Figure this out as though no digits are present. You can choose 8 of the 26 letters and that's it.
26^8 [you can allow repeating letters] = 2.088 * 10^11
The total number of ways that can be chosen with letters and digits intermixed = 36^8
The probability of getting no numbers is 26^8 / 36^8 or (26/36)^8 = 0.07402
So the probability that there were be at least one digit is
1 - 0.07402 = 0.92598
I think B
J U S T I F I C A T I O N
Semester 1:
let the number of students in the art class be 2a, and the number of the students in the gym class be 7a. (check: the ratio is 2a:7a = 2:7)
so the total number of students is 9a.
semester 2:
the 9a students are go to the art class and gym class at a a ratio of 5: 4,
so 5a students go to the art class, and 4a students go to the gym class.
<span>75 students are in art class in second semester means that 5a=75,
so a=75/5=15.
In the 1st semester the number of students was:
art class: 2a=2*15=30
gym class: 7a=7*15=105</span>
Answer:
(-6,9,-3)
Step-by-step explanation:
-3x -y +z=6
-3x-y+3z =0
x-3z =3
Multiply the second equation by -1
-1 *(-3x-y+3z) =0*-1
3x +y -3z =0
Add this to the first equation
-3x -y +z=6
3x +y -3z =0
----------------------
0 + 0 + -2z = 6
Divide by -2
-2z/-2 = 6/-2
z = 6/-2
z=-3
Take the third equation to find x
x-3z=3
x-3(-3) = 3
x+9=3
Subtract 9 from each side
x+9-9 =3-9
x=-6
Now we need to find y
3x +y -3z =0
3(-6) +y -3(-3) =0
-18 +y +9=0
-9+y =0
Add 9 to each side
-9+9+y = 0+9
y=9
(-6,9,-3)
