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>.
Answer:
The surface area that Sergio needs to frost on each cake is 3,238 square centimeters
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The surface area of the cylindrical cake is equal to the lateral area plus the area of the top of cylinder (remember that the bottom of the cake does not need frosting)
so
we have
---> the radius is half the diameter
substitute the given values
Round up to the nearest whole number
therefore
The surface area that Sergio needs to frost on each cake is 3,238 square centimeters
Answer:
-18
Step-by-step explanation:
3(-4) - 6
-12 - 6 = -18
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Sometimes the quadratic is easier to graph if written in vertex form.
y = -x^2 -6x -3
= -(x^2 +6x) -3
= -(x^2 +6x +9) -3 +9
= -(x +3)^2 +6
This is a parabola that opens downward, with its vertex at (-3, 6). Unlike the one shown in the graph already, its scale factor is 1, so it will appear narrower than the one given with the problem statement.
x= A ticket
y=b ticket
x+y=500
10x+60y=6000
-------------------
10x+60y=6000
- x+y=500 (*10) ---> 10x+10y=5000
-------------------
10x+60y=6000
- 10x+10y=5000
-------------------
50y=1000
y=1000/50
y=20
b ticket =20
x+y=500
x+20=500
x=500-20
x=480
a ticket=480
answer is the last option ,
