The final answer would be:
r+2
Exact steps are shown in the attached picture.
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:
x = 44
Step-by-step explanation:
log4(x + 20) = 3
Raise each side to the power of 4
4^ log4(x + 20) = 4^3
x+20 = 4^3
x+20 = 64
Subtract 20 from each side
x+20-20 = 64-20
x = 44
Trigonometric values (sin, cos, tan etc.), represents the ratio between two sides.
In this case the triangle is dilated, which means the size will change but the shape will stay proportional.
Because the sides grew proportional their ratio stays the same; so, the tan in the second triangle is 22/5 too.
Moreover, because the sides grew/shrunk proportional, the angles stay the same.
Because same angles have the same trigonometric values, tan(x) in second triangle becomes 22/5.
Answer:
1.944
Step-by-step explanation:
if the problem was written just like the 2.4(0.81) then yes you multiply
