Solve the following equation for x: x^2 +8x=33 a. x=2 and x=4 b. x=1 and x=33 c. x=-3 and x=11 d. x=3 and x= -11

Julie buys 2kg of apples and 7kg of pears ? 12.70. the pears cost ? 1.30 per kilogram what is the price per kilogram of the apples? show your working out

Which statement is true about a number and its additive inverse? a. their product is always one. b. their sum is always one. c. they are always reciprocals of each other. d. their sum is always zero.

Assume the population consists of the values 1, 3, 14. assume samples of 2 values are randomly selected with replacement (see page 23 for a definition) from this population. all the samples of n=2 with replacement are 1 and 1, 1 and 3, 1 and 14, 3 and 1, 3 and 3, 3 and 14, 14 and 1, 14 and 3, and 14 and 14. for part a) of this project, find the variance σ2 of the population {1, 3, 14}. for part b) of this project, list the 9 different possible samples of 2 values selected with replacement, then find sample variance s2 (which includes division by n-1) for each of them, and finally find the mean of the sample variances s2. for part c), for each of the 9 different samples of 2 values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population variance, which includes division by n), then find the mean of those population variances. for part d), which approach results in values that are better estimates of σ2 from part a): part b) or part c)? why? when computing variances of samples, should you use division by n or n-1? upload your answers for a), b), c), and d). the preceding parts show that s2 is an unbiased estimator of σ2. is s and unbiased estimator of σ? the above problem is from triola’s essentials of statistics, 4th edition.