Answer:
a) 0.06
b) 0.778
Step-by-step explanation:
Let's suppose a community of 100 families just to facilitate the calculation.
30% of the families own a dog
Dog = 30% of 100 = 30
20% of the families that own a dog also own a cat = 20% of 30 = 6
27% of all the families own a cat = 27% of 100 = 27
So, 6 families own a dog and a cat.
As 30 families own a dog, [30 - 6 =] 24 families own only dogs
As 27 families own a cat, [27 - 6 = ] 21 families own only cats
See picture attached.
a) What is the probability that a randomly selected family owns both a dog and a cat?
P(dog and cat) = dog ∩ cat/total = 6/100 = 0.06
b) What is the conditional probability that a randomly selected family doesn't own a dog given that it owns a cat?
So, only cat/total cat
P (not dog|cat) = 21/27 = 0.778
A line and a point always intersect
The slope of the line is 
Explanation:
Given that a coordinate plane with a straight line passing through the points
,
and 
We need to determine the slope of the line.
The slope of the line can be determined using the formula,

Since, the points
,
and
lie on the straight line and the slope of all the points in a straight line have the same slope.
Hence, let us consider the points
and 
Let us substitute these points in the slope formula, we have,

Simplifying, we get,

Dividing, we get,

Hence, the slope of the line is 
Answer:
L×W×B
10×7×6
=420cm of triangular prism
Answer:

The vertex form for a parabola is given by this expression:

By direct comparison we see that for this case:

And we know from the general expression that the vertex is:

So then the vertex for this case is:

Step-by-step explanation:
For this case we have the following function:

And we need to take in count that the vertex form for a parabola is given by this expression:

By direct comparison we see that for this case:

And we know from the general expression that the vertex is:

So then the vertex for this case is:
