I'm not able to reach it with a valid mathematical process.
thank you.

The number 75 can be written as the sum of the squares of 3 different positive integers. What is the sum of these integers?

hi, could you please explain to me the following problem and the reasoning behind the solution? thank you!

5 numbers have an average (arithmetic mean) of 124 and a median of 140. What is the max possible value of the lowest number?

could someone please help me with these 2 problems explaining the reasoning behind them?
thank you.

PROBLEM 1

figure doc.1

The figure shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has probability 1/2 of passing through the opening immediately to the left of that peg and probability 1/2 of passing through the opening immediately to the right. What is the probability that when the ball passes throught the first two pegs at the top it will end up in cell 2?

PROBLEM 2

figure doc.2

A person walks from point A to point B along a route confined to the grid of four streets and three avenues shown in the figure. How many routes from A to B can the person take that have minimum possible lenght?

could you please help me work this problems out?

FIRST PROBLEM
The equation:

|x/2| + |y/2| = 5

encloses a certain region on a coordinate plane. What is the area of this region?

SECOND PROBLEM
How many different numbers are there such that   ax + b = c  (a,b,and c are constants)  ?
1.   c>b
2.   a>1

A. Statement 1. is sufficient
B. Statement 2. is sufficient
C. Statements 1. and 2. together are sufficient
D. Each statement alone is sufficient
E. Both statements together are not sufficient

thank you
   

thank you.