Math Answers

A supermarket owner believes that the mean income of its customers is P50,000 per month.One-hundred customers are randomly selected and asked of their monthly income.The sample mean is P48,500 per month and the standard deviation is P3,200.Is there sufficient evidence to indicate that the mean income of the customers of the supermarket is P50,000 per month? Use a=0.05

Subtract the given numbers using the indicated complements. Also show your answers in non-complement form, using (+) and (-) to indicate the sign of the number.

a. 848₁₀ – 692₁₀ in 10’s complement

b. 618₁₆ – 8E3₁₆ in 16’s complement

c. 10001100₂ – 11100011₂ in 2’s complement

d. 11000101₂ – 10001110₂ in 1’s complement

e. 4020₈ – 2021₈ in 8’s complement 

Work out the following and give answers in the indicated bases/codes. (Show your ALL working):

a. 1660₈ – 530₁₆ in base 8

b. AB.75₁₆ – 830.5₁₀ in base 2

c. 4028₁₀ + 475.08₁₆ in base 16

d. 1024₁₀ – 11010111₂ in base 2 

Subtract the following numbers in the indicated bases (do not make any conversion to a different base):

a. 4607₈ - 1705₈

b. F32₁₆ - A65₁₆ 

c. 110010₂ - 010101₂

d. 1234₅ - 432₅ 

1. Add the following numbers in the indicated bases (do not make any conversion to a different base):

a. 4607.54₈ + 1705.63₈

b. A65₁₆ + F32₁₆

c. 110010₂ + 010101₂

d. 432₅ + 1234₅

Find the centroid of the region.

The triangle with vertices (0, 0), (2, 0), and (0, 1).

The average public high school has 468 students with a standard deviation of 87.

a. If a public school is selected what is the probability that the number of student enrolled is greater than 400?

b. If a random sample of 38:public elementary schools is selected what is the probability that the number of students enrolled is between 445 and 485?

A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.

(a). assuming that the tank is half-filled with water.

Assume that 10 ft-lb of work is required to stretch a spring 1 ft beyond its natural length. What is the spring constant?

A spring exerts a force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m beyond its natural length?