Answer:
f(x) = -(x+2)(x-1)
Step-by-step explanation:
We know the zeros are at 1 and -2
f(x) = a *(x-b1)(x-b2) where b1 and b2 are the zeros and a is a constant
f(x) =a(x-1)(x- -2)
f(x) =a(x-1)(x+2)
We know that a must be negative since the parabola opens down so
The only choice is choice D where a = -1
f(x) = -(x+2)(x-1)
Given:
The growth of a sample of bacteria can be modeled by the function
where, b is the number of bacteria and t is time in hours.
To find:
The number of total bacteria after 3 hours.
Solution:
We have,
Here, b(t) number of total bacteria after t hours.
Substitute t=3 in the given function, to find the number of total bacteria after 3 hours.
Therefore, the number of total bacteria after 3 hours is 119.1016.
60 minutes is an hour , you haven't given out what the 15, 30 and 60 are , and the 1 , 2 and 4 are(minutes or hours?)
So the waiting time for a bus has density f(t)=λe−λtf(t)=λe−λt, where λλ is the rate. To understand the rate, you know that f(t)dtf(t)dt is a probability, so λλ has units of 1/[t]1/[t]. Thus if your bus arrives rr times per hour, the rate would be λ=rλ=r. Since the expectation of an exponential distribution is 1/λ1/λ, the higher your rate, the quicker you'll see a bus, which makes sense.
So define <span><span>X=min(<span>B1</span>,<span>B2</span>)</span><span>X=min(<span>B1</span>,<span>B2</span>)</span></span>, where <span><span>B1</span><span>B1</span></span> is exponential with rate <span>33</span> and <span><span>B2</span><span>B2</span></span> has rate <span>44</span>. It's easy to show the minimum of two independent exponentials is another exponential with rate <span><span><span>λ1</span>+<span>λ2</span></span><span><span>λ1</span>+<span>λ2</span></span></span>. So you want:
<span><span>P(X>20 minutes)=P(X>1/3)=1−F(1/3),</span><span>P(X>20 minutes)=P(X>1/3)=1−F(1/3),</span></span>
where <span><span>F(t)=1−<span>e<span>−t(<span>λ1</span>+<span>λ2</span>)</span></span></span><span>F(t)=1−<span>e<span>−t(<span>λ1</span>+<span>λ2</span>)</span></span></span></span>.
