E) jack and kevin are creating a mosaic by using fragments of broken tiles for art class. they want the mosaic to have 100 sections. if each section requires 31.5 tiles, how many tiles will they need to complete the mosaic? explain your reasoning with a place value chart.

Number of sections in mosaic=100 section

Number of tiles required in each section=31.5 tiles

Total number of tiles required in mosaic

                      =31.5 × 100

                      =3150 tiles

5=Tenth place

1=Unit Place

3=Tens Place

As 31.5 has to be multiplied by 100, there is single digit after decimal, so 0, will be placed at right end of number to get correct number of tiles.  

 Also,

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.