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?

Question

*
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?
*
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 solve each question step-by-step.

1. Cost of gas for 2,727 miles: \[ \text{Miles per gallon} = 27 \text{ mpg} \] \[ \text{Total gallons used} = \frac{2727 \text{ miles}}{27 \text{ mpg}} = 101 \text{ gallons} \] \[ \text{Cost of gas} = 101 \text{ gallons} \times 4.04 \text{ dollars/gallon} = 408.04 \text{ dollars} \] Thus, the answer is $408.04.

2. Value of \(3x^2 – 2y\) exceeds \(2x^2 – 3y\) when \(x = 3\) and \(y = 5\): \[ 3x^2 - 2y = 3(3^2) - 2(5) = 3(9) - 10 = 27 - 10 = 17 \] \[ 2x^2 - 3y = 2(3^2) - 3(5) = 2(9) - 15 = 18 - 15 = 3 \] The difference is: \[ 17 - 3 = 14 \] Thus, the answer is 14.

3. Greatest common factor of 42, 126, and 210:

   • Factors of \(42 = 2 \times 3 \times 7\)
   • Factors of \(126 = 2 \times 3^2 \times 7\)
   • Factors of \(210 = 2 \times 3 \times 5 \times 7\) The common factors are \(2\), \(3\), and \(7\). Calculation of GCF: \[ GCF = 2 \times 3 \times 7 = 42 \] Thus, the answer is 42.

4. Sales for the first year: Let \(x\) be the sales for the first year.

   • Sales for the second year = \(x + 3\)
   • Sales for the third year = \(2(x + 3) = 38\) \[ 2(x + 3) = 38 \] \[ x + 3 = 19 \implies x = 16 \] Thus, the answer is 16 million dollars.

5. Angle measures \(\angle DEF\) and \(\angle GEF\): Since \(F\) is equidistant from points \(D\) and \(G\) and both segments stem from the same point \(E\), by construction, the angles are equal. Thus, the answer is are equal.

6. Probability of red marbles: Let \(r\) be the number of additional red marbles. The total number of marbles becomes \(24 + r\) and the number of red marbles is \(8 + r\). The probability of drawing a red marble should equal \(\frac{5}{3}\): \[ \frac{8 + r}{24 + r} = \frac{5}{3} \] Cross-multiplying: \[ 3(8 + r) = 5(24 + r) \] \[ 24 + 3r = 120 + 5r \implies 120 - 24 = 5r - 3r \implies 96 = 2r \implies r = 48 \] Thus, we want to solve for \(r\): \[ 8 + r = N \] \[ r = 48 \Rightarrow R + 8 \Rightarrow R = 32 \] Thus, the answer is 32 additional red marbles.

7. Thomas's pay calculation: Thomas worked 40 regular hours and 6 overtime hours. \[ \text{Regular pay} = 40 \times 15 = 600 \] \[ \text{Overtime pay} = 6 \times 15 \times 1.5 = 135 \] Total gross pay: \[ 600 + 135 = 735 \] After deductions: \[ 735 - 117 = 618 \] Thus, the answer is $618.

8. Graph with no vertical line of symmetry: A scalene triangle has no sides of equal length and thus does not possess vertical symmetry. Thus, the answer is Scalene triangle.

9. Radius of circle: The formula for circumference is \(C = 2 \pi r\). Given \(C = 16 \pi\): \[ 2 \pi r = 16 \pi \implies r = 8 \] Thus, the answer is 8 feet.

Here are all the answers summarized:

1. $408.04
2. 14
3. 42
4. 16
5. are equal
6. 32
7. $618
8. Scalene triangle
9. 8