Sam applies a force at 30° to the horizontal to move a football tackling dummy 10 m horizontally. He does 160 J of mechanical work. Determine the magnitude of the force by using vector dot product.

Solve this system of equations. 12x − 18y = 27 4x − 6y = 10

If f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)

Consider a bag that contains 220 coins of which 6 are rare indian pennies. for the given pair of events a and b, complete parts (a) and (b) below. a: when one of the 220 coins is randomly selected, it is one of the 6 indian pennies. b: when another one of the 220 coins is randomly selected (with replacement), it is also one of the 6 indian pennies. a. determine whether events a and b are independent or dependent. b. find p(a and b), the probability that events a and b both occur.