Answer is 9.
-3x^2 + 243 = 0
Bring 243 to the right.
-3x^2 = -243
Divide by -3.
x^2 = 243/3 = 81
Tak the square root of both sides.
x = 81^1/2 = 9.
Answer:
609
Step-by-step explanation:
Standard deviation =
= $30
Margin of error = E = $2
Confidence level = 90%
Since the distribution is said to be normal, we will use z scores to solve this problem.
The z score for 90% confidence level = z = 1.645
Sample size= n = ?
The formula to calculate the margin of error is:

Using the values in above equation, we get:

This means, the minimum number of observations required is 609
Answer:
5.5
Step-by-step explanation:
2,3,3,4,5,7,8,8,8,10,10,12
The mean of this data is 7.5. So what you are trying to figure out is the mean between 2 and 7. Since that is 3 and 4 it would be 3.5. So 3.5 is the Q1. Now you have to figure out the mean between 8 and 12. That is 9. This is Q3. You have to subtract 9-3.5 and that is the interquartile range. So 5.5 is the answer. I hope that made sense.
Answer:
(a) 120 choices
(b) 110 choices
Step-by-step explanation:
The number of ways in which we can select k element from a group n elements is given by:

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

Then each student have 120 possible choices.
On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:
1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:
50 + 50 + 10 = 110
Answer:
2
Step-by-step explanation:
You can find slope using the slope equation :
- Plug in the two points :

- Calculate by adding the numbers:

The slope is 2