Edexcel Functional Skills Maths Level 2 Quiz Exam

To solve the expression 8 + 2 × (3 + 5) – 4 ÷ 2, we must follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). 1. First, we solve the expression inside the brackets: (3 + 5) = 8. 2. Next, we rewrite the expression with this value: 8 + 2 × 8 – 4 ÷ 2. 3. Now, we perform multiplication and division from left to right: – First, calculate 2 × 8 = 16. – Then, calculate 4 ÷ 2 = 2. 4. Now, substitute these values back into the expression: 8 + 16 – 2. 5. Finally, we perform the addition and subtraction from left to right: – First, 8 + 16 = 24. – Then, 24 – 2 = 22. Thus, the final answer is 22.

To determine the actual length represented by a measurement on a scale, we first need to understand the scale’s ratio. In this case, the scale indicates that 1 cm on the scale represents 5 meters in reality. If a measurement on the scale reads 7 cm, we can calculate the actual length by multiplying the scale measurement by the scale factor. Calculation: Actual Length = Scale Measurement × Scale Factor Actual Length = 7 cm × 5 m/cm = 35 m Thus, the actual length represented by the 7 cm measurement on the scale is 35 meters. This question tests the understanding of how to interpret scale measurements accurately. It is essential to grasp that scales are often used in maps, models, and diagrams to represent larger distances or sizes in a manageable format. The ability to convert scale measurements into real-world dimensions is a critical skill in various fields, including engineering, architecture, and geography. Misinterpreting scales can lead to significant errors in planning and execution, making it vital for students to practice these conversions.

To evaluate the validity of the argument presented, we first need to analyze the given mathematical statement: “If a number is even, then it is divisible by 2.” We can test this statement by considering an even number, such as 8. Dividing 8 by 2 gives us 4, which is an integer, confirming that 8 is indeed divisible by 2. Next, we can consider an odd number, such as 7. If we apply the same logic, dividing 7 by 2 results in 3.5, which is not an integer, thus confirming that 7 is not divisible by 2. This reinforces the original statement that only even numbers are divisible by 2. To further validate the argument, we can use a counterexample. If we take the number 10, which is even, dividing it by 2 gives us 5, an integer. This supports the claim. Therefore, the argument holds true as it consistently applies to all even numbers. In conclusion, the statement is valid as it accurately describes the relationship between even numbers and their divisibility by 2. The correct answer is that the argument is valid.

To solve the problem, we first need to determine the total cost of the items purchased. The customer buys 3 notebooks at £2.50 each and 5 pens at £1.20 each. Calculating the total cost of the notebooks: Total cost of notebooks = Number of notebooks × Price per notebook Total cost of notebooks = 3 × £2.50 = £7.50 Calculating the total cost of the pens: Total cost of pens = Number of pens × Price per pen Total cost of pens = 5 × £1.20 = £6.00 Now, we add the total costs of the notebooks and pens to find the overall total: Total cost = Total cost of notebooks + Total cost of pens Total cost = £7.50 + £6.00 = £13.50 The customer pays with a £20 note, so we need to calculate the change: Change = Amount paid – Total cost Change = £20.00 – £13.50 = £6.50 Thus, the change the customer receives is £6.50. In this scenario, the question tests the student’s ability to perform basic arithmetic operations, including multiplication and addition, as well as understanding how to calculate change from a transaction. It requires careful attention to detail in ensuring that each step is correctly calculated and that the final answer reflects the total amount spent and the change given. This type of problem is common in real-life situations, making it relevant for functional skills in mathematics.

To find the area of a rectangle, we use the formula: Area = Length × Width. In this scenario, the length of the rectangle is given as 12 meters and the width is 8 meters. Calculating the area: Area = 12 m × 8 m = 96 m². The area of the rectangle is 96 square meters. This calculation is straightforward, but understanding the application of the formula in practical contexts is crucial. For instance, if a gardener wants to plant grass in a rectangular garden that measures 12 meters in length and 8 meters in width, knowing the area helps them determine how much grass seed is needed. If the seed covers 1 m², they would need 96 packets of seed. This example illustrates the importance of using formulas not just for calculations but for making informed decisions in real-world scenarios. Additionally, it emphasizes the need for accuracy in measurements and calculations, as any error could lead to insufficient or excessive resources being used.

