The numbers 1 through 15 were each written on individual pieces of paper, 1 number per piece. Then the 15 pieces of paper were put in a jar. One piece of paper will be drawn from the jar at random. What is the probability of drawing a piece of paper with a number less than 9 written on it?

Question

*
1 point
1/9
1/15
6/15
7/15
8/15
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
*
1 point
$44.44
$118.80
$444.40
$109.08
$408.04
When x = 3 and y = 5, by how much does the value of 3x2 – 2y exceed the value of 2x2 – 3y ?
*
1 point
4
14
16
20
50
What is the greatest common factor of 42, 126, and 210 ?
*
1 point
2
6
14
21
42
Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?
*
1 point
16
17.5
20.5
22
35
In the figure, ray EF was constructed starting from rays ED and EG. By using a compass D and G were marked equidistant from E on rays ED and EG. The compass was then used to locate a point F, distinct from E, so that F is equidistant from D and G. For all constructions defined by the above steps, the measures of ∠DEF and ∠GEF:
*
1 point
Captionless Image
are equal
are NOT equal
sum to 30 degrees
sum to 45 degrees
A bag contains 8 red marbles, 9 yellow marbles, and 7 green marbles. How many additional red marbles must be added to the 24 marbles already in the bag so that the probability of randomly drawing a red marble is 5/3 ?
*
1 point
11
16
20
24
32
At his job, the first 40 hours of each week that Thomas works is regular time, and any additional time that he works is overtime. Thomas gets paid $15 per hour during regular time. During overtime Thomas gets paid 1.5 times as much as he gets paid during regular time. Thomas works 46 hours in 1 week and gets $117 in deductions taken out of his pay for this week. After the deductions are taken out, how much of Thomas’s pay for this week remains?
*
1 point
$492
$573
$609
$618
$735
Regardless of how the graph is oriented in the standard (x,y) coordinate plane, NO graph in one of the following categories has a vertical line of symmetry. Which one?
(This question has been updated - the original answer was incorrectly noted.)
*
1 point
Square
Line
Pentagon
Scalene triangle
Parallelogram
A circle has a circumference of 16 π feet. What is the radius of the circle, in feet?
*
1 point
8
12
16
24
32

Answer 1

Let's go through each question one by one:

1. Probability of drawing a piece of paper with a number less than 9:

   • The numbers less than 9 are 1, 2, 3, 4, 5, 6, 7, 8 (which gives us 8 numbers).
   • Total numbers = 15.
   • Probability = Number of favorable outcomes / Total outcomes = 8/15.
   • Answer: 8/15

2. Gas cost for traveling 2,727 miles:

   • Miles per gallon = 27.
   • Gallons needed = Total miles / Miles per gallon = 2727 / 27 = 101.
   • Cost = Gallons needed * Cost per gallon = 101 * $4.04 = $408.04.
   • Answer: $408.04

3. Calculate value of expressions:

   • When \( x = 3 \) and \( y = 5 \):
     • \( 3x^2 - 2y = 3(3^2) - 2(5) = 3(9) - 10 = 27 - 10 = 17 \).
     • \( 2x^2 - 3y = 2(3^2) - 3(5) = 2(9) - 15 = 18 - 15 = 3 \).
     • Difference = \( 17 - 3 = 14 \).
   • Answer: 14

4. Greatest common factor (GCF) of 42, 126, and 210:

   • The prime factors are:
     • 42 = 2 × 3 × 7
     • 126 = 2 × 3^2 × 7
     • 210 = 2 × 3 × 5 × 7
   • The common prime factors are \( 2, 3, \) and \( 7 \).
   • GCF = \( 2 × 3 × 7 = 42 \).
   • Answer: 42

5. Sales for the first year:

   • Let \( x \) be the sales for the first year.
   • Second year sales = \( x + 3 \).
   • Third year sales = \( 2(x + 3) = 38 \).
   • Solving: \( 2(x + 3) = 38 \) → \( x + 3 = 19 \) → \( x = 16 \).
   • Answer: 16

6. Measures of angles ∠DEF and ∠GEF:

   • Since point F is equidistant from D and G on rays ED and EG, the angles ∠DEF and ∠GEF are equal.
   • Answer: are equal

7. Probability of drawing a red marble:

   • Initial marbles: 8 red + 9 yellow + 7 green = 24 marbles.
   • Let \( r \) be additional red marbles. Total marbles = \( 24 + r \).
   • Probability = Number of red marbles / Total marbles = \( \frac{8 + r}{24 + r} = \frac{5}{3} \).
   • Cross multiply: \( 3(8 + r) = 5(24 + r) \) → \( 24 + 3r = 120 + 5r \) → \( 2r = 96 \) → \( r = 48 \).
   • (Since no options match, let's reassess): If target probability is \( 5/3\) instead of 3, we set \( 8 + r = 5k \) etc., and find the solution if hiccup.
   • Answer: There seems to be no appropriate value fitting options given.

8. Thomas’s pay for the week:

   • Regular hours = 40, Overtime = 6 hours (since 46-40).
   • Regular pay = 40 * $15 = $600. Overtime rate = $15 * 1.5 = $22.5, so Overtime pay = 6 * $22.5 = $135.
   • Total pay before deductions = $600 + $135 = $735.
   • After deductions of $117: \( 735 - 117 = 618 \).
   • Answer: $618

9. No vertical line of symmetry:

   • A scalene triangle is defined such that all sides are different, thus no line of symmetry exists.
   • Answer: Scalene triangle

10. Radius of a circle:

• Circumference = \( 2\pi r = 16\pi \).
• Solving for \( r \): \( r = 16/2 = 8 \).
• Answer: 8

If further clarifications or corrections apply, please input!