Mastering Fractions, Percentages, and Data Concepts

To convert the fraction 3/4 into a decimal, you divide the numerator (3) by the denominator (4). Performing the division, 3 divided by 4 equals 0.75. This means that 3/4 is equivalent to 0.75 in decimal form, representing three parts out of four total parts.

To convert a percentage to a fraction, you can express the percentage as a fraction over 100. For 20%, this is written as 20/100. Simplifying this fraction involves dividing both the numerator and denominator by their greatest common divisor, which is 20. Thus, 20 ÷ 20 = 1 and 100 ÷ 20 = 5, resulting in the simplified fraction 1/5.

To calculate the percentage profit, first determine the profit amount by subtracting the cost price from the selling price: $60 - $50 = $10. Next, divide the profit by the cost price: $10 ÷ $50 = 0.2. To express this as a percentage, multiply by 100: 0.2 × 100 = 20%. However, the percentage profit is calculated using the formula: (Profit / Cost Price) × 100. Thus, the profit percentage is 25%, as it represents the profit relative to the cost price.

To find the median, first arrange the data set in ascending order: 3, 5, 7, 9, 12. The median is the middle number in a sorted list. Since there are five numbers in this set, the median is the third number, which is 7. This value effectively divides the data into two equal halves, with two numbers on either side.

The mode of a set of numbers is the value that appears most frequently. In the given list (4, 1, 2, 4, 3, 4, 2), the number 4 appears three times, while all other numbers appear less frequently. Therefore, 4 is the mode, as it is the number with the highest frequency in the dataset.

To find the percentage of boys in the class, first determine the number of boys. With 30 students total and 12 girls, there are 30 - 12 = 18 boys. To find the percentage of boys, divide the number of boys by the total number of students and multiply by 100: (18 boys / 30 students) × 100 = 60%. Thus, 60% of the class consists of boys.

A standard six-sided die has six equally likely outcomes, numbered 1 through 6. Each number has an equal chance of being rolled. Since there is only one outcome that results in rolling a 3, the probability of this event is calculated as the number of favorable outcomes (1) divided by the total number of possible outcomes (6). Therefore, the probability of rolling a 3 is 1/6.

To find the probability of picking a red marble from a bag containing 10 marbles, where 4 are red, we use the formula for probability: the number of favorable outcomes divided by the total number of outcomes. Here, the favorable outcomes are the 4 red marbles, and the total outcomes are the 10 marbles. Thus, the probability is calculated as 4 (red marbles) divided by 10 (total marbles), resulting in 4/10, which can also be simplified to 2/5.

To determine the amount of sugar needed for 9 cups of flour using the 2:3 ratio, first, recognize that for every 2 parts of sugar, there are 3 parts of flour. This means for every 3 cups of flour, 2 cups of sugar are required. To find the sugar for 9 cups of flour, set up a proportion: (2 cups sugar / 3 cups flour) = (x cups sugar / 9 cups flour). Solving for x yields 6 cups of sugar, maintaining the specified ratio.

The range of a data set is calculated by subtracting the smallest value from the largest value. In this case, the smallest number is 5 and the largest number is 20. Therefore, the range is 20 - 5, which equals 15. This value represents the spread or dispersion of the data set, indicating how much the numbers vary from the minimum to the maximum.

To convert a decimal to a percentage, you multiply the decimal by 100. In this case, 0.6 multiplied by 100 equals 60. This means that 0.6 represents 60 out of 100, or 60%. Thus, 0.6 as a percentage is 60%.

To find the average speed of the car, divide the total distance traveled by the total time taken. In this case, the car travels 120 miles in 2 hours. By performing the calculation: 120 miles ÷ 2 hours = 60 miles per hour (mph). This means the car's average speed is 60 mph, which indicates how fast it was traveling over the entire distance.

In a standard deck of 52 playing cards, there are 4 suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards. Therefore, the probability of drawing a heart can be calculated by dividing the number of hearts (13) by the total number of cards (52). This simplifies to 13/52, which reduces to 1/4. Thus, the probability of drawing a heart from a standard deck is 1/4.

To find the sale price after a 25% discount on a $200 item, first calculate the discount amount. Multiply $200 by 25%, which equals $50. Then, subtract the discount from the original price: $200 - $50 = $150. Thus, the sale price of the item after applying the discount is $150.

In Euclidean geometry, the sum of the interior angles of a triangle is always 180 degrees. This property holds true regardless of the type of triangle, whether it is scalene, isosceles, or equilateral. The reasoning behind this can be visualized by drawing a line parallel to one side of the triangle and using alternate interior angles, which confirms that the angles add up to 180 degrees. This fundamental principle is a cornerstone of triangle geometry and is essential for various applications in mathematics and related fields.

To find the probability of picking a blue ball, first determine the total number of balls in the box, which is 5 red + 3 blue + 2 green = 10 balls. The probability of picking a blue ball is the number of blue balls divided by the total number of balls. There are 3 blue balls, so the probability is 3/10. This fraction represents the likelihood of selecting a blue ball from the box.

To find the mean of a set of numbers, you add all the numbers together and then divide by the total count of the numbers. In this case, the numbers are 2, 4, 6, 8, and 10. Adding these gives 2 + 4 + 6 + 8 + 10 = 30. There are 5 numbers in total. Dividing the sum by the count, 30 ÷ 5, results in 6. Therefore, the mean of the given numbers is 6.

To determine the amount of sugar needed for 15 parts of flour, we first establish the ratio of flour to sugar, which is 3:2. This means for every 3 parts of flour, there are 2 parts of sugar. To find the equivalent amount of sugar for 15 parts of flour, we can set up a proportion: if 3 parts of flour corresponds to 2 parts of sugar, then 15 parts of flour corresponds to \( \frac{2}{3} \times 15 = 10 \) parts of sugar. Thus, 10 parts of sugar are needed.

When flipping a fair coin, there are two equally likely outcomes: heads or tails. Since there are no other possibilities, the probability of getting heads is calculated by dividing the number of favorable outcomes (1 for heads) by the total number of outcomes (2: heads and tails). Thus, the probability is 1 (for heads) divided by 2 (total outcomes), resulting in a probability of 1/2.

To calculate the percentage score, divide the obtained score by the total possible score and then multiply by 100. In this case, the student scored 80 out of 100. Thus, the calculation is (80/100) × 100, which equals 80%. This indicates that the student achieved 80% of the total marks available on the test.