Answer:
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Step-by-step explanation:
Answer:

Step-by-step explanation:
Total possibilities when we a roll a die at a time are 6
given we should have four for first time and then three
let us assume we rolled the dice we may get 1,2,3,4,5,6(any of these) the probability to get 4 is
PROBABILITY=
Favourable chances=1
Total chances=6
Probability=
the prabability to get 4 in first roll is
.
let us assume we rolled the dice for second time again we may get 1,2,3,4,5,6(any of these) the probability to get 3 is
Favourable chances=1
total chances=6
probability=
the probability to get 3 in second roll irrespective of first one is 
the probability to get 4 in first time and then 3 is
The probability to occur both events at a time is multiplication of individual probabilities
So,
probablility to get 4 in first roll=
probability to get 3 in second roll=
probability to occur both at a same time is =

=
Answer:
Length of rug in original design is 36 inches .
Width of rug in original design is 60 inches .
The problem says that the new design has length 3x inches longer and x inches wider than the rug in the original plans .
New length of rug would be 3x inches longer than the original design which is 36 inches .
Thus new length of rug is ( 3x + 36 ) inches .
New width of rug is x inches wider than the rug in the original plans which is 60 inches in original plan .
Thus new width of rug is ( x + 60 ) inches .
Area of rectangle is Length * Width
Area of new rug is ( 3x + 36 ) * ( x + 60 )
We distribute the terms using FOIL method .
( 3x + 36 ) *( x + 60 ) = 3x ( x + 60 ) + 36 ( x + 60 )
= 3x² + 3x * 60 + 36 x + 36 * 60
= 3x² + 180 x + 36 x + 2160
Combining like terms , 3x² + 216 x + 2160
Thus the area of the rug with the new dimensions is
( 3x + 36) ( x + 60 ) = 3x² + 216 x + 2160 .