<span>along with units digit being < tens digit....let see if we can come up with something.
ones unit must be 0,2,4,6,or 8.
if 0 then tens unit can be 1-9 case1
if 2 then tens unit can be 3-9 case2
if 4 then tens unit can be 5-9 case3
if 6 then tens unit can be 7-9 case4
if 8 then tens unit can be 9 case5
:
108 is covered in case1 because 0<8
:</span><span>case5: 98----9+8=17 to be divisible by 9 hunderds unit has to be 1 and 198
is not divisible by 12
:
case4:96,86,76...96---9+6=16 to be div by 9 100's unit has to be 3 and that is more than 200. 86 ...8+6=14 to be div by 9 100's unit has to be 4....to big
same problem with 76
:
case3:94,84,74,64,54...9+4, 8+4,7+4,6+4,5+4 all present problems with #'s larger than 200
:
case2:92,82,72,62,52,42,32 ...92,82,and 72 all get throw out because #'s larger than 200. 62 is 6+2=8..to be divisble by 9 100's unit must be 1...162..not divisible by 12 take 52,42,32 end up with being over 200
:
case1:90,80,70,60,50,40,30,20,10... 90 larger than 200...80 is 8+0=8 in order to be divisible by 9 100's unit has to be 1. 180.......guess what this number is divisible by 9 and 12 and is less than 200
applying divisibility rules for the rest of the numbers in this case make all the numbers to large >200
:
SO WE HAVE GONE THROUGH ALL THE CASES AND 180 is the only one that qualified
there could be a simpler way but I will have to think on that</span>lets work backwards
Complete Question
A certain university estimated that the proportion of students who prefer 2 day a week classes to 1 day a week classes was somewhere in the interval (0.451, 0.872) . If a 95% confidence interval was used, find the point estimate of the proportion and the margin of error
Answer:
The point estimate is
The margin of error is
Step-by-step explanation:
From the question we are that
The estimate of the proportion of students who prefer 2 day a week classes to 1 day a week classes is (0.451, 0.872)
Generally the point estimate is mathematically represented as
=>
Generally the margin of error is mathematically represented as
=>
First, the factor pairs for 18 are:
1, 18
2, 9
3, 6
Since the middle term is -3, the two factors must be 3 apart. The only pair that is 3 values apart is 3, 6.
Since the middle value is negative, the larger number is negative. This means that the 6 is negative.
z = -6
z = 3
Set each equal to 0;
z = -6
z + 6 = 0
z = 3
z - 3 =0
So your factors are (z+6) and (z-3), or answer B.