Rectangle ABCD with coordinates A(1,1), B(4,1), C(4,2) and D(1,2) dilates with respect to the origin to give rectangle A’B’C’D’.
2 answers:
Answer: Option C.
Step-by-step explanation:
You need to find the distance AB with the formula for calculate the distance between two points:
Then, substituting the coordinates of the points A(1,1) and B(4,1), you get:
You know that A'B'=6, then the scale factor of dilation can be calculated with:
Substituting values, you get:
This matches with the option C.
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Answer:
The probability that the yellow M&M came from the 1994 bag is 0.07407 or 7.407%
Step-by-step explanation:
Given
Before 1995
(Br) Brown = 30%
(Y) Yellow = 20% =0.2
(R) Red = 20%
(G) Green =10% =0.1
(O) Orange = 10%
(T) Tan = 10%
After 1995
(Br) Brown = 13%
(Y) Yellow = 14% =0.14
(R) Red = 13%
(G) Green = 20% = 0.2
(O) Orange = 16%
(Bl) Blue = 24%
Since there are two bags, let A be the bag from 1994, and B be the bag from 1996
Then let AY imply we drew a yellow M&M from the 1994 bag
AG implies we drew a green M&M from the 1994 bag
BY implies imply we drew a yellow M&M from the 1996 bag
BG implies we drew a green M&M from the 1996 bag
P(AY) =0.2
P (BY) = 0.14
P(AG) =0.1
P(BG) =0.2
Since the draws from the 1994 and 1996 bag are independent,
therefore
The draws can happen in either of the 2 ways in (1) and (2) above
therefore total probability E is given as
E =
For the yellow one to be from 1994, it implies that the event to be chosen is
Since the total probability is given as E=0.054
then
Concluding statement: This is the condition for the Yellow one to come from 1994 and green from 1996 provided that they obey the condition from E
Answer:
It is proved that exixts at (0,0) but not differentiable there.
Step-by-step explanation:
Given function is,
- To show exixtance of
we take,
exists.
And,
exists.
- To show f(x,y) is not differentiable at the origin cheaking continuity at origin be such that,
where m is a variable.
which depends on various values of m, therefore limit does not exists. So f(x,y) is not continuous at (0,0). Hence it is not differentiable at (0,0).