To solve the problem, we first need to calculate the total cost of the items purchased. The customer buys 3 notebooks at £2.50 each and 5 pens at £1.20 each. Calculating the total cost of the notebooks: Total cost of notebooks = Number of notebooks × Price per notebook Total cost of notebooks = 3 × £2.50 = £7.50 Calculating the total cost of the pens: Total cost of pens = Number of pens × Price per pen Total cost of pens = 5 × £1.20 = £6.00 Now, we add the total costs of the notebooks and pens to find the overall total cost: Total cost = Total cost of notebooks + Total cost of pens Total cost = £7.50 + £6.00 = £13.50 The customer pays with a £20 note, so we need to calculate the change: Change = Amount paid – Total cost Change = £20.00 – £13.50 = £6.50 Therefore, the change the customer receives is £6.50.

To find the total number of items, we need to add the quantities from each category. The quantities are as follows: 245, 378, and 412. First, we add 245 and 378: 245 + 378 = 623 Next, we add the result to 412: 623 + 412 = 1035 Thus, the total number of items is 1035. This question tests the student’s ability to perform addition with larger numbers and to understand the concept of combining quantities. In real-world scenarios, such as inventory management or budgeting, being able to accurately sum multiple figures is crucial. The ability to handle numbers up to 1,000,000 is essential in various contexts, including finance, logistics, and data analysis. This question also encourages students to check their work and ensure that they are correctly adding each step, as mistakes can easily occur when dealing with larger numbers.

To find the total number of students who prefer each type of fruit, we first need to analyze the data presented in the table. Let’s assume the table shows the following preferences for fruits among 100 students: – Apples: 30 students – Bananas: 25 students – Oranges: 20 students – Grapes: 25 students To calculate the percentage of students who prefer each fruit, we use the formula: Percentage = (Number of students preferring the fruit / Total number of students) × 100 Calculating for each fruit: 1. Apples: (30 / 100) × 100 = 30% 2. Bananas: (25 / 100) × 100 = 25% 3. Oranges: (20 / 100) × 100 = 20% 4. Grapes: (25 / 100) × 100 = 25% Now, if we want to present this data in a pie chart, we would represent each fruit’s percentage as a sector of the pie. The total of all percentages should equal 100%, which confirms our calculations are correct. The question asks for the percentage of students who prefer apples. From our calculations, we found that 30 students prefer apples, which corresponds to 30% of the total student population surveyed. This understanding of how to collect, organize, and present data is crucial in functional skills mathematics, as it allows for effective communication of information through visual means like charts and tables.

To solve the problem, we need to evaluate the expression -5 + 3 – 8. We start by adding -5 and 3. When adding a negative number to a positive number, we subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value. Here, the absolute values are 5 and 3. Thus, we calculate: -5 + 3 = -2 Next, we take this result and subtract 8: -2 – 8 = -10 So, the final answer is -10. This question tests the understanding of negative numbers and their operations. It requires the student to apply the rules of addition and subtraction involving negative numbers, which can often be confusing. The key is to remember that subtracting a positive number from a negative number results in a more negative number. This is a common area of misunderstanding, as students may mistakenly think that subtracting a larger number from a smaller one will yield a positive result. Understanding how to navigate through negative numbers is crucial in various real-life applications, such as financial calculations, temperature changes, and other scenarios where values can drop below zero.

To find the total cost of the items purchased, we first need to calculate the cost of each item. The first item costs £15.75, the second item costs £22.50, and the third item costs £9.99. We will add these amounts together to find the total. Total cost = Cost of item 1 + Cost of item 2 + Cost of item 3 Total cost = £15.75 + £22.50 + £9.99 Total cost = £48.24 Now, if the customer has a discount of 10% on the total cost, we need to calculate the discount amount and then subtract it from the total cost. Discount amount = Total cost × Discount rate Discount amount = £48.24 × 0.10 Discount amount = £4.824 Now, we will round the discount amount to two decimal places, which gives us £4.82. Finally, we subtract the discount from the total cost to find the final amount to be paid. Final amount = Total cost – Discount amount Final amount = £48.24 – £4.82 Final amount = £43.42 Thus, the final amount the customer needs to pay after applying the discount is £43.42.

To find the total cost of the items purchased, we first need to calculate the cost of each item and then sum them up. The prices of the items are as follows: a notebook costs £2.50, a pen costs £1.20, and a pack of markers costs £3.80. Calculating the total cost: Cost of notebook = £2.50 Cost of pen = £1.20 Cost of markers = £3.80 Total cost = Cost of notebook + Cost of pen + Cost of markers Total cost = £2.50 + £1.20 + £3.80 Total cost = £7.50 Now, if the student pays with a £10 note, we need to determine how much change they will receive. Change = Amount given – Total cost Change = £10.00 – £7.50 Change = £2.50 Thus, the total change the student will receive after their purchase is £2.50.

