curiouskids

Due: Aug 8th

Questions

Comprehension and statistics

  1. Solve for x: x + 3.5 = 10.2
  2. Solve for x: 2.5x = 15
  3. Write an equation to represent the relationship: the cost of p pounds of apples at $2.5 per pound.
  4. Find the area of a rectangle with length 5 units and width 3 units.
  5. Find the surface area of a cube with side length 4 units.
  6. Find the volume of a cylinder with radius 3 units and height 7 units.
  7. On a number line, position the number -2.5 and its opposite.
  8. Which is greater: -2/3 or -3/5?
  9. Find the absolute value of -45.
  10. Represent the solution of the inequality x + 3 < 7 on a number line.
  11. Is the question, “How many siblings do you have?” a statistical question? Explain.
  12. A set of five test scores is: 85, 87, 89, 91, 93. Find the mean and the median of the set.
  13. Find the interquartile range of the data set 5, 7, 9, 12, 15, 18, 20.
  14. The following data set shows the number of pages in seven books: 120, 150, 170, 180, 190, 200, 230. Find the mean absolute deviation.
  15. Describe the distribution of the following data set: 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7.

Solutions

  1. To solve for x in x + 3.5 = 10.2, you subtract 3.5 from both sides of the equation, getting x = 10.2 - 3.5 = 6.7.

  2. To solve for x in 2.5x = 15, you divide both sides of the equation by 2.5, getting x = 15 / 2.5 = 6.

  3. An equation to represent the relationship could be C = 2.5p, where C is the cost and p is the number of pounds of apples.

  4. The area of a rectangle is given by Area = length * width = 5 units * 3 units = 15 square units.

  5. The surface area of a cube is given by Surface Area = 6 * (side length)^2 = 6 * (4 units)^2 = 96 square units.

  6. The volume of a cylinder is given by Volume = π * (radius)^2 * height = π * (3 units)^2 * 7 units = 63π cubic units.

  7. On a number line, -2.5 would be placed to the left of 0 and its opposite, 2.5, would be placed to the right of 0.

  8. To determine which is greater between -2/3 and -3/5, you can compare them as fractions or as decimal values. -2/3 is approximately -0.67 and -3/5 is -0.60. Therefore, -3/5 > -2/3.

  9. The absolute value of -45 is 45.

  10. To represent the solution of the inequality x + 3 < 7 on a number line, you would first solve for x to get x < 7 - 3 or x < 4. On a number line, you’d draw an open circle at 4 and a line extending to the left from this point.

  11. Yes, the question, “How many siblings do you have?” is a statistical question because it anticipates a variety of responses and allows for the data to be collected, analyzed, and interpreted.

  12. The mean of the set is the sum of the numbers divided by the count of numbers, or (85 + 87 + 89 + 91 + 93)/5 = 89. The median of the set is the middle number when the numbers are listed in order, or 89.

  13. The interquartile range of a data set is the difference between the third quartile and the first quartile. For the given data, Q1 is 7, Q3 is 18, so the interquartile range is 18 - 7 = 11.

  14. The mean absolute deviation is the average of the absolute differences between each data point and the mean. For the given data, the mean is 178.57. The differences are 58.57, 28.57, 8.57, 1.43, 11.43, 21.43, and 51.43. Their average is 29.29.

  15. The distribution of the data set is slightly skewed to the right because the right side (greater values) has a longer tail. Most of the data is concentrated around 4 and 5.

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