Algebra and Probability Problems

The video tutorial covers a series of math problems, including calculating the time to fill a pool, solving algebraic equations for x and y, determining the percentage of sodium chloride in a solution after evaporation, calculating the probability of selecting a woman from a committee, factorizing integers, and finding the area of a circular path. Each problem is broken down step-by-step to demonstrate the solution process.

If a pool is filled at a constant rate and takes 8 hours to fill 3/5 of its capacity, how much longer will it take to fill the remaining 2/5?

• 6 hours

• 5 hours and 20 minutes

• 4 hours and 30 minutes

• 7 hours

If a pool is filled at a rate of 3/40 pools per hour, how long does it take to fill the entire pool?

• 15 hours

• 10 hours

• 13 hours and 20 minutes

• 12 hours

A positive number x is multiplied by 2 and then divided by 3. If the square root of the result equals x, what is the value of x?

• 2/3

• 3/4

• 1/3

• 1/2

In the equation 2x/3 = x^2, what is the value of x if x is positive?

• 1/3

• 3/4

• 1/4

• 2/3

A tank contains 10,000 gallons of a 5% sodium chloride solution. After 2,500 gallons of water evaporate, what is the new concentration of sodium chloride?

• 8%

• 7.5%

• 6.67%

• 5.5%

After 2,500 gallons of water evaporate from a 10,000-gallon tank of 5% sodium chloride solution, what is the remaining volume of the solution?

• 5,000 gallons

• 6,500 gallons

• 7,500 gallons

• 8,000 gallons

If x + 5y = 16 and x = -3y, what is the value of y?

• 8

• 6

• 4

• 10

A committee has w women and m men. If 3 women and 2 men are added, what is the probability of selecting a woman from the enlarged committee?

• (w + 2) / (w + m + 2)

• (w + 3) / (w + m + 5)

• (w + 2) / (w + m + 5)

• (w + 3) / (w + m + 2)

If the product of integers w, x, y, and z is 770 and 1 < w < x < y < z, what is w + z?

• 12

• 13

• 14

• 15

What is the area of a circular path that is 3 feet wide surrounding a flowerbed with a radius of 8 feet?

• 60π square feet

• 57π square feet

• 50π square feet

• 64π square feet