Search & Filtering
Use deductive reasoning to show that the following procedure produces a number that is three times
the original number. Procedure: Pick a number. Multiply the number by 6, add 10 to the product, divide
the sum by 2, and subtract 5. Hint: Let n represent the original number.
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.
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.
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.
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.
eric wants to know if cooperative grouping is an effective strategy in improving the mathematics performance of grade 11 students. Twenty students were included in the experimental group while another 20 students were included in the controlled group. The mean achievement score of the students in the experimental group was 82.5 with a standard deviation of 3 while the mean of the students in the control group was 80 with a standards deviation of 6. the two groups come from normally distributed population. the confidence level adopted was 95%.
If P (A|B) = 0.5, P (A) = 0.45 and P (B) = ?
