Answer:
c
Step-by-step explanation:
=1/81
=3
=
=1/81
LoJao(37-3八):log 20 (3rniay)
1 answer:
Hello,
if the question is to solve the equation:
1) log must exist:
a)==>2r²-27>0==>(r-√(27/2))(r+√(27/2))==> outside the roots
r<-√(27/2) or r>√(27/2)
b)==>3r²+12r>0 ==>3r(r+4)>0 ==>outside the roots
r>0 or r<-4
==>r<-4 or r>√(27/2)=3.6742...
If this is realized:
2r-27=3r²+12r
==>r²+12r+27=0
Δ=12²-4*27=36=6²
r=(-12+6)/2=-3 or r=(-12-6)/2=-9
One solution r=-9
Proof
if the question is to solve the equation:
1) log must exist:
a)==>2r²-27>0==>(r-√(27/2))(r+√(27/2))==> outside the roots
r<-√(27/2) or r>√(27/2)
b)==>3r²+12r>0 ==>3r(r+4)>0 ==>outside the roots
r>0 or r<-4
==>r<-4 or r>√(27/2)=3.6742...
If this is realized:
2r-27=3r²+12r
==>r²+12r+27=0
Δ=12²-4*27=36=6²
r=(-12+6)/2=-3 or r=(-12-6)/2=-9
One solution r=-9
Proof
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Answer:
(a)
(b)5,832 Mosquitoes
(c)5 days
Step-by-step explanation:
(a)Given an original amount at t=0. The population of the colony with a growth rate
, where k is a constant is given as:
(b)If and the population after 1 day, N(1)=1800
Then, from our model:
N(1)=1800
Therefore, our model is:
In 3 days time
The population of mosquitoes in 3 days time will be approximately 5832.
(c)If the population N(t)=20,000,we want to determine how many days it takes to attain that value.
From our model
In approximately 5 days, the population of mosquitoes will be 20,000.
The box-and-whisker plot is attached.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.
We first order the data from least to greatest:
67,68,68,69,70,72,73,74,75,75,76,78,79,79,80,83,84,85,85,88
Now we find the median. Since there are 20 data values, the median is between 75 and 76:
(75+76)/2 = 151/2 = 75.5
Now we find the Lower Quartile (LQ). We do this by finding the median of the lower half of data (from the median down). There are 10 values here; the median is between 70 and 72:
(70+72)/2 = 142/2 = 71
Find the Upper Quartile (UQ). Do this by finding the median of the upper half of data (from the median up). There are 10 values here; the median is between 80 and 83:
(80+83)/2 = 163/2 = 81.5
The middle bar of the box is over the median. The left hand side of the box is over LQ, and the right hand side of the box is over UQ. Now we draw a whisker from the box to the highest value, 88, and from the box to the lowest value, 67.