Question

lydia runs an experiment to determine if a coin is fair by counting the number of times a coin lands heads up. the table shows her data. coin fairness test number of coin flips 0 10 20 30 40 50 60 70 80 90 number of heads up 0 7 12 18 23 30 35 38 42 45 according to the line of best fit, about how many times would the coin land heads up in 100 flips? 48 50 51 53

Explanation:

Step1: Calculate the ratio of heads - up to coin - flips for the given data points

We can take two points, say (10, 7) and (90, 45). The slope $m$ of the line of best - fit using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ where $x$ is the number of coin flips and $y$ is the number of heads - up.
$m=\frac{45 - 7}{90 - 10}=\frac{38}{80}=0.475$
The line of best - fit has the form $y=mx + b$. Using the point - slope form with the point (10, 7), we have $y - 7=0.475(x - 10)$.
Expanding gives $y-7 = 0.475x-4.75$, so $y = 0.475x+2.25$.

Step2: Predict the number of heads - up for 100 coin flips

Substitute $x = 100$ into the equation $y = 0.475x+2.25$.
$y=0.475\times100 + 2.25=47.5+2.25 = 49.75\approx50$

Answer:

50