Question

1. the speed limit on a highway is 70 miles per hour. what is the approximate speed in kilometers per hour? use 1 kilometer = 0.621 mile. a. 112.7 km/h b. 105.3 km/h c. 86.1 km/h d. 43.5 km/h 2. the relationship shown in the table is proportional. what is the missing value in the table? gas purchased (gal) cost ($) 2 5.78 5 14.45 x 23.12 11 31.79 a. 9 b. 8 c. 7 d. 6 3. in a recipe, cups of flour (y), is proportional to cups of sugar (x). the equation y = 4x is used to calculate cups of flour needed. what is the constant of proportionality? a. 4 b. 3 c. 0.4 d. $\frac{1}{4}$ 4. in a floor design, for every 7 blue tiles (x), there are 12 orange tiles (y). on a graph of this relationship, what are the coordinates of the point for 60 orange tiles? a. (60, 21) b. (35, 60) c. (21, 60) d. (60, 35) 5. a graph passes through $(-\frac{2}{3}, -1)$ and $(1,\frac{3}{2})$. what is the constant of proportionality? a. $-\frac{3}{2}$ b. $-\frac{2}{3}$ c. $\frac{2}{3}$ d. $\frac{3}{2}$ 6. the relationship between the number of bushels of apples and the number of apple trees is shown. how many bushels of apples will 12 apple trees produce? a. 300 bushels b. 330 bushels c. 360 bushels d. 390 bushels 7. george cleans 14 windows per hour. which equation shows the relationship between windows cleaned (w), and the time in hours (h)? a. w = 14h b. w = $\frac{14}{h}$ c. w = 14 + h d. w = $\frac{h}{14}$ 8. jan completes 60% of a 1,500 - piece puzzle. how many puzzle pieces is this? a. 1,200 pieces b. 1,050 pieces c. 900 pieces d. 750 pieces 9. finn hikes 588 miles, which is 27% of the length of the appalachian trail. how long is the appalachian trail? a. 15,876 mi b. 2,178 mi c. 159 mi d. 22 mi 10. daniella and hasson take the same test. daniella answers 150 questions correctly, and hasson answers 12% fewer questions correctly than she did. how many more questions does daniella answer correctly than hasson? a. 132 b. 36 c. 18 d. 12

Explanation:

Step1: Convert speed from miles to kilometers

We know 1 kilometer = 0.621 mile. To convert 70 miles per hour to kilometers per hour, we use the formula $k=\frac{m}{0.621}$, where $m = 70$. So $k=\frac{70}{0.621}\approx112.7$ km/h.

Step2: Find missing value in proportional - table

The relationship is proportional, so the ratio of cost to gas purchased is constant. The ratio for the first row is $\frac{5.78}{2}=2.89$. For the third row, if $\frac{23.12}{x}=2.89$, then $x=\frac{23.12}{2.89}=8$.

Step3: Identify constant of proportionality

The equation of proportionality is $y = kx$. Given $y = 4x$, the constant of proportionality $k = 4$.

Step4: Find coordinates for tile - relationship

The ratio of blue tiles to orange tiles is $\frac{x}{y}=\frac{7}{12}$. If $y = 60$, then $x=\frac{7\times60}{12}=35$. So the coordinates are $(35,60)$.

Step5: Find constant of proportionality for two - points

The equation for proportionality is $y=kx$. Substitute $(x_1,y_1)=(-\frac{2}{3},-1)$ and $(x_2,y_2)=(1,\frac{3}{2})$ into $y = kx$. Using the first - point $-1=k\times(-\frac{2}{3})$, then $k=\frac{3}{2}$.

Step6: Find number of bushels from graph

From the graph, when $x = 12$ (number of apple trees), $y = 360$ (number of bushels of apples).

Step7: Find equation for window - cleaning

If George cleans 14 windows per hour, the relationship between the number of windows cleaned $w$ and time $h$ is $w = 14h$.

Step8: Find number of puzzle pieces

Jan completes 60% of a 1500 - piece puzzle. The number of pieces is $0.6\times1500 = 900$.

Step9: Find length of Appalachian Trail

If 588 miles is 27% of the length $L$ of the Appalachian Trail, then $L=\frac{588}{0.27}\approx2178$ mi.

Step10: Find difference in correct answers

Hasson answers 12% fewer questions correctly than Daniella. The number of questions Hasson answers correctly is $150\times(1 - 0.12)=150\times0.88 = 132$. The difference is $150-132 = 18$.

Answer:

1. A. 112.7 km/h
2. B. 8
3. A. 4
4. B. (35, 60)
5. D. $\frac{3}{2}$
6. C. 360 bushels
7. A. $w = 14h$
8. C. 900 pieces
9. B. 2,178 mi
10. C. 18