1.At a road section, an average of 15 vehicles arrive during a 10-minute interval. If vehicles arrive according to a Poisson distribution, what is the probability that the number of vehicles ­arriving during a 3-minute interval is between 2 and 5 (i.e., 2 ≤ k ≤ 5)?

a.0.110

b.0.171

c.0.642

d.0.653

e.0.703

2.At a specific point on a highway, it is known that the time headways between successive vehicles are exponentially distributed and that 65% of the headways are greater than 3 seconds. What is the probability that less than two vehicles arrive during a 20-second interval?

a.0.219

b.0.233

c.0.350

d.0.397

e.0.412

Construction of a new fright terminal along a rural highway has been proposed. During certain periods of the day, significant numbers of large trucks are expected to depart the terminal’s one-lane driveway to access an interstate highway. Developers would like to know if there are an adequate number of time gaps (headways) in the highway traffic to permit about 40 trucks per hour to enter the highway without the need for a traffic signal. To permit a truck to safely enter the highway, a time gap of at least 8 seconds is needed. Assuming that there will be a flow of 850 vehicles on the highway during a design hour, how many gaps or opportunities will there be during the design hour for trucks to enter the highway without a traffic signal? Assume that vehicle arrivals follow a Poisson distribution.

a.849

b.425

c.340

d.212

e.128

Determine the number of moles of the compound and determine the number of moles of each type of atom in
each of the following:
(a) 2.12 g of potassium bromide, KBr
(b) 0.1488 g of phosphoric acid, H3PO4
(c) 23 kg of calcium carbonate, CaCO3
(d) 78.452 g of aluminum sulfate, Al2(SO4)3
(e) 0.1250 mg of caffeine, C8H10N4O2

The number of effective workers takes into account the number of workers and the:

a) amount of capital available to each worker

b) rate of growth of the number of workers

c) efficiency of each worker

d) saving rate of each worker

An element has an atomic number of 76. The number of protons and electrons in a neutral atom of the element are?

Number of units produced                           30, 000

Number of units sold                                     28,000

Selling price                                                           $20

Beginning inventory                                                 0

Fixed selling and administrative costs      $ 20,000

Fixed manufacturing overhead                  $ 150,000

Direct materials cost per unit                                      2

Direct manufacturing labor                                          6

Variable manufacturing overhead per unit       4

Variable selling expenses per unit                              2

FMOH per unit                                                               5

1.Operating Income under Absorption method is         

2.If Sales Revenue $560,000 then Gross Margin under Absorption method is

3.Cost of Goods Sold and Ending inventory under Absorption costing method are:

4.What is Cost of Goods Manufactured under Variable costing method

5.What is Cost of goods manufactured under Absorption costing method

7. Ask the user to type in a number and compare this number with 8. The user could try twice.

If the first user input was 8 then print out “Correct!” and terminate the program, otherwise ask user to type in a number for the second time. If the second input was 8 then print out “Correct”, otherwise print “Game over!”

Finish the assembly code segment for the above requirement.

.data

message: .asciiz "Please enter a random number:"

right_str: .asciiz "Correct!\n"

wrong_str: .asciiz "Game over! \n"

.text

            li $t0,8 # true answer

            li $t1,0 #counter, two chances           

loopcheck:  

            la $a0, message # ask user type in

            li $v0, 4

            syscall

            li $v0, 5

            syscall

            move $s1, $v0 # s1 is the user input

            …. # your answer here

           …. # your answer here

printGameOver:

            la $a0, wrong_str

            li $v0, 4

            syscall

            j done

printright:

            la $a0, right_str

            li $v0, 4

            syscall           

done: #exit

li $v0, 10

syscall

Show that the number of triangulations of a regular n-gon is the same as the number of Catalan paths from (0,0) to (n−2, n−2).

A Catalan path is defined as the following:

we want to count the number of distinct paths from the point (0,0) to the point (n, n) subject to the following rules:

•We must stay inside the box [0, n]×[0, n].

•We move one step at a time, either moving one unit East or one unit North.

•We cannot visit the same point twice.

•The path must always stay at or below the line y = x.

Is the number of tornadoes increasing? In the last homework, data on the number of tornadoes in the United States between 1953 and 2014 were analyzed to see if there was a linear trend over time. Some argue that it’s not the number of tornadoes increasing over time, but rather the probability of sighting them because there are more people living in the United States. Let’s investigate this by including the U.S. census count (in thousands) as an additional explanatory variable (data in EX11-24TWISTER.csv).

Perform a multiple regression using both year and census count as explanatory variables. Write down the fitted model. Are year and census count respectively significant in the MLR model?