The total volume of the cylindrical can is found by multiplying the area of the base of the can, 75 cm², by the height of the can, 10 cm, which yields 750 cm³. If the syrup needed to fill the can has a volume of 110 cm³, then the remaining volume for the pieces of fruit is 750 – 110 = 640 cm³.

Choice A is incorrect because if the fruit had a volume of 7.5 cm³, there would be 750 – 7.5 = 742.5 cm³ of syrup needed to fill the can to the top. Choice B is incorrect because if the fruit had a volume of 185 cm³,there would be 750 – 185 = 565 cm³ of syrup needed to fill the can to the top. Choice D is incorrect because it is the total volume of the can,not just of the pieces of fruit.

The median of a set of numbers is the middle value of the set values when ordered from least to greatest. If the percents in the table are ordered from least to greatest, the middle value is 27.9%. The difference between 27.9% and 26.95% is 0.95%.

Choice A is incorrect and may be the result of calculation errors or not finding the median of the data in the table correctly. Choice C is incorrect and may be the result of finding the mean instead of the median. Choice D is incorrect and may be the result of using the middle value of the unordered list.

The predicted increase in total fat, in grams, for every increase of 1 gram in total protein is represented by the slope of the line of best fit. Any two points on the line can be used to calculate the slope of the line as the change in total fat over the change in total protein. For instance, it can be estimated that the points (20, 34) and (30, 48) are on the line of best fit, and the slope of the line that passes through them is \(\frac{48 − 34}{30 − 20}=\frac{14}{10}\)​, or 1.4. Of the choices given, 1.5 is the closest to the slope of the line of best fit.

Choices A, B, and D are incorrect and may be the result of incorrectly finding ordered pairs that lie on the line of best fit or of incorrectly calculating the slope.

If Mosteller’s and Current’s formulas give the same estimate for A, then the right-hand sides of these two equations are equal; that is,\(\frac{\sqrt{hw}}{60}=\frac{4+w}{30}\)​. Multiplying each side of this equation \(\sqrt{hw}\) 60 to isolate the expression \(\sqrt{hw}\) gives \(\sqrt{hw}\) = 60 ​\(\left ( \frac{4+w}{30} \right )\) or \(\left ( \frac{4+w}{30} \right )\) = 2 (4 + w). Therefore, if Mosteller’s and Current’s formulas give the same estimate for A, then \(\sqrt{hw}\) is equivalent to 2(4 + w).

An alternate approach is to multiply the numerator and denominator of Current’s formula by 2, which gives \(\frac{2(4 + w)}{60}\)​. Since it is given that Mosteller’s and Current’s formulas give the same estimate for A,\(\frac{2(4+w)}{60}=\frac{\sqrt{hw}}{60}\)​. Therefore,\(\sqrt{hw}\) = 2(4 + w).

Choices A, B, and D are incorrect and may result from errors in the algebraic manipulation of the equations.

Current’s formula is A = \(\frac{4+w}{30}\)​.Multiplying each side of the equation by 30 gives 30A = 4 + w. Subtracting 4 from each side of 30A = 4 + w gives w = 30A – 4.

Choices B, C, and D are incorrect and may result from errors in choosing and applying operations to isolate w as one side of the equation in Current’s formula.

The charity with the greatest percent of total expenses spent on programs is represented by the highest point on the scatterplot; this is the point that has a vertical coordinate slightly less than halfway between 90 and 95 and a horizontal coordinate slightly less than halfway between 3,000 and 4,000. Thus, the charity represented by this point has a total income of about $3,400 million and spends about 92% of its total expenses on programs. The percent predicted by the line of best fit is the vertical coordinate of the point on the line of best fit with horizontal coordinate $3,400 million; this vertical coordinate is very slightly more than 85. Thus, the line of best fit predicts that the charity with the greatest percent of total expenses spent on programs will spend slightly more than 85% on programs. Therefore, the difference between the actual percent (92%) and the prediction (slightly more than 85%) is slightly less than 7%.

Choice A is incorrect. There is no charity represented in the scatterplot for which the difference between the actual percent of total expenses spent on programs and the percent predicted by the line of best fit is as much as 10%. Choices C and D are incorrect. These choices may result from misidentifying in the scatterplot the point that represents the charity with the greatest percent of total expenses spent on programs.

