Nokea
What is a factor?
- A. A number that you multiply to get another number
- B. A number that divides evenly into another number
- C. A number that can be both multiplied and divided by another number
- D. A number that is greater than 1
Correct Answer: A
Rationale: A factor is a number that can be multiplied by another number to produce a third number. When you multiply factors together, you get the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because these numbers can be multiplied in pairs to give the product 12. Choice B is incorrect as it describes a divisor. Choice C is incorrect because factors are only multiplied, not divided. Choice D is incorrect because factors can be any number, not just those greater than 1.
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If a box of 55 syringes costs $660.00, what is the cost of four syringes?
- A. $51.00
- B. $26.00
- C. $32.00
- D. $48.00
Correct Answer: D
Rationale: To find the cost of one syringe, divide the total cost by the number of syringes: $660.00 · 55 = $12. Therefore, the cost of four syringes is 4 x $12 = $48. Choices A, B, and C are incorrect because they do not correctly calculate the cost per syringe or the total cost of four syringes.
The scatter plot below shows the relationship between the students' exam scores and their heights. Which type of correlation is depicted in the scatter plot?
- A. Positive
- B. Positive and Negative
- C. Negative
- D. No correlation
Correct Answer: D
Rationale: The scatter plot illustrates the relationship between students' exam scores and heights. There is no correlation between these variables, as height is not expected to have a direct impact on exam scores. Therefore, choice D, 'No correlation,' is the correct answer. Choices A, 'Positive,' and C, 'Negative,' are incorrect because the scatter plot does not indicate a positive or negative correlation between exam scores and heights. Choice B, 'Positive and Negative,' is also incorrect because the scatter plot does not exhibit both positive and negative correlations simultaneously.
Which of the following relationships represents no correlation between two variables?
- A. As a student's class attendance decreases, the student's overall grade remains the same
- B. As the number of hours a person exercises decreases, the weight of that person increases
- C. As the number of miles driven increases, the amount of gasoline in the tank decreases
- D. As the amount of water a plant receives increases, the growth rate of the plant increases
Correct Answer: A
Rationale: Choice A represents no correlation between two variables as it states that as a student's class attendance decreases, the student's overall grade remains the same. This scenario shows no relationship between class attendance and grade. In contrast, choices B, C, and D show clear correlations between the variables mentioned. Choice B indicates a negative correlation between exercise hours and weight gain, choice C indicates a negative correlation between miles driven and gasoline in the tank, and choice D indicates a positive correlation between water intake and plant growth rate, making them all examples of correlated relationships.
As a company's stocks increase, production, sales, and investments also increase. Which of the following is the independent variable?
- A. Sales
- B. Stocks
- C. Production
- D. Investments
Correct Answer: B
Rationale: The independent variable in this scenario is 'Stocks.' An independent variable is the one that is manipulated or controlled by the experimenter. In this case, stocks are the factor that is changing and influencing the other variables - production, sales, and investments. Production, sales, and investments are dependent on the changes in stocks; hence, they are the dependent variables. While production, sales, and investments may increase as a result of changes in stocks, the stocks themselves are the driving force behind these changes, making them the independent variable.
A recipe calls for 2.5 teaspoons of vanilla. 1 teaspoon equals approximately 4.93 mL. Which of the following is the correct amount of vanilla in mL?
- A. 5.33 mL
- B. 7.43 mL
- C. 12.325 mL
- D. 0.507 mL
Correct Answer: C
Rationale: To convert 2.5 teaspoons of vanilla to milliliters, you multiply by the conversion factor: 2.5 teaspoons * 4.93 mL = 12.325 mL. Therefore, the correct amount of vanilla in milliliters is 12.325 mL. Choice A (5.33 mL) is incorrect because it does not account for the correct conversion factor. Choice B (7.43 mL) is incorrect as it also does not use the accurate conversion factor. Choice D (0.507 mL) is incorrect as it represents a miscalculation of the conversion.