Robert is taking a road trip from Jacksonville to Fort Lauderdale. He drives 150 miles at 70 miles per hour and then drives another 150 miles at 50 miles per hour. What is his average speed?
Answer(s): B
Speed is equivalent to distance over time: Speed = (Distance / Time). The total distance of this trip is 150 + 150 = 300 milesBreak down the question into 2 components, one for each speed and distance traveled.First 150 miles:Time = (Distance / Speed) = (150 / 70) = 2.14 hoursSecond 150 miles:Time= (Distance / Speed) = (150 / 50) = 3.0 hours Total time is therefore: 2.14 + 3.0 = 5.14 hours Thus, returning back to the Speed=(distance/time)Speed = (Distance / Time) = (300 miles) / (5.14 hours) = 58.4 miles per hour
Find the value of x in 3x – 3 = 93x − 7:
Answer(s): A
Begin by finding a common base root. Left side is 31(x − 3); right is 32(3x − 7). The 3’s cancel out on both sides, and you have: 1(x − 3) = 2(3x − 7). Simplifying gives:x – 3 = 6x − 14 −3 = 5x − 14 11 = 5x x = 2.2
A wall that is 9 ft × 10 ft costs $88 to paint. How much would it cost to paint a wall that is 21 ft × 30 ft?
Answer(s): D
It will cost $88 to paint an area of 90 square feet (9 ft × 10 ft). The new wall has 630 square feet (21 ft × 30 ft). Thus, the new area is 7x bigger (630 square feet / 90 square feet = 7), and thus, 7x more expensive.7 × $88 = $616
Solve for x:(42)8x = 265
(42)8x = 4428x = 4 28x = 22 8x = 2 x = 1/4
w = ?
Answer(s): C
This is a simple algebraic problem. Multiply both sides by 3 to get ‘w’ alone. This results in 15/8, which is equivalent to 1 7/8.
8 dogs must line up behind each other in single file to get a treat. How many different ways can the dogs line up?
Answer(s): E
This question is asking for the different ways the 8 dogs can be arranged, without repeats. This is represented by the factorial (!). Thus, 8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320. Thus, the number of ways to arrange the 8 equal dogs is 40320.
What is the sum of the interior angles of a regular nonagon?
The sum of interior angles for any regular shaped polygon can be determined with the following equation:(n − 2) × 180°Where n is # of sides. In this case, a nonagon is a 9-sided polygon. Plugging in 9 in the equation gives 1260° for all 9 sides combined. If asked for EACH angle, then you would just divide 1260° by 9.
A man decided to buy new furniture from Futuristic Furniture for $2600. Futuristic Furniture gave the man two choices: pay the entire amount in one payment with cash, or pay $1000 as a down payment and $120 per month for two full years in the financial plan. If the man chooses the financial plan, how much more would he pay?
Multiply $120 by 24 months (a full two years) to get $2880. Add the thousand dollars for the down payment to get $3880. Find the difference between the entire amount all at once ($2600) and the amount paid in the plan ($3880). To find the difference, you subtract. The difference shows that $1280 more is paid with the installment plan.
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