Use the given graph to determine the limit, if it exists.   Find and . (5 points)

A beam is singly reinforced with the reinforcement in two rows. The bottom row contains 6 No. 6 bars at a depth of 20 in. The top row contains 4 No. 8 bars at a depth of 14 in. Determine the effective (centroidal) depth, d, of the steel.

(05.01 LC)  Samuel, a quality assurance inspector at a donut factory, checks for product quality using a random sample of 7 donuts from a batch of 38, with 14 cake donuts and 24 glazed donuts. Let p̂ be the proportion of cake donuts in the sample. Part A: Is the 10% condition met in this case? Justify your answer. (5 points) Part B: Is the Normal condition met in this case? Justify your answer. (5 points) (10 points)

Find an equation for the nth term of the arithmetic sequence. a16 = 21, a17 = -1 (7 points)

Find the first six terms of the sequence. a1 = -7, an = 2 • an-1 (5 points)

Please select ALL the following that are true about fats as they pertain to our diet/eating: 

Find a • b. a = 4i + 3j, b = -4i + 4j (5 points)  

(05.05 MC)  An ecological group suspects lobsters are consuming dangerous levels of mercury in a region of the world. Dangerous levels of mercury are classified when they reach beyond 6.5 parts per million. A random sample of 25 lobsters in the region were tested and the data is shown in the stemplot. Key: 2|2 = 2.2 parts per million Part A: What proportion of the lobsters in the sample have dangerous levels of mercury in their systems? (4 points)Part B: Construct and interpret a 95% confidence interval for the mean mercury levels of the lobsters if the sample of 25 lobsters has a mean mercury level of 5.05 parts per million and standard deviation of 1.45 parts per million. (6 points)(10 points)

Find the limit of the function by using direct substitution. (6 points)  

A beam has dimensions of b = 14 in., h = 28 in., d’ = 2.5 in., and d = 25.5 in. It is reinforced with 2 No. 5 bars on the compression side and 5 No. 8 bars on the tension side. The concrete strength is 3,700 psi, and the yield strength of the reinforcement is 60,000 psi. If the depth of the neutral axis is c = 5.588 in., determine the strain in the compression reinforcement, ε’s.