Let's solve each question step-by-step.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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:
- $408.04
- 14
- 42
- 16
- are equal
- 32
- $618
- Scalene triangle
- 8