Answer:
c= 1 d=1
Step-by-step explanation:
Answer:
0.1724 or 17.24%
Step-by-step explanation:
There are
10+13+7 = 30 people
so there are C(30,5) combinations of 30 elements taken 5 at a time ways to select groups of 5 people.
There are C(10,2) combinations of 10 elements taken 2 at a time ways to select the 2 Democrats
There are C(13,2) combinations of 13 elements taken 2 at a time ways to select the 2 Republicans
There are C(7,1) combinations of 7 elements taken 1 at a time ways to select the Independent
By the Fundamental Principle of Counting, there are
45*78*7 = 24,570
ways of making the group of 5 people with 2 Democrats, 2 Republicans and 1 independent, and the probability of forming the group is
or 17.24%
Answer:
a) The 90% confidence interval for the mean noise level at such locations
(112.46 , 163.54)
b) The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
Step-by-step explanation:
<u><em>Step(i)</em></u> :-
Noise levels at 3 airports were measured in decibels yielding the following data
108 146 160
Mean of given data
x : 108 146 160
x-x⁻ : -30 8 22
(x-x⁻ )² : 900 64 484
Variance σ ² = ∑(x-x⁻ )²/ n-1
=
Standard deviation
σ = √724 = 26.90
<u><em>Step(ii):</em></u>-
The 90% confidence interval for the mean noise level at such locations
The critical value that should be used in constructing the confidence interval
Z₀.₁₀ = 1.645
( 138 - 25.54 , 138 + 25.54 )
(112.46 , 163.54)
There are two cases to consider.
A) The removed square is in an odd-numbered column (and row). In this case, the board is divided by that column and row into parts with an even number of columns, which can always be tiled by dominos, and the column the square is in, which has an even number of remaining squares that can also be tiled by dominos.
B) The removed square is in an even-numbered column (and row). In this case, the top row to the left of that column (including that column) can be tiled by dominos, as can the bottom row to the right of that column (including that column). The remaining untiled sections of the board have even numbers of rows, so can be tiled by dominos.
_____
Perhaps the shorter answer is that in an odd-sized board, the corner squares are the ones that there is one of in excess. Cutting out one that is of that color leaves an even number of squares, and equal numbers of each color. Such a board seems like it <em>ought</em> to be able to be tiled by dominos, but the above shows there is actually an algorithm for doing so.