Search & Filtering
A study of the amount of rainfall and the quantity of air pollution removed produced the following data
Daily Rainfall, Particulate Removed,
(0.01 cm) x y (µg/m3)
4.3. 126
4.5. 121
5.9. 116
5.6. 118
6.1. 114
5.2. 118
3.8. 132
2.1. 141
7.5. 108
Find the Pearson r Correlation Coefficient: r = Blank 1
Find the equation of the regression line: y = Blank 2x + Blank 3
Estimate the amount of particulate removed when the daily rainfall is x = 4.8 units: Blank 4 μg/m3
Test the significance of the correlation coefficient calculated in the question above at α = 0.05. Use the steps in conducting hypothesis tests
Two functions f : R → R and g : R → R are defined by f(x) = 5x3 + 1 and g(x) = 2x − 3 for all x ∈ R.
Determine the inverse of (f -1 ◦ g) and (g ◦ f )(2) and ( f ◦ g)(2).
For sets A = {-3, -2,…,3} and B = {0, 1,…,10} B’ = {0, 1, 4, 5, 8, 9} and C = {1, 2,…,10}, let f :
A → B and g : B’ → C be functions defined by f(n) = n2
for all n ∈ A and g(n) = n + 1 for all
n ∈ B’.
a. Show that the composition g o f : A → C is defined
b. For "n\\in A", determine (g o f)(n)
Solve the inequalities. Give your answer in interval notation, and indicate the answer
geometrically on the real-number line.
a. t + 6 ≤ 2 + 3t
b. 3(2 – 3x) > 4(1 – 4x)
In the following problems, perform the operations and simplify as much as possible.
a. (x2 + 2x)/(3x2 – 18x + 24) ÷ (x2 – x – 6)/(x
2 – 4x + 4)
b. (x2 + 6x + 9)/x/(x + 3)
c. 1/(3x – 1) + x/(x2 – 9)
Let the function f : R → R and g : R → R be defined by f(x) 2x + 3 and g(x) = -3x + 5.
a. Show that f is one-to-one and onto.
b. Show that g is one-to-one and onto.
c. Determine the composition function g o f
d. Determine the inverse functions f -1 and g -1 .
e. Determine the inverse function (g o f) -1 of g o f and the composite f -1 o g -1 .
A ship is 20km west of another ship B. If a sails at 10km/hr. and at the same time B sails north 30km/hr. Find the rate of change of distance between them at the end of half hour.
The following data were collected to determine the relationship between pressure and the corresponding scale reading for the purpose of calibration
Pressure, x (lb/sq in.)
Scale Reading, y
10 13
10 18
10 16
10. 15
10. 20
50. 86
50. 90
50. 88
50. 88
50. 92
- Find the Pearson r Correlation Coefficient: r = Blank 1
- Find the equation of the regression line: y = Blank 2x + Blank 3
- The purpose of calibration in this application is to estimate pressure from an observed scale reading. Estimate the pressure for a scale reading of 54: Pressure = Blank 4lb/sq. in
Test the significance of the correlation coefficient calculated in the given question above at α = 0.05. Use the steps in conducting hypothesis tests
Using the number 5, 10, 15, 20, 25, and 30 as the element of the population, construct the sampling distribution of the sample means with a sample size of 2. Find the population and sample mean, population and sample variance, and population and sample standard deviation.
According to NSC statistics,the life expectancy of Filipino women is 70.1 years. Suppose a random sample of 30 women in town B yields a mean of 72.5 years with a population variance of 4.76 years, would you say that the life expextancy of the women in town B is greater than the average?Formulate the null and alternative hypothesis and in symbol.
