Mathematics and Vocabulary Basics

LUTE→MUTE and FATE→GATE show the pattern: first letter is replaced by the next letter in alphabet (L→M, F→G). The rest of the word remains unchanged. For BLUE: B→C gives CLUE, with LUE unchanged.

When adding a positive number to a negative number, you subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value. Here, 14 - 4 = 10, and since -14 has the larger magnitude, the result is -10.

The average of four numbers is 9, so their sum is 4 × 9 = 36. Three numbers are given: 5 + 9 + 12 = 26. The fourth number is 36 - 26 = 10. Option A is correct.

A helix is a smooth curve in three-dimensional space that has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Spirals and screws are common examples.

Lisa needs 6 cans of soda total (one for herself + 5 friends). Each can costs $0.65. Total cost = 6 × $0.65 = $3.90. Option A is correct.

34% of trees are oaks, so 100% - 34% = 66% are NOT oaks. 66% of 500 trees = 0.66 × 500 = 330 trees. Option A is correct. Option B (170) is the number OF oak trees, which is the opposite of what's asked.

40% of CDs are rap, so the remaining 60% are hip hop. 60% of 80 = 0.60 × 80 = 48 hip hop CDs. Option A is correct. Option B (32) is the number of rap CDs, not hip hop.

To convert centimeters to inches, divide by 2.54. 22.86 ÷ 2.54 = 9 inches. Option D is correct. This is a straightforward unit conversion problem.

A chord is any line segment connecting two points on a circle's circumference. A diameter is a special chord passing through the center, while a radius extends from the center to the circumference. An arc is a curved portion of the circle, not a straight line.