Ametallurgist is designing an experiment to determine the effect of flux, base metal, and energy input on the hardness of a weld. she wants to study four different fluxes, two different base metals, and three different amounts of energy input. if each run of the experiment involves a choice of one flux, one base metal, and one amount of energy input, how many different runs are possible?

24

Step-by-step explanation:

Given : A metallurgist wants to study four different fluxes, two different base metals, and three different amounts of energy input.

i.e. 4 different choices for fluxes.

2 different choices for base metals.

3 different choices for amounts of energy input.

If each run of the experiment involves a choice of one flux, one base metal, and one amount of energy input.

Then , the number of runs are possible :-

Hence, there are 24 different runs are possible .

step-by-step explanation:

1. the cylinder is a. 54

2.   a.108 /

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.