Math Answers

1. A certain radioactive element has a half-life of 5 hours. If its initial mass is at

6,470 grams, how many grams are left after 2 days?

2. Carlo’s online investment is worth Php870,000 on its 3rd year and Php650, 000

on its 7th year. What is the worth of his initial investment?

3. The pressure exerted on us by the atmosphere decreases exponentially as you

go up. The pressure at ground level is 1,013 hPa and decreases to 965 hPa at

381 meters. What is the pressure at the summit of Mt. Apo which is at 2,954

meters?

4. A strain of bacteria growing on the palm of your hands is 9 bacteria after 6

minutes. If you start with only one bacterium and follows an exponential growth

model, how many bacteria could be present at the end of 1 hour?

5. A certain breed of rats doubles its population every 2 months. Assuming there

were only 6 rats initially at a certain area, how many months will it take for the

population to grow to 68 rats?

Identify the t-value given the following. Use the T-table provided in this module.

Confidence Level

Tailed Test

Given

T critical Value

90%

Two - Tailed Test

df = 23

95%

One - Tailed Test

df = 12

99%

Two - Tailed Test

n = 25

90%

One - Tailed Test

n = 11

1.An investigator predicts that dog owners in the country spend more time walking their dogs than do dog owners in the city. The investigator gets a sample of 12 country owners and 15 city owners. The mean number of hours per week that city owners spend walking their dogs is 10.0. The standard deviation of hours spent walking the dog by city owners is 4.0. The mean number of hours country owners spent walking their dogs per week was 12.0. The standard deviation of the number of hours spent walking the dog by owners in the country was 5.0. Do dog owners in the country spend more time walking their dogs than do dog owners in the city?

Accomplish the table below:

Dog Owners

Mean

Standard Deviation

Sample Size

Country

City

A researcher wishes to determine the performance level of students with pre-school education and with no preschool education. Fifteen senior high school students with pre-school education and fifteen senior high school students with no pre-school education were randomly selected and the results are tabulated below.

Education

 (mean)

 (standard deviation)

 (sample size)

With pre-school education

89.4

3.25

15

With no pre-school education

85.2

2.85

15

Is it safe to conclude that those with pre-school education have a better performance than those with no pre-school education? Use 99% level of confidence

A TV manufacturer claims that the life span of its regular TV sets is longer than 10 years. Using a random sample of their 25 TV sets, the average life span is found to be 11.9 years with a standard deviation of 1.8 years. Test the hypothesis that the TV sets' life span is longer than 10 years at cx = 0.10

A soda manufacturer is interested in determining whether it's bottling machine tends to overfill. Each bottle is supposed to contain 15 ounces of fluid. A random sample of 30 bottles was taken and found that the mean amount of soda of the sample of bottles is 13.4 ounces with a standard deviation of 2.98 ounces. if the manufacturer decides on a significance level od 0.05 test, should the null hypothesis be rejected?

Instruction: Find the solution set of the following using 3 methods. Show your solutions, then submit your answer to your eLMS dropbox.

1.2x + y = 15

x - y = 9

2. 3x - 2y = 12

2x + 5y = 7

In the context of a choosing a whole, explain when a fifth is not always equal to a fifth.

A car travels between 2 towns 60 miles apart in 2 hours.What is its average speed?

A research conducted on a certain company last year revealed that 25% of the employees prefer drinking milk tea than coffee during break time The company has decided to give free milk tea during break time in a recent study out of 100 randomly sampled employees 28% said that they would rather drink milk tea than coffee. What is the z-value?