I'm assuming you want us to solve for the unknown variable z
Combine like terms on the right side
Use the distributive property on the left side
Add both sides by 20 to cancel out the "-20" on the left side
Divide both sides by 10
That is the value of the known variable, z, in this equation. Let me know if you need any clarifications, thanks!
~ Padoru
Answer:
<em>is the increased number.</em>
Step-by-step explanation:
<em>The first step would be to turn the percentage into a decimal. To do that, divide it by 100.</em>
Then, multiply that by 90.
Add both together to get the increased price.
<em>:)</em>
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>.
So first, you have to get two of the same variables to cancel out. Let's do this for x. In order for the x's to cancel out, we could multiply the bottom problem by 2.
(2) 3x-6y=24
After multiplying all the numbers by 2, you get the equation 6x-12y=48
The set of equations is now
-6x+2y=12
6x-12y=48
Now you can add them. The x variables cancel out, so you are left with the y variable.
2y+-12y=-10y and 12+48=60
Then you would divide 60 by -10 to get y=-6.
You would plug the answer for y into one of the original equations, lets do the top one. -6x+2y=12 becomes -6x+2(-6)=12
You'd multiply the 2 and -6 to get -12 so the equation is
-6x-12=12
The negative 12 turn positive and you add to both sides to get the -6x alone.
-6x-12=12
+12=12
-6x=24
Then divide 24 by -6
X=4
(-4,-6) is your final answer.
