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sertanlavr [38]
3 years ago
6

Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 min

utes or more, which inequality best represents his practice time?
Mathematics
2 answers:
Free_Kalibri [48]3 years ago
8 0

The answer to the equation is: x + y ≥ 45

Arte-miy333 [17]3 years ago
5 0
<span>In the question "Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?" Since the total time he spent on both is 45 minutes or more, it means that the sum of x and y is greater than or equal to 45. Therefore, the required equation is x + y ≥ 45.</span>
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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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