Answer:
a² + b² = c · (e + d) = c × c = c²
a² + b² = c²
Please see attachment
Step-by-step explanation:
Statement, Reason
ΔADC ~ ΔACB, Given
AC/AD = BA/AC, The ratio of corresponding sides of similar triangles
b/e = c/b
b² = c·e
ΔBDC ~ ΔBCA, Given
BC/BA = BD/BC, The ratio of corresponding sides of similar triangles
a/c = d/a
a² = c·d
a² + b² = c·e + c·d
a² + b² = c · (e + d)
e + d = c, Addition of segment
a² + b² = c × c = c²
Therefore, a² + b² = c²
Answer:
1. The 95% confidence interval for the difference between means is (-5.34, 11.34).
2. The standard error of (x-bar1)-(x-bar2) is 4.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1, of size n1=10 has a mean of 45 and a standard deviation of √85=9.2195.
The sample 2, of size n2=12 has a mean of 42 and a standard deviation of √90=9.4868.
The difference between sample means is Md=3.
The estimated standard error of the difference between means is computed using the formula:
The critical t-value for a 95% confidence interval is t=2.086.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference between means is (-5.34, 11.34).