ATI TEAS 7 Math Version 2 Questions

Explanation

<h2>The student travels a distance of 37.4 kilometers to go to class.</h2> To convert miles into kilometers, the distance in miles is divided by 0.62. When 23.2 miles is divided by 0.62, the result is approximately 37.4 kilometers. <b>A) 37.4 km</b> This is the correct answer. By dividing the distance in miles (23.2) by the conversion factor of 0.62 miles per kilometer, you get approximately 37.4 kilometers. <b>B) 14.4 km</b> This choice appears to be a result of incorrectly dividing the distance in kilometers by the conversion factor instead of the distance in miles. Thus, it is not the correct conversion. <b>C) 61.1 km</b> This seems to be the result of a multiplication of the distance in miles by the conversion factor rather than a division, hence generating a larger and incorrect value in kilometers. <b>D) 23.6 km</b> This value is very close to the original distance in miles, suggesting a confusion between the two units and neglecting to apply the conversion factor. <b>Conclusion</b> In order to correctly convert a distance from miles to kilometers, one must divide the given distance in miles by the conversion factor (0.62 mi/km). In this case, dividing the distance from the student's home to their college (23.2 miles) by 0.62, results in approximately 37.4 kilometers. The other options represent common mistakes made when converting units, such as neglecting to convert at all or using the conversion factor incorrectly.

Explanation

<h2>The correct conversion of 95F to degrees Celsius is 35C.</h2> The conversion formula from Fahrenheit to Celsius is C = 5/9[F - 32]. When you substitute 95 for F in the formula, it gives 35 for C. This is the accurate conversion for 95F to degrees Celsius. <b>A) 113C</b> This choice is incorrect because it does not follow the conversion formula from Fahrenheit to Celsius. Plugging 95 into the formula C = 5/9[F - 32] does not yield 113C. <b>B) 63C</b> This choice is also incorrect because it does not follow the conversion formula from Fahrenheit to Celsius. If we substitute 95 for F in the formula C = 5/9[F - 32], the result is not 63C. <b>D) 21C</b> This choice is incorrect as well. Using the conversion formula C = 5/9[F - 32] and substituting 95F does not result in 21C. <b>Conclusion</b> The correct conversion of 95F to degrees Celsius follows the formula C = 5/9[F - 32]. Substituting 95 for F in this formula provides 35C. The other choices - 113C, 63C, and 21C - do not follow this formula, making them incorrect answers for the conversion of 95F to degrees Celsius.

Explanation

<h2>x = y(nw + z)</h2> In the equation "(x/y) - z = nw", to solve for x, you need to isolate x on one side of the equation. This involves multiplying both sides by y and adding zy to both sides. <b>A) x = y(nw + z)</b> This is the correct solution. First, you multiply both sides of the equation "(x/y) - z = nw" by y. This results in "x - yz = ynw", then you add yz to both sides of the equation, which gives you "x = y(nw + z)". <b>B) x = y(2 + rw)</b> This is not correct because it does not follow the correct algebraic steps to solve the equation for x. There is no term 2 or rw in the original equation, so this option introduces variables and constants that are not present in the original equation. <b>C) x = yw + yz</b> This is not correct either. While it appears to use the variables from the original equation, the operations are incorrect. In the original equation, z is subtracted, not added, and the term yw does not appear in the original equation. <b>D) x = y(nw - z)</b> This is also incorrect. It incorrectly subtracts z from nw in the parentheses, whereas the correct operation, according to the original equation, is to add z to nw. <b>Conclusion</b> In order to solve the equation "(x/y) - z = nw" for x, you must isolate x. This involves two steps: first, multiplying both sides of the equation by y; second, adding yz to both sides of the equation. The correct result is "x = y(nw + z)", not any of the other choices. The other choices either introduce variables and constants not present in the original equation, or incorrectly manipulate the variables in the equation.

Explanation

<h2>The length of the board in centimeters is 1230 cm.</h2> To convert meters to centimeters, the appropriate conversion factor is 100 cm/1 m. Therefore, the length of the board, when converted from meters to centimeters, is 12.3 m * 100 cm/1 m = 1230 cm. <b>A) 1230 cm</b> This is the correct answer. As indicated above, multiplying the length of the board in meters (12.3 m) by the conversion factor of 100 cm/1 m results in a length of 1230 cm. <b>B) 0.123 cm</b> This answer would be correct if we were converting meters to kilometers, not centimeters. One meter is equivalent to 0.001 kilometers, so 12.3 m would indeed be 0.0123 km. However, since we're converting to centimeters, this answer is not correct. <b>C) 12300 cm</b> This answer would be correct if the original length of the board was 123 m, not 12.3 m. When converting from meters to centimeters, we multiply by 100, so 123 m would indeed be 12300 cm. However, the length of the board is 12.3 m, so this answer is not correct. <b>D) 12.3 cm</b> This answer would be correct if the original length of the board was 12.3 cm, not 12.3 m. One meter is equivalent to 100 centimeters, so 12.3 m is much larger than 12.3 cm. Therefore, this answer is not correct. <b>Conclusion</b> The length of the board, when converted from meters to centimeters, is 1230 cm. The other options incorrectly apply the conversion factor or assume a different original length for the board. Understanding unit conversion is critical in many fields, including engineering, physics, and everyday life, as it allows us to express measurements in different scales and compare quantities accurately.

Explanation

<h2>The estimated total cost for the coffee is $840.00.</h2> The employer plans to round the number of employees to the nearest ten and the cost of the coffee to the nearest dollar for estimation. Thus, 214 employees round to 210 and $3.95 rounds to $4.00. Multiplying these rounded values gives an estimated total cost of $840.00. <b>A) $845.30</b> This choice might be the result of rounding only the number of employees (214 to 210) but not the cost of coffee. Multiplying 210 employees with the exact cost of coffee ($3.95) results in $829.50, not $845.30. Therefore, this option is incorrect. <b>B) $840.00</b> This choice correctly represents the product of the rounded number of employees (210) and the rounded cost of coffee ($4.00). Hence, this is the correct answer. <b>C) $829.50</b> This choice appears to be the result of an error in rounding. It seems the number of employees was rounded correctly to 210 but the cost of the coffee was not rounded. Multiplying 210 employees with the exact cost of coffee ($3.95) results in $829.50. However, the employer wanted to round both values for estimation, so this option is incorrect. <b>D) $850.00</b> This choice seems to be the result of an overestimate. Neither the rounded number of employees (210) nor the rounded cost of coffee ($4.00) would result in this total. Therefore, this option is incorrect. <b>Conclusion</b> In this situation, the employer wants to estimate the total cost by rounding both the number of employees and the cost of coffee. By rounding 214 employees to 210 and the cost of coffee from $3.95 to $4.00, the estimated total comes to $840.00. All other choices appear to be based on errors in rounding or calculation.