Answer:
a) P(x=3)=0.089
b) P(x≥3)=0.938
c) 1.5 arrivals
Step-by-step explanation:
Let t be the time (in hours), then random variable X is the number of people arriving for treatment at an emergency room.
The variable X is modeled by a Poisson process with a rate parameter of λ=6.
The probability of exactly k arrivals in a particular hour can be written as:
a) The probability that exactly 3 arrivals occur during a particular hour is:
b) The probability that <em>at least</em> 3 people arrive during a particular hour is:
![P(x\geq3)=1-[P(x=0)+P(x=1)+P(x=2)]\\\\\\P(0)=6^{0} \cdot e^{-6}/0!=1*0.0025/1=0.002\\\\P(1)=6^{1} \cdot e^{-6}/1!=6*0.0025/1=0.015\\\\P(2)=6^{2} \cdot e^{-6}/2!=36*0.0025/2=0.045\\\\\\P(x\geq3)=1-[0.002+0.015+0.045]=1-0.062=0.938](https://tex.z-dn.net/?f=P%28x%5Cgeq3%29%3D1-%5BP%28x%3D0%29%2BP%28x%3D1%29%2BP%28x%3D2%29%5D%5C%5C%5C%5C%5C%5CP%280%29%3D6%5E%7B0%7D%20%5Ccdot%20e%5E%7B-6%7D%2F0%21%3D1%2A0.0025%2F1%3D0.002%5C%5C%5C%5CP%281%29%3D6%5E%7B1%7D%20%5Ccdot%20e%5E%7B-6%7D%2F1%21%3D6%2A0.0025%2F1%3D0.015%5C%5C%5C%5CP%282%29%3D6%5E%7B2%7D%20%5Ccdot%20e%5E%7B-6%7D%2F2%21%3D36%2A0.0025%2F2%3D0.045%5C%5C%5C%5C%5C%5CP%28x%5Cgeq3%29%3D1-%5B0.002%2B0.015%2B0.045%5D%3D1-0.062%3D0.938)
c) In this case, t=0.25, so we recalculate the parameter as:
The expected value for a Poisson distribution is equal to its parameter λ, so in this case we expect 1.5 arrivals in a period of 15 minutes.
Answer:
1. 73
2.-63
Step-by-step explanation:
1. 30+43=73
2. -84+21= 21-84=-63
Answer:
see explanation
Step-by-step explanation:
Using the trigonometric identity
sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x
Given
sin²x + 7cosx + 17
=1 - cos²x + 7cosx + 17
= - cos²x + 7cosx + 18 ← factor out - 1 from each term
= - (cos²x - 7cosx - 18)
Consider the factors of the constant term (- 18) which sum to give the coefficient of the cosx term (- 7)
The factors are - 9 and + 2, thus
= - (cosx - 9)(cosx + 2) ← in factored form
Answer:
3 dimes
Step-by-step explanation:
Part A: 0.10x + 0.25 = 0.80 (dimes are 10 cents or 0.10 dollars, quarters are 0.25 dollars)
Part B: Plug in what you DO know and solve the one you DON’T:
0.10x + 0.25(2) = 0.80
0.10x + 0.50 = 0.80. Subtract 0.50 from both sides:
0.10x = 0.30 (Divide both sides by 0.10)
x = 3