To find the volume of a cylinder, we use the formula: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. In this scenario, the cylinder has a radius of 3 cm and a height of 10 cm. First, we calculate the area of the base: \[ A = \pi r^2 = \pi (3^2) = \pi (9) = 9\pi \] Next, we multiply the area of the base by the height to find the volume: \[ V = 9\pi \times 10 = 90\pi \] Using the approximation \( \pi \approx 3.14 \): \[ V \approx 90 \times 3.14 = 282.6 \text{ cm}^3 \] Thus, the volume of the cylinder is approximately 282.6 cm³. In this question, we are assessing the understanding of the volume calculation of a cylinder, which is a fundamental concept in geometry. The volume represents the amount of space inside the cylinder, and knowing how to calculate it is essential for various real-world applications, such as determining the capacity of containers. The options provided challenge the student to think critically about the calculations and the application of the formula. The incorrect options are designed to reflect common mistakes, such as miscalculating the radius or height, or confusing the formula with that of another shape.

To find the probability of drawing a red card from a standard deck of 52 playing cards, we first need to identify the total number of favorable outcomes and the total number of possible outcomes. A standard deck contains 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades). The probability (P) of an event is calculated using the formula: \[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] In this case, the number of favorable outcomes (red cards) is 26, and the total number of possible outcomes (total cards) is 52. Therefore, the probability of drawing a red card is: \[ P(\text{Red card}) = \frac{26}{52} = \frac{1}{2} \] Thus, the probability of drawing a red card from a standard deck of cards is 0.5 or 50%.

To find the total cost of the materials needed for the project, we first need to calculate the cost of each type of material. The project requires 5 rolls of fabric at £12 each, 3 packs of paint at £8 each, and 2 boxes of nails at £5 each. Calculating the total cost: – Cost of fabric: 5 rolls × £12/roll = £60 – Cost of paint: 3 packs × £8/pack = £24 – Cost of nails: 2 boxes × £5/box = £10 Now, we add these costs together to find the total: Total cost = Cost of fabric + Cost of paint + Cost of nails Total cost = £60 + £24 + £10 = £94 Therefore, the total cost of materials needed for the project is £94.

To solve the expression 8 + 2 × (3 + 5) – 4 ÷ 2, we must follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). 1. Start with the brackets: (3 + 5) = 8. 2. Substitute back into the expression: 8 + 2 × 8 – 4 ÷ 2. 3. Next, perform the multiplication and division from left to right: 2 × 8 = 16, 4 ÷ 2 = 2. 4. Now, substitute these values back into the expression: 8 + 16 – 2. 5. Finally, perform the addition and subtraction from left to right: 8 + 16 = 24, 24 – 2 = 22. Thus, the final answer is 22. This question tests the understanding of the order of operations, which is crucial in mathematics to ensure that calculations are performed correctly. Many students may struggle with this concept, especially when multiple operations are involved. It is essential to remember that operations within brackets must be completed first, followed by multiplication and division, and finally addition and subtraction. This systematic approach prevents errors and ensures accurate results. Misunderstanding the order can lead to incorrect answers, highlighting the importance of mastering this fundamental principle in mathematics.

To determine the total cost of the items purchased, we first need to identify the assumptions made regarding the prices and quantities. Let’s assume the following: – The price of item A is $p_A = 15$. – The price of item B is $p_B = 10$. – The quantity of item A purchased is $q_A = 3$. – The quantity of item B purchased is $q_B = 5$. The total cost $C$ can be calculated using the formula: $$ C = (p_A \cdot q_A) + (p_B \cdot q_B) $$ Substituting the values into the equation: $$ C = (15 \cdot 3) + (10 \cdot 5) $$ Calculating each term: $$ C = 45 + 50 = 95 $$ Thus, the total cost is $C = 95$. Now, let’s analyze the assumptions and biases in this scenario. The assumption here is that the prices of the items remain constant and that there are no discounts or additional costs (like taxes or shipping). If we were to assume that there is a discount of 10% on item A, the new price would be: $$ p_A’ = p_A – (0.1 \cdot p_A) = 15 – 1.5 = 13.5 $$ Recalculating the total cost with the new price: $$ C’ = (p_A’ \cdot q_A) + (p_B \cdot q_B) = (13.5 \cdot 3) + (10 \cdot 5) = 40.5 + 50 = 90.5 $$ This shows how assumptions about pricing can significantly affect the total cost. Therefore, it is crucial to identify and evaluate these assumptions when solving problems.

