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Prove that the function f(x)= cosx-cos3x is periodc

Sum of prime numbers in the input

Compute for Profit.



Sales: 50,000



Paid Rent: 2,500



Paid utility fees: 4,679.18



Supplies: 10,789.86



Delivery Cost: 589.00



Employee's salary:



A: 450.00 (15 days) (4person)



B: 650.00(15 days) (1 person)



Income: ?

Suppose that the manufacturing company of Exercise 5.36 decides to change its acceptance scheme. Under the new scheme, an inspector takes 1 item at random, inspects it, and then replaces it in the box; a second inspector does likewise. Finally, a third inspector goes through the same procedure. The box is not shipped if any of the three inspectors find a defective. Answer the questions in Exercise 5.36 for this new plan


A city when its operation is normal uses a supply of drinking water

containing 15 mg /L of chloride (Cl-), but during periods of high water demand,

mixes with groundwater containing 65 mg/L Cl-. The two waters mix

completely in a 1400 m3 tank and then sent to the distribution system. the

demand for many days has been ~500 m3/d, and all the water has come from

the main supply. So, the demand increases to 700 m3 /d, and the additional

200 m3/d is extracted from the groundwater supply. How long can

continue with this operating strategy before the water entering the

distribution system contains ≥ 20 mg/L Cl-? (Note: chloride is not reactive).


Briefly explain the evolution of microbiology, discuss the scientist contribution, the spontaneous generation

What type of reaction is formed when a phenol reacts with aluminum oxide under basic condition (pH8).what type of bonding is formed when phenol is begin adsorbed onto Al2O3


Force between two point charges: Two point charges,


and , are separated by a distance


(Refer to the figure below). Find the magnitude


and direction of the electric force (a) that exerts on and (b)


that exerts on .

The shaft of a steam turbine produces 600 Nm torque at 50rev/s. Calculate the work transfer rate from the steam


The weight of teenagers in Barangay Payapa approaches a normal distribution with a mean of 52.9 kg and a standard deviation of 7.2 kg. If a teenager is a chosen at random from Barangay Payapa, what is the probability that his/her weight is above 48.5 kg?


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