Answer:
Option A is correct.
Solution for the given equation is,
Step-by-step explanation:
Given that :
Let
then our equation become;
.....[1]
A quadratic equation is of the form:
.....[2] where a, b and c are coefficient and the solution is given by;
Comparing equation [1] and [2] we get;
a = 2 b = -1 and c =-1
then;
Simplify:
or
or
and
Simplify:
y = 1 and
Substitute y = cos x we have;
⇒
and
⇒
The solution set:
Therefore, the solution for the given equation is,
Answer:
The 99% confidence interval for the mean germination time is (12.3, 19.3).
Step-by-step explanation:
<em>The question is incomplete:</em>
<em>Recorded here are the germination times (in days) for ten randomly chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.</em>
<em />
We start calculating the sample mean M and standard deviation s:
We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=15.8.
The sample size is N=10.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
The degrees of freedom for this sample size are:
df=n-1=10-1=9
The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the mean germination time is (12.3, 19.3).