Which of the following options correctly orders the numbers below from least to greatest? 235.971, 145.884, -271.906, -193.823

A. -271.906, -193.823, 145.884, 235.971

B. -271.971, 235.971, -193.823, 145.884

C. 145.884, -193.823, 235.971, -271.906

D. -193.823, -271.906, 145.884, 235.971

Answer Explanation:

From the given options, we can arrange the numbers from the smallest to the largest as:

-271.906, -193.823, 145.884, 235.971

From the above, it can be noted that -271 is less than -193 while 235 is more than 145.

Therefore, the Correct Answer is A.

Q #1: A girl and a dog are playing tug of war with a piece of rope. The girl pulls on the rope with a force of 165 newtons (N) towards the east, and the dog pulls with a force of 190 N towards the west. What is the net force on the rope?

A. 25 N towards the west

B. 190 N towards the west

C. 165 N towards the east

D. 35 N towards the east

Answer Explanation

To find the net force, we choose east direction as positive and west as negative. From this, we can present the tag of war in the diagram below.

So, the force on the dog is -190 N and that of the girl is 165 N.

The net force is the sum of the two forces

The resulting force is negative, meaning it is in the west direction. Thus, the net force is 25 N to the west.
Q #2: The hypotenuse (side C) of a triangle is 13 inches long. Which of the following pairs of measurements could be the correct for the lengths of the other two sides of the triangle? (Note: A2 + B2= C2)

A. 5 inches, 12 inches

B. 2.5 inches, 6 inches

C. 2.5 inches, 4 inches

D. 5 inches, 8 inches

Answer Explanation

In this problem, we take the triangle as a right-angled triangle and label it as follows:

From the Pythagoras theorem A2 + B2= C2, we can look for a combination of A and B that when the squares of A and B are summed give a square of 13. Mathematically,

But C=13 inches

If we take A=5 inches and B=12 inches, then

Next, we take A=2.5 inches, B=6 inches

Next, we take A=2.5 inches, B=4 inches

6.25+16=169

22.25≠169

Taking A=5 inches and B=8 inches

From the above computation, the combination of A=5 inches and B=12 inches give a triangle with a hypothenuse of 13 inches.
Q #3: An employee discovers that 0.0025 of all products produced at a factory contain defects. Which of the following percentage does this represent?

A. 0.25%

B. 25%

C. 2.5%

D. 0.025%

Answer Explanation

all products represent 100%. Then, the portion of defect products is:

0.0025 of 100%

‘of’ means multiply

0.0025 *100%=0.25%