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Find the unit vector that is orthogonal to the vectors A=2i+j+k and B=-i+2j+k. Let the position of vectors of the vertices of triangle ∆ADC be OA=-2i+4j+k, OB=4i+j+k and OC=-7i+6k respectively. Use this information to answer
a)find the cosine of the angle between the side AB and AC
b)what is the the projection of the vector AC onto AB?
c)the area of the triangle ∆ABC can be calculated using?
d)find the area of the triangle ABC
A 9N force F1 and a 10N force F2 act in the same directions 2i+j-2k and 4i-3j respectively.
a) Find the resultant of the two forces
b)Find the total work done that the forces make the object move 2m along the vector s= i+j+k
c)find F1•F2
d)find F1 * F2
e)find the unit vector alone which the object will move to achieve maximum work done
f)what is the maximum work done that can be achieve if the tje forces displace the object by 1m
Read and analyze the following situations and supply the values of the following variables (if
there is any). On the third column, write known on the space provided if the situation gives
or can compute the value of the variance, otherwise write unknown. Identify also the formula
to be used to estimate the standard error of the mean by writing the symbols of, when the
population variance is known and sawhen the population variance is unknown,
Situation :
Given the population mean of 12, and a sample standard deviation of 3 in a sample size of 125
Given :
Answer :
Standard error formula :
If 50 of them are taken as samples, what is the probability that their mean height is less than 150cm?
4. A solution of HF contains 12 grams in 500.0mL. (5 marks)
a. Find [H+]. Make sure to show the ionization equation (with water)
. b. Calculate the pH of the above solution.
5. Predict the products of the following neutralization reactions (be sure to balance the equation and include states as well). (2 marks) a. HCl(aq) + Mg(OH)2(s) b. H3PO4(aq) + KOH(s)
What is the probability of getting a perfect square from the numbers 1 to 100?
A.
1/4
B.
1/10
C.
1/25
D.
1/5
E.
None of the above
The probability that two events, A and B, will both occur is represented by the following multiplication rule:
A.
P(A ∩ B) = P(A│B) × P(B)
B.
P (A ∩ B) = P(A) × P(B)
C.
P(A ∩ B) = P(B│A) × P(B)
D.
Both B and C.
E.
None of the above
Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.
Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.
A 23 kg object is pushed up an inclined plane with angle of inclination of 14 degrees. The coefficient of kinetic friction between the object and the incline is 0.30. Determine the acceleration of the object if it is pushed by a 250 N force that is acting parallel to the incline.
The weight (in kg) of grade 11 students in section Z follows a normal distribution with a mean 48 and a standard deviation of . Find the probability that students choosen at random has a weight less than 45
#340153 on Dec 2023