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zlopas [31]
3 years ago
12

Which number is a solution of the inequality 8 - 1/4 b > 27?

Mathematics
1 answer:
vodomira [7]3 years ago
5 0

Answer:

b< -76

Step-by-step explanation:

  • 8 - 1/4 b > 27         ⇒ add -8 to both sides
  • -1/4b > 27 - 8      
  • -1/4 b > 19              ⇒ multiply both sides by -4
  • b < - 4*19               ⇒ change inequality sing to opposite due to multiplication to negative number
  • b < - 76                  ⇒ answer

Answer is any number smaller than -76

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Step-by-step explanation:  Given that a bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles.

Let S be the sample space for the experiment of pulling a marble.

Then, n(S) = 12 + 8 + 5 = 25.

Let, E, F and G represents the events of pulling a red marble, a blue marble and a green marble respectively.

The, n(E) = 12, n(F) = 8  and  n(G) = 5.

Therefore, the probabilities of each of these three events E, F and G will be

P(E)=\dfrac{n(E)}{n(S)}=\dfrac{12}{25}=\dfrac{12}{25}\times100\%=48\%,\\\\\\P(F)=\dfrac{n(F)}{n(S)}=\dfrac{8}{25}=\dfrac{8}{25}\times100\%=32\%,\\\\\\P(G)=\dfrac{n(G)}{n(S)}=\dfrac{5}{25}=\dfrac{5}{25}\times100\%=20\%.

Now, the probability of pulling three green marbles out with replacement is given by

P(G)\times P(G)\times P(G)=\dfrac{5}{25}\times\dfrac{5}{25}\times \dfrac{5}{25}=\dfrac{1}{125}=\dfrac{1}{125}\times100\%=0.8\%.

Thus, the probability of pulling a red marble is 48%, probability of pulling a blue marble is 32%, probability of pulling a green marble is 20%

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the probability of pulling three green marbles out with replacement is 0.8%.

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