Question (1 point) A random variable X can be modeled by the Exponential distribution, where ß= 0 = 3,1=1 (a) Complete the sentence. The distribution of X is with px = !!! and ox = (Enter numerical answers to two decimals.) (b) Find P(2 < X <5). Use four decimals. (c) Find the 25-th percentile. Enter your answer to two decimals. Use two decimals in your answer. X 25 (1 point) A random variable X can be modeled by the Exponential distribution, where ß= 0 = 3,1=1 (a) Complete the sentence. The distribution of X is with px = !!! and ox = (Enter numerical answers to two decimals.) (b) Find P(2 < X <5). Use four decimals. (c) Find the 25-th percentile. Enter your answer to two decimals. Use two decimals in your answer. X 25 = (d) Find P(X > 9). Use four decimals in your answer.

[10 points] Problem 5. Let today's high temperature be denoted as a random variable \( T \). For this time of the year in Amherst, let's assume that \( T \) is a normal random variable with mean \( \mu=50 \) and \( \sigma^{2}=25 \). Let's say Andrew feels comfortable if the temperature is between two integers \( A \) and \( B \), i.e., \( A \leq T \leq B \). He hasn't been here for long and is a little unsure about what to expect. So his lower temperature threshold \( A \) is a discrete random variable and takes two equally-likely values: 40 and 45 . Similarly, his high temperature threshold \( B \) is also a discrete random variable and takes two equally-likely values: 55 and 60 . Further assume that \( A \) and \( B \) are independent. What is the probability that Andrew feels comfortable today?

?Q. No.3 Nagano International has 420 accounts receivable in its subsidiary ledger. All accounts are due in 20 days. On December 31, an aging schedule was prepared. The results are summarized below: Customer total Not yet due 1-30 3 1-60 61-90 over 90Days Days Days Dayspast due past due past due past due (418 names) Subtotals S863,125 $458,975 $236,700 $108,350 $22,500 $36.600Two accounts receivable were accidently omitted from this schedule. The following data are available regarding these accounts: I. J.Ardis owes S10,625 from two invoices: invoice no. 218, dated September 14, in the amount of$3,375 : and invoice no. 641 dated December 5, in the amount of $6,025.Instructionsa. Complete the aging schedule as of December 31 by adding to the column subtotals an aging ofthe account of Ardis and Selstad. b. Prepare a schedule to compute the estimated portion of each age group that will proveuncollectible and the required balance in the Allowances for Doubtful Accounts. Arrange your schedule in the format illustrated on pae 292. The following percentages of each age group are estimated to be uncollectible: Not yet due, 1%; 1-30 days, 4%, 31-60 days, 10%: 61-90 days,30% over 90 days, 50% c. Prepare the journal entry to bring the Allowances for Doubtful Accounts up to its requiredbalance at December 31. Prior to making this adjustment, the account has a credit balance ofS34,500. d. Show how accounts receivable would appear in the company's balance sheet at December 31. e. On January 7 of the following year, the credit manager of Nagano International leams that the$10,625 account receivable from J.Arids is uncollectible because Arids has declared bankruptcy. Prepare the journal entry to write off his account.

The image(constants in there are D1 and D2 )below shows a phase reaction equation at the temperature of 600K with rate constants D1= 500 L.mol-1.hr-1 and D2 = 0.032 hr-1i)At 1 atm supposed the feed contains 0.25 mol% of Br2 with no inert, find the equilibrium conversionii)Explain why the formation of C2H4Br2 proceed to an appreciable extent ? iii)At 85% of the equilibrium conversion,find and explain the number of possible batches in a day (Assume downtime is one and half hours.) Thanks,this is a full question. 

The conditions for the operation of a short circuit asynchronous motor controlled by three switches (S0, S1, S2) and connected to the energy source via contactor K1 are given as follows:  The S1 button is pressed and released, then if the S2 button is pressed within 5 seconds, the motor will be activated.  If the S0 button is pressed while the motor is on or if it is overloaded (F2F), the motor will be deactivated. a) Draw the appropriate state diagram to implement this control function with a relay. b) Write the logical functions related to this diagram and draw the electrical (relay) control circuit.

1. [7 marks] (a) (2 marks] Suppose that two distinct complex numbers u and v have the same modulus, and u+v+0. U – V (i) Show that the real part of is zero. u+v (ii) Show that u – v and u + v are orthogonal. a — с (b) [3 marks] Suppose that a and b are distinct points in C, that m is the midpoint of the line segment with endpoints a and b, and that c is a 1. [7 marks] (a) (2 marks] Suppose that two distinct complex numbers u and v have the same modulus, and u+v+0. U – V (i) Show that the real part of is zero. u+v (ii) Show that u – v and u + v are orthogonal. a — с (b) [3 marks] Suppose that a and b are distinct points in C, that m is the midpoint of the line segment with endpoints a and b, and that c is a point on the circle C(m, ž\b – al) with centre m and radius 316 – all such that c + a and c #b. Use the ratio and the fact that a - c= a - m + m - c and b-c=b- m + m - c to show that Zacb is a right angle. (c) [2 marks] Prove the assertion in (b) using the geometry of triangles in the Euclidean plane only. a - C

17.7 Bedeivable: A Sive Problem Nagano International has 420 accounts receivable in its subsidiary ledger. All accounts are due in 30 days. On December 31, an aging schedule was prepared. The results are summarized below: Not Yet Due 1-30 Days Past Due 31-60 Days Past Due 61-90 Days Past Due Over 90 Days Past Due Total Customer (418 names) Subtotals $863,125 $458,975 $236,700 $108,350 $22.500 $36.600 Two accounts receivable were accidentally omitted from this schedule. The following data are available regarding these accounts: 1. J. Ardis owes $10,625 from two invoices: invoice no. 218, dated September 14, in the amount of $7.450; and invoice no. 568, dated November 9, in the amount of $3.175. 2. N. Selstad owes 59,400 from two invoices: invoice no. 574, dated November 19, in the amount of $3,375; and invoice no. 641, dated December 5, in the amount of 6,025. Instructions a. Complete the aging schedule as of December 31 by adding to the column subtotals an aging of the accounts of Ardis and Selstad. b. Prepare a schedule to compute the estimated portion of each age group that will prove uncol- lectible and the required balance in the Allowance for Doubtful Accounts. Arrange your sched ule in the format illustrated on page 292. The following percentages of each age group are es- timated to be uncollectible: Not yet due, 1%; 1-30 days, 4%; 31-60 days, 10%; 61-90 days, 30%, over 90 days, 50%. c. Prepare the journal entry to bring the Allowance for Doubtful Accounts up to its required bal ance at December 31. Prior to making this adjustment, the account has a credit balance of $34,500. d. Show how accounts receivabıle would appear in the company's balance sheet at Decem ber 31 e. On January 7 of the following year, the credit manager of Nagano International learns that the $10,625 account receivable from J. Ardis is uncollectible because Ardis has declared bank ruptcy. Prepare the journal entry to write off this account.