Mark, chase, and beatrice are running a 100-meter race. which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? if there were four runners and three positions to be won, what would the sample size be?

a.)the sample space is {mbc, bcm, cmb}. if there were four runners, the sample size would be 4.
b.)the sample space is {mbc, mcb, bcm, bmc, cbm, cmb}. if there were four runners, the sample size would be 24.
c.)the sample space is {mbc, bcm, cmb}. if there were four runners, the sample size would be 4.
d.)the sample space is {mbc, mcb, bcm, bmc, cbm, cmb}. if there were four runners, the sample size would be 16.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

b. f(x) = –√x + 3this is the correct answer

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