Step-by-step explanation:
The equation for the best fitting line is y = 2.599x + 105.08. When x is set to 20, the predicted height becomes y = 157.06. However, the actual height recorded is 160 cm, therefore, the residual is calculated as:
160 cm − 157.06 cm = 2.94 cm
Approximately 2, I believe... I calculated it to be around 2.10.
Given that,
Julia completes a 20-mile bike ride in 1.2 hours.
The distance Julia covers is 20 miles and her time taken is 1.2 hours.
Therefore, Julia's speed =
= 16.67 mph
Katie finishes the same 20-mile ride in 1.6 hours.
Katie’s distance is 20 miles and her time is 1.6 hours.
Hence, Katie's speed =
= 12.5 mph
To determine how much faster Julia rides compared to Katie, subtract Katie’s speed from Julia’s speed.
Thus, 16.67 mph minus 12.5 mph equals 4.17 mph, approximately 4.2 mph.
Consequently, Julia cycles 4.2 mph faster than Katie.
Answer:
m = - 3
Step-by-step explanation:
a³ + 27 can be recognized as a sum of cubes, which factors generally as
a³ + b³ = (a + b)(a² - ab + b²). Therefore:
a³ + 27
= a³ + 3³
= (a + 3)(a² - 3a + 9).
By comparing a² - 3a + 9 to a² + ma + 9, we find that
m = - 3.