Answer: Probability that the proportion of students who graduated is greater than 0.743 is P = 0.4755
Step-by-step explanation:
Given that,
Probability of freshmen entering public high schools in 2006 graduated with their class in 2010, p = 0.74
Random sample of freshman, n = 81
Utilizing central limit theorem,

So,

= P( Z > 0.0616)
= 0.4755 ⇒ probability that the proportion of students who graduated is greater than 0.743.
Each ticket is 26.25, but since three friends are going, all you have to do is:
26.25 x 3
<em>Which is $78.75</em>
Answer:
The answer is "9 and 7".
Step-by-step explanation:
Given:
![A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right]](https://tex.z-dn.net/?f=A%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D)
Using formula:

![\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\](https://tex.z-dn.net/?f=%5Cto%20%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D-%5Clambda%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%20%7C%3D0%5C%5C%5C%5C%5C%5C%20%5Cto%20%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7%269%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D-%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5Clambda%260%5C%5C0%26%5Clambda%5Cend%7Barray%7D%5Cright%5D%20%7C%3D0%5C%5C%5C%5C%5C%5C%5Cto%7C%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D7-%5Clambda%20%269%5C%5C0%269-%5Clambda%5Cend%7Barray%7D%5Cright%5D%7C%3D0%5C%5C%5C%5C%5C%5C%5Cto%7C%287-%5Clambda%29%289-%5Clambda%29%7C%3D0%5C%5C%5C%5C%5Cto%20%287-%5Clambda%29%289-%5Clambda%29%3D0%5C%5C%5C%5C%5Cto%207-%5Clambda%3D0%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%209-%5Clambda%3D0%5C%5C%5C%5C)

Answer:
The value of a which equation have 2 , -
Step-by-step explanation:
Given expression as :
2 a - 4 x = 4 - a² × x
The equation lies in the interval ( - 8 , - 2 )
∵ equation lies in the interval , so it must satisfy the equation
So , 2 a - 4 × ( - 8 ) = 4 - a² × ( - 8 )
Or, 2 a + 32 = 4 + 8 a²
Or, a + 16 = 2 + 4 a²
So, equation can be written as :
4 a² - a - 14 = 0
Or, 4 a² - 8 a + 7 a - 14 = 0
Or, 4 a ( a - 2 ) + 7 ( a - 2 ) = 0
Or, ( a - 2 ) ( 4 a + 7 ) = 0
∴ a = 2 And -
Hence The value of a which equation have 2 , -
Answer
Answer:
Step-by-step explanation:
<u>The filling speed is 30 hours or:</u>
<u>The draining speed is 34 hours or: </u>
<u>If both lines are open simultaneously, the filling speed is:</u>
- 1/30 - 1/34 =
- 17/510 - 15/ 510 =
- 2/510 =
- 1/255 in an hour
<u>If the tank is 1/5 full, then we need to fill the 4/5 of level and it will take:</u>
- 4/5 : 1/255 =
- 4/5 *255 =
- 204 hours