Translate the phrase 'Five less than twice the number' into a mathematical expression.
Your Answer: Option(s)
Correct Answer: Option(s) B
Rationale
2x-5 is the mathematical expression that translates the phrase 'Five less than twice the number'.
In mathematics, the phrase 'Five less than twice the number' means we first multiply a number by two (twice the number) and then subtract five from the result. This operation can be represented as 2x-5, where x stands for the number.
A) 5x-2
This expression represents 'Two less than five times the number', not 'Five less than twice the number'. In this expression, the number is first multiplied by five (five times the number) and then two is subtracted from it, which is different from the original phrase.
B) 2x-5
The mathematical expression 2x-5 translates the phrase 'Five less than twice the number'. The term 'twice the number' is represented by '2x' and 'Five less than' is represented by '-5'. The expression is read as 'two times x, minus five', which matches the phrase.
C) 2-5x
This expression represents 'Two less than five times the number', not 'Five less than twice the number'. In this expression, the number is first multiplied by five (five times the number), and then subtracted from two, changing the order of operations from the original phrase.
D) 5-2x
This expression represents 'Five less than two times the number', not 'Five less than twice the number'. In this expression, two is multiplied by the number (two times the number) and then subtracted from five, which again changes the order of operations from the original phrase.
Conclusion
In the given phrase 'Five less than twice the number', 'twice the number' translates to '2x' and 'Five less than' translates to '-5'. Therefore, the correct mathematical expression is 2x-5. All other expressions either misinterpret the phrase or change the order of operations.
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Question 2
Which of the following expressions has the greatest value?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
A) 34 + 96 has the greatest value.
The sum of 34 and 96 is 130, which is greater than the other choices provided.
A) 34 + 96
The sum of 34 and 96 is 130. This is the largest value amongst the options provided.
B) 0.372
0.372 is a decimal number and less than 1, making it much smaller than the sum of 34 and 96.
C) 03-Aug
03-Aug seems to be a date, and as such, it does not have a numerical value that can be compared to the other choices.
D) 37%
37% is equivalent to 0.37 when converted to decimal form, which is significantly less than 130, the sum of 34 and 96.
Conclusion
The comparison of the values of the given expressions shows that the sum of 34 and 96, which is 130, is the greatest value. The other options either have much smaller numerical values (0.372 and 37%), or do not represent a numerical value that can be compared to the others (03-Aug). Therefore, A) 34 + 96 is the correct answer.
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Question 3
A farmer grows apple, orange, lemon, banana, and pear trees. The number of trees planted this year is shown in the table above. Which of the following would best display the data?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
A bar graph would best display the data.
A bar graph is a common tool used to represent categorical data. The number of trees for each fruit type (apple, orange, lemon, banana, and pear) represents categorical data, making a bar graph the most suitable choice.
A) Bar graph
A bar graph is typically used to compare different categories. In this case, the categories would be the types of fruit trees (apple, orange, lemon, banana, and pear) and the variable being measured would be the number of trees. Each bar would represent a category and the height of the bar would correspond to the number of trees.
B) Scatter plot
A scatter plot is used to display data along two dimensions and is typically used to show the relationship between two quantitative variables. In this context, there is not a second quantitative variable to be compared with the number of trees, making a scatter plot inappropriate for displaying this data.
C) Stem-and-leaf plot
Stem-and-leaf plots are used to display quantitative data and are particularly useful when the distribution of data is of interest. However, in this instance, the data is categorical (types of trees) rather than quantitative. Therefore, a stem-and-leaf plot would not be the best choice for displaying this data.
D) Line graph
Line graphs are used to show how a variable changes over time. Since the data provided does not involve a time component, a line graph would not be the best choice for displaying this data.
Conclusion
Given that the data involves different categories (types of fruit trees) and a variable to be measured (number of trees), a bar graph is the most appropriate choice. A bar graph will clearly show the number of each type of tree the farmer has planted. Other graph types like scatter plots, stem-and-leaf plots, and line graphs are not suitable as they are designed to display different types of data or relationships that are not applicable in this situation.
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Question 4
A worker earns $8000.00 per week before any tax deductions. The following taxes are deducted each week: $83.00 federal income tax, $38.00 state income tax, and $79.00 social security tax. How much will the worker make in 4 weeks after taxes are deducted?
Your Answer: Option(s)
Correct Answer: Option(s) A
Rationale
The worker will make $31,200.00 in 4 weeks after taxes are deducted.
The worker's weekly earnings after tax deductions are calculated by subtracting the total tax amount ($83.00 + $38.00 + $79.00 = $200.00) from the gross weekly earnings ($8000.00). This results in net weekly earnings of $7800.00. Multiplying this by 4 gives the total earnings after 4 weeks, which is $31,200.00.
A) $31,200.00
This is the correct answer. After deducting the total tax amount of $200.00 from the gross weekly earnings of $8000.00, the worker earns $7800.00 per week. Over 4 weeks, this amounts to $31,200.00.
B) $29,200.00
This answer incorrectly assumes that the worker's weekly earnings after tax deductions are $7300.00 ($8000.00 - $700.00). However, the total tax amount is $200.00, not $700.00, resulting in weekly earnings of $7800.00, not $7300.00.
C) $26,000.00
This answer incorrectly assumes that the worker's weekly earnings after tax deductions are $6500.00 ($8000.00 - $1500.00). However, the total tax amount is $200.00, not $1500.00, resulting in weekly earnings of $7800.00, not $6500.00.
D) $24,000.00
This answer incorrectly assumes that the worker's weekly earnings after tax deductions are $6000.00 ($8000.00 - $2000.00). However, the total tax amount is $200.00, not $2000.00, resulting in weekly earnings of $7800.00, not $6000.00.
Conclusion
In order to determine the worker's earnings after 4 weeks, it is necessary to subtract the total tax deductions from the gross weekly earnings and then multiply the result by 4. This gives the correct answer of $31,200.00, not $29,200.00, $26,000.00, or $24,000.00. The other options incorrectly calculate the weekly tax deductions, resulting in lower estimated earnings.
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Question 5
If a box of 35 syringes costs $560.00, what is the cost for two syringes?
Your Answer: Option(s)
Correct Answer: Option(s) D
Rationale
The cost for two syringes is $32.00.
To find the cost of two syringes, we first need to determine the price of a single syringe. We do this by dividing the total cost of the box ($560) by the number of syringes in the box (35). This gives us a cost of $16 per syringe. Then, we multiply this by 2 to get the cost for two syringes, which is $32.
A) $8.00
This choice is incorrect because it does not properly calculate the cost of two syringes. To get this answer, one might incorrectly assume that each syringe costs $4. However, we determined that each syringe actually costs $16, so two syringes would cost $32, not $8.
B) $16.00
This choice is incorrect because it represents the cost of a single syringe, not two. We determined that each syringe costs $16, so two syringes would cost $32.
C) $15.00
This choice is incorrect because it does not align with any correct calculations from the given information. Each syringe costs $16, so the cost of two syringes would be $32, not $15.
D) $32.00
This is the correct answer. We determined that each syringe costs $16, so the cost of two syringes would be $32.
Conclusion
Understanding how to calculate the cost per item given a total cost and quantity is a fundamental concept in mathematics. In this case, by dividing the total cost of the box by the number of syringes, we find the cost per syringe. Multiplying this by the desired quantity (two syringes) gives us the correct answer of $32. It's essential to ensure the correct calculation method is used to avoid incorrect answers like $8, $16, or $15.
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