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Use inductive reasoning to predict the most probable next number in the following lists.
a) 5, 10, 15, 20, 25, ?
b) 2, 5, 10, 17, 26, ?
Consider the following procedure: Pick a number. Multiply the number by 9, add 15 to the product,
divide the sum by 3, and subtract 5. Complete the above procedure for several different numbers. Use
inductive reasoning to make a conjecture about the relationship between the size of the resulting number
and the size of the original number.
The standard enthalpy of formation, ΔH˚f of liquid ethanol, C2H5OH(l) @ 25C is -277.63 kJ/mol. Calculate its heat of combustion at constant pressure from the given reaction, C2H5OH(l)+ 3 O2(g) → 2 CO2(g) + 3 H2O(l). ΔH˚f CO2=-393.50 kJ/mol ΔH˚fH2O= -285.84 kJ/mol
A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years with a standard deviation of 1.5 years. Using a random sample of their 16 TV sets, the average life span is found to be 11.5 years. Test the hypothesis that the TV sets' life span is longer than 10 years at a = 0.01.
A chemical company alleged that the average weight of its bag of chemical is 50 kgs. with a standard deviation of 0.9 kg. A sample of 29 bags was taken and revealed a mean weight of 48.1 kgs. Shall we accept the allegation of the chemical company? Use a = 0.01.
Two simple clutch disks of equal mass 6.3 kg are initially separate. They also have equal radii of R=0.55 m. One of the disks is accelerated to 5.7 rad/s in time Δt = 1.8 s. They are then brought in contact and both start to sping together. Calculate the angular velocity of the two disks together.
Activity 2
Directions :Solve the logistics problem. show your solution.
The population of a certain bacteria follows the logistic growth pattern, initially, there are 10 g of bacteria present in the culture. Two hours later, the culture weighs 25 g. The maximum weight of the culture is 100g.
a.Write the corresponding logistic model for the bacterial growth?
b. What is the weight of the culture after 5 hours?
c. When will the culture's weight be 75 g?
Activity 1:
Solve the following problems applying the concepts learned above. Write your answer on a separate sheet of paper. (Show your solution)
1. The rate of change x is proportional to x. When t =0, x0 = 3 and when t =2, x=6. What is the value of x when t =4?
2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately 15% of the original amount decomposes in 100 years. How much amount of the substance has decayed after 600 years? Also, find the half - life t1/2 of this radioactive substance ; that is, find the time required for this substance to decay to one- half of its original amount.
Solid lime (CaO) reacts with chlorine gas (Cl2) to form laundry bleach (CaOCl2). Calculate how many moles of chlorine gas is required to produce 1.000 kg of laundry bleach.
In a public senior high school, a survey conducted last year showed that 25%
of the students’ parents are farmers. This year, a new survey was conducted
randomly on 150 students from the same school. It was found that 63 of them
have parents who are farmers. Test if the claim was higher at α = 0.01 level.
#340153 on Dec 2023