Step-by-step explanation:
Flour needed to make birthday cakes = 2x
Flour needed to make holiday cakes = 1y = y
Maximum amount of Flour allowed = 20 (No more than 20)
Therefore
2x + y must not be more than 20
I need help asap pls
2 answers:
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Answer:
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this case, assume that 104 eligible voters aged 18-24 are randomly selected.
This means that .
Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
This means that
Mean and standard deviation:
Probability that exactly 27 voted
By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.
X = 27.5
has a p-value of 0.8621
X = 26.5
has a p-value of 0.8051
0.8621 - 0.8051 = 0.057
The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.
Answer:
For maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.
Step-by-step explanation:
Let the length of the rectangular exercise run = l ft
and width of the run = w ft
Sinoman has to cover a rectangular exercise run from three sides with the fencing material,
So length of the material = (l + 2w) ft
l + 2w = 100
l = 100 - 2w --------(1)
Area of the rectangular area covered = Length × width
A = lw
A = w(100 - 2w) [(l = 100 - 2w)from equation (1)
For maximum area we find the derivative of area and equate it to zero.
A' = 100 - 4w
For A' = 0
100 - 4w = 0
4w = 100
w = 25 ft
From equation (1)
l = 100 - 2w
l = 100 - 2×(25)
l = 50 ft
Therefore, for maximum area of the rectangular exercise run dimensions will be 50ft by 25ft.
