<u>Question Completion</u>
(b) Use the possibility diagram to calculate the probability that the product of the two numbers is
I) A prime number
ii) Not a perfect square
iii) A multiple of 5
iv) Less than or equal to 21
v) Divisible by 4 or 6
Answer:
I) 0.125 (ii)0.828125 (iii)0.234375 (iv) 0.625 (v)0.65625
Step-by-step explanation:
The sample space for an 8-sided fair die rolled twice is:
![[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]\\](https://tex.z-dn.net/?f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
(a) The possibility diagram of the product of the two numbers appearing on the die in each throw
(b)
I) A prime number
Number of Products which are prime numbers = 8
ii) Not a perfect square
Number of products which are perfect squares =11
iii) A multiple of 5
Number of Products that are multiples of 5=15
iv) Less than or equal to 21
Number of products less than or equal to 21=40
v) Divisible by 4 or 6
Products Divisible by 4 or 6= 42
Answer:
The answer to your question is:
a) f(a) -2 = a² - 3
b) f(a - 2) = a² - 4a + 3
c) f(b + d) = b² + 2bd + d² - 1
Step-by-step explanation:
a. f(a) - 2 = (a)² - 1 - 2
f(a) -2 = a² - 3
b. f(a - 2) = (a - 2)² - 1
f(a - 2) = a² - 4a + 4 - 1
f(a - 2) = a² - 4a + 3
c. f(b + d) = (b + d)² - 1
f(b + d) = b² + 2bd + d² - 1
Answer: If the dimension of V is n, then V has n elements.
Now, dim(U) + dim(W) = n, this means that the addition of the dimensions of U and W also has n elements.
and because U and W are subspaces of V, you know that every element on U and W is also an element of V.
If U ∩ W = ∅, means that there are no elements in common between U and W.
Because there are no elements in common, then Dim(U) + Dim(W) = dim(U ∪ W) = n
So U ∪ W has the same number of elements as V, and every element of W and U is also an element of V
this means that U ∪ W = V.
Answer:
96
Step-by-step explanation:
Rectangle area:
(8)(10)=80
Triangle area:
(1/2)(4)(8)=16
Total area:
16+80=96
The answer is A‼️the first one
