The electric field strength at any point from a charged particle is given by E = kq/r^2 and we can use this to calculate the field strength of the two fields individually at the midpoint.
The field strength at midway (r = 0.171/2 = 0.0885 m) for particle 1 is E = (8.99x10^9)(-1* 10^-7)/(0.0885)^2 = -7.041 N/C and the field strength at midway for particle 2 is E = (8.99x10^9)(5.98* 10^-7)/(0.0935)^2 = <span>-7.041 N/C
</span>
Note the sign of the field for particle 1 is negative so this is attractive for a test charge whereas for particle 2 it is positive therefore their equal magnitudes will add to give the magnitude of the net field, 2*<span>7.041 N/C </span>= 14.082 N/C
Answer:
a) 0.2416
b) 0.4172
c) 0.0253
Step-by-step explanation:
Since the result of the test should be independent of the time , then the that the test number of times that test proves correct is independent of the days the river is correct .
denoting event a A=the test proves correct and B=the river is polluted
a) the test indicates pollution when
- the river is polluted and the test is correct
- the river is not polluted and the test fails
then
P(test indicates pollution)= P(A)*P(B)+ (1-P(A))*(1-P(B)) = 0.12*0.84+0.88*0.16 = 0.2416
b) according to Bayes
P(A∩B)= P(A/B)*P(B) → P(A/B)=P(A∩B)/P(B)
then
P(pollution exists/test indicates pollution)=P(A∩B)/P(B) = 0.84*0.12 / 0.2416 = 0.4172
c) since
P(test indicates no pollution)= P(A)*(1-P(B))+ (1-P(A))*P(B) = 0.84*0.88+ 0.16*0.12 = 0.7584
the rate of false positives is
P(river is polluted/test indicates no pollution) = 0.12*0.16 / 0.7584 = 0.0253
Answer:
<h2>22 hours and 10 hours </h2>
Step-by-step explanation:
let the jobs be x and y, so that
x+y=32--------1
9x+7y=248----2
x=32-y
substitute x=32-y for x in equation 2 we have
9(32-y)+7y=248
open bracket we have
288-9y+7y=248
-2y=248-288
-2y=-40
2y=40
divide both sides by 2 we have
y=40/2
y= 10 hours
subtitute y=10 for y in equation 1 to find x
x+10=32--------1
x=32-10
x=22
x=22 hours
Answer:
D) (x, y) → (1/3x , 1/3 y)
Step-by-step explanation:
A dilation is a change of size, if the dilation factor is greater than 1, then the figure is enlarged. If the dilation factor is smaller than 1, the figure is shrinked. In both cases, the coordinates are MULTIPLIED by the dilation factor.
Among the 4 choices, only 2 are dilations. One is with a dilation factor of 3 (A), which means the shape was enlarged. And the other is with dilation factor of 1/3, meaning the shape was shrinked.
Since we went from MNOP (LARGE one) to M'N'O'P' (small one), the dilation factor was < 1... so 1/3 is the answer.
Answers B and C show a translation/movement of the shape, not a dilation.
Answer:
4
Step-by-step explanation:
5
