Determine whether the following is always true or not always true. Given reasons for your answers.(u × v) ? w = u ? (w × v)
What will be an ideal response?
Not always true; (u × v) ? w = u ? (v × w), but v × w = -(w × v) from which it follows that the original equation false if 
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Calculate the product. -4 ? 8
A. 4 B. -4 C. 32 D. -32
Find the Taylor series for the given function.f(x) = 
A. 
B. 
C. 
D. 
Solve the problem.The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring and 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $30 and on an SST ring is $60?
A. 0 VIP and 24 SST B. 8 VIP and 16 SST C. 16 VIP and 8 SST D. 12 VIP and 12 SST
Provide an appropriate response.The probability distribution for the random variable X is: 
What is the expected value of X?
A. 0.62 B. 0.26 C. 0.22 D. 0.50