The work of a student to solve a set of equations is shown:
equation 1: m = 8 + 2n
equation 2: 4m = 4 + 4n
step 1: −4(m) = −4(8 + 2n) [equation 1 is multiplied by −4.]
4m = 4 + 4n [equation 2]
step 2: −4m = −32 − 8n [equation 1 in step 1 is simplified.]
4m = 4 + 4n [equation 2]
step 3: −4m + 4m = −32 − 8n + 4n [equations in step 2 are added.]
step 4: 0 = −32 − 4n
step 5: n = −8
in which step did the student first make an error?
step 1
step 2
step 3
step 4

Which is the standard form for this number? (4 x 1 100 ) + (8 x 1 1,000 ) + ( 3 x 1 100,000 ) ? a) 0.004803 b) 0.04803 c) 0.0483 d) 0.483

The weight of full–grown tomatoes at a farm is modeled by a normal distribution with a standard deviation of 18.4 grams. the 95 percent confidence interval for the mean weight of the tomatoes is calculated using a sample of 100 tomatoes. what is the margin of error (half the width of the confidence interval)?

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).