Search & Filtering
Identify the critical value of each given problem. Find the rejection region and sketch the curve on a separate sheet of paper.
“According to the radio announcer, the average price of kilogram of pork liempo is more than ₱210.00. However, a sample of 15 prices randomly collected from different markets showed an average of ₱215.00 and standard deviation of ₱9.00. Using 0.05 level of significance, is there sufficient evidence to conclude that the average price of pork liempo is more than ₱210.00?”
A coffee vending machine is designed to dispense 180 ml of coffee but its owner
suspects that it is dispensing more than what is designed for. He took a random
sample of 40 and found out that the mean is 192 ml with a standard deviation of
4 ml. do you think the owner is right about his suspicion? Test at 0.05 level of
significance.
Find (x̅, y̅): R = {(x, y): 0 ≤ y ≤ √x^2 + 1 , 0 ≤ x ≤ 1} about the x-axis.
Find the center of mass of the solid generated by the area bounded by x = 1, x = 3, y = 0
and y = x^2 by revolving about the x-axis.
2. Don, a canteen owner claims that the average meal cost of his usual costumers
is 190 pesos. In order to test his claim, Don took a random sample of 25
costumers and found out that the meal cost is 210 with a standard deviation of
30 pesos. Test the hypothesis at 0.01 level of significance.
Using shell method, find the volume of R, when it is bounded by √x + √y = √a , x =
0 , y = 0 about the line x = a.
Differentiate:
f(x)= (2x⁴+5x+2)
g(x)= 3x²√6x³+5x²+1
h(x)= 4x²/√x+7
find the surface area of the portion of the curve x^2+y^2=4 from x=0 to x=2 when it is revolved about the y-axis
Topic: Implicit Differentiation
1. Find y’ in 𝑥3 + 2𝑦3 = 3𝑥2𝑦.
2. Find the derivative of 𝑦 = √𝑠𝑖𝑛𝑥𝑦
Topic: Optimization
1. A close right circular cylinder is to be constructed to hold a 1 liter oil can shape.
What dimensions will minimize the amount of material, assuming that the
thickness of the material is uniform?
2. Find two positive numbers whose sum is 9 and whose product is a maximum.
