Question

The pitch, vkHz, of the chirps made by a cricket was recorded at 15 different temperatures, t, between 10 and 30 C C. The data are summarised in the following sums: ∑t=308,∑v=114,∑t2 =6771.86,∑v 2 =1121.16,∑tv=2522.03 a) A line of best fit, v=a+bt, is found for the data. Find the value of b to 3 decimal places. b= b) Find the value of a in v=a+bt. Give your answer to 3 decimal places. a= Using the model, predict the pitch of the cricket's chirps at 20.6C° . Give your answer to 1 decimal place. kHz d) Match the answers that best describe the meanings of a and b in this context.

Answer 1

The answer is: 8.7khz

To find the value of b in the line of best fit, we can use the formula b = (n∑(xy) - ∑x∑y) / (n∑(x^2) - (∑x)^2). Substituting the given values, we have b = (15 * 2522.03 - 308 * 114) / (15 * 6771.86 - 308^2), which gives us b ≈ 0.263.

To find the value of a, we can use the formula a = (∑y - b∑x) / n. Substituting the given values, we have a = (114 - 0.263 * 308) / 15, which gives us a ≈ 3.291.

Using the model, we can predict the pitch of the cricket’s chirps at 20.6°C by substituting the value of t into the equation v = a + bt. This gives us v = 3.291 + 0.263 * 20.6, which is approximately equal to 8.7 kHz.