MATHEMATICS COLLEGE

A computer processes jobs on a first-come, first served basis in a time-sharing environment. The jobs have Poisson arrival rates average 0.6 jobs per minute. The objective in processing these jobs is that they spend no more than 5 minutes, on average, in the system. Assuming exponential service times, how fast does the computer have to process jobs (in minutes), on average, to meet this objective

Answers

Answer 1

Answer:

Answer:

0.8 minutes

Step-by-step explanation:

From the given information:

The arrival time for the jobs to the computer obeys a Poisson distribution;

Thus, the arrival rate is:

$\lambda = 0.6 \ jobs \ per \ minute$

Assuming the average time spent on the jobs in the system is denoted by:

$W_s= 5 \ minutes$

The average time a job process in the system can be expressed as follows:

$W_s = (1)/(\mu - \lambda)$

From above formula:

$\mu =$ service rate

$\lambda =$ arrival rate

replacing the values;

$5 = (1)/(\mu - 0.6)$

$5(\mu - 0.6) = 1$

Open brackets

$5 \mu - 3 = 1$

$5 \mu = 3+ 1 \n \n \mu = (4)/(5)$

$\mu =$ 0.8 minutes

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Answer the following...

Given the formula for the perimeter of a rectangle where l represents the length and w represents the width. 2(l + w) What does the 2 represent in this formula?

Answers

The fact that there are two length sides and two width sides.

A local BBQ restaurants offers 2 side dishes with a lunch plate. There are 7 side dishes. How many choices of side dishes does a customer have

Answers

Step-by-step explanation:

This is a question that bothers combination. Combination has to do with selection.

When selecting r objects out of a pool of n objects, the number of ways this can be done is:

nCr = n!/(n-r)!r!

If a local BBQ restaurants offers 2 side dishes with a lunch plate, and there are 7 side dishes, the number of choices that the customer have is expressed as:

7C2 = 7!/(7-2)!2!

7C2 = 7!/(5)!2!

7C2 = 7*6*5!/5! * 2

7C2 = 7*6/2

7C2 = 42/2

7C2 = 21 choices

Hence the customer has 21 choices of side dishes to make

What is the sum of the infinite geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 144) (one-half) Superscript n minus 1

Answers

Step-by-step explanation:

∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹

This is a finite geometric series with n = 4, a₁ = -144, and r = ½.

S = a₁ (1 − rⁿ) / (1 − r)

S = -144 (1 − (½)⁴) / (1 − ½)

S = -270

If you wanted to find the infinite sum (n = ∞):

S = a₁ / (1 − r)

S = -144 / (1 − ½)

S = -288

Answer:

It's A: -288

Step-by-step explanation:

on edge 2021

MP of an article is $1400. Find the SP of that article in cents if the shopkeeper adds 13% VAT after allowing 45% discount. (100 cents =$1)

Answers

Answer:

87,010 cents is the SP.

Step-by-step explanation:

MP = $1400

VAT = 13%

Discount = 45%

so,

discount amount = 45% of MP

= 45% of $1400

= 45/100 * $1400

= 9/20 * $1400

= 9* $70

= $630

so,

MP - discount amount

= $1400 - $630

= $770(SP)

so,

VAT amount = 13% of SP

= 13% of $770

= 13/100 * $770

= $100.1

so,

SP + VAT

= $770 + $100.1

= $870.1

so,

$1 = 100 cents

$870.1 = 100*870.1

= 87,010 cents

As a promotional offer, a new gym is offering a 30% discount to those who sign up in the first month. Patty and her 2 siblings take advantage of the offer and sign up for a total amount of €210. What were the total savings mode? Work out the average savings per person