Answer:
Step-by-step explanation:
#3
(i)
- P(A and B) = P(A) * P(B) = 3/8*2/7 = 3/28
(ii)
- P(A or B) = P(A) + P(B) - P(A and B) = 3/8 + 2/7 - 3/28 = 1/56(21 + 16 - 6) = 31/56
(iii)
- P(not A and not B) = P(not A) * P(not B) = (1 - 3/8)*(1 - 2/7) = 5/8*5/7 = 25/56
<u>Another way:</u>
- P(not A and not B) = 1 - P(A or B) = 1 - 31/56 = 25/56
#4
Outcomes with two fair coins: TT, TH, HT, HH
Outcomes with normal dice: 1 to 6
a)
- P(odd number) = 3/6 = 1/2
b)
- P(two heads and an even number) = 1/4*3/6 = 1/8
c)
- P(head and tail) = 1/2
- P(prime) = 3/6 = 1/2 (primes are 2, 3 and 5)
- P(head, tail and prime) = 1/2*1/2 = 1/4
d)
- P(two tails and odd number) = 1/4*3/6 = 1/8
Answer:
1¹/₈ hours
Joelle spent 1¹/₂ hours reading and Rileigh spent 3/4 of that time.
To find out how much time Rileigh spent, multiply the fractions but first convert the improper fraction to a proper fraction:
= 1¹/₂ = 3/2
= 3/2 * 3/4
= 9/8
= 1¹/₈ hours
Step-by-step explanation:
Answer:
Answer=44
Step-by-step explanation:
Rectangle: 6x4=24.
Triangle: 4x4=16, and 16/2=8.
Semicircle: Pi x radius squared, so pi x 2 squared is 16.something, and since it's a semicircle, we divide by 2, so it's 8 again.
Overall: 24+8+8=44 cm squared.
Answer:129
Step-by-step explanation:
630/5 is 126. Add 126, two numbers below it, and two above it. So, 124+125+126+127+128=630. The next page is 129
]Eigenvectors are found by the equation
implying that
. We then can write:
![A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]](https://tex.z-dn.net/?f=%20A-%5Clambda%20I%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204-%5Clambda%20%26%202%20%5C%5C%205%20%26%201-%5Clambda%20%5Cend%7Barray%7D%5Cright%20%5D%20)
And:
Gives us the characteristic polynomial:
So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line
We can see then that 3 is the answer.
