Answer:
False.
Step-by-step explanation:
I believe this is a false statement, due to the fact '6' is larger than four. In this case, the six is negative. Therefore, negative numbers are always closer to zero than positive numbers.
Hope it helped :)
Expand
f(x)=-x²-8x-12
take derivitive
f'(x)=-2x-8
zero at x=-4
in x<-4, the derivitive is positive so the function is increasing
in x>-4, the derivitive is negative so the function is decreasing
increasing in (-infinity,-4)
decreasing in (-4,infinity)
first option
The probability you're asked to find is
![\mathbb P(A\cup B)-\mathbb P(A\cap B)](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Ccup%20B%29-%5Cmathbb%20P%28A%5Ccap%20B%29)
where
![A\cup B](https://tex.z-dn.net/?f=A%5Ccup%20B)
is the event that either event occurs (A, B, or both), and
![A\cap B](https://tex.z-dn.net/?f=A%5Ccap%20B)
is the event that both events occur.
Recall that
![\mathbb P(A\cup B)=\mathbb P(A)+\mathbb P(B)-\mathbb P(A\cap B)](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Ccup%20B%29%3D%5Cmathbb%20P%28A%29%2B%5Cmathbb%20P%28B%29-%5Cmathbb%20P%28A%5Ccap%20B%29)
which means
![\mathbb P(A\cup B)-\mathbb P(A\cap B)=\mathbb P(A)+\mathbb P(B)-2\mathbb P(A\cap B)](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Ccup%20B%29-%5Cmathbb%20P%28A%5Ccap%20B%29%3D%5Cmathbb%20P%28A%29%2B%5Cmathbb%20P%28B%29-2%5Cmathbb%20P%28A%5Ccap%20B%29)
You're told that
![\mathbb P(A)=0.5](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%29%3D0.5)
,
![\mathbb P(B)=0.7](https://tex.z-dn.net/?f=%5Cmathbb%20P%28B%29%3D0.7)
, and (if I'm reading the diagram correctly)
![\mathbb P(A\cap B)=0.3](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Ccap%20B%29%3D0.3)
.
So,
![\mathbb P(A\cup B)-\mathbb P(A\cap B)=0.5+0.7-2\times0.3=0.6](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Ccup%20B%29-%5Cmathbb%20P%28A%5Ccap%20B%29%3D0.5%2B0.7-2%5Ctimes0.3%3D0.6)
Another way of seeing this is that the event A consists of the regions "A not B" and "A and B". So the probability that "A not B" occurs is
![\mathbb P(A\setminus B)=\mathbb P(A)-\mathbb P(A\cap B)=0.5-0.3=0.2](https://tex.z-dn.net/?f=%5Cmathbb%20P%28A%5Csetminus%20B%29%3D%5Cmathbb%20P%28A%29-%5Cmathbb%20P%28A%5Ccap%20B%29%3D0.5-0.3%3D0.2)
Similarly, B consists of "B not A" and "A and B", so you have
![\mathbb P(B\setminus A)=\mathbb P(B)-\mathbb P(A\cap B)=0.7-0.3=0.4](https://tex.z-dn.net/?f=%5Cmathbb%20P%28B%5Csetminus%20A%29%3D%5Cmathbb%20P%28B%29-%5Cmathbb%20P%28A%5Ccap%20B%29%3D0.7-0.3%3D0.4)
So the probability that A or B, but not both, occur is
Answer:
L = 324 cm²
S = 359.1 cm²
Step-by-step explanation:
Lateral surface area of a triangular prism is given by,
Lateral surface area = Perimeter of the triangular base × Height
= (9 + 9 + 9)×12
= 27 × 12
= 324 cm²
Surface area area of the triangular prism = Lateral area of the prism + Area of the triangular bases
= 324 + ![\frac{1}{2}(Base)(Height)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%28Base%29%28Height%29)
= 324 + ![\frac{1}{2}(9)(7.8)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%289%29%287.8%29)
= 324 + 35.1
= 359.1 cm²
Answer:
7%
Step-by-step explanation:
Given Data:
mean =$1000
standard deviation s = $370
number of employee n 80
weekly salary at most of $75
the value of z can be determined
![n = [z\times \frac{s}{E}]^2](https://tex.z-dn.net/?f=n%20%3D%20%5Bz%5Ctimes%20%5Cfrac%7Bs%7D%7BE%7D%5D%5E2)
![80 = [z \times \frac{370}{75}]^2](https://tex.z-dn.net/?f=80%20%3D%20%5Bz%20%5Ctimes%20%5Cfrac%7B370%7D%7B75%7D%5D%5E2)
![\sqrt(80) = 4.93z](https://tex.z-dn.net/?f=%5Csqrt%2880%29%20%3D%204.93z)
z = 1.81
From standard table of z
P(z > 1.81) = 0.035
P(condition described) = 2*0.035 = 7%
Z DISTRIBUTION