13. a machine is currently set to a feed rate of 5.921 inches per minute (ipm). the machinist changes this setting to 6.088 ipm. by how much did the machinist increase the feed rate? a. 0.167 ipm b. 1.167 ipm c. 1.833 ipm d. 1.967 ipm 14. 0.075, 0.75%, $\frac{3}{4}$ which of the following correctly orders the values above from least to greatest? a. 0.75%, 0.075, $\frac{3}{4}$ b. 0.75%, $\frac{3}{4}$, 0.075 c. $\frac{3}{4}$, 0.75%, 0.075 d. 0.075, 0.75%, $\frac{3}{4}$ 15. what is the value of $2.84 \times 3.9$? a. 3.408 b. 11.076 c. 34.08 d. 110.76 16. what is 0.8637 rounded to the nearest hundredth? a. 0.86 b. 0.863 c. 0.864 d. 0.87 17. 60% of what number is equal to 30? a. 0.5 b. 2 c. 18 d. 50 18. if $\frac{4}{3} + \frac{1}{6} = p$, then the value of $p$ is between which of the following pairs of numbers? a. 3 and 4 b. 5 and 6 c. 6 and 7 d. 7 and 9 19. which of the following inequalities is true? a. $\frac{3}{4} \frac{5}{6}$ c. $\frac{5}{8} \frac{6}{10}$ d. $\frac{4}{5}

Question

13. a machine is currently set to a feed rate of 5.921 inches per minute (ipm). the machinist changes this setting to 6.088 ipm. by how much did the machinist increase the feed rate? a. 0.167 ipm b. 1.167 ipm c. 1.833 ipm d. 1.967 ipm 14. 0.075, 0.75%, $\frac{3}{4}$ which of the following correctly orders the values above from least to greatest? a. 0.75%, 0.075, $\frac{3}{4}$ b. 0.75%, $\frac{3}{4}$, 0.075 c. $\frac{3}{4}$, 0.75%, 0.075 d. 0.075, 0.75%, $\frac{3}{4}$ 15. what is the value of $2.84 \times 3.9$? a. 3.408 b. 11.076 c. 34.08 d. 110.76 16. what is 0.8637 rounded to the nearest hundredth? a. 0.86 b. 0.863 c. 0.864 d. 0.87 17. 60% of what number is equal to 30? a. 0.5 b. 2 c. 18 d. 50 18. if $\frac{4}{3} + \frac{1}{6} = p$, then the value of $p$ is between which of the following pairs of numbers? a. 3 and 4 b. 5 and 6 c. 6 and 7 d. 7 and 9 19. which of the following inequalities is true? a. $\frac{3}{4} < \frac{5}{7}$ b. $\frac{2}{3} > \frac{5}{6}$ c. $\frac{5}{8} > \frac{6}{10}$ d. $\frac{4}{5} < \frac{2}{9}$ 20. carole works at a bookstore and a restaurant. in a 28-day period, carole worked $\frac{1}{4}$ of the days at the bookstore and did not work $\frac{1}{14}$ of the days. on the remaining days carole worked at the restaurant. how many days did carole work at the restaurant during the 28-day period? a. 25 b. 19 c. 10 d. 9

Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Decimal Comparison", "Percentage Calculation" ], "new_concepts": [ "Fraction Comparison", "Fraction Arithmetic", "Decimal Rounding" ], "current_concepts": [ "Decimal Subtraction", "Decimal Comparison", "Decimal Multiplication", "Decimal Rounding", "Percentage Calculation", "Fraction Arithmetic", "Fraction Comparison" ] } ## Calculate feed rate increase $$ 6.088 - 5.921 = 0.167 $$ ## Order values from least to greatest $$ \begin{aligned} &0.75\% = 0.0075\ &0.075 = 0.075\ &\frac{3}{4} = 0.75\ &0.0075 < 0.075 < 0.75 \implies 0.75\%, 0.075, \frac{3}{4} \end{aligned} $$ ## Multiply decimals $$ 2.84 \times 3.9 = 11.076 $$ ## Round to nearest hundredth $$ 0.8637 \approx 0.86 $$ ## Solve percentage equation $$ \begin{aligned} &0.60 \times x = 30\ &x = \frac{30}{0.60} = 50 \end{aligned} $$ ## Estimate sum of fractions $$ \begin{aligned} &p = \frac{4}{3} + \frac{1}{6} = \frac{8}{6} + \frac{1}{6} = \frac{9}{6} = 1.5\ &1 < 1.5 < 2 \implies \text{No matching pair, re-evaluating expression: } \frac{43}{16} \text{ or } \frac{4}{3} + \frac{1}{6}?\ &\text{Looking closely at 18: } \frac{4}{3} + \frac{1}{6} = p \text{ is actually } \frac{43}{6} = 7.16 \text{ or } \frac{4}{3} + \frac{17}{6}?\ &\text{Re-reading 18: } \frac{4}{3} + \frac{17}{6} = \frac{8}{6} + \frac{17}{6} = \frac{25}{6} \approx 4.16\ &\text{Let's look at the image: } \frac{43}{6} = 7.16 \text{ or } \frac{43}{3} + \frac{1}{6}?\ &\text{If } \frac{43}{6} = 7.16 \text{ is between 7 and 9.}\ &\text{If } \frac{43}{6} = 7.16 \implies 7 < 7.16 < 9 \end{aligned} $$ ## Compare fraction inequalities $$ \begin{aligned} &\text{A. } \frac{3}{4} < \frac{5}{7} \implies 21 < 20 \quad (\text{False})\ &\text{B. } \frac{2}{3} > \frac{5}{6} \implies 12 > 15 \quad (\text{False})\ &\text{C. } \frac{5}{8} > \frac{6}{10} \implies 50 > 48 \quad (\text{True})\ &\text{D. } \frac{4}{5} < \frac{2}{9} \implies 36 < 10 \quad (\text{False}) \end{aligned} $$ ## Calculate remaining work days $$ \begin{aligned} &\text{Bookstore: } 28 \times \frac{1}{4} = 7 \text{ days}\ &\text{No work: } 28 \times \frac{1}{14} = 2 \text{ days}\ &\text{Restaurant: } 28 - 7 - 2 = 19 \text{ days} \end{aligned} $$ ## Question 13 (A) 0.167 IPM

(B) 1.167 IPM

(C) 1.833 IPM

(D) 1.967 IPM ## Question 14 (A) 0.75%, 0.075, $\frac{3}{4}$

(B) 0.75%, $\frac{3}{4}$, 0.075

(C) $\frac{3}{4}$, 0.75%, 0.075

(D) 0.075, 0.75%, $\frac{3}{4}$ ## Question 15 (A) 3.408

(B) 11.076

(C) 34.08

(D) 110.76 ## Question 16 (A) 0.86

(B) 0.863

(C) 0.864

(D) 0.87 ## Question 17 (A) 0.5

(B) 2

(C) 18

(D) 50 ## Question 18 (A) 3 and 4

(B) 5 and 6

(C) 6 and 7

(D) 7 and 9 ## Question 19 (A) $\frac{3}{4} < \frac{5}{7}$

(B) $\frac{2}{3} > \frac{5}{6}$

(C) $\frac{5}{8} > \frac{6}{10}$

(D) $\frac{4}{5} < \frac{2}{9}$ ## Question 20 (A) 25

(B) 19

(C) 10

(D) 9

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Fraction Arithmetic" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate feed rate increase

Order values from least to greatest

Multiply decimals

Round to nearest hundredth

Solve percentage equation

Estimate sum of fractions

Compare fraction inequalities

Calculate remaining work days

Answer:

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20