Answer:
(x+5)(x-4)(x-3)
Step-by-step explanation:
Divide (e+5) into e³-2e²-23e+60 using polynomial long division (picture attached below). Since it divides in evenly, we can see it is a factor.
So we can say e³-2e²-23e+60 = (e+5)(e²-7e+12)
To complete the factorisation, factorise e²-7e+12.
Note that (x+a)(x+b)=x²+(a+b)x+ab. So find the multiples or 12 which can be added or subtracted to get -7: -4 and -3.
e²-7e+12=(x-4)(x-3)
So e³-2e²-23e+60 = (x+5)(x-4)(x-3)
Answer:
0.25
Step-by-step explanation:
We are given that Rob created the Venn Diagram shown below which gives us,
The probability of teenagers who like to eat hot dogs = P(HD) = 0.3
The probability of teenagers who like to eat hamburger = P(HB) 0.4
The probability of teenagers who like to eat both = P( HD ∩ HB ) =0.1
The probability of teenagers who like to eat none = 0.2
It is required to find the probability that a teenager eats hot dogs when it is given that he/she eats hamburger i.e. P( HD | HB ).
Now, we know that the probability that an event B occurs given that event A has already occurred is given by,
![P(B|A) = \frac{P(A \bigcap B)}{P(B)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Cbigcap%20B%29%7D%7BP%28B%29%7D)
So, ![P(HD|HB) = \frac{P(HD \bigcap HB)}{P(HB)}](https://tex.z-dn.net/?f=P%28HD%7CHB%29%20%3D%20%5Cfrac%7BP%28HD%20%5Cbigcap%20HB%29%7D%7BP%28HB%29%7D)
i.e. ![P(HD|HB) = \frac{0.1}{0.4}](https://tex.z-dn.net/?f=P%28HD%7CHB%29%20%3D%20%5Cfrac%7B0.1%7D%7B0.4%7D)
i.e. ![P(HD|HB) = 0.25](https://tex.z-dn.net/?f=P%28HD%7CHB%29%20%3D%200.25)
Hence, the probability that a teenager eats hot dogs when it is given that he/she eats hamburger is 0.25.
Answer:
14hrs
Step-by-step explanation:
5 1/2+8 1/2
Answer:
Step-by-step explanation:
x^2-(2+2)x+4=0
or, x^2-2x-2x+4=0
or, x(x-2)-2(x-2)=0
or, (x-2)(x-2)=0
Now,
Either, x-2=0
=2
Or, x-2=0
=2