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Evaluate:
a) ∫∫D (e^(y^2) + 1) dA where D is the triangle with vertices (0,0), (-2,4) and (8,4).
b) ∫∫D x^(5)sin(y^4) dA where D is the region in the 2nd quadrant bounded by y =3x^2, y = 12 and the y-axis.
The velocity of a particle moving on the x-axis is given by v(t) = t^(3) − 6t^(2) for the time interval 0 ≤ t ≤ 10.
a) When is the particle farthest to the left?
b) When is the velocity of the particle increasing the fastest?
Evaluate ∫∫∫E 6z^2dV where E is the region below 4x + 2y + 2z = 10 in the first octant.
Find favg for the functions given on the interval and determine the value of c in the given
interval for which f(c) = favg.
a) f(x) = 9 − 2e^(4x+1) on [2,6]
b) 8 − cos (x/4) on [0 4π]
Make a venn diagram Suppose that 53 of the 55 Information Technology students of University of Northern Philippines are taking atleast one of the mathematics subjects Mathematics in the Modern World, Discrete Mathematics, and Data management. Also suppose that: 24 taking Mathematics in the Modern World, 26 taking Discrete Mathematics, and 20 taking Data Management, 5 taking Mathematics in the Modern World and Discrete Mathematics, 7 taking Mathematics in the Modern World and Data Management, 8 taking Discrete Mathematics and Data Management.
There are 7 boys and 5 girls in a youngsters’ club. A committee of 3 boys and 2 girls is to be chosen. How many different possibilities are there?
How many ways can 4 baseball players and 3 basketball players be selected from 12 baseball players and 9 basketball players?
Student , Height , X²
Hazel Kim , 1.47 , 2.16
Mee Ann Mae , 1.58 , 2.50
Grace Ann , 1.67 , 2.79
Jethro , 1.69 , 2.86
Chelsea Mae , 1.51 , 2.28
TOTAL: 9.92 , 12.59
1. Solve for the mean of the population μ.
2. Solve for the mean of the sampling distribution of the sample means Hr.
3. Compare u and ur.
4. Solve for the variance (a) and the standard deviation (a) of the population.
5. Solve the variance (or) and the standard deviation (ar) of the sampling distribution of the sample means Hr.
6. Compare a and or.
A professor only gives two types of exams, "easy" and "difficult". you will
get a difficult exam with a probability of 0.80. The probability that the first question
on the exam will be marked as difficult is 0.90 if the exam is difficult and 0.15 otherwise.
What is the probability that the first question on your exam is marked as difficult. How many
the probability that your exam is difficult to remember the first question on the exam is marked as
difficult?For each binary operation ∗ defined below say whether the following is
a group or not
a) Define ∗ 𝑜𝑛 𝑍 by 𝑎 ∗ 𝑏 = 𝑎 − 𝑏
b) Define ∗ 𝑜𝑛 𝑍 by 𝑎 ∗ 𝑏 = 𝑎𝑏
c) Define ∗ 𝑜𝑛 𝑅+by 𝑎 ∗ 𝑏 = 𝑎𝑏
d) Define ∗ 𝑜𝑛 𝑄 by 𝑎 ∗ 𝑏 = 𝑎𝑏
