a. If any letters and numbers are allowed, there will be
... 26×26×26×10×10×10 = 260³ = 17,576,000 possible plates
b. If the letters and numbers cannot repeat, there will be
... 26×25×24×10×9×8 = 11,232,000 possible plates with no repeats
c. The proabaility that a randomly chosen plate has no repeats is
... 11,232,000/17,576,000 = 108/169 ≈ 0,63905
_____
When no repeats are allowed, the first letter choice can be any of the 26 letters. The second letter choice must exclude the first letter, so there are only 25 different letters to choose from. Likewise, the third letter choice cannot be either of the first two, so there are only 24 letters to choose from. The reasoning applies to numbers in similar fashion.
Answer:
Solution set = {25}
Step-by-step explanation:
=>
Dividing both sides by -1
=>
Taking square on both sides
=> x = 25
<em><u>Solution set = {25}</u></em>
Answer:
The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .
The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .
Step-by-step explanation:
Parallel means equal slopes. Hence, the slope of the line parallel to y=4/3x+3 is 4/3 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.
y−y1=m(x−x1)
y−6=4/3(x−4)
y−6=4/3x−16/3
y=4/3x−7/3
The equation of the line parallel to y=4/3x−4 that passes through (-4,6) is y=4/3x−10/3 .
Question #2:
Perpendicular means negative reciprocal slopes. Hence, the slope perpendicular to y=4/3x+3 is y=−3/4 . We know our slope and we know a point. We can therefore use point-slope form to determine the equation of the new line.
y−y1=m(x−x1)
y−6=−3/4(x-4)
y−6=−3/4x+6
y=−3/4x+10
The equation of the line perpendicular to y=43x−4 that passes through (-4,6) is y=−3/4x+10 .
A = -11
B= -12
This is because of how calculations work in negatives. Because they are both negative they work similarly to addition
<span>President has 19 options
Vice President has 18 options (19 - 1 president)
Secretary has 17 options (19 - president and vice president)
19*18*17 = 5,814 different combinations are possible for the office positions</span>