answer:We want to find the value of X in the given situation. We are told that Phil has X green marbles and 3 purple marbles in a bag. He removes a marble at random, records the color, puts it back, and repeats this process until he has withdrawn 6 marbles. To find the probability that exactly three of the marbles he removes are green, we can use the concept of combinations. The total number of marbles in the bag is X + 3. The total number of ways to choose 6 marbles from X + 3 marbles is given by the combination formula: C(n, r) = frac{n!}{r!(n-r)!} In this case, n is X + 3 (total number of marbles) and r is 6 (number of marbles Phil removes). The number of ways to choose exactly 3 green marbles from X green marbles is given by the combination formula: C(X, 3) = frac{X!}{3!(X-3)!} The probability of choosing exactly 3 green marbles out of 6 marbles is the ratio of the number of ways to choose 3 green marbles to the total number of ways to choose 6 marbles: Probability = frac{C(X, 3)}{C(X+3, 6)} Given that the probability is 0.185, we can set up the equation: 0.185 = frac{C(X, 3)}{C(X+3, 6)} To solve for X, we can try different values and calculate the probability. Let's start with X = 5: 0.185 = frac{C(5, 3)}{C(8, 6)} 0.185 = frac{10}{28} The equation does not hold true for X = 5. Let's try X = 6: 0.185 = frac{C(6, 3)}{C(9, 6)} 0.185 = frac{20}{84} The equation does not hold true for X = 6. Let's try X = 7: 0.185 = frac{C(7, 3)}{C(10, 6)} 0.185 = frac{35}{210} The equation holds true for X = 7. Therefore, the value of X is 7. The answer is: 7

answer:Georgie can run 40 yards within x seconds. If he improves his speed by forty percent, he will be able to run 40 + 40% of 40 = 40 + (40/100)*40 = 40 + 16 = 56 yards within x seconds. We are given that Georgie will be able to run 112 yards within 10 seconds, so we can write: 56/x = 112/10. Cross-multiplying, we get: 56*10 = 112*x. Simplifying, we get: 560 = 112*x. Dividing both sides by 112, we get: x = 5. The value of x is 5. 5 The answer is: 5

answer:If the number of lions is 200, then the number of leopards is 200/2 = 100. The combined number of lions and leopards is 200 + 100 = 300. The number of elephants is half the combined number of lions and leopards, so it is 300/2 = 150. The total population of the three animals in the park is 200 + 100 + 150 = 450. 450 The answer is: 450

answer:If 4 shirts weigh 1 pound, then 1 shirt weighs 1/4 = 0.25 pounds. Similarly, if 2 pairs of pants weigh 1 pound, then 1 pair of pants weighs 1/2 = 0.5 pounds. Jon has 20 shirts, so they weigh 20 * 0.25 = 5 pounds. Jon also has 20 pairs of pants, so they weigh 20 * 0.5 = 10 pounds. In total, Jon needs to wash 5 + 10 = 15 pounds of laundry. Since Jon's laundry machine can handle 5 pounds of laundry at a time, he needs to do 15 / 5 = 3 loads of laundry. 3 The answer is: 3