Applied Math Level 7

Tina completed \(\frac{3}{8}\) of the project in \(2 \frac{1}{2}\) weeks. If she continues progressing at the same rate, how many more days will she need to bring the project to completion? Round your answer to the nearest whole number.

Compute the volume of the cylinder shown below in cubic inches. Round your answer to the nearest tenth. There are 16.39 cubic centimeters (cm³) in 1 cubic inch (in³).

Volume of a cylinder ≈ 3.14 × (radius)² × height

GrassLoppers Incorporated has 5 employees dedicated to cutting grass. The fastest employee is able to mow one acre in 30 minutes; the 3 average employees are each able to mow one acre in 45 minutes; and the slowest employee is able to mow one acre in 60 minutes. How many acres can this team of 5 employees mow in one hour?

An online database company offers two plans. Plan A costs $9 per month plus $0.006 per transaction. Plan B costs $39 per month plus $0.002 per transaction. If you anticipate having 12,000 transactions per month, what will be the expected average unit transaction cost (as defined below) if you select the plan that provides the lowest cost for your situation?

\( \text{Average Unit Transaction Cost}\)

\(= \dfrac{\text{Total Cost Per Month}}{\text{Transactions Per Month}}\)

The illustration below shows the dimensions of the existing cone-shaped container. A new cone-shaped container needs to be designed such that its volume is twice that of the existing container’s volume. Its radius will need to be increased to meet the new volume requirement, but the height of the new container will remain the same (12 cm). What will be the radius of the new container? Round to the nearest tenth.

\(V_{\text{cone}} ≈ \dfrac{3.14 × r^2 × h}{3}\)

(Where \(r\) is the radius and \(h\) is the height.)

\(2\frac{1}{4}\) metric tons of ore have just been mined. It is expected that 0.2% of the ore is lithium. How many grams of Lithium are expected to be present in the ore? (1 metric ton = 1000 kg and 1 kg = 1000 g)

For vacation you reserve a room at a beach hotel. The standard rate of the room is $190 per night. On weekends, the rate is increased by $60. The holiday rate is 40% more than the weekend rate. For your stay, 5 nights will be at the standard rate, 2 nights will be at the weekend rate, and 2 nights will be at the holiday rate. What will be the weighted average amount paid per night for the room?

Your company owns a small fleet of vehicles that all-together travel an average of 2,500 miles per week. The fleet has an average fuel economy of 28 miles per gallon. Normally profits have been $500 per week, but recent increases in gas prices have caused profits to decrease by 30%. What fuel surcharge should be added per gallon to restore profits to their normal level?

In a certain midwestern city, the number of hours of daylight during the shortest day of the year is 0.631 that of the longest day of the year. On the shortest day of the year the sun sets at 5:18 pm. The longest day of the year has daylight that lasts 14 hours and 55 minutes. What time does the sun rise on the shortest day of the year?

A paint company creates different paint colors by varying the ratio of Cyan (C), Magenta (M), and Yellow (Y) pigments. One of their signature paint colors uses these pigments in the C:M:Y ratio of 3:4:5 (3 parts Cyan: 4 parts Magenta: 5 parts Yellow). They had a container storing 6 liters of this paint color. A new employee later mistakenly added an additional 2 liters of Magenta pigment to the 6 liters of paint already in the container which changed the color. To correct his mistake, he decides to add Cyan and Yellow pigments to restore the original C:M:Y ratio of 3:4:5. How many liters of Yellow pigment should he add?