Answer:
[(1/12)(5/5) + (1/20)(3/3)](x hours) = 1
(5/60 + 3/60)x = 1
(8/60)x = 1 we can reduce 8/60 by dividing out a 4
(2/15)x = 1 x both sides by 15/2
x = 15/2
x = 7 1/2 or 7.5 hours
Answer:
Area of the wall to be painted = (11x² + 12x) square units
Step-by-step explanation:
The figure that should be attached to this question is missing. The figure was obtained and is attached to this solution provided.
From the image attached, it is given that the dimension of the rectangular wall to be painted is (4x+3) by (4x), the dimensions of the window is (2x) by (x) and the dimensions of the door is (x) by (3x).
Since, the window space and the door space cannot be painted along with the wall, the Area of the rectangular wall that will be painted will be given by the expression
(Total Area of the rectangular wall) - [(Area of window space) + (Area of door space)]
Area of a rectangular figure = Length × Breadth
Total area of rectangular wall = (4x+3) × 4x = (16x² + 12x) square units
Area of window space = (2x) × (x) = (2x²) square units
Area of door space = (x) × (3x) = (3x²) square units
Area of the wall to be painted = (16x² + 12x) - (2x² + 3x²)
= 16x² + 12x - 5x²
= (11x² + 12x) square units
Hope this Helps!!!
Ohhhh nasty ! What a delightful little problem !
The first card can be any one of the 52 in the deck. For each one ...
The second card can be any one of the 39 in the other 3 suits. For each one ...
The third card can be any one of the 26 in the other 2 suits. For each one ...
The fourth card can be any one of the 13 in the last suit.
Total possible ways to draw them = (52 x 39 x 26 x 13) = 685,464 ways.
But wait ! That's not the answer yet.
Once you have the 4 cards in your hand, you can arrange them
in (4 x 3 x 2 x 1) = 24 different arrangements. That tells you that
the same hand could have been drawn in 24 different ways. So
the number of different 4-card hands is only ...
(685,464) / (24) = <em>28,561 hands</em>.
I love it !