Determine whether or not the following expressions are valid, i. e., whether the left- and right-hand sides represent same function. use truth table method for b, c and boolean algebra for a. draw the logic circuits for the left hand side expression for a, b,c

(a) x1'x3 + x1x2x3' + x1'x2 + x1x2' = x2'x3 + x1x3' + x2x3' + x1'x2x3

(b)x1x3' +x2x3 +x2'x3' =(x1 +x2' +x3)(x1 +x2 +x3')(x1' +x2 +x3')

(c)(x1 +x3)(x1' +x2' +x3')(x1' +x2)=(x1 +x2)(x2 +x3)(x1' +x3')

Which graph represents the parent function of y=(x+2)(x-2)

Asalsa recipe uses green pepper, onion, and tomato in the extended ratio 3: 5: 7. how many cups of tomato are needed to make 105 cups of salsa? a. 7 b. 21 c. 35 d. 49

Arandom sample of 15 observations is used to estimate the population mean. the sample mean and the standard deviation are calculated as 172 and 63, respectively. assume that the population is normally distributed. a. with 99 confidence, what is the margin of error for the estimation of the population mean? b. construct the 99% confidence interval for the population mean. c. construct the 95% confidence interval for the population mean. d. construct the 83% confidence interval for the population mean. hint: you need to use excel function =t. inv.2t to find the value of t for the interval calculation.