Question a. John Bulldock would like to put away money for a down payment on a house during the next ten years. How much money should John deposit quarterly in an account paying 3.5% annual interest rate so he can have $60,000 10 years. b. The Marginal Cost (MC) of producing a certain good is set as $15 +.0025Q. If Profit is maximized where the selling price is equal to the Marginal Cost, find the profit maximizing quantity of output, if the good sells for $35.00?

For the following exercises, find the lengths of the functions of y over the given interval. If you cannot evaluate the integral exactly, use technology to approximate it. 181. y = 5 - 3x from y = 0 to y = 4 – 4

Coursework 3.3 Write the state-space representation for the following systems: Yilt 7. 421t) К. M2 KI m W fit) bi yait) be -Ma RA 2. 20 + yilt) Ta í It) = Uzlt) Milt=VLE R2 R2

Help please A thin walled cylindrical pressure vessel is subjected to an internal pressure which varies from 750 KPa to 3550 KPa continuously. The diameter of the shell is 1.5 m. Find the required thickness of the cylinder wall based on yield point of 480 MPa, net endurance limit of 205 MPa and a factor of safety of 2.5. A camshaft 19 mm. in diameter is mounted on ball bearings and carries a cam midway from the bearings. The follower, which weighs 2.8 KN, is out of adjustment so that impact is produced when it is contacted by the cam. The height h of fall equals 0.254 mm. The shaft is made of AISI C1045 steel. Determine the maximum bending stress in the shaft.

Biostatistics ESSAY A firm investigates the length of telephone conversations of their office staff. Ten consecutive conversations had lengths, in minutes: 10.7, 9.5, 11.1, 7.8, 11.9, 4.1, 10.0, 9.2, 6.5, 9.2. Derive a 95% confidence interval for the mean conversation length. Test whether the mean length of a conversation is eight minutes.(25 MARKS)

P3.5 The sales revenue, food cost of sales, and guests served for a small fast- food carryout division of a restaurant for the past six months are given below. Sales Month Cost of Revenue Guests Served Sales, Food 1 2. 4 $258,200 274,800 285,600 289,400 298,300 304,600 $ 96,200 104,300 110,500 113,100 118,900 123,700 10,200 10,400 10,300 10,100 10,400 10,500 6 For each of the six months calculate average check and average costs of sales food. Using these averages, calculate an index number. Set the in- dex for month 1 at 100 and complete index numbers for the remaining five months. With the index numbers identified, convert sales revenue and cost of sales food from historic to current dollars.

Victory Company uses weighted average process costing. The company has two production processes. Conversion cost is added evenly throughout each process. Direct materials are added at the beginning of the first process Additional information for the first process follows Direct Materials Conversion Percent Percent Units Complete Complete Beginning work in process inventory 72, eee 100% 80% Units started this period 833,eee Units completed and transferred out 71e,eee Ending work in process inventory 195, eee 1ees 50% Beginning work in process inventory Direct materials $ 411,775 Conversion 100,938 $ 512, 713 Costs added this period Direct materials 2,755,725 Conversion 1,917,812 4,673,537 Total costs to account for $ 5,186,250 Required: 1. Compute equivalent units of production for both direct materials and conversion Equivalent Units of Production (EUP). Weighted Average Method Units % Materials EUP-Materials % Conversion EUP. Conversion Total units 2. Compute cost per equivalent unit of production for both direct materials and conversion Cost per equivalent unit of production Materials Conversion Costs Costs Total costs Equivalent units of production (from part 1) Cost per equivalent unit of production EUP EUP 0 0 3. Assign costs to the department's output-specifically, to the units transferred out and to the units in ending work in process Inventory (Round "Cost per EUP" to 2 decimal places.) EUP Cost per EUP Total cost Cost assignment-Weighted average Completed and transferred out Direct materials Conversion Total completed and transferred out Ending work in process Direct materials Conversion Total ending work in process Total costs accounted for $ 0 0.00 $ 0.00 S 0