Solve the following problems using MATLAB script (write one .m file per problem): Create two variables x and y and store numbers in them. Write an expression that would be true if the value of x is greater than 5 or if the value of y is less than 10, but not if both of those are true. 1. 2. An environmental engineer has determined that the cost C of a containment tank will be based on the radius r of the tank: 32430 I Create a variable for the radius, and then for the cost. C = +428TI The geometric mean g of n numbers x is defined as the nth root of the product of X: Xi g = X1 X2 X3...Xn (This is useful, e.g., in finding the average rate of return for an investment, which is something you'd do in engineering economics.) If an investment returns 15% the first year, 50% the second, and 30% the third year, the average rate of return would be (1.15*1.50*1.30)/3). Compute this. 3. 4. 5. A sphere has a radius of 24 cm. A rectangular prism has sides of a, a/2, and a/4. (a) Determine a of a prism that has the same volume as the sphere. (b) Determine a of a prism that has the same surface area as the sphere. n! r!(n-r)! a/2 The number of combinations C,, of taking r objects out of objects is given by: a/4 C6, 2C43, 4 C49,6 (Use the built-in function factorial.) Cnr (a) Determine how many combinations are possible in a lottery game for selecting 6 numbers that are drawn out of 49. (b) Using the following formula, determine the probability of guessing two out of the six drawn numbers.