The sum of the angles x and y are 127 degrees. If the measure of x is 34 more than half the measure of y, what is the measure of
1 answer:
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Answer: (-0.4, 6.8)
The graph is attached
Step-by-step explanation:
We can find the axis of symmetry using the formula x = -b/2a
x = - -4/2(-5)
x = 4/-10
x = 0.04
Substitute for x and calculate y
y =
y = 6.8
Answer:
Probability that 300 or more will be recycled is 0.0314.
Step-by-step explanation:
We are given that one environmental group did a study of recycling habits in a California community. It found that 73% of the aluminum cans sold in the area were recycled.
Also, 388 cans are sold today.
The above situation can be represented through Binomial distribution;
where, n = number of trials (samples) taken = 388 cans
r = number of success = 300 or more
p = probability of success which in our question is % of aluminum
cans sold in the area that were recycled, i.e; 73%
<em>LET X = Number of cans that are recycled</em>
SO, X ~ Binom(n = 388, p = 0.73)
<em>Now, here we can't find the probability that 300 or more will be recycled using binomial distribution because the sample size is very large here (n > 30), so we will use Normal approximation to find the respective probability.</em>
So, mean of binomial distribution = E(X) =
= = 283.24
Standard deviation of binomial distribution = S.D.(X) =
=
= 8.74
<em />
<em>Let Y = Number of cans that are recycled for normal approximation;</em>
So, Y ~ Normal()
The z-score probability distribution for normal distribution is given by;
<em> </em> Z = ~ N(0,1)
Now, probability that 300 or more will be recycled is given by = P(Y 300) = P(Y > 299.5) --------------{using continuity correction}
<em> </em> P(Y > 299.5) = P( >
) = P(Z > 1.86) = 1 - P(Z
1.86)
= 1 - 0.9686 = 0.0314
<em>The above probability is calculated using z table by looking value of x = 1.86 in z-table.</em>
<em />
Therefore, the probability that 300 or more will be recycled is 0.0314.