Answer:
70707mmm = 111nnn
Step-by-step explanation:
Using the basic equation of a line:
y = mx + c;. where m is slope and c is intercept on y axis.
Let mmm = y and nnn = x
(i) 333 = 212121m + c
(ii) 555 = 353535m + c
Making c the subject of the formula in both (i) and (ii)
c = 333 - 212121m = 555 - 353535m
353535m -212121m = 555 - 333
141414m = 222
m = 111/70707
Substitute in (i) above
c = 333 -333 = 0
Hence; y = 111/70707x + c
Finally, mmm = 111/70707 nnn
i.e. 70707mmm = 111nnn
Hope this helps.
Answer:
Part 1) The exponential function is equal to 
Part 2) The population in 2010 was 
Step-by-step explanation:
Part 1) Write an exponential decay function that models this situation
we know that
In this problem we have a exponential function of the form
where
y ----> the fish population of Lake Collins since 2004
x ----> the time in years
a is the initial value
b is the base
we have
substitute
----> exponential function that represent this scenario
Part 2) Find the population in 2010
we have
so
For 
substitute
Answer:
1/30 of an hour
Step-by-step explanation:
Answer:
a) probability that is cracked=1/30 (3.33%)
b) probability that is discoloured = 29/600 (4.83%)
c) probability that is cracked and discoloured = 11/600 (1.83%)
Step-by-step explanation:
assuming that each stone is equally likely to be chosen then defining the events C= the stone is cracked , D= the stone is discoloured , N= the stone is neither cracked or discoloured, then
P(C)= number of favourable outcomes/total number of outcomes = 20 stones/600 stones = 1/30 (3.33%)
P(D)= number of favourable outcomes/total number of outcomes = 29 stones/600 stones = 29/600 (4.83%)
the probability that is discoloured and cracked is P(C∩D) , where
P(C∪D)=P(C) + P(D)-P(C∩D)
and
P(C∪D)= 1- P(N)
thus
1- P(N)=P(C) + P(D)-P(C∩D)
P(C∩D)= P(N)+P(C)+P(D) -1
replacing values
P(C∩D)= P(N)+P(C)+P(D)=562/600 + 20/600 + 29/600 -1= 611/600 -1 = 11/600
thus
P(C∩D)= 11/600 (1.83%)
