A manufacturer of dustless chalk instituted a quality control program to monitor chalk density. The sample standard deviations of densities for 24 different subgroups, each consisting of n = 8 chalk specimens, were as follows: (0.203, 0.316, 0.096, 0.183, 0.233, 0.213, 0.320,
0.285, 0.144, 0.208, 0.053, 0.144, 0.275, 0.351,
0.159, 0.216, 0.389, 0.185, 0.153, 0.227, 0.275,
0.118, 0.089, 0.055)

Required:
Calculate limits for an S chart, construct the chart, and check for out-of-control points. If there is an out-of-control point, delete it and repeat the process

Una caja de galletas contiene 16 paquetes y cada una de estas tiene 12 galletas y se quieren repartir entre 6 niños ¿de cuantas galletas le toca a cada niño?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

What is the effect on the graph of the function f(x)=x when f(x) is replaced with -f(x)+4