Answer:
• for the first inequality:
• for the second inequality:
substitute for a:
• substitute to get value of a: [ first inequality ]
[ second inequality ]
Given expression: 1/4 (16-12x).
Solution: We can see that 1/4 is in front of paranthesis.
That represents multiplication of 1/4 with (16-12x)
In order to 1/4 with (16-12x), we need to distribute 1/4 over (16-12x).
On distributing 1/4 over (16-12x), we get
1/4 (16-2x) = 1/4 * 16 + 1/4 * (-12x).
On multiplying 1/4*16, we get 16/4 and 1/4 * (-12x) = -12x/4.
16/4 could be simplify to 4 and -12x/4 could be simplify to -3x.
So, final answer would be 4 - 3x.
Therefore, second option is our correct option, that is 4 - 3x.
Very easy!
6 people= 12 servings so 1 person= 2 servings
We have 112 people so we need 112 x 2= 224 servings
So she will make 224 servings with an 8 servings pan, 224/8= 28 pans.
The minimum number of pans she need in order to serve 112 people is 28 pans!
Using binomial distribution where success is the appearing of any of the top 10 most common names, thus probability of success (p) is 9.6% = 0.096 and the probability of failure = 1 - 0.096 = 0.904. Number of trials is 11.
Binomial distribution probability is given by P(x) = nCx (p)^x (q)^(n - x)
Probability that none of the top 10 most common names appears is P(0) = 11C0 (0.096)^0 (0.904)^(11 - 0) = (0.904)^11 = 0.3295
Thus, the probability that at least one of the 10 most common names appear is 1 - 0.3295 = 0.6705
Therefore, I will be supprised that none of the names of the authors were among the 10 most common names given that the probability that at least one of the names appear is 67%.
Answer:
p = 0.68 and p^ = 0.6
Step-by-step explanation:
Jackie received 68% of the votes in an election.
Here p is the decimal equivalent of 68 %.Hence ,
p = 0.68
Now we have taken a sample of 30 people from the total number of voters and we have to find the percentage of votes that Jackie gets in this .
Out of 30 people Jackie got 18 votes. Hence,
p^ = = 0.6
Hence the values are
p = 0.68 and p^ = 0.6
In the random sample we have taken the probability of Jackie has decreased but it will be compensated by another sample where it will be more.