Answer:
a) C. No, a carton can have a puncture and a smashed corner.
b) The probability that a carton has a puncture or a smashed corner is P(X ∪ Y) = 0.104.
Step-by-step explanation:
To be mutually exclusive, the probability of the two events happening at the same time should be 0. But the probability that a carton has a puncture and has a smashed corner is 0.004 and not 0.
Then, we can conclude the events "selecting a carton with a puncture" and "selecting a carton with a smashed corner" are not mutually exclusive.
The answer is "C. No, a carton can have a puncture and a smashed corner."
We can calculate the probability that the carton has a puncture <em>or </em>has a smashed comer simply by adding the probability of each event:
P(X ∪ Y): probability that a carton has a puncture or a smashed corner.
The association between the given lines is that they are 'neither perpendicular nor parallel.'
To prove, let's convert the given equations in their slope-intercept form i.e. 'y = mx + b'
-7x + 2y = 3
2y = 7x + 3
y = 7/2x + 3/2
-6x + 3y = 2
3y = 6x + 2
y = 2x + 2/3
This shows that both the lines have different slopes, as well as, intercepts of y. And,
= 2 * 7/2 ≠ -1
Thus, it is not perpendicular also.
Therefore, <u>option D</u> i.e. 'neither perpendicular nor parallel' is the correct answer.
Learn more about 'slope' here:
brainly.com/question/10973849
Answer:
Step-by-step explanation:
( g ° f )(x) = ( x + 7 )² = x² + 14x + 49
20 + 3(x² + 14x + 49) = - 34
20 + 3x² + 42x + 147 = - 34
3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0
D = 196 - 268 = - 72 < 0
There is no any roots in set of real numbers.
The values of x in set of complex numbers are:
= ±
= - 7 ± 3√2 i
The 4/9 is greater than 4/10
Given:
The surface area of a right circular cone is 32 sq. cm.
Scale factor for enlargement = 3
To find:
The surface area of the new cone.
Solution:
We know that enlargement of a shape forms a similar shape and area of the similar shapes is proportional to the square of their corresponding sides.
Let the surface area of new cone be A and r be the radius of original cone
By cross multiplication, we get
The surface area of the new cone is 288 sq. cm.
Therefore, the correct option is C.