Three stoplights on different streets each operate on their own independent schedules, as follows: the first stoplight is red 1 minute out of every 2 minutes (1 minute red, then 1 minute green), the second is red 2 minutes out of every 3 minutes (2 minutes red, then 1 minute green) and the third is red 3 minutes out of every 5 minutes (3 minutes red, then 2 minutes green.) At 9:00 am each stoplight turns red. The lights are either red or green (don’t worry about yellow). What time is it when the next 1-minute segment of time in which all three stoplights are red begins? 

A path crosses a rectangular field on a diagonal. If someone travels across the field on the diagonal, instead of walking along the sides, what is the greatest possible percent reduction in total distance traveled? Express your answer to the nearest whole number.

An old puzzle asks you to use the numbers 1 through 9 to equal 100.

Example:

123 – 45 – 67 + 89 = 100

OR

1.234 + 98.765 = 100

Can you find one or two more possibilities?

Vijay gives Sanjay a set of four weights of 1, 3, 8 and 26 grams. When Sanjay places weights on either side of a balance, what is the smallest positive integer number of grams that he cannot measure with this set?

what can be the smallest value of a in 6x - a = 5x + 8?

make two number equal  to \(\dfrac{1}{4}\)

of the first number .the two number are 441. find the two number

Rayshon has 51 coins consisting of dimes and nickels that total $3.55. How many dimes does he have?

Given x,y satisfy 16x² - 9y² \(\ge\) 144 .

Show that : |2x - y + 1| \(\ge\) \(2\sqrt{5}-1\)

An advertisement states that 4 out of 7 dentists recommend Minty Fresh Mouthwash. If 1421 dentists were surveyed, how many dentists recommended Minty Fresh Mouthwash?

The shape shown is formed by a circle with radius of length r units and two smaller semicircular regions, each with diameter of length r units. What is the perimeter of the shaded portion of the large circle? Express your answer in terms of r and π.