For a certain automobile, M(x)=−.015x^2+1.42x−7.8, 30≤x≤60, represents the miles per gallon obtained at a speed of x miles per hour. (a) Find the absolute maximum miles per gallon and the speed at which it occurs. (b) Find the absolute minimum miles per gallon and the speed at which it occurs.

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Step-by-step explanation:

A graph can be helpful. It can show the locations of the maximum and minimum.

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The maximum is found at the vertex of the parabola, located where ...

  x = -b/(2a)

  x = -1.42/(2(-0.015)) = 47 1/3

The value M(47 1/3) is ...

  M(47 1/3) = (-0.015(47 1/3) +1.42)(47 1/3) -7.8 = 0.71(47 1/3) -7.8 = 25 121/150

The maximum gas mileage is 25 121/150 ≈ 25.8067 mpg at 47 1/3 mph.

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The minimum will be at one end or the other of the interval. Here, the maximum is farther from the lower end of the domain, so we expect to find the minimum there:

  M(30) = (-0.015(30) +1.42)(30) -7.8 = 0.97(30) -7.8 = 21.3

The absolute minimum gas mileage is 21.3 mpg at 30 mph.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

its kind of blurry. can you put a clearer pic?

step-by-step explanation: