Answer:
The 80% confidence interval for the the population mean nitrate concentration is (0.144, 0.186).
Critical value t=1.318
Step-by-step explanation:
We have to calculate a 80% 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=0.165.
The sample size is N=25.
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:

The t-value for a 80% confidence interval and 24 degrees of freedom is t=1.318.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:

The 80% confidence interval for the population mean nitrate concentration is (0.144, 0.186).
Answer:
slope = 7/5
y-int = -3
Step-by-step explanation:
this equation is in slope-intercept form. in thsi form, the slope will always be the coefficient of x, and the y-intercept will always be the last constant, or the "b" term (dont forget to include the negative!)
Example:

This suggests two solutions,

and

.
However, upon plugging these solutions back into the equation, you get

which checks out, but

does not because

is defined only for

(assuming you're looking for real solutions only). So, we call

an extraneous solution, and the complete solution set (over the real numbers) is

.
Answer: x = 10.6666666 or 10 2/3
Step-by-step explanation:
6x + 8 = 72
- 8 -8
6x = 64
6x/6 = 64/6
x = 10.6666666 aka 10 2/3