The distance that a spring will stretch varies directly as the force applied to the spring. A force of 6060 pounds is needed to stretch a spring 66 inches. What force is required to stretch the spring 1414 inches?

Forced need to stretch 1414 inches = 129830.91 pounds

Step-by-step explanation:

Force ∝ Distance

F = KD where K is constant of proportionality

K = F/D = 6060/66 = 91.818182

Hence Force needed to stretch 1414 inches =

F = 6060/66 x 1414 = 129830.91 pounds

a) N(A∩B) = 0.9

b) N(A∩B) = 4.9

c) N(A or B) = 4.2

Step-by-step explanation:

Given that A and B each randomly, and independently, choose 3 of 10 objects;

P(A) = P(B) = 3/10 = 0.3

P(A') = P(B') = 1 - 0.3 = 0.7

a) chosen by both;

Probability of being chosen by both;

P(A∩B) = 0.3 × 0.3 = 0.09

Expected Number of objects being chosen by both;

N(A∩B) = P(A∩B) × N(total) = 0.09×10

N(A∩B) = 0.9

b) not chosen by either A or B;

Probability of not being chosen by either A or B;

P(A'∩B') = 0.7 × 0.7 = 0.49

Expected Number of objects being chosen by both;

N(A'∩B') = P(A'∩B') × N(total) = 0.49×10

N(A∩B) = 4.9

c) chosen by exactly one of A and B.

Probability of being chosen by exactly one of A and B

P(A∩B') + P(A'∩B) = 0.3×0.7 + 0.7 × 0.3 = 0.42

Expected Number of objects being chosen by both;

N(A or B) = 0.42 × 10

N(A or B) = 4.2