Math Answers

ABC Company, a manufacturer of automobile tires claims that the average life of the product is 45,600 miles. A random sample of 15 tires was chosen and resulted in a mean life of 43,500 miles with a standard deviation of 3,000 miles. Based on the above results, can you accept the manufacturer’s claim? Use α = 0.05

Tank A initially contains 200 liters of brine containing 225 N of salt. Eight liters of fresh water per minute enter A and the mixture, assumed uniform, passes from A to B, initially containing 200 liters of fresh water, at 8 liters per minute. The resulting mixture, also kept uniform, leaves B at the rate of 8 liters per minute. Find the amount of salt in tank B after one hour.

Application of First Order of Differential Equation

one sample z test A report in LTO stated that the average age of taxis in the Philippines is 9 years. An operations manager of a large taxi company selects a sample of 40 taxis and finds the average age of the taxis is 8.2 years. The o if the population is 2.3 years. At a = 0.05, can it be concluded that the average age of the taxis in his company is less than the national average?

If the matrix R =[-5 2]

[M -4]

is singular, determine the

value of m .

A box contains black marbles and white marbles. A person selects two marbles without replacement. If the probability of selecting a black marbles and a white marbles is 15/56, and the probability of selecting a black marble on the first draw is 3/8, find the probability of selecting the white marble on the second draw, given that the first marble selected was a black marble.

(Show tree diagram).

x=e^t, y=sint, z=x^2+xy

dz/dt = ???

Determine and sketech the set of pairs (x, y) in R×R that satisfy: i)|x|=|y| ii)|x|-|y|=2

Find all x belongs to R that satisfy the following inequalities: i)|x|+|x+1|<2 ii)|x^2-1|<_3

Solve the following triangles:

13. A side and a diagonal of a parallelogram are 12 inches and 19 inches respectively. The angle between the diagonals, opposite the given side, is 124°. Find the length of the other diagonal and the length of the other side.

14. A lighthouse is 10 miles northeast of a dock. A ship leaves the dock at noon, and sails east at a speed of 12 miles an hour. At what time will it be 8 miles from the lighthouse?

15.A vertical pole 35 feet high, standing on sloping ground, is braced by a wire which extends from the top of the pole to a point on the ground 25 feet from the foot of the pole. If the pole. subtends an angle of 30° at the point where the wire reaches the ground, how long is the wire?

16.A tower 125 feet high stands on the side of a hill. At a point 240 feet from the foot of the tower, measured straight down the hill, the tower subtends an angle of 25°. What angle does the side of the hill make with the horizontal?

1 Determine k for which line (k + 2)x + (k^2 -9)y + 3k^2 - 8k + 5 =0 is 1, parallel to y axis 2, parallel to x axis 3, pass through origin 4, pass through (1,1)