answer:Let the first term of the arithmetic series be a, and let the common difference be d. Then the sum of an arithmetic series is given by frac{n}{2}(2a + (n-1)d), where n is the number of terms. Thus we have frac{15}{2}(2a + 14d) = 615, which simplifies to (2a + 14d) = 82. We are also given that the fifth term is 53, so a + 4d = 53. Subtracting twice the second equation from the first, we get (2a + 14d) - 2(a + 4d) = 82 - 2(53), which simplifies to 6d = 70, or d = boxed{frac{35}{3}}.

answer:To calculate the labor efficiency variance, we need to compare the actual direct labor hours worked to the standard direct labor hours allowed for the production of the actual output. Actual direct labor hours worked = 1,550 hours Actual output = 1,000 Zippies Standard direct labor hours allowed = (1.5 standard hours per Zippy) * (1,000 Zippies) = 1,500 hours Labor efficiency variance (LEV) = Actual direct labor hours worked - Standard direct labor hours allowed LEV = 1,550 hours - 1,500 hours LEV = 50 hours The labor efficiency variance (LEV) is 50 hours. Now, we need to calculate the dollar value of the labor efficiency variance. To do this, we multiply the labor efficiency variance by the standard labor rate. Standard labor rate = 12.00 per direct labor hour Dollar value of LEV = LEV * Standard labor rate Dollar value of LEV = 50 hours * 12.00 per hour Dollar value of LEV = 600 Since the LEV is a measure of favorable or unfavorable performance, and the actual labor hours worked exceeded the standard labor hours allowed, the labor efficiency variance (LEV) is unfavorable. Therefore, the correct answer is c. 600 unfavorable.

answer:To calculate the rate variance for variable manufacturing overhead, we need to compare the actual variable manufacturing overhead rate per labor-hour to the standard variable manufacturing overhead rate per labor-hour. Actual variable manufacturing overhead rate per labor-hour = Variable manufacturing overhead spent / Labor-hours worked Actual variable manufacturing overhead rate per labor-hour = 5,115 / 1,550 labor-hours Actual variable manufacturing overhead rate per labor-hour = 3.31 per labor-hour Standard variable manufacturing overhead rate per labor-hour = 3.00 per labor-hour Rate variance (VMRV) = (Actual variable manufacturing overhead rate per labor-hour - Standard variable manufacturing overhead rate per labor-hour) * Labor-hours worked VMRV = (3.31 per labor-hour - 3.00 per labor-hour) * 1,550 labor-hours VMRV = 0.31 per labor-hour * 1,550 labor-hours VMRV = 479.50 The rate variance for variable manufacturing overhead (VMRV) is 479.50. Since the rate variance is a measure of favorable or unfavorable performance, and the actual variable manufacturing overhead rate per labor-hour exceeds the standard variable manufacturing overhead rate per labor-hour, the rate variance is unfavorable. Therefore, the correct answer is a. 465 unfavorable.

answer:To calculate the efficiency variance for variable manufacturing overhead, we need to compare the actual labor-hours worked to the standard labor-hours allowed for the production of the actual output. Actual labor-hours worked = 1,550 labor-hours Actual output = 1,000 Zippies Standard labor-hours allowed = (1.5 standard labor-hours per Zippy) * (1,000 Zippies) = 1,500 labor-hours Efficiency variance (VMEV) = Actual labor-hours worked - Standard labor-hours allowed VMEV = 1,550 labor-hours - 1,500 labor-hours VMEV = 50 labor-hours The efficiency variance (VMEV) is 50 labor-hours. Now, we need to calculate the dollar value of the efficiency variance. To do this, we multiply the efficiency variance by the standard variable manufacturing overhead rate per labor-hour. Standard variable manufacturing overhead rate per labor-hour = 3.00 Dollar value of VMEV = VMEV * Standard variable manufacturing overhead rate per labor-hour Dollar value of VMEV = 50 labor-hours * 3.00 per labor-hour Dollar value of VMEV = 150 Since the VMEV is a measure of favorable or unfavorable performance, and the actual labor-hours worked exceeded the standard labor-hours allowed, the efficiency variance (VMEV) is unfavorable. Therefore, the correct answer is c. 150 unfavorable.