Answer:
Step-by-step explanation:
given that a deck of cards is shuffled.
we know in a deck there are 52 cards, 13 cards of each variety spade, clubs hearts and dice. Red are 26 and black are 26. kings, will be 4.
(a) the top card is the king of spades and the bottom card is the queen of spades?
(iii) 1/52 × 1/52
Top has 1/52 and bottom has 1/52 and these are independent.
(b) the top card is the king of spades and the bottom card is the king of spades?
(viii) None of the above
Because it is impossible.
(c) the top card is the king of spades or the bottom card is the king of spades?
(iv) 1/52 + 1/52
This is the sum of probabilities because there is no common event for these two.
(d) the top card is the king of spades or the bottom card is the queen of spades?
(ii) 1/52 + 1/51 (once king of spades is there, then probability is 1/51 for bottom card)
(e) of the top and bottom cards, one is the king of spades and the other is the queen of spades?
(vii) 2/52 × 1/51
Because this is twice of probability d.
Answer:
(a) 
(b) Domain:
<em>(See attachment for graph)</em>
(c) 
Step-by-step explanation:
Given



Solving (a): A function; l in terms of w
All we need to do is make l the subject in 
Divide through by 2

Subtract w from both sides


Reorder

Solving (b): The graph
In (a), we have:

Since l and w are the dimensions of the fence, they can't be less than 1
So, the domain of the function can be 
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To check this
When 



When 


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<em>See attachment for graph</em>
<em></em>
Solving (c): Write l as a function 
In (a), we have:

Writing l as a function, we have:

Substitute
for l in 
becomes

Answer:
2 - 
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) =
and the exact values
tan45° = 1 , tan60° =
, then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= 
=
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 +
is 1 -
=
← expand numerator/denominator using FOIL
= 
= 
=
+ 
= 2 - 
Answer:
Step-by-step explanation:
The equation for solving for density is:
Density = mass / volume
Then plug in the values:
Density = 6 g / 12 mL
Divide and don't forget the units!
Density = 0.5 g/mL