<p>Help/explanation of the correct answer to any of these questions would be appreciated. </p>
<p>1) A car traveled 10 miles at an average speed of 20 miles per hour and then traveled the next 10 miles at an average speed of 40 miles per hour. What was the average speed, in miles per hour, of the car for the 20 miles? (Grid-in type of question)</p>
<p>2) Set S consists of the positive multiples of 6 that are less than 50, and set T consists of the positive multiples of 8 that are less than 50. How many numbers do sets S and T have in common?
a. none
b. one
c. two
d. four
e. eight</p>
<p>3) A certain ice-cream parlor offers 6 different toppings for sundaes. How many combinations of 2 different topping from those offered are possible?
a. 6
b. 12
c. 15
d. 36
e. 64</p>
<p>4) For a certain tire, the manufacturer recommends that the air pressure be between 30 and 34 pounds per square inch. If x pounds per square inch is the air pressure in a tire that meets this recommendation, which of the following represents all possible values of x?
a. |x-32| < 2
b. |x+32| < 2
c. |x-32| > 2
d. |x+32| > 2
e. |x-32| = 2</p>
<ol>
<li><p>The car drove at 20mph for 30 minutes, and at 40mph for 15 minutes. Therefore it took 45 minutes for the car to drive 20 miles, so set up a proportion 45/20 = 60/x and solve it to get x = 25, so 25mph. </p></li>
<li><p>This question basically wants you to find all the numbers that are multiples of both 6 and 8 and less than 50. 24 and 48 are the only numbers that fulfill this criteria, so C is the correct answer. </p></li>
<li><p>The first topping can be paired with any other topping besides itself, giving 5 possible combinations. The second topping can be paired with any other topping besides itself and the first topping, so 4 combinations, and so forth. Add these combinations - 5+4+3+2+1=15, so C. </p></li>
<li><p>32 is the middle number out of the possible pressures allowed, so when 32 is subtracted from any of the allowed pressures, the absolute value should not exceed 2, since 32-30=2 and 34-32=2. It should be A.</p></li>
</ol>
<p>If you don’t understand the above explanation, just plug in all of the allowed pressures to eliminate the wrong choices. XD</p>
<ol>
<li><p>To find the average of the 20 miles, find the total time for each 10 mile ride. So, for the 10 miles driven with an average speed of 20 miles/hour, the time was 30 minutes and for the 10 miles driven with an average of speed of 40 miles/hour, the time was 15 minutes. Add the time together (45 minutes). So you know you rode 20 miles in 45 minutes or 80/3 miles per hour.</p></li>
<li><p>Compute all the multiples of 6 and 8 that are less than 50. So, for multiples of 6, they would be 6, 12, 18, 24, 30, 36, 42, and 48; multiples of 8 are 8, 16, 24, 32, 40, and 48. There’s only two common numbers (24 & 48)</p></li>
</ol>
<p>. </p>
<ol>
<li>The answer is A because you can rewrite the inequality two ways: you can rewrite it the way it is and by taking away the sign and adding a negative. So, x-32<2 or x<34 is one way of rewriting it and the other way is x-32>-2 or x>30. Both these expressions fit the recommendation that the tire has to be less than 34 but greater than 30 psi.</li>
</ol>