To determine the coordinates of the image of a triangle after a reflection across the line y = x, we need to swap the x and y coordinates of each vertex of the triangle. The original vertices of the triangle are A(2, 3), B(4, 5), and C(6, 1). Reflecting point A(2, 3): – The new coordinates will be A'(3, 2). Reflecting point B(4, 5): – The new coordinates will be B'(5, 4). Reflecting point C(6, 1): – The new coordinates will be C'(1, 6). Thus, the coordinates of the reflected triangle A’B’C’ are (3, 2), (5, 4), and (1, 6). Now, to find the perimeter of triangle A’B’C’, we can use the distance formula to calculate the lengths of the sides. The distance formula is given by: \[ d = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2} \] Calculating the lengths of the sides: 1. Length of A’B’: \[ d_{A’B’} = \sqrt{(5 – 3)^2 + (4 – 2)^2} = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \] 2. Length of B’C’: \[ d_{B’C’} = \sqrt{(1 – 5)^2 + (6 – 4)^2} = \sqrt{(-4)^2 + (2)^2} = \sqrt{16 + 4} = \sqrt{20} = 2\sqrt{5} \] 3. Length of C’A’: \[ d_{C’A’} = \sqrt{(3 – 1)^2 + (2 – 6)^2} = \sqrt{(2)^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} = 2\sqrt{5} \] Now, adding these lengths together to find the perimeter: \[ \text{Perimeter} = 2\sqrt{2} + 2\sqrt{5} + 2\sqrt{5} = 2\sqrt{2} + 4\sqrt{5} \] Thus, the perimeter of triangle A’B’C’ is \( 2\sqrt{2} + 4\sqrt{5} \).

To compare the numbers 3.75, 3.8, 3.7, and 3.75, we first convert them into a consistent format. The decimal numbers can be compared directly since they are all in decimal form. – 3.75 is equal to 3.75. – 3.8 can be expressed as 3.80 for easier comparison. – 3.7 can be expressed as 3.70 for easier comparison. Now we can compare: – 3.75 (which is the same as 3.75) – 3.80 (which is greater than 3.75) – 3.70 (which is less than 3.75) Ordering these from smallest to largest gives us: 3.70, 3.75, 3.75, 3.80. Thus, the largest number in this set is 3.80. Therefore, the correct answer is 3.80.

To convert the improper fraction \( \frac{17}{5} \) into a mixed number, we start by dividing the numerator (17) by the denominator (5). Performing the division, we find that \( 17 \div 5 = 3 \) with a remainder of 2. This means that 5 fits into 17 three times completely, which gives us the whole number part of the mixed number. The remainder (2) becomes the numerator of the fractional part, while the denominator remains the same (5). Therefore, we can express \( \frac{17}{5} \) as \( 3 \frac{2}{5} \). In summary, the improper fraction \( \frac{17}{5} \) converts to the mixed number \( 3 \frac{2}{5} \). This process illustrates the relationship between improper fractions and mixed numbers, emphasizing the importance of division and understanding remainders in the conversion process. It also highlights how mixed numbers can represent the same value as improper fractions but in a more intuitive way, particularly for those who may find whole numbers easier to visualize. Understanding this conversion is crucial for various applications in mathematics, including measurements, cooking, and financial calculations, where mixed numbers are often more practical.

To find 25% of £240, we first convert the percentage into a decimal. This is done by dividing the percentage by 100: 25% = 25/100 = 0.25. Next, we multiply this decimal by the total amount (£240): 0.25 × £240 = £60. Thus, 25% of £240 is £60. Now, to understand the reasoning behind this calculation, it’s important to recognize that percentages represent a part of a whole. In this case, we are determining what one-quarter (25%) of £240 amounts to. This is a common calculation in financial contexts, such as discounts, tax calculations, or profit sharing. Understanding how to manipulate percentages is crucial for effective budgeting and financial planning. By converting the percentage to a decimal, we simplify the multiplication process, allowing for a straightforward calculation. This skill is essential for functional mathematics, as it enables individuals to make informed decisions based on numerical data.

