a) The dimensions of original rectangle are length= 5 and width= 4.
b) The dimensions of new rectangle are length= 15 and width=8.
<u>Step-by-step explanation</u>:
- length of a rectangle = l
- width of a rectangle = w
- Perimeter of a rectangle = 2(l+w)
<u>Original rectangle</u> :
18 = 2(l+w)
18 = 2l + 2w ---------(1)
<u>New rectangle</u> :
46 = 2(3l+2w)
46 = 6l + 4w ---------(2)
<u>Solving the equations</u> :
Multiply (1) by 2 and subtract (2) from (1)
4l + 4w = 36
-(<u>6l + 4w = 46</u>)
<u>-2l = -10</u>
l = 10/2
length = 5 inches.
Substitute l=5 in (1)
18 = 2(5)+2w
18 = 10+2w
2w = 8
w = 8/2
width = 4 inches.
length of new rectangle = 3(l) = 3
5 = 15 inches.
width of new rectangle = 2(w) = 24 = 8 inches.
Answer:
Step-by-step explanation:
A. The steady state probability vectorπ= (π1, π2, π3, π4, π5, π6, π7) satisfies the system ofequations:πP=π,7Xi=1πi= 1which has solutionπ= (π1, π2, π3, π4, π5, π6, π7) = (0.1389,0.1389,0.1390,0.1383,0.1411,0.1302,0.1736)
(B) At any time period, an emergency delivery will be needed ifXn= 1 and the demands either 2 or 3, or ifXn= 2 and the demand is 3. The long-run proportion of time the chain will be in state 1 isπ1 and in-state 2π2.
<h3>
Answer: 9 units</h3>
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Explanation:
Let's calculate the volume of one small spherical bead
V = (4/3)*pi*r^3
V = (4/3)*pi*3^3
V = 36pi
The volume of 27 such identical beads is 27*36pi = 972pi cubic units.
----------
This is the new volume and we'll use this to find the radius r of the larger sphere.
V = (4/3)*pi*r^3
972pi = (4/3)*pi*r^3
3*972pi = 4pi*r^3
2916pi = 4pi*r^3
r^3 = (2916pi)/(4pi)
r^3 = 729
r = (729)^(1/3)
r = 9 units is the radius of the larger gold sphere
Answer:
x=24, y=15
Step-by-step explanation:
(3x-29)+(8y+17)=180
(8y+17)=(6x-7)
Answer:
B) The subset consists of all the matches where Manchester United won or lost.
Step-by-step explanation:
1 - Manchester united lost
2 - Manchester United won
4 - Manchester United won
6 - Manchester United lost
7 - Manchester United won
Hence, 1, 2, 4, 6, 7 consists of matches where Manchester United either won or lost.
Therefore, 1,2,4,6,7 is a subset of the sample space where Manchester United won or Lost
