The required work to pump water is 3,325,140 Joules. Step-by-step explanation: Work done by the pump is calculated by multiplying the force exerted on the pump by the distance the water is moved. Force equates to mass multiplied by gravitational acceleration. Consequently, Force = (water density × tank volume) × gravitational acceleration, leading to F = ρVg. Therefore, Work done = (ρVg) * d. Given the values of ρ = 1000 kg/m³, g = 9.8 m/s², d = 3 m, we compute the work done: Work = 1000 * 113.10 * 9.8 * 3 = 3,325,140 Joules.
P(f | weekend) = p(f & weekend)/p(weekend)
.. = 10%/25%
.. = 0.4 = 2/5
a) P(identified as explosive) equals P(actual explosive & identified as explosive) + P(not explosive & identified as explosive) = (10/(4*10^6))*0.95+(1-10/(4*10^6))*0.005 = 0.005002363. Thus, the probability that it actually contains explosives given that it's identified as containing explosives is (10/(4*10^6))*0.95/0.005002363 = 0.000475. b) Let the probability of correctly identifying a bag without explosives be a. Therefore, a = 0.99999763, approximately 99.999763%. c) No, even if this becomes 1, the true proportion of explosives will always be below half of the total detected.
Answer: To remove fractions prior to solving, each term in the equation must be multiplied by 
.
Step-by-step explanation:
Consider the given expression:
It is essential to simplify this before attempting to solve it.
Since the denominators differ, identifying the Least Common Denominator (LCD) is necessary.
Break down the denominators into their prime components:
Select 
, as it possesses the greatest exponent. Thus:
Ultimately, to remove the fractions before solving, multiply both sides by 4:
Answer:
To inspect a batch consisting of 20 semiconductor chips, a sample of 3 is selected. Out of these, 10 chips fail to meet customer specifications.
a) Total distinct samples possible = 20C3 = 
=1140
b) For exactly 2 good chips and 1 bad chip
Total samples = 10C2 * 10C1 = 45 * 10 =450
c) Combinations of 2 good 1 bad, 1 good 2 bad, and 3 bad chips
Total samples = 10C2 * 10C1 + 10C1 * 10C2 + 10C3
= 