To estimate the total cost of 15 items priced at £4.79 each, we first round the price to the nearest whole number. Rounding £4.79 gives us approximately £5.00. Next, we multiply the rounded price by the number of items: 15 items × £5.00/item = £75.00. Now, let’s calculate the exact total cost for comparison. The exact calculation is: 15 × £4.79 = £71.85. Now, we can see that our estimation of £75.00 is close to the exact total of £71.85. The purpose of estimation is to provide a quick way to assess the total without needing to perform precise calculations, which can be useful in budgeting or when making quick decisions. In this case, the estimation method allows us to quickly gauge that the total cost is around £75.00, which is useful for determining if we have enough funds available. However, it is important to note that while estimation is a valuable tool, it is also essential to check the exact figures when accuracy is required, especially in financial contexts.

To determine the coordinates of the image of a triangle after a reflection across the line y = x, we need to switch the x and y coordinates of each vertex of the triangle. The original triangle has vertices at A(2, 3), B(4, 5), and C(6, 1). For point A(2, 3): – After reflection, the new coordinates will be A'(3, 2). For point B(4, 5): – After reflection, the new coordinates will be B'(5, 4). For point C(6, 1): – After reflection, the new coordinates will be C'(1, 6). Now, we can summarize the new coordinates of the triangle after reflection: – A’ = (3, 2) – B’ = (5, 4) – C’ = (1, 6) To find the area of the new triangle formed by these points, we can use the formula for the area of a triangle given by vertices (x1, y1), (x2, y2), (x3, y3): Area = 0.5 * |x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)| Substituting the coordinates of A’, B’, and C’: Area = 0.5 * |3(4 – 6) + 5(6 – 2) + 1(2 – 4)| = 0.5 * |3(-2) + 5(4) + 1(-2)| = 0.5 * |-6 + 20 – 2| = 0.5 * |12| = 6 Thus, the area of the triangle after reflection is 6 square units.

To find the probability of drawing a red card from a standard deck of 52 playing cards, we first need to identify how many red cards are in the deck. A standard deck contains 26 red cards (13 hearts and 13 diamonds). The probability (P) of an event is calculated using the formula: P(Event) = Number of favorable outcomes / Total number of outcomes In this case, the number of favorable outcomes (red cards) is 26, and the total number of outcomes (total cards) is 52. Therefore, the calculation is: P(Red Card) = 26 / 52 = 1/2 This fraction can also be expressed as a decimal, which is 0.5, or as a percentage, which is 50%. Thus, the probability of drawing a red card from a standard deck of cards is 1/2. Understanding probability is crucial in various real-life situations, such as games, risk assessment, and decision-making processes. It helps individuals make informed choices based on the likelihood of different outcomes. In this scenario, recognizing that half of the cards are red allows players to strategize effectively when playing card games or making bets.

To find the total number of items, we need to add the quantities of each type of item together. The quantities given are: – Type A: 245,000 – Type B: 378,000 – Type C: 156,000 Now, we perform the addition step-by-step: 1. First, add Type A and Type B: 245,000 + 378,000 = 623,000 2. Next, add the result to Type C: 623,000 + 156,000 = 779,000 Thus, the total number of items is 779,000. This question tests the understanding of large numbers and the ability to perform addition with them. It is essential to be comfortable with handling numbers in the hundreds of thousands and to ensure accuracy in calculations. In real-world scenarios, such as inventory management or financial reporting, being able to quickly and accurately add large quantities is crucial. This question also emphasizes the importance of checking each step in the calculation process to avoid errors, which is a valuable skill in both academic and professional settings.

To find the total cost of the items purchased, we first need to calculate the cost of each item. The first item costs £15.75, the second item costs £22.50, and the third item costs £9.99. We will add these amounts together to find the total. Total Cost = Cost of Item 1 + Cost of Item 2 + Cost of Item 3 Total Cost = £15.75 + £22.50 + £9.99 Total Cost = £48.24 Now, if the customer has a discount of 10% on the total cost, we need to calculate the discount amount and then subtract it from the total cost. Discount Amount = Total Cost × Discount Rate Discount Amount = £48.24 × 0.10 Discount Amount = £4.824 Now, we will round the discount amount to two decimal places, which gives us £4.82. Final Amount to Pay = Total Cost – Discount Amount Final Amount to Pay = £48.24 – £4.82 Final Amount to Pay = £43.42 Thus, the final amount the customer needs to pay after applying the discount is £43.42.