The y-intercept of the graph of y = 19.99 + 1.50x in the xy-plane is the point on the graph with an x-coordinate equal to 0. In the model represented by the equation, the x-coordinate represents the number of miles a rental truck is driven during a one-day rental, and so the y-intercept represents the charge, in dollars, for the rental when the truck is driven 0 miles; that is, the y-intercept represents the cost, in dollars, of the flat fee. Since the y-intercept of the graph of y = 19.99 + 1.50x is (0, 19.99), the y-intercept represents a flat fee of $19.99 in terms of the model.

Choice B is incorrect. The slope of the graph of y = 19.99 + 1.50x in the xy-plane, not the y-intercept, represents a driving charge per mile of $1.50 in terms of the model. Choice C is incorrect. Since the coefficient of x in the equation is 1.50, the charge per mile for driving the rental truck is $1.50, not $19.99. Choice D is incorrect. The sum of 19.99 and 1.50, which is 21.49, represents the cost, in dollars, for renting the truck for one day and driving the truck 1 mile; however, the total daily charges for renting the truck does not need to be $21.49.

If ^b⁄₂ ​ = 10, then multiplying each side of this equation by 2 gives b = 20. Substituting 20 for b in the equation a − b = 12 gives a − 20 = 12. Adding 20 to each side of this equation gives a = 32. Since a = 32 and b = 20, it follows that the value of a + b is 32 + 20, or 52.

Choice A is incorrect. If the value of a + b were less than the value of a − b, it would follow that b is negative. But if ^b⁄₂ ​ = 10, then b must be positive. This contradiction shows that the value of a + b cannot be 2. Choice B is incorrect. If the value of a + b were equal to the value of a – b, then it would follow that b = 0. However, b cannot equal zero because it is given that ^b⁄₂ ​ = 10. Choice C is incorrect. This is the value of a, but the question asks for the value of a + b.

A column of 50 stacked one-cent coins is about 3⁷⁄₈ ​ inches tall, which is slightly less than 4 inches tall. Therefore a column of stacked one-cent coins that is 4 inches tall would contain slightly more than 50 one-cent coins. It can then be reasoned that because 8 inches is twice 4 inches, a column of stacked one-cent coins that is 8 inches tall would contain slightly more than twice as many coins; that is, slightly more than 100 one-cent coins. An alternate approach is to set up a proportion comparing the column height to the number of one-cent coins, or \(\frac{3\frac{7}{8}inches}{50\, coins}=\frac{8\, inches}{x\, coins}\)​, where x is the number of coins in an 8-inch-tall column. Multiplying each side of the proportion by 50x gives 3⁷⁄₈ x = 400. Solving for x gives x =\(\frac{400 \times 8}{31}\)​,which is approximately 103. Therefore, of the given choices, 100 is closest to the number of one-cent coins it would take to build an 8-inch-tall column.

Choice A is incorrect. A column of 75 stacked one-cent coins would be slightly less than 6 inches tall. Choice C is incorrect. A column of 200 stacked one-cent coins would be more than 15 inches tall. Choice D is incorrect. A column of 390 stacked one-cent coins would be over 30 inches tall.

The figure is a quadrilateral, so the sum of the measures of its interior angles is 360°. The value of x can be found by using the equation 45 + 3x = 360. Subtracting 45 from both sides of the equation results in 3x = 315, and dividing both sides of the resulting equation by 3 yields x = 105. Therefore, the value of x in the figure is 105.

Choice A is incorrect. If the value of x were 45, the sum of the measures of the angles in the figure would be 45 + 3(45), or 180°, but the sum of the measures of the angles in a quadrilateral is 360°. Choice B is incorrect. If the value of x were 90, the sum of the measures of the angles in the figure would be 45 + 3(90), or 315°, but the sum of the measures of the angles in a quadrilateral is 360°. Choice C is incorrect. If the value of x were 100, the sum of the measures of the angles in the figure would be 45 + 3(100), or 345°, but the sum of the measures of the angles in a quadrilateral is 360°.