An officer at a prison was studying recidivism among the prison inmates. The officer questioned cach inmate to find out how many times the inmate had been convicted prior to the inmate's current conviction. The officer came up with the following table that shows the relative frequencies of X, the number of times previously convicted:

d

step-by-step explanation:

d

step-by-step explanation:

yes

step-by-step explanation:

they have to be opposite and reciprocal of eachother.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west