A bank has kept records of the checking balances of its 4000 customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected. Please answer the following questions.

(a) What is the probability that the sample mean will be more than $309?

(b) What is the probability that the sample mean will be between $291 and $307?

(c) Suppose the number of customers decreases from 4000 to 2000. What is the probability that the sample mean will be between $296 and $306?

A steam thermoelectric plant operates a Rankine cycle with overheating. Water enters the pump as saturated liquid , 7.7 kg/s. The efficiency of the pump is 0.9 The water enters the high pression turbine at 12 500 kPa and 550°C, after that steam overheats at a constant pressure of 2000 kPa until 450°C before it expands on the low pressure turbine. The efficiency of both turbines is 0.85. The vapor quality when it enters to the condenser is 0.95 Determine the thermal efficiency of the cycle.

A gas decomposes to hydrogen and a liquid in a compressed cylinder of 16 liters. Assuming 298 K, find the maximum pressure the cylinder can withstand (ie, the pressure of hydrogen gas). Formula: 5A(g)-> 2B(l)+ 4H2(g)

Mass of A initial: 2000 g
Molar Mass of A: 30 g/mol
Molar Mass of B: 70 g
Density of B: 600 g/mL

If you can't assume Ideal Gas, how would one do this with Vapor Pressures?

The cost function C and the price-demand function p are given. Assume that the value of C(x) and p(x) are in dollars. Complete the following. C(x) = x2 100 + 7x + 2000; p(x) = − x 40 + 5 (a) Determine the revenue function R and the profit function P. R(x) = P(x) = (b) Determine the marginal cost function MC and the marginal profit function MP. MC(x) = MP(x) =

Here is a picture of the problem: https://gyazo.com/6ce694b737f7dd4cfb20fbb9d1917420

A steam thermoelectric plant operates a Rankine cycle with overheating. Water enters the pump as saturated liquid , 7.7 kg/s. The efficiency of the pump is 0.9 The water enters the high pression turbine at 12 500 kPa and 550°C, after that steam overheats at a constant pressure of 2000 kPa until 450°C before it expands on the low pressure turbine. The efficiency of both turbines is 0.85. The vapor quality when it enters to the condenser is 0.95 Determine the thermal efficiency of the cycle.

Consider a perfectly competitive market where each firm’s total cost function is TC = q^3 – 10q^2 + 50q.

a) What is the long run equilibrium price and quantity for each firm?

b) The industry demand function is Qd=2000-10p. How many firms are there in the industry in the long run?

c) The demand has changed to Qd=4000-18p. Describe the industry’s response to the demand shock and calculate the change in the number of firms in the long run equilibrium.

16a)Consider a 550 nm light falling on a single slit of width 0.75 μm.  At what angle (in degrees) is the first minimum for the light?

16b)  Sodium vapor light (average wavelength 610 nm) falls on a single slit of width 7.3 μm. At what angle θ, in degrees, does it produces its second minimum?

16c) A diffraction grating has 2000 lines per centimeter. At what angle, in degrees, will the first-order maximum be for 505-nm wavelength green light?

Question 2 [20 Marks]

You are provided with the following information. Conduct an ABC analysis, categorising each item of stock appropriately. (80% = A, 15% = B, 5%=C

>Prepare t-accounts for cash, A/R, the allowance for DA, Income statement

>Prepare journal entries for each situation

>Find net accounts receivable

-Nonprofit organization begins 2019 with a balance in A/R of $14,000.

-The company has an allowance for doubtful accounts beginning balance of 2000.

-During 2019, the company has credit sales of $300,000.

-Bad debt expense is 2% of credit sales.

-Cash collections of A/R are $290,000.

-Accounts written off were 4500 for the year.