Answer:
The number of test required is: 55
Explanation:
Using combination formula:
n!/x!(n-x)!
= 11!/2!(9)!
= 55
Answer:
21/676
Step-by-step explanation:
The total number of letters of the alphabet will be the total outcome which is 26 alphabets.
If consonant numbers are drawn out, the probability of drawing a consonant will be total consonants/total alphabets
Total consonants in the alphabet is 21.
Probability of drawing consonants = 21/26.
Since all the consonants are replaced before drawing a Z, our total outcome will not change i.e it will still be 26.
Probability of drawing a letter Z will be 1/26.
Therefore, the probability of drawing a consonant,replacing it, and then drawing a Z will be;
21/26×1/26
= 21/676
Xy=10
x+y=29
subtract x from both sides for second equation
y=-x-29
subsitute in second equaiton
x(-x-29)=10
-x^2-29x=10
add x^2+29x to both sides
x^2+29x+10=0
quadratic formula
if you have
ax^2+bx+c=0,
x=
![\frac{-b+/- \sqrt{b^{2}-4ac} }{2a}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-b%2B%2F-%20%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%20%7D%7B2a%7D%20)
so
x^2+29x+10=0
a=1
b=29
c=10
x=
x=
x=
![\frac{-29+/- \sqrt{801} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-29%2B%2F-%20%5Csqrt%7B801%7D%20%7D%7B2%7D%20)
x=
![\frac{-29+/- 3\sqrt{89} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-29%2B%2F-%203%5Csqrt%7B89%7D%20%7D%7B2%7D%20)
x=
![\frac{-29- 3\sqrt{89} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-29-%203%5Csqrt%7B89%7D%20%7D%7B2%7D%20)
or
![\frac{-29+ 3\sqrt{89} }{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-29%2B%203%5Csqrt%7B89%7D%20%7D%7B2%7D%20)
those are the 2 numbers
aprox=-28.65 and -0.349
Every 30 min the tank fills up to 40 gallons