Answer:
probability that actual service time will be less than or equal to five minutes = P(X <= 5) = 1 - e-15(5/60) = 0.714 or 71.4%
Step-by-step explanation:
The identification of the average arrival rate of customers(v) and the average service rate(u) must be done in order to solve this kind of problem .
In this case, on average, 12 customers arrive each hour. On average, the service rate is 15 customers per hour.
The arrival rate follows the exponential distribution.
probability that actual service time will be less than or equal to 't' minutes P(X <= t) = 1 - e-u(t/60)
probability that actual service time will be less than or equal to five minutes = P(X <= 5) = 1 - e-15(5/60) = 0.714 or 71.4%
<u>In a parallelogram,</u>
⇒the angles adjacent to each other
⇒ are of the same measure
⇒so
∠A = ∠C
∠B = ∠D
<u>Let's solve</u>:
![7z +5 = 8z - 10\\5+10=8z-7z\\8z-7z=5+10\\z = 15](https://tex.z-dn.net/?f=7z%20%2B5%20%3D%208z%20-%2010%5C%5C5%2B10%3D8z-7z%5C%5C8z-7z%3D5%2B10%5C%5Cz%20%3D%2015)
![5w-30=3w+10\\5w-3w=30+10\\2w = 40\\w=20](https://tex.z-dn.net/?f=5w-30%3D3w%2B10%5C%5C5w-3w%3D30%2B10%5C%5C2w%20%3D%2040%5C%5Cw%3D20)
<u>Let's check</u>:
⇒ for all quadrilaterals like a parallelogram
⇒all the angle measures added up to 360, so:
![(7z+5)+(8z-10)+(5w-30)+(3w+10)=360\\(7(15)+5)+(8(15)-10)+(5(20)-30)+(3(20)+10)=360\\(105+5)+(120-10)+(100-30)+(60+10)=360\\110+110+70+70=360\\220+140=360\\360=360](https://tex.z-dn.net/?f=%287z%2B5%29%2B%288z-10%29%2B%285w-30%29%2B%283w%2B10%29%3D360%5C%5C%287%2815%29%2B5%29%2B%288%2815%29-10%29%2B%285%2820%29-30%29%2B%283%2820%29%2B10%29%3D360%5C%5C%28105%2B5%29%2B%28120-10%29%2B%28100-30%29%2B%2860%2B10%29%3D360%5C%5C110%2B110%2B70%2B70%3D360%5C%5C220%2B140%3D360%5C%5C360%3D360)
<u>Thus</u>:
<u>Answer: w = 20 and z = 15</u>
Hope that helps!
Answer:
yes becasue their sides have the same length and angles
Step-by-step explanation:
A. Karel should charge less than $2 if she wants to be the cheapest (x<$2). x would represent what she charges.
B. She should charge $2.75 if she wants to charge what most other sitters are charged because this amount occurs more than any other(the mode).
C. She should also charge $2.75 if she wants to be in the middle (median).
D. When deciding on a rate, Karel should also consider if there are any rates that are a lot lower or a lot higher because there might be a reason (more kids, unusual hours, relatives, etc...).