A project manager is analyzing the budget for a new initiative. The cost C (in thousands of dollars) is related to the number of resources R by the function C(R) = R^2 - 10R + 30. For what number of resources will the cost be 15 thousand dollars?

Correct answer: D. 3 or 7 resources

Set C(R) = 15: R^2 - 10R + 30 = 15. Subtract 15 from both sides to set the equation to zero: R^2 - 10R + 15 = 0. This quadratic equation can be solved using the quadratic formula or by factoring if possible. (R-3)(R-7) = R^2 - 7R - 3R + 21 = R^2 - 10R + 21. This is incorrect. R^2 - 10R + 15 = 0. Using the quadratic formula, R = [-(-10) ± sqrt((-10)^2 - 4(1)(15))] / (2*1) = [10 ± sqrt(100 - 60)] / 2 = [10 ± sqrt(40)] / 2 = [10 ± 2sqrt(10)] / 2 = 5 ± sqrt(10). Wait, the options are integers. Let me re-check the question setup: R^2 - 10R + 30 = 15. R^2 - 10R + 15 = 0. This quadratic does not factor cleanly into integers. Let's re-evaluate the options. If R=3, C(3) = 3^2 - 10(3) + 30 = 9 - 30 + 30 = 9. Not 15. If R=7, C(7) = 7^2 - 10(7) + 30 = 49 - 70 + 30 = 9. Not 15. Let me re-evaluate my options, there's a problem here. The initial question setup for this difficulty needs integer answers. Let's adjust the question or options. Let's say the cost is 9 thousand dollars. Then R^2 - 10R + 30 = 9. R^2 - 10R + 21 = 0. This factors to (R-3)(R-7) = 0. So R=3 or R=7. This matches option D. I'll correct the problem statement to match this solution. The question should be: 'For what number of resources will the cost be 9 thousand dollars?' Corrected Explanation: Set C(R) = 9: R^2 - 10R + 30 = 9. Subtract 9 from both sides to set the equation to zero: R^2 - 10R + 21 = 0. This quadratic equation can be factored as (R - 3)(R - 7) = 0. Therefore, R = 3 or R = 7.