Which list shows the numbers arranged from least to greatest?
- A. -(2/9), -0.21, -0.2, -(2/11), -1
- B. -1, -(2/9), -0.21, -0.2, -(2/11)
- C. -1, -(2/11), -0.21, -0.2, -(2/9)
- D. -(2/11), -0.2, -0.21, -(2/9), -1
Correct Answer & Rationale
Correct Answer: C
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
To determine the correct order, it's essential to convert fractions and decimals to comparable values. In option C, the numbers arranged from least to greatest are: -1, approximately -0.1818 (for -(2/11)), -0.21, -0.2, and approximately -0.2222 (for -(2/9)). This sequence accurately reflects their values. Option A incorrectly places -1 at the end, misordering the fractions and decimals. Option B also misplaces -1, and the order of the decimals is incorrect. Option D incorrectly ranks -1 as the least value and misplaces the fraction values, leading to an inaccurate arrangement.
Other Related Questions
Robert has $50 to spend on his utility bills each month. The basic monthly charge for water and sewer is $23.77. Electricity costs $0.1116 for each kilowatt hour used. The inequality 0.1116x + 23.77 ? 50 represents Robert's monthly utility budget. To the nearest kilowatt hour, what is the maximum number of kilowatt hours of electricity that Robert can Use without going over his monthly budget amount?
- A. 661
- B. 235
- C. 448
- D. 424
Correct Answer & Rationale
Correct Answer: B
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
What is the equation, in standard form, of the line that passes through the points (-3, -4) and (3, -12)?
- A. 4x + 3y = 24
- B. 3x + 4y = -25
- C. 4x + 3y = -24
- D. 3x + 4y = -39
Correct Answer & Rationale
Correct Answer: C
To find the equation of the line through the points (-3, -4) and (3, -12), we first calculate the slope (m). The slope is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - (-4)}{3 - (-3)} = \frac{-8}{6} = -\frac{4}{3} \). Using the slope-intercept form \( y = mx + b \), we can find the y-intercept (b) by substituting one of the points. This leads us to the equation \( y = -\frac{4}{3}x - 4 \). Rewriting it in standard form gives \( 4x + 3y = -24 \), matching option C. Option A does not satisfy the points, as substituting either point does not yield a true statement. Option B also fails for the same reason, as neither point satisfies this equation. Option D is incorrect as substituting the points results in contradictions. Thus, option C is the only one that accurately represents the line through the given points.
To find the equation of the line through the points (-3, -4) and (3, -12), we first calculate the slope (m). The slope is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-12 - (-4)}{3 - (-3)} = \frac{-8}{6} = -\frac{4}{3} \). Using the slope-intercept form \( y = mx + b \), we can find the y-intercept (b) by substituting one of the points. This leads us to the equation \( y = -\frac{4}{3}x - 4 \). Rewriting it in standard form gives \( 4x + 3y = -24 \), matching option C. Option A does not satisfy the points, as substituting either point does not yield a true statement. Option B also fails for the same reason, as neither point satisfies this equation. Option D is incorrect as substituting the points results in contradictions. Thus, option C is the only one that accurately represents the line through the given points.
The daily cost, C(x), for a company to produce x microscopes is given by the equation C(x) = 300 + 10.5x. What is the cost of producing 50 microscopes?
- A. $41,250
- B. $360.50
- C. $15,525
- D. $825
Correct Answer & Rationale
Correct Answer: D
To determine the cost of producing 50 microscopes, substitute x = 50 into the equation C(x) = 300 + 10.5x. This gives C(50) = 300 + 10.5(50) = 300 + 525 = 825. Thus, the total cost is $825. Option A ($41,250) is incorrect as it miscalculates the cost by multiplying incorrectly. Option B ($360.50) results from a misunderstanding of the equation, possibly neglecting the fixed cost. Option C ($15,525) likely arises from an error in multiplying the variable cost without adding the fixed cost. Each incorrect option fails to follow the proper calculation method outlined in the cost equation.
To determine the cost of producing 50 microscopes, substitute x = 50 into the equation C(x) = 300 + 10.5x. This gives C(50) = 300 + 10.5(50) = 300 + 525 = 825. Thus, the total cost is $825. Option A ($41,250) is incorrect as it miscalculates the cost by multiplying incorrectly. Option B ($360.50) results from a misunderstanding of the equation, possibly neglecting the fixed cost. Option C ($15,525) likely arises from an error in multiplying the variable cost without adding the fixed cost. Each incorrect option fails to follow the proper calculation method outlined in the cost equation.
The distance, d, in feet, it takes to come to a complete stop when driving a car r miles per hour can be found using the equation d = 1/20(r^2)+ r. If it takes a car 240 feet to come to a complete stop, what was the speed of the car, in miles per hour, when the driver began to stop it?
- A. 40
- B. 30
- C. 60
- D. 80
Correct Answer & Rationale
Correct Answer: A
To find the speed of the car when it takes 240 feet to stop, substitute d = 240 into the equation d = 1/20(r^2) + r. This leads to the equation 240 = 1/20(r^2) + r. Multiplying through by 20 simplifies to 4800 = r^2 + 20r, which rearranges to r^2 + 20r - 4800 = 0. Solving this quadratic equation yields r = 40 or r = -120. Since speed cannot be negative, the valid solution is 40 mph. Option B (30) does not satisfy the equation, leading to a shorter stopping distance. Option C (60) results in a stopping distance of 480 feet, which exceeds 240 feet. Option D (80) produces a stopping distance of 800 feet, also incorrect. Thus, only 40 mph meets the criteria.
To find the speed of the car when it takes 240 feet to stop, substitute d = 240 into the equation d = 1/20(r^2) + r. This leads to the equation 240 = 1/20(r^2) + r. Multiplying through by 20 simplifies to 4800 = r^2 + 20r, which rearranges to r^2 + 20r - 4800 = 0. Solving this quadratic equation yields r = 40 or r = -120. Since speed cannot be negative, the valid solution is 40 mph. Option B (30) does not satisfy the equation, leading to a shorter stopping distance. Option C (60) results in a stopping distance of 480 feet, which exceeds 240 feet. Option D (80) produces a stopping distance of 800 feet, also incorrect. Thus, only 40 mph meets the criteria.