Hi! I'm new here...and Math is actually my weak subject, it'll be awesome if you could help me answer these questions. Pretty please? (If the rationale will be included--will appreciate it more!)

1. A pipe can alone fill a tank in 5 hours, while a drain can do the contrary in 12 hours. How long would it take the pipe to fill the tank if the drain was simultaneously opened during the duration of the filling job and if the tank were entirely emptied at the start?

2. A 24-foot ladder just reaches the sill of a window that is 12 feet above ground level. What angle of measure is the ladder inclined?

3. A man left 1/2 of his state to his wife, 1/8 to his daughter, and the remainder, an amount of 30, 000 to his son. How much was the entire estate?

4. In a particular 30day month, records show that there is more than 1cm of rain in 2 days, some rain but less than 1cm on 5 days and no rain on 23 days. If a day is chosen at random, what is the probability that it rained on that day?

5. A license plate consists of 3 letters and 3 numbers, where the 1st number can't be zero. What is the probability that a car's license plate is greater than 400?

1. A pipe can alone fill a tank in 5 hours, while a drain can do the contrary in 12 hours. How long would it take the pipe to fill the tank if the drain was simultaneously opened during the duration of the filling job and if the tank were entirely emptied at the start?

2. A 24-foot ladder just reaches the sill of a window that is 12 feet above ground level. What angle of measure is the ladder inclined?

3. A man left 1/2 of his state to his wife, 1/8 to his daughter, and the remainder, an amount of 30, 000 to his son. How much was the entire estate?

4. In a particular 30day month, records show that there is more than 1cm of rain in 2 days, some rain but less than 1cm on 5 days and no rain on 23 days. If a day is chosen at random, what is the probability that it rained on that day?

5. A license plate consists of 3 letters and 3 numbers, where the 1st number can't be zero. What is the probability that a car's license plate is greater than 400?

LeEpikia Mar 17, 2014

#1**+2 **

1. This is a "thinking" problem. For every fifth part of the tank that is filled, 1/12th of it is being drained away. In effect, the draining is retarding the filling.

So we have: (The portion of the tank being filled per hour) * (time it takes to fill) = (whole tank filled)

In math terms this equates to: (1/5 - 1/12) * X = 1

So we have: (7/60) * X = 1

I'll let you finish this one......just solve for X......your answer will be in hrs.

2. This is a trig problem. We have a triangle whose opposite side is 12 and whose hypotenuse is 24. To find the incline angle, take the sine inverse of 12/24.

3.If the wife gets 1/2 and the daughter gets 1/8, the son gets what's left = 3/8. Then, 3/8 of the estate is 30000.

Let X be the total amount of the estate.

In math terms, we have............. 3/8 * X = 30000

Again, I'll let you finish this one for yourself.

4. Since it rained 7 days out of 30, the probability it rained on any one day is just......... 7/30.

5. The letters don't matter. The first digit is a non-zero number and the other two digits can be any digit from 0-9 inclusive.

So, the possible numbers are from 100 - 999 inclusive. We have 900 of these......... (999-100+1)

So, the total numbers that are 400 or greater = (999-400+1) = 600

Therefore, the probability that a number is greater than 400 is just 600/900 = 2/3.

Hope that helps......good luck!!

So we have: (The portion of the tank being filled per hour) * (time it takes to fill) = (whole tank filled)

In math terms this equates to: (1/5 - 1/12) * X = 1

So we have: (7/60) * X = 1

I'll let you finish this one......just solve for X......your answer will be in hrs.

2. This is a trig problem. We have a triangle whose opposite side is 12 and whose hypotenuse is 24. To find the incline angle, take the sine inverse of 12/24.

3.If the wife gets 1/2 and the daughter gets 1/8, the son gets what's left = 3/8. Then, 3/8 of the estate is 30000.

Let X be the total amount of the estate.

In math terms, we have............. 3/8 * X = 30000

Again, I'll let you finish this one for yourself.

4. Since it rained 7 days out of 30, the probability it rained on any one day is just......... 7/30.

5. The letters don't matter. The first digit is a non-zero number and the other two digits can be any digit from 0-9 inclusive.

So, the possible numbers are from 100 - 999 inclusive. We have 900 of these......... (999-100+1)

So, the total numbers that are 400 or greater = (999-400+1) = 600

Therefore, the probability that a number is greater than 400 is just 600/900 = 2/3.

Hope that helps......good luck!!

CPhill Mar 17, 2014