The base of a rectangular prism is 5.4 centimeters long and 4.9 centimeters wide. It is 3.8 centimeters tall. What is the volume
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<u>Answer: </u>
The probability of rolling a number greater than 4 or less than 3 is
<u>Solution: </u>
In the given question there are two events as follows:
(a) Rolling a number greater than 4 i.e. A = {5,6}
(b) Rolling a number less than 3 i.e. B = {1,2}
Since a die has 6 numbers,
P(A) = where P(A) is the probability of occurrence of event A and P(B) =
Since, Event A and Event B has nothing in common therefore they are mutually exclusive events.
P(A∪B) = P(A) + P(B)
Therefore the probability of getting a number greater than 4 or less than 3 is
As shown in the figure, we have two straight line. One of them has a negative slope and the other has a positive one. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form by:
being m the slope of the line and <span>b the y-intercept of it.
On the other hand, if x = 0 then y = b.
First of all we will order the equations above without </span>inequalities<span> like this:
A. </span>
, 
<span>B. </span>, 
C.
,
D., 
<span>
As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:
</span>
For C, b = 1 and b = 4
For D, b = -1 and b = -4
Let's analyze A and B. So:
For A, m = 5 and m = 3
For B, m = 5 and m = -3
Therefore, we discard A because of the statement above.
Finally the answer is B. So, the inequalities are:
(1)
(2)
Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:
(1)
(2)
In fact, this is true.
being m the slope of the line and <span>b the y-intercept of it.
On the other hand, if x = 0 then y = b.
First of all we will order the equations above without </span>inequalities<span> like this:
A. </span>
<span>B. </span>
C.
D.
As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:
</span>
For C, b = 1 and b = 4
For D, b = -1 and b = -4
Let's analyze A and B. So:
For A, m = 5 and m = 3
For B, m = 5 and m = -3
Therefore, we discard A because of the statement above.
Finally the answer is B. So, the inequalities are:
(1)
(2)
Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:
(1)
(2)
In fact, this is true.