Answer:
|-2| + |5|
Step-by-step explanation:
Dennis walks from (–5, –2) to (–5, 5) on the map.
Point on the format (x,y). On the x-coordinate, he stayed at the same position, x = -5, so it does not enter the distance calculation.
On the y-coordinate, he went from -2 to 5, so the distance is of:
![d = 5 - (-2) = 5 + 2 = |5| + |2| = |5| + |-2| = 7](https://tex.z-dn.net/?f=d%20%3D%205%20-%20%28-2%29%20%3D%205%20%2B%202%20%3D%20%7C5%7C%20%2B%20%7C2%7C%20%3D%20%7C5%7C%20%2B%20%7C-2%7C%20%3D%207)
So the correct option is |-2| + |5|
1/3+1/3.5=6.5/10.5
1/(6.5/10.5)=10.5/6.5 hours=1.65384 hours to mow the lawn working together
☺☺☺☺
Answer:
The proportion of the population which is infected is =0.07692
Step-by-step explanation:
Let the events be,
A: a person is infected.
B: the test result is positve
According to the question we have,
![P(B|A)=90/100=0.9,](https://tex.z-dn.net/?f=P%28B%7CA%29%3D90%2F100%3D0.9%2C)
![P(B^c|A^c)=95/100=0.95](https://tex.z-dn.net/?f=P%28B%5Ec%7CA%5Ec%29%3D95%2F100%3D0.95)
![P(A|B)=0.6](https://tex.z-dn.net/?f=P%28A%7CB%29%3D0.6)
So
![P(B|A)=0.9 \Rightarrow \frac{P(A\cap B)}{P(A)}=0.9 \Rightarrow P(A\cap B)=0.9P(A)](https://tex.z-dn.net/?f=P%28B%7CA%29%3D0.9%20%5CRightarrow%20%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28A%29%7D%3D0.9%20%5CRightarrow%20P%28A%5Ccap%20B%29%3D0.9P%28A%29)
![P(A|B)=0.6 \Rightarrow \frac{P(A\cap B)}{P(B)}=0.6 \Rightarrow P(A\cap B)=0.6P(B)](https://tex.z-dn.net/?f=P%28A%7CB%29%3D0.6%20%5CRightarrow%20%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D%3D0.6%20%5CRightarrow%20P%28A%5Ccap%20B%29%3D0.6P%28B%29)
Hence,
![0.6P(B)=0.9P(A) \Rightarrow P(B)=1.5P(A)](https://tex.z-dn.net/?f=0.6P%28B%29%3D0.9P%28A%29%20%5CRightarrow%20P%28B%29%3D1.5P%28A%29)
Now
![P(B^c|A^c)=0.95 \Rightarrow \frac{P(A^c\cap B^c)}{P(A^c)}=0.95 \Rightarrow \frac{P(A\cup B)^c}{1-P(A)}=0.95](https://tex.z-dn.net/?f=P%28B%5Ec%7CA%5Ec%29%3D0.95%20%5CRightarrow%20%5Cfrac%7BP%28A%5Ec%5Ccap%20B%5Ec%29%7D%7BP%28A%5Ec%29%7D%3D0.95%20%5CRightarrow%20%5Cfrac%7BP%28A%5Ccup%20B%29%5Ec%7D%7B1-P%28A%29%7D%3D0.95)
![\Rightarrow \frac{1-P(A\cup B)}{1-P(A)}=0.95](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B1-P%28A%5Ccup%20B%29%7D%7B1-P%28A%29%7D%3D0.95)
![\Rightarrow 1-[P(A)+P(B)-P(A\cap B)]=0.95-0.95P(A)](https://tex.z-dn.net/?f=%5CRightarrow%201-%5BP%28A%29%2BP%28B%29-P%28A%5Ccap%20B%29%5D%3D0.95-0.95P%28A%29)
![\Rightarrow 1-P(A)-1.5P(A)+0.9(A)+0.95P(A)=0.95 \Rightarrow 0.65P(A)=0.05](https://tex.z-dn.net/?f=%5CRightarrow%201-P%28A%29-1.5P%28A%29%2B0.9%28A%29%2B0.95P%28A%29%3D0.95%20%5CRightarrow%200.65P%28A%29%3D0.05)
![\Rightarrow P(A)=\frac{1}{13}\Rightarrow P(A)=0.07692](https://tex.z-dn.net/?f=%5CRightarrow%20P%28A%29%3D%5Cfrac%7B1%7D%7B13%7D%5CRightarrow%20P%28A%29%3D0.07692)
The probability that a person is infected is ![\frac{1}{13}=0.07692.](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B13%7D%3D0.07692.)
So the probability that a person is infected is =0.07692.
The proportion of the population which is infected is ![\frac{1}{13}=0.07692](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B13%7D%3D0.07692)
Hence the proportion of the population which is infected is =0.07692
Answer:
9 or 81/9
Step-by-step explanation:
The four consecutive odd integers are x, x+2, x+4, x+6
x+x+2+x+4+x+6=216
4x+12=216
4x=204
x=51
they are 51, 53, 55, 57