For the given claim, complete parts (a) and (b) below.

Claim: High school teachers have incomes with a standard deviation that is more than $19, 250. A recent study of 149 high school teacher incomes showed a standard deviation of $21,250.

a. Express the original claim in symbolic form.

b. Identify the null and the alternative hypotheses that should be used to arrive at a conclusion that supports the claim: H0: ___ ___ H1:___ ___ ___

Which multiplicative property is being illustrated below? (type commutative, associative, or identity) 5 × 2 × 4 = 2 × 5 × 4

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Is there a direction u in which the rate of change of f(x,y)equals=x squared minus 3 xy plus 4 y squaredx2−3xy+4y2 at p(1,2) equals 14? give reasons for your answer. choose the correct answer below. a. no. the given rate of change is smaller than the minimum rate of change. b. no. the given rate of change is larger than the maximum rate of change. c. yes. the given rate of change is larger than the minimum rate of change and smaller than the maximum rate of change.