square. The opposite angles are equal, the diagonals intersect at midpoint, opposite sides remain parallel, and the diagonals bisect the angles.
(a) The multiplicative inverse of 1234 (mod 4321) is x so that 1234*x ≡ 1 (mod 4321). We can apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now we will express 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
This reduces to
1 ≡ -1082 * 1234 (mod 4321)
Thus, the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Since both 24140 and 40902 are even, their GCD cannot equal 1, indicating no inverse exists.
<span>The outcome = probability of choosing exactly 2, 3, 4, or 5 passing plays.
The probability of selecting exactly two passing plays is given by:
(8C2)*(9*8)*
(15*14*13*12*11*10)
/(26*28*.....19)
where:
8C2 represents the combinations of choosing two from 8 and
probability that the first passing play is selected = 9/26
probability that the second passing play is chosen = 10/25, and so forth
you can similarly calculate the other three scenarios and sum them to find the total probability.</span>
You can easily calculate the result for each segment and then sum them to determine the perimeter of triangle MNK.
