Perpendicular lines refers to a pair of straight lines that intercept each other. The slopes of this lines are opposite reciprocal, meaning that it's multiplication is -1.
On this case they give you the equation of a line and a point, and is asked to find the equation of a line that is perpendicular to the given one, and that passes through this point.
-2x+3y=-6 Add 2x in both sides
3y=2x-6 Divide by 3 in both sides to isolate y
y=2/3x-6/3
The slope of the given line is 2/3, which means that the slope of a line perpendicular to this one, needs to be -3/2. Now you need to find the value of b or the y-intercept by substituting the given point into the formula y=mx+b, where letter m represents the slope.
y=mx+b Substitute the given point and the previous slope found
-2=(-3/2)(6)+b Combine like terms
-2=-9+b Add 9 in both sides to isolate b
7=b
The equation that represents the line perpendicular to -2x+3y=-6 and that passes through the point (6,-2), is y=-3/2x+7.
The most simplified version of it is 49/50
Answer:
A
Step-by-step explanation:
Cylinder volume= V = π r ^2 h
So you times Pie by the radius (diametre divided by two- 3.5) you then square this. After that, times it by the height (10)
So the volume is 384.85.
You then find 30% of this, so times 384.85 by 30%.
You then get an answer of 115.455, and this is equal to A.
I hope this helps, have a lovely day.
Answer:
And the z score for 0.4 is
And then the probability desired would be:
Step-by-step explanation:
The normal approximation for this case is satisfied since the value for p is near to 0.5 and the sample size is large enough, and we have:
For this case we can assume that the population proportion have the following distribution
Where:
And we want to find this probability:
And we can use the z score formula given by:
And the z score for 0.4 is
And then the probability desired would be:
