Answer:
[300.202 , 329.798]
Step-by-step explanation:
The 95% confidence interval is given by the interval
![\large [\bar x-t^*\frac{s}{\sqrt n}, \bar x+t^*\frac{s}{\sqrt n}]](https://tex.z-dn.net/?f=%5Clarge%20%5B%5Cbar%20x-t%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%2C%20%5Cbar%20x%2Bt%5E%2A%5Cfrac%7Bs%7D%7B%5Csqrt%20n%7D%5D)
where
<em>is the sample mean </em>
<em>s is the sample standard deviation </em>
<em>n is the sample size (n = 7) </em>
is the 0.05 (5%) upper critical value for the Student's t-distribution with 6 degrees of freedom (sample size -1), which is <em>an approximation to the Normal distribution for small samples (n<30).</em>
Either by using a table or the computer, we find
and our 95% confidence interval is
![\large [315-2.447*\frac{16}{\sqrt{7}}, 315+2.447*\frac{16}{\sqrt{7}}]=\boxed{[300.202,329.798]}](https://tex.z-dn.net/?f=%5Clarge%20%5B315-2.447%2A%5Cfrac%7B16%7D%7B%5Csqrt%7B7%7D%7D%2C%20315%2B2.447%2A%5Cfrac%7B16%7D%7B%5Csqrt%7B7%7D%7D%5D%3D%5Cboxed%7B%5B300.202%2C329.798%5D%7D)
Answer:
1. 5 + y = 7
⇒ y = 7 - 5
⇒<u>y = 5</u>
2. 3.8 = a + 2.5
⇒ a = 2.5 - 3.8
⇒ <u>a = -1.3</u>
3. 5 + p = 9 1/3
⇒ p = 9 1/3 - 5
⇒ p = 28/3 - 5
⇒ p = 28/3 - 15/3
⇒ p = 13/3
⇒<u> </u><u>p = 4 1/3</u>
Answer: x=7.21
Step-by-step explanation: This is a right triangle- remember the Pythagorean theorem: a² + b² = c². To find leg a, you'd use a = √(c² - b²) **leg a would be the side that is labeled with 12. To find leg b, you'd use b = √(c² - a²) *this is the equation we need. To find the hypotenuse, or <em>c</em>, you'd use c = √(a² + b²). This equation works for right triangles only.
Hope this helps :)
