Find b and c so that y=-8x^2+bx+c has vertex (−6,6).
1 answer:
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Answer:
a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 48 - 1 = 47
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0117
The margin of error is:
M = T*s = 2.0117*2.3 = 4.6
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day
The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day
a) Compute the 95% confidence interval for the mean.
The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) Explain your confidence interval from part (a) in context.
The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
Answer:
There are 67626 ways of distributing the chairs.
Step-by-step explanation:
This is a combinatorial problem of balls and sticks. In order to represent a way of distributing n identical chairs to k classrooms we can align n balls and k-1 sticks. The first classroom will receive as many chairs as the amount of balls before the first stick. The second one will receive as many chairs as the amount of balls between the first and the second stick, the third classroom will receive the amount between the second and third stick and so on (if 2 sticks are one next to the other, then the respective classroom receives 0 chairs).
The total amount of ways to distribute n chairs to k classrooms as a result, is the total amount of ways to put k-1 sticks and n balls in a line. This can be represented by picking k-1 places for the sticks from n+k-1 places available; thus the cardinality will be the combinatorial number of n+k-1 with k-1, .
For the 2 largest classrooms we distribute n = 50 chairs. Here k = 2, thus the total amount of ways to distribute them is .
For the 3 remaining classrooms (k=3) we need to distribute the remaining 50 chairs, here we have ways of making the distribution.
As a result, the total amount of possibilities for the chairs to be distributed is 51*1326 = 67626.