1. Alden fills his backpack with \( 0.45 kg \) of apples, \( 0.18 kg \) of cheese, and a water bottle that weighs \( 1.4 kg \) . How heavy are the contents of his backpack?
A recipe for vegetable frittata calls for \( 10 \) chard leaves for every \( 6 \) eggs. Eggs are available either by the dozen for \( \$ 3.20 \) or by the half-dozen for \( \$ 1.70 \) . Marissa wants to use \( 25 \) chard leaves to make a frittata. What is the minimum she must spend on eggs to use all of the chard leaves while keeping the recipe in the correct proportion?
A) \( \$ 3.20 \)
B) \( \$ 4.00 \)
C) \( \$ 4.90 \)
D) \( \$ 5.10\)
One gram of fat is equivalent to \( 9 \) calories, \( 1 \) gram of protein is equivalent to \( 4 \) calories, and \( 1 \) gram of carbohydrates is equivalent to \( 4 \) calories. If a granola bar weighs \( 1.4 \) oz and is \( 37.5 \% \) fat by weight, \( 15 \% \) protein by weight, and \( 40 \% \) carbohydrates by weight, how many calories, to the nearest calorie, are in the granola bar, if \( 1 \) ounce is \( 28.34 \) grams?
With a certain medical insurance policy, the customer must first pay an annual \( \$ 350 \) deductible, and then the policy covers \( 70 \% \) of the cost of x-rays. The first insurance claims for a specific year submitted by a person are for two \( x \) -rays. The first x-ray cost \( \$ 670 \) , and the second \( x \) -ray cost \( \$ 940 \) . How much, in total, will he need to pay for these \( x \) -rays?
Manny has an investment account that compounds interest continuously at a rate of \( 3.1 \% \) . After \( 2 \) years, he has \( \$ 7500 \) in the account. How much money did he initially place in the account? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer.
Provide your answer below:
Alice is opening a savings account that earns \( 2.2 \% \) interest, compounded continuously. How much will she need to deposit in the account so that she has \( \$ 6,200 \) after \( 3 \) years? Round your answer to the nearest dollar. Do NOT round until you have calculated the final answer. Provide your answer below: