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question:f a bag contains six green balls and four red balls, and two balls are randomly drawn with replacement, what is the probability that the two balls are the same color?
answer:There are two cases: either both balls are green or both balls are red. The probability that both balls are green is left(frac{6}{10}right)^2 = frac{36}{100}. The probability that both balls are red is left(frac{4}{10}right)^2 = frac{16}{100}. So, the total probability is frac{36}{100} + frac{16}{100} = frac{52}{100} = boxed{frac{13}{25}}. The answer is: frac{13}{25}
question:After breaking his leg and needing to visit the doctor, Tom incurred a cost of 300 for the visit and 200 for the cast. If his insurance covered 60% of the total cost, what was Tom's out-of-pocket cost?
answer:The total cost of the visit and cast is 300 + 200 = 500. His insurance covered 60% of the total cost, so they paid for 60% * 500 = 300. Tom's out-of-pocket cost is the remaining 40% of the total cost, which is 40% * 500 = 200. 200 The answer is: 200
question:Tom went to the store to buy fruit. Lemons cost x, papayas cost 1, and mangos cost 4. For every 4 fruits that customers buy, the store offers a 1 discount. Tom buys 6 lemons, 4 papayas, and 2 mangos. How much will he pay? If we know the answer to the above question is 21, what is the value of unknown variable x?
answer:Tom buys 6 lemons, which means he pays 6x dollars for lemons. Tom buys 4 papayas, which means he pays 4 * 1 = 4 for papayas. Tom buys 2 mangos, which means he pays 2 * 4 = 8 for mangos. The total cost before the discount is 6x + 4 + 8 = 6x + 12. Since Tom buys a total of 6 + 4 + 2 = 12 fruits, he qualifies for 12/4 = 3 discounts of 1 each. The total discount is 3 * 1 = 3. The final cost that Tom will pay is 6x + 12 - 3 = 6x + 9. We are given that the final cost is 21, so we can write: 6x + 9 = 21. Solving for x, we get: 6x = 12. Dividing both sides by 6, we get: x = 2. The value of x is 2. 2 The answer is: 2
question:Scott wants to buy a skateboard. To make money, Scott sold berry smoothies for 3 a cup and cakes for 2 each. He sold 40 cups of smoothies and x cakes. He made 156 money. What is the value of unknown variable x? What is the value of unknown variable x?
answer:To solve this problem, we need to determine the value of x, which represents the number of cakes Scott sold. Let's break down the information given: Number of cups of smoothies sold: 40 Price per cup of smoothie: 3 Number of cakes sold: x Price per cake: 2 Total amount of money made: 156 We can set up the equation as follows: (Number of cups of smoothies sold * Price per cup of smoothie) + (Number of cakes sold * Price per cake) = Total amount of money made (40 * 3) + (x * 2) = 156 Let's simplify and solve for x: 120 + 2x = 156 To isolate x, we subtract 120 from both sides of the equation: 120 - 120 + 2x = 156 - 120 2x = 36 To solve for x, we divide both sides of the equation by 2: x = 36 / 2 x = 18 The value of x is 18. 18 The answer is: 18