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Fittoniya [83]
3 years ago
8

Is the difference between a positive mixed number and a negative mixed number always, sometimes, or never positive?

Mathematics
1 answer:
Annette [7]3 years ago
5 0
Ok It depends upon what the order of the terms might be

 

If we consider that the positive mixed number is the first term and the negative mixed number is the second term and we consider "difference" to be subtraction.....then the result is positive

 

For example

(3 + 1/2) -  [ -(1 + 1/2)] =

 

(3 +1/2) + (1 + 1/2) = 5   since subtracting a negative results in a positve

 

But....if we had the reverse order with the same operation, we would have

 

-(1 + 1/2) - (3 + 1/2)   and the result is - 5

 

Hence.......I would go with "sometimes"

 

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Read 2 more answers
An 8-sided fair die is rolled twice and the product of the two numbers obtained when the die is rolled two times is calculated.
marissa [1.9K]

<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)]\\

(a) The possibility diagram of the product of the two numbers appearing on the die in each throw

1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64

(b)

I) A prime number

Number of Products which are prime numbers = 8 

P$(Product is a prime number)=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125

ii) Not a perfect square  

Number of products which are perfect squares =11

 P$(Product is Not a perfect square)=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125

iii) A multiple of 5

Number of Products that are multiples of 5=15

P$(A multiple of 5)=\dfrac{15}{64}\\=0.234375

iv) Less than or equal to 21

Number of products less than or equal to 21=40

P$(Less than or equal to 21)=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625

v) Divisible by 4 or 6

Products Divisible by 4 or 6= 42

P$(Divisible by 4 or 6)=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625

5 0
3 years ago
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