Suppose you decide to invest in a new account that offers continuously compounding interest. You decide to invest $50 for a period of 3 years with an interest rate of 7%. The bank tells you that you can calculate how much will be in your account at the end of the 3 years by calculating the composition of two formulas (f o g)(3), where f(t) = 50e^(t) and g(t) = t * .07. How much money do you have in the account after 3 years? Round to two decimal places.
The composition of two formulas means that (f o g)(3) = f(g(3)). First, let's find g(3) by plugging t=3 into g(t): g(3) = 3 * .07 = .21. Next, let's plus g(3) into f(t), f(g(3)) = 50e^(.21) = 61.68
Suppose you've conducted a survey about whether your classmates believe in mermaids. According to your results, 8% of your classmates actually believe in mermaids. If you surveyed 30 classmates, what's the average number of classmates who believe?
This is a binomial problem in statistics. You can recognize that it's binomial problem because we are given a fixed number of trials (30 classmates) that are independent of each other, where each can only have two possible outcomes (believing or not). We can find the average of a binomial distribution by simply multiplying the given probability of a success by the number of trials. Therefore, the average number of classmates who believe is: .08 * 30 = 2.4.
If x represents the sum of y and 4, and y represents the product of x and -3, what value is x?
Given in the problem: x = y + 4 and y = (-3)x. We can substitute the second equation into the first. This means that every time we see a "y" in the first equation, we can rewrite it as "(-3)x" instead. Then, x = (-3)x + 4. Now we just need to get x by itself. First we subtract (-3)x from both sides, which gives us x - (-3)x = (-3)x + 4 - (-3)x x + 3x = 4 4x = 4 Dividing both sides by four gives us the final result: x = 1.