To interpret the pie chart, we first need to understand the total amount represented by the chart. Let’s assume the pie chart represents the distribution of a budget of £8000 among four categories: A, B, C, and D. If the angles of the pie chart for categories A, B, C, and D are 90°, 120°, 150°, and 180° respectively, we can calculate the budget allocation for each category. The total angle in a pie chart is 360°. Therefore, the fraction of the budget for each category can be calculated as follows: – Category A: (90° / 360°) * £8000 = £2000 – Category B: (120° / 360°) * £8000 = £2666.67 – Category C: (150° / 360°) * £8000 = £3333.33 – Category D: (180° / 360°) * £8000 = £4000 Now, if we want to find out which category has the highest budget allocation, we can see that Category D has the highest allocation of £4000. Thus, the answer to the question regarding which category has the largest budget allocation is £4000.

To find the probability of drawing a red card from a standard deck of 52 playing cards, we first need to identify the total number of favorable outcomes and the total number of possible outcomes. A standard deck contains 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades). The probability (P) of an event is calculated using the formula: P(Event) = Number of favorable outcomes / Total number of possible outcomes In this case: Number of favorable outcomes (red cards) = 26 Total number of possible outcomes (total cards) = 52 Thus, the probability of drawing a red card is: P(Red Card) = 26 / 52 = 1/2 = 0.5 Therefore, the probability of drawing a red card from a standard deck of cards is 0.5. This question tests the understanding of basic probability concepts, specifically how to calculate the likelihood of a single event occurring. It requires students to recognize the total number of outcomes and the specific outcomes that meet the criteria of the event in question. Understanding this concept is crucial for more complex probability problems, as it lays the foundation for calculating probabilities in various scenarios, including those involving multiple events or conditional probabilities.

To solve the problem, we first need to calculate the total cost of the items purchased. The customer buys 3 notebooks at £2.50 each and 5 pens at £1.20 each. Calculating the total cost of the notebooks: 3 notebooks × £2.50 = £7.50 Calculating the total cost of the pens: 5 pens × £1.20 = £6.00 Now, we add the total costs of the notebooks and pens together: Total cost = Cost of notebooks + Cost of pens Total cost = £7.50 + £6.00 = £13.50 Next, the customer pays with a £20 note. To find out how much change the customer will receive, we subtract the total cost from the amount paid: Change = Amount paid – Total cost Change = £20.00 – £13.50 = £6.50 Thus, the customer will receive £6.50 in change. This problem tests the understanding of basic operations involving multiplication and addition, as well as the ability to perform subtraction to find change. It requires careful attention to detail in calculating the costs of multiple items and understanding the concept of change from a transaction. The ability to break down the problem into manageable parts is crucial for arriving at the correct answer.

To determine the total cost of the items purchased, we first need to identify the individual costs and any assumptions made regarding discounts. Let’s assume the following costs for the items: – Item A: $20 – Item B: $15 – Item C: $10 If a discount of 10% is applied to the total cost, we first calculate the total cost without the discount: $$ \text{Total Cost} = \text{Cost of Item A} + \text{Cost of Item B} + \text{Cost of Item C} = 20 + 15 + 10 = 45 $$ Next, we apply the 10% discount: $$ \text{Discount Amount} = 0.10 \times \text{Total Cost} = 0.10 \times 45 = 4.5 $$ Now, we subtract the discount from the total cost: $$ \text{Final Cost} = \text{Total Cost} – \text{Discount Amount} = 45 – 4.5 = 40.5 $$ Thus, the final cost after applying the discount is $40.50. In this scenario, the assumption made is that the discount applies to the total cost of all items combined. This assumption is crucial because if the discount were to apply to individual items instead, the final cost would differ. For example, if we applied the discount to each item separately, the calculations would yield different results. Therefore, understanding the assumptions behind the calculations is essential for accurate problem-solving in real-world scenarios.

To find the probability of drawing a red card from a standard deck of 52 playing cards, we first need to identify the total number of favorable outcomes and the total number of possible outcomes. A standard deck contains 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades). The probability (P) of an event is calculated using the formula: P(Event) = Number of favorable outcomes / Total number of possible outcomes In this case: Number of favorable outcomes (red cards) = 26 Total number of possible outcomes (total cards) = 52 Thus, the probability of drawing a red card is: P(Red Card) = 26 / 52 = 1/2 = 0.5 Therefore, the probability of drawing a red card from a standard deck of cards is 0.5. This question tests the understanding of basic probability concepts, specifically how to calculate the likelihood of a single event occurring. It requires students to recognize the total number of outcomes and the specific outcomes that are favorable to the event in question. Understanding this concept is crucial for more complex probability problems, as it lays the foundation for calculating probabilities in various scenarios, including those involving multiple events or conditional probabilities.