Math

A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?

$4.12 because; Divide the total cost, $28.84, by the number of hours (7) that the wallpaper steamer was rented.

What is the value of 36x - 8y2 when x = 3 and y = -6?

-180 because; Substitute the given values x and y into the expression, then follow the rules for order of operations to find the value of the expression.

Dominic earns $285 per week plus an 8% commission rate on all his sales. If Dominic sells $4,213 worth of merchandise in one week, how much will his total earnings for the week be?

$622.04 because; This question requires you to calculate Dominic's commission using the amount of sales, then add the result to his weekly salary. Answer Rationale: This question requires a two-step percentage calculation. The first step is to determine the commission on the sales for the week by calculating 8% of $4,213. .08 x 4213 = 337.04, the commission amountThe result is then added to the weekly salary to arrive at the final answer.285 + 337.04 = 622.04

An office uses paper drinking cups in the shape of a cone, with dimensions as shown. To the nearest tenth of a cubic inch, what is the volume of each drinking cup?

7.9 because; Explanation: Question Overview: This question involves determining the volume of a cone by substituting the appropriate values into the formula. The first step is recognizing that the diameter is given, rather than the radius, requiring you to divide the diameter by 2. After substituting values into the formula, you must convert the result from a mixed number to a decimal. Or, you may convert the mixed number measurements to decimals before substituting values into the formula. Answer Rationale: The paper drinking cup is in the shape of a cone. In order to determine the volume of the cone, you must first find the radius. The diameter of the cone is 2 3/4 or 11/4 inches. Because the radius is half of the diameter, the radius is 11/8 inches. You must substitute these and other measurements into the formula for the volume of a cone, which results in V = 1/3 π (11/8)2(4), which is equal to approximately 7.9 cubic inches.

A scientist is studying red maple tree growth in a state park. She measured the trunk diameters of a sample of trees in the same month every other year. The tables show the data for two of the trees. This is the final year in which she will collect data. When her data collection is complete, she will predict future red maple tree growth. The scientist plots the data for tree 2 on a coordinate grid.Which point is correct for year 3?

Point B because; This question requires graphing the point for Year 3 on a coordinate grid from values in the data table for Tree 2. Answer Rationale: To graph the correct point for Tree 2, review the Tree 2 table. In Year 3, the diameter of the trunk is 12.0 inches. On the coordinate grid, the year is plotted on the x-axis and the tree's diameter is plotted on the y-axis. So the coordinates for Year 3 are (3, 12). To plot the point (3, 12), you need to begin at (0, 0), then move 3 units to the right and then 12 units up.

The graph shows the level of ibuprofen, y units, in a patient's bloodstream x hours after the ibuprofen was taken. Select the correct answer to complete the blanks in the sentence:"The level of ibuprofen in the patient's bloodstream increased from _____ hours to _____ hours."

0 hours to 2/3 hours because; This question involves interpreting a data display, specifically to identify the interval in which the graph is increasing. This requires interpreting the data display in order to determine the beginning and ending points of the increase and then selecting the correct values. Answer Rationale: 0 represents the x- coordinate of the starting point of the only line segment that increases from left to right. The x- coordinates on the graph show the number of hours after taking ibuprofen. 2/3 represents the x- coordinate of the ending point of the only line segment that increases from left to right. The x- coordinates on the graph indicate the time.

In year 13, the scientist will put tree wrap around tree 1 to protect it from the winter snow. The height of the tree wrap needs to be 45 inches.The wrap is priced by the square foot. To the nearest square foot, how many square feet of wrap does she need?

22 because; This question requires you to recognize that the tree wrap is in the shape of a cylinder without the top and bottom bases. The area of the tree wrap is represented by the lateral area of the cylinder. The lateral surface of a cylinder is a rectangle, where the base of the rectangle equals the circumference of the cylinder and the height of the rectangle equals the height of the cylinder. Answer Rationale: First, you must subtract the area of the two circular bases from the formula for the surface area of a cylinder. The result is the formula for lateral area of a cylinder, LA = 2πrh or LA = πdh. In the table for Tree 1, the diameter in year 13 is 22.2 inches. Using 3.14 as the value for π, you must substitute these values into the formula, which results in LA = (3.14)(22.2)(45) = 3,136.86. Because tree wrap measurements are priced by the square foot, you must convert the lateral surface area from square inches to square feet. There are 144 square inches in 1 square foot; therefore, dividing the lateral area by 144 gives the lateral area in square feet: 3,136.86/144 = 22 square feet.

+Annie is planning a business meeting for her company. She has a budget of $1,325 for renting a meeting room at a local hotel and providing lunch. She expects 26 people to attend the meeting. The cost of renting the meeting room is $270. Which inequality shows how to find the amount, x, Annie can spend on lunch for each person?

26x+270<_ 1,325 because; This question requires you to determine which inequality describes the situation. First, the total cost of lunch must be accounted for by the term 26x, where 26 is the number of people at the meeting and x represents the cost of lunch per person. This is combined with the amount of $270 to represent the total cost. This sum is then compared to the budget of $1,325; since this is the maximum amount that can be spent, the 'less than or equal to' symbol is used. This question tests translating between different types of mathematical representations. Answer Rationale: The given situation must be modeled (a multi-step linear inquality) as described in the Question Overview.

The scientist creates an equation that models her data for each tree so that she can predict the diameter in the future. Select the linear equation that fits the data for tree 1, where x is the year and y is the trunk diameter, in inches.

3-y=0.3x+18.3 because; This question requires you create the equation of a line using data from the table. Answer Rationale: You may use any two points from the table to find the slope of the line. For instance, you could use the points (1, 18.6) and (3, 19.2). Substitute these values into the slope formula, (y2 - y1) / (x2 - x1), in order to calculate the slope of the line, m, which is 0.3. You must then substitute 0.3 for m and the x- and y- coordinates from one of the points in the table into the slope-intercept form of a linear equation, y = mx + b. This will allow you to solve for the y- intercept, b, which is 18.3. The makes the final equation y = 0.3x + 18.3.

-There are s steps from the pedestal to the head of the Statue of Liberty. The number of steps in the Washington Monument is 27 less than 6 times the number of steps in the Statue of Liberty. Which expression presents the number of steps in the Washington Monument in terms of s?

6s-27 because; Question Overview: This question requires translating text and numbers into an equivalent algebraic representation. Step one is interpreting the meaning of the numbers given in the question and how they relate both to each other and to the appropriate operation-subtraction. Step two is realizing that the correct expression is not represented by the distributive property, but by a straightforward application of the order of operations. Answer Rationale: The term "times" indicates multiplication, and "less than" indicates subtraction. 6s - 27 correctly translates the phrase "27 less than 6 times the number of steps, with s representing the number of steps."