The Hour Hand Of A Watch Rotates 30 Degrees Every Hour. How Many Complete Rotations Does The Hour Hand Make In 6 Days?

Jake’s final grade in math class is determined by the average he gets on six tests in the class. So far, Jake has earned a 97, 89, 85, 90, and 99 on the first five tests. What grade must Jake earn on the sixth test in order to get a 93 average in the class?

98

The average is found by adding the total of all scores and dividing it by the number of scores. Since we know the average Jake wants (93), and we have all the scores from Jake’s tests except one, we can set up an equation, with A representing Jake’s score on the 6th test.
(97 + 89 + 85 + 90 + 99 + A) ÷ 6 = 93
97 + 89 + 85 + 90 + 99 + A = 93 × 6
460 + A = 558
A = 558 - 460 = 98

If a gas tank can hold 30 gallons, how many gallons does it contain when it is three-fifths full?

18

$30gallons \times \frac{\mathrm{3} }{\mathrm{5} } = 18$

Will is filling up his pool for the summer, and water from the hose flows into the pool at 6 gallons per minute. The pool holds 17,280 gallons. How long, in hours, does it take to fill the pool?

48 hours

The water is flowing into the pool at a rate of 6 gallons per minute. Do the math to see how long it takes to get to 17,280 gallons: 17,280 gallons ÷ 6 gallons/minute = 2,880 minutes. To convert to hours, divide by 60 minutes: 2,880 minutes ÷ 60 minutes/hour = 48 hours.

Sofía is driving to Texas. She travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. Over the 7 hour time period what was Sofía’s average speed?

65 km/h

To find the average over the entire trip, use:
Average Speed = Total Distance ÷ Total Time.
Begin by calculating the total distance traveled:
Total Distance = 2(70) + 5(63) = 140 + 315 = 455 km
While the total time 7 hours.
Substitute these values into the average speed formula to solve:
Average Speed = 455 ÷ 7 = 65 km/h.

A plane left San Francisco at 6:15 pm PST and arrived in Philadelphia at 2:45 am EST. How long was the flight?

$5\frac{\mathrm{1} }{\mathrm{2} }$ hours

PST stands for Pacific Standard Time. EST is known as Eastern Standard Time. EST is 3 hours ahead of PST.
First, convert 6:15 PST to 9:15 EST. The flight then took from 9:15 pm EST to 2:45 am EST. That means that the flight took $5\frac{\mathrm{1} }{\mathrm{2} }$ hours.

Cooks are needed to prepare for a large party. Each cook can bake either 5 large cakes or 14 small cakes per hour. The kitchen is available for 3 hours and 29 large cakes and 260 small cakes need to be baked.
How many cooks are required to bake the required number of cakes during the time the kitchen is available?

9

If a single cook can bake 5 large cakes per hour and the kitchen is available for 3 hours, a single cook can bake 5 x 3 = 15 large cakes during that time. 29 large cakes are needed for the party so 29/15 = 1 and 14/15 cooks are needed to bake the required number of large cakes.
If a single cook can bake 14 small cakes per hour and the kitchen is available for 3 hours, a single cook can bake 14 x 3 = 42 small cakes during that time. 260 small cakes are needed for the party so 260/42 = 6 and 4/21 cooks are needed to bake the required number of small cakes.
Because you can't employ a fractional cook, round the number of cooks needed for each type of cake up to the next whole number resulting in 2 + 7 = 9 cooks.

If $|a| = 7$, which of the following best describes a?

a = 7 or a = -7

The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: |−7|=7. In the case of a variable absolute value (|a|=7) the value of a can be either positive or negative (a = -7 or a = 7).

The supervisor of a small company is designing a new open office layout and thinks that employees will need 4 chairs for every 2 desks. How many office chairs will be needed for an office building with 40 desks?

80 chairs

2 desks require 4 chairs then each desk need 2 chairs. Therefore number of chairs needed for 40 desks: 2*40=80 (chairs).

Simplify: 7x × (8-3) ÷ 5

7x

Simplify by using the order of operations. It’s easy to do if you remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
$7x(8 - 3) \div 5 = 56x - 21x \div 5$
$= 35x \div 5 = 7x$

Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire. Robert has taken 12 more photos than Claire. How many photos has Claire taken?

6

Call the number of pictures Claire taken is x. Lisa has taken 3 times as many photos as Claire then Lisa took is 3x. Robert has taken 12 more photos than Claire then it is x+12. Lisa and Robert have taken the same number of photos: 3x = x+12. Solve the equation we have x=6.

A book regularly sells for $28. If the book is on sale for "20% off", how much is the sales price of the book?

$22.40

20% of $28 = 28x0.2=$5.60. The sales price is then $28-$5.6 = $22.40

Aisha wants to paint the walls of a room. She knows that each can of paint contains one gallon. A half gallon will completely cover a 55 square feet of wall. Each of the four walls of the room is 10 feet high. Two of the walls are 10 feet wide and two of the walls are 15 feet wide. How many 1-gallon buckets of paint does Aisha need to buy in order to fully paint the room?

5

The total number of buckets necessary will be the total area of the walls divided by the total area covered by each bucket. First, calculate the area of the walls Aisha wants to paint. Two of the walls are 10 × 10 and two of the walls are 10 × 15:
2 (10 × 10) = 200 sq. ft.
2 (10 × 15) = 300 sq. ft.
So the total square footage of the walls is 500. If a half gallon of paint will cover 55 square feet, then each gallon will cover 2 × 55 = 110 square feet. Four gallons can only cover 440 square feet. Five gallons will cover 550 square feet, which will be enough for the entire area of the walls.

A scale on a map says that 1 inch represents 60 miles. If the distance between two points on the map is $2 \frac{\mathrm{1} }{\mathrm{2} }$ inches, how many miles are between the two points?

150

$2 \frac{\mathrm{1} }{\mathrm{2} } \times 60 = 150$

With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?

10,000

The decimal must be moved four places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 10,000.

The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days?