A card is drawn from a standard deck of 52 cards. What is the theoretical probability, as a decimal, of drawing a number 8? Roun
1 answer:
We know that in a standard deck of 52 cards there are 4 suits and each suit has one card with the number 8. Thus, 4 suits will have 4 cards with the number 8. Therefore, the total number of events in the sample space is 52 and the total number of favorable events is 4.
Thus, if a card is drawn from a standard deck of 52 cards, the theoretical probability of drawing a number 8 is given by:
Thus, round the decimal to the nearest hundredth, the theoretical probability of drawing a number 8 from a standard deck of 52 cards is given by 0.08.
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Answer:
The parabola has a horizontal tangent line at the point (2,4)
The parabola has a vertical tangent line at the point (1,5)
Step-by-step explanation:
Ir order to perform the implicit differentiation, you have to differentiate with respect to x. Then, you have to use the conditions for horizontal and vertical tangent lines.
-To obtain horizontal tangent lines, the condition is:
(The slope is zero)
--To obtain vertical tangent lines, the condition is:
(The slope is undefined, therefore the denominator is set to zero)
Derivating respect to x:
=
Solving for dy/dx:
Applying the first conditon (slope is zero)
Solving for y (Adding 2x+4, dividing by 2)
y=x+2 (I)
Replacing (I) in the given equation:
Replacing it in (I)
y=(2)+2
y=4
Therefore, the parabola has a horizontal tangent line at the point (2,4)
Applying the second condition (slope is undefined where denominator is zero)
2y-2x-8=0
Adding 2x+8 both sides and dividing by 2:
y=x+4(II)
Replacing (II) in the given equation:
Replacing it in (II)
y=1+4
y=5
The parabola has vertical tangent lines at the point (1,5)