Square root of 27 is the answer
x is less than or equal to -4 or x is greater than or equal to 5
x <= -4 or x>= 5
There is no intersection of both inequalities when we graph it in number line So, we write the interval notation separately for each inequality
for x<=-4 , x starts at -4 and goes to -infinity because we have less than symbol. Also we have = sign so we use square brackets
Interval notation is (-∞ , -4]
for x>= 5 , x starts at 5 and goes to infinity because we have greater than symbol. Also we have = sign so we use square bracket at 5
Interval notation is [5 , ∞)
Now combine both notation by a 'U' symbol Union
(-∞ , -4] U [5 , ∞)
Answer: The point slope solution is y+4 = -(1/2)(x-4) which is y + 4 = -(.5)x + 2 or y = -(.5)x -2.
Step-by-step explanation:
Answer:
0.3
Step-by-step explanation:
The margin of error is calculated as ...
(standard deviation)/√(sample size) × (z*-score)
where the z*-score is chosen based on the desired confidence level.
Here, you have ...
- standard deviation = 2.7
- √(sample size) = √225 = 15
- z*-score for 90% confidence level = 1.645
Putting these values in the above expression for margin of error gives ...
2.7/15·1.645 = 0.2961 ≈ 0.3
Answer:
The circle's centre is at the position (3, 5), and it has a radius of 2
Step-by-step explanation:
First let's put it in a useful format by completing the squares:
x² + y² - 6x - 10y + 30 = 0
x² - 6x + y² - 10y = -30
x² - 6x + 9 + y² - 10y + 25 = -30 + 9 + 25
(x - 3)² + (y - 5)² = 4
This tells us that the centre position is (3, 5) and the radius is √4, or 2
