A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in2) and additive concentration is Tensile Strength Concentration of Additive 100 150 200 0.02 0.05 0.06 0.11 0.04 0.01 0.08 0.10 0.06 0.04 0.08 0.17 0.08 0.04 0.14 0.12 a. What are the marginal probability mass functions for X (additive concentration) and Y (tensile strength)

which expression represents the approximate length of bc?

step-by-step explanation:

she will travel a distance in the range of 3 - 11 miles

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough