Find the least common denominator (LCD) of 7/9 and 5/6

Mathematics

1 answer:

AnnZ [28]2 years ago

8 0

Answer: 18

Step-by-step explanation:

The least common denominator of $\frac{7}{9}$ and $\frac{5}{6}$ is going to be a multiple of 9 and 6. Let us list them out:

9: 9, <u>18</u>, 27, 36, 45, 54, 63, 72, 81, 90

6: 6, 12, <u>18</u>, 24, 30, 36, 42, 28, 54, 60

You can see I bolded and underlined 18. Why? This is the first common multiple of 9 and 6 so it is our least common denominator (LCD).

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Disjoint, Independent, and Complement State whether the two events (A and B) described are disjoint, independent, and/or complem

just olya [345]

Answer:

Independent Events

Step-by-step explanation:

Two events are mutually exclusive or disjoint if they cannot both occur at the same time.

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Australia plays Argentina for the championship in the Rugby World Cup.

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3 years ago

A jar contains 3 red, 2 white, and 1 green marble. Aside from color, the marbles are indistinguishable. Two marbles are drawn at

IRISSAK [1]

Answer:

0.6

Step-by-step explanation:

A permutation is an arrangement of outcomes whereas a combination is a grouping of outcomes.

Order matters in case of permutations but does not matter in combinations.

Given:

Number of red marbles = 3

Number of white marbles = 2

Number of green marbles = 1

To find: probability of picking 4 marbles and getting one of each color

Solution:

Total number of outcomes = $6_C__4$ = $\frac{6!}{4!\,2!}=\frac{6\times 5\times 4!}{4!\times 2}=15$

Number of favourable outcomes = 2 red, 1 white and 1 green marble + 1 red, 2 white and 1 green marble = $3_C_2\,2_C_1\,1_C_1+3_C_1\,2_C_2\,1_C_1$ = $\frac{3!}{2!\,1!}\times \frac{2!}{1!\,1!}\times 1+\frac{3!}{2!\,1!}\times 1\times 1=6+3=9$

So, probability of picking 4 marbles and getting one of each color = Number of favourable outcomes/Total number of outcomes = $\frac{9}{15}=\frac{3}{5}=0.6$