Hello,
Let's assume the last digit given by the function last(x).
last(7^0)=1
last(7)=7
last(7^2)=last(49)=9
last(7^3)=last(last(7^2)*7)=last(9*7)=last(63)=3
last(7^4)=1
If the exponent n is 0,4,8,12,.... a multiple of 4 last(7^n)=1
If the exponent n is 1,5,9,13,.... a multiple of 4 + 1 last(7^n)=7
If the exponent n is 2,6,10,14,.... a multiple of 4 + 2 last(7^n)=9
If the exponent n is 3,7,11,15,.... a multiple of 4 + 3 last(7^n)=37
Here exponent is 282=70*4+2
last(7^282)=9
^^ .............................
This given problem asks for the y-intercept of the linear equation.
The first step we need to is to transform the original equation into its slope-intercept form, y = mx + b (where m = slope, and b = y-intercept).
3x = 5y - 6
Subtract 3x on both sides:
3x - 5y - 3x = - 3x - 6
-5y = - 3x - 6
Divide both sides by -5:
-5y/-5 = (- 3x - 6) / -5
y = 3/5x + 6/5 (This is the slope-intercept form).
To solve for the y-intercept of the line, we must set x = 0 (because the y-intercept is the value of y when x = 0). The coordinate of the y-intercept is (0, b).
y = 3/5x + 6/5
y = 3/5(0) + 6/5
y = 0 + 6/5
y = 6/5
Therefore, the y-coordinate of the point where ‘L’ cuts the y-axis is 6/5.
5/6 x 5/6 x 5/6 x 5/6 x 1/6
625/7776
This is the probability of her rolling a 1 on her <span>fifth roll and not before.
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