Search & Filtering
n= 15 Percentile= 99.5th t(a,df)=
Determine whether if lim f(c) = f(c)
x→c
1. f(x) = x+2; c = -1
2. f(x) = x-2; c = 0
3. (at c = -1 )
f(x) = {x ² - 1 if x < -1}
f(x) = { (x - 1) ² - 4 if x ≥ -1}
4. (at c = 1 )
f(x) = {x³ - 1 if x < 1}
f(x) = { x² + 4 if x ≥ 1}
The average time it takes for a high school students to complete certain examination is 46.2 minutes. The standard deviation is 8 minutes. There will be 50 random samples to be selected. Assume that the variable is normally distributed.
1. What is the population mean in the given problem?
a. 0
b. 8
c. 46.2
d. 50
2. What is the value of n in the given problem?
a. 0
b. 8
c. 46.2
d. 50
3. If 50 random selected high school students take the exam, what is the probability that the mean time it takes the group to complete the test will be less than 43 minutes?
a. 0.23%
b. 2.3%
c. 3%
d. 23%
What is the standard deviation of sampling distribution if standard deviation of population is 35 and sample size is 9?
Activity in Limit Theorems
Compute the following limits.
1. lim (4 • f(x))
x→c
2. lim (g(x) - h (x))
x→c ________
3. lim √12 • f(x)
x→c
4. lim (g(x) + h(x)) / f(x)
x→c
5. lim (f(x) + h(x))
x→c
Activity in Limit Theorems
Directions: Assume the following.
lim f(x) = 3/4;
x→c
lim g(x) = 12;
x→c
lim h(x) = -3;
x→c
3. An ideal shock absorption system would use a critically damped oscillator to absorb shock loads. The location of the absorbing piston (𝑥) is described by 𝑥 = 𝜏𝑒−𝛾𝑡 where:
- 𝜏 is the linear damping coefficient
- 𝛾 is the exponential damping constant
- 𝑡 is the time (𝑠)
- 𝑥 is the displacement of piston (𝑚)
The tasks are to:
a) Draw a graph of displacement against time for 𝜏 = 12 and 𝛾 = 2, between 𝑡 = 0𝑠 and 𝑡 = 10𝑠.
b) Calculate the gradient at 𝑡 = 2𝑠 and 𝑡 = 4𝑠.
QD099_September_2017
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c) Differentiate the function of 𝑥 and calculate the value of 𝑑𝑥 at 𝑡 = 2𝑠 and 𝑡 = 4𝑠. 𝑑𝑡
d) Compare your answers for part b and part c. (M1)
e) Calculate the derivative for the velocity function(𝑑2𝑥).
Determine whether if
lim f(c) = f(c)
x→c
1. f(x) = x+2; c = -1
2. f(x) = x-2; c = 0
3. (at c = -1 )
f(x) = {x ² - 1 if x < -1}
f(x) = { (x - 1) ² - 4 if x ≥ -1}
4. (at c = 1 )
f(x) = {x³ - 1 if x < 1}
f(x) = { x² + 4 if x ≥ 1}
Which of the following is a correct statement?
If the primal problem is in its standard form, dual variables will be non-negative.
Dual simplex method is applicable to an LPP, if initial basic feasible
solution is not optimum.
Dual simplex method always leads to degenerate basic feasible solution.
If the number of primal variables is very small and the number of
constraints is very large, then it is more efficient to solve the dual rather
than the primal problem.
Determine each of the following areas and show these graphically. Use the
probability notation in your final answer.
1.) above z = 1.46
2.) below = -0.58
3.) between z = -78 and z = -1.95
4.) between z = 0.76 and z = 2.88
5.) to the right of z =1.32
6.) to the left of z = 2.78
#340153 on Dec 2023