Answer:
120*2.75*60/5280
= 3.75
Step-by-step explanation:
Considering James takes 120 steps in a minute, with 60 minutes in an hour and a mile consisting of 5,280 feet, we can establish his walking pace. By multiplying his steps per minute by the distance of each step (120 * 2.75), we determine the distance he covers in one minute. This value is then multiplied by 60 to account for the total hour. Finally, the total distance is divided by the feet in a mile (5,280), which results in a speed of 3.75 miles per hour. Thus, the calculation becomes 120*2.75*60/5280
Answer:
Option 1 is valid, which entails 2 hours of walking and 12 hours of running.
Step-by-step explanation:
The equations provided are:
3w + 6r ≥ 36
3w + 6r ≤ 90
We'll assess which options comply with these equations.
1) 2 hours walking; 12 hours running
w = 2 and r = 12
3w + 6r ≥ 36
3(2) + 6(12) ≥ 36
6+72 ≥ 36
78 ≥ 36
3w + 6r ≤ 90
3(2) + 6(12) ≤ 90
6+72 ≤ 90
78 ≤ 90
Both equations are satisfied. Option 1 is valid.
2) 4 hours walking; 3 hours running
w = 4 and r = 3
3w + 6r ≥ 36
3(4) + 6(3) ≥ 36
12+18 ≥ 36
30 ≥ 36 (this does not hold since 30 < 36)
3w + 6r ≤ 90
3(4) + 6(3) ≤ 90
12+18 ≤ 90
30 ≤ 90
Thus, Option 2 is invalid.
3) 9 hours running; 12 hours walking
w = 9 and r = 12
3w + 6r ≥ 36
3(9) + 6(12) ≥ 36
27+72 ≥ 36
99 ≥ 36
3w + 6r ≤ 90
3(9) + 6(12) ≤ 90
27+72 ≤ 90
99 ≤ 90 (this does not hold since 99 > 90)
Option 3 is invalid.
4) 12 hours walking; 10 hours running
w = 12 and r = 10
3w + 6r ≥ 36
3(12) + 6(10) ≥ 36
36+60 ≥ 36
96 ≥ 36
3w + 6r ≤ 90
3(12) + 6(10) ≤ 90
36 + 60 ≤ 90
96 ≤ 90 (this does not hold since 96 > 90)
So, Option 4 is invalid.
Response: a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Detailed explanation:
In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:
Given that
Applying the Poisson process, we find that
(a) at most 12
probability= 
(b) exactly 13
probability=
(c) more than 12
probability=
(d) exactly 20
probability=
(e) within the range of 10 to 15, inclusive
probability=
Thus, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Answer: The least amount spent amounts to £12.92 Step-by-step explanation: Given Number of Cartons = 38 A carton costs 45 pence 4 cartons cost £1.56 In order to minimize expenses, one must opt for the cheaper choice. Since there are 100 pence in £1, this means that £1.36 is equivalent to x pence, where x * 1 = 1.36 * 100, leading to x = 136 pence for four cartons. To find the cost of a single carton, divide x by 4; thus, x/4 = 136p/4, resulting in x/4 = 34 pence. This indicates that a carton of juice can be purchased at 34 pence and 45 pence, with 34 pence being the better deal. Therefore, the total expenditure equals 34 * 38, which converts to 1292p and subsequently to £12.92.
Answer:
Step-by-step explanation:
Initial Charge = $ 65
Hourly Rate = $ 28
Hours Worked = H
Cost for H hours = 28 * H = 28H
Inequality:
65 + 28H ≤ 250
