Alimnologist wishes to estimate the mean phosphate content per unit volume of lake water. it is knownfrom studies in previous years that the standard deviation has a fairly stable value ofσ= 4. how manyindependent water samples must the limnologist analyze to be 90% certain that the error of estimation [halfwidth of 90% confidence interval] does not exceed 0.8 milligrams?

68

Step-by-step explanation:

As per given , we have

Population standard deviation :

Critical value for  90% confidence interval =

Margin of error : E= 0.8 milligrams

The formula to find the sample size is given by :-

i.e.

Hence, the limnologist must analyze 68 samples.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)