Appearance
question:Susie Q has 1000 dollars to invest. She invests some of the money at the Pretty Penny Bank, which compounds annually at 3 percent. She invests the rest of the money at the Five and Dime Bank, which compounds annually at X percent. After two years, Susie has a total of 1090.02. How much did Susie Q originally invest at the Pretty Penny Bank, In dollars, the answer is 300. What is the value of unknown variable X?
answer:To solve this problem, we need to determine the value of x, which represents the annual interest rate at the Five and Dime Bank. Let's break down the information given: Initial investment at the Pretty Penny Bank: 300 Initial investment at the Five and Dime Bank: 1000 - 300 = 700 Annual interest rate at the Pretty Penny Bank: 3% Total amount after two years: 1090.02 We can set up the equation as follows: Amount at the Pretty Penny Bank after two years + Amount at the Five and Dime Bank after two years = Total amount after two years Let's calculate the amount at the Pretty Penny Bank after two years: Amount at the Pretty Penny Bank after two years = Initial investment at the Pretty Penny Bank * (1 + Annual interest rate)^2 Amount at the Pretty Penny Bank after two years = 300 * (1 + 0.03)^2 Let's calculate the amount at the Five and Dime Bank after two years: Amount at the Five and Dime Bank after two years = Initial investment at the Five and Dime Bank * (1 + x/100)^2 Amount at the Five and Dime Bank after two years = 700 * (1 + x/100)^2 Now, let's set up the equation and solve for x: 300 * (1 + 0.03)^2 + 700 * (1 + x/100)^2 = 1090.02 Let's simplify and solve for x: 300 * (1.03)^2 + 700 * (1 + x/100)^2 = 1090.02 300 * 1.0609 + 700 * (1 + x/100)^2 = 1090.02 318.27 + 700 * (1 + x/100)^2 = 1090.02 To isolate x, we subtract 318.27 from both sides of the equation: 318.27 + 700 * (1 + x/100)^2 - 318.27 = 1090.02 - 318.27 700 * (1 + x/100)^2 = 771.75 To solve for x, we divide both sides of the equation by 700 and then take the square root of both sides: (1 + x/100)^2 = 771.75 / 700 1 + x/100 = sqrt(1.1025) To isolate x, we subtract 1 from both sides of the equation: 1 + x/100 - 1 = sqrt(1.1025) - 1 x/100 = sqrt(1.1025) - 1 To solve for x, we multiply both sides of the equation by 100: x = 100 * (sqrt(1.1025) - 1) Now, let's calculate the value of x: x = 100 * (1.05 - 1) x = 100 * 0.05 x = 5 The value of x is 5. The answer is: 5
question:f the population of Maryville was approximately 450,000 in 2000 and increased to about 467,000 in 2005, what is the average number of people added each year?
answer:To find the average number of people added each year, we need to calculate the total increase in population over the 5-year period and then divide it by the number of years. The population increase is 467,000 - 450,000 = 17,000 The number of years is 2005 - 2000 = 5 So, the average number of people added each year is 17,000 / 5 = 3,400 3400 The answer is: 3400
question:how many ways can I choose a 4-person committee from a club of 9 people?
answer:We can choose a 4-person committee from a group of 9 people in binom{9}{4} ways. Using the formula for combinations, this is equal to frac{9!}{4!(9-4)!} = frac{9!}{4!5!} = frac{9times8times7times6}{4times3times2times1} = boxed{126} ways. The answer is: 126
question:Brenda and nine of her friends want to order a pizza. They decide that each person will eat 2 slices. If each pizza has 4 slices, how many pizzas should they order?
answer:There are 10 people in total, and each person will eat 2 slices, so they will need 10 * 2 = 20 slices in total. If each pizza has 4 slices, then they will need 20 / 4 = 5 pizzas in total. 5 The answer is: 5