Answer:
v= 13
w= -32
Step-by-step explanation:
2v+6w=-36
5v+2w=1
2w= 1-5v
2v+ (3)(1-5v)= -36
2v+3-15v= -36
3-13v =-36
3--36= 13v
39= 13v
13 = V
5×13+2w=1
65+2w=1
1-65= 2w
-64=2w
-32=w
Answer:
% Po lost = 100[1 - e^(-0.005t)] %; 73.0 g
Step-by-step explanation:
p(t) = 100e^(-0.005t)
Initial amount: p(0) = 100
Amount remaining: p(t) = 100e^(-0.005t)
Amount lost: p(0) – p(t) = 100 - 100e^(-0.005t) = 100[1 - e^(-0.005t)]
% of Po lost = amount lost/initial amount × 100 %
= [1 - e^(-0.005t)] × 100 % = 100[1 - e^(-0.005t)] %
p(63) = 100e^(-0.005 × 63) = 100e^(-0.315) = 100 × 0.730 = 73 g
The mass of polonium remaining after 63 days is 73 g.
Answer:
The steady state proportion for the U (uninvolved) fraction is 0.4.
Step-by-step explanation:
This can be modeled as a Markov chain, with two states:
U: uninvolved
M: matched
The transitions probability matrix is:

The steady state is that satisfies this product of matrixs:
![[\pi] \cdot [P]=[\pi]](https://tex.z-dn.net/?f=%5B%5Cpi%5D%20%5Ccdot%20%5BP%5D%3D%5B%5Cpi%5D)
being π the matrix of steady-state proportions and P the transition matrix.
If we multiply, we have:

Now we have to solve this equations

We choose one of the equations and solve:

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.
Answer:
134 sneakers and 66 sandals
Step-by-step explanation:
Sneakers= x, sandals= y
Profit rate:
- sneakers: (10-2)/8= 25%
- sandals: (17-14)/14= 21.4%
Sneakers are more profitable, so it should be maximized.
Cost:
8x+14y≤2000
x+y≤200
if we assume the maximum of 200 shoes stocked, then:
x= 200-y
8(200-y)+14y ≤ 2000
1600 - 8y +14y ≤ 2000
6y≤400
y≤66 and x=134 is the best option
If you would like to match each time with a time above, you can do this using the following steps:
a 3h 18m 7s = 11887s<span>
3h = 3 * 60m = 180m; 180m + 18m = 198m; 198m = 198 * 60s = </span>11880s; 11880s + 7s = 11887s
b <span> 8300min = approximately 5 days 18 hours
8300min = 8300 * 60s = </span>498000s
8300 min / 60 min = 138h 20min; 138h / 24h = 5 days 18 hours 20min
c 1461 days
1461 days = 1461 * 24 hours = 35064 hours
d <span>44640min. = 31 days
</span><span>44640min / 60min = 744 hours; 744 hours / 24 hours = 31 days
e </span><span>10:21:2.5
</span>10:21:2.5 = 10 hours, 21 minutes, 2 seconds, 50 milliseconds<span>
</span>