A rectangular pool is 20 feet wide and 50 feet long. A deck used for sunning surrounds the pool. The deck is the same width all the way around the pool. The total area of the deck is 456 square feet. How wide is the walkway?A. 2 feet
B. 3 feet
C. 4 feet
D. 5 feet
Answers
Firstly we find the expression for the area (using x as the walk way):
>50x * 2 (the left and right)
>20x * 2 (the top and bottom)
>4 * x^2 (the corners)
Add them all together , Area = 140x + 4x^2
Now we place the deck's area, 456 into the expression
456 = 140x + 4x^2
Solve for x
I'm a bit rusty on this i'm afraid, but I believe the only way to solve this is to factorise it
0 = 4x^2 + 140x - 456
0 = 4(x+38)(x-3) <
x must = -38 or = +3 (the numbers inside the brackets inverted)
x must = +3 as it's logical, you can't have a negative width
The walkway is 3 feet wide, we can put this into our expression to double check this,
456 = 140*(3) + 4(3)^2
456 = 420 + 4*9
456 = 420 + 36
456 = 456
Yes, 3 feet wide is correct.
*Note, I tried to keep this simple, please let me know if I didn't go into enough detail anywhere
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The chance is not pretty big. It's pretty small.
The chance of guessing the first card correctly is (1/52) = 0.0192
The chance of guessing the 2nd card correctly is (1/51) = 0.0196
The chance of guessing the 3rd card correctly is (1/50) = 0.02
The chance of guessing the 4th card correctly is (1/49) = 0.0204
The chance of guessing the 5th card correctly is (1/48) = 0.0208
The chance of guessing the 6th card correctly is (1/47) = 0.0217
The chance of guessing the 7th card correctly is (1/46) = 0.0217
The chance of guessing the 8th card correctly is (1/45) = 0.0222
The chance of guessing the 9th card correctly is (1/44) = 0.0227
The chance of guessing the 10th card correctly is (1/43) = 0.0233
.
.
.
and you keep going like that. Then the chance of guessing ALL of them
correctly is the product of all of the individual chances.
After the first ten, listed above, you're already down to
0.00000 00000 00000 00000 00000 00000 00000 00000 00000 00000 0712 .
You're not even 1 tenth of the way through the deck yet, and it just keeps
getting smaller as you keep going.
The chance of guessing the first 10 correctly is ( 42 ! ) / ( 52 ! ) .
That's the number I just wrote up there, with 51 zeroes after the decimal point.
The chance of guessing the whole deck correctly is 1 / ( 52 !) .
That number starts out with roughly 51 more zeroes.
You might say that it's roughly 1 percent of 1 "googoleth".
My estimation is: It's almost identical to zero.
Answers
We have to take a look at the numerator and the denominator
Why? Because to simplify we need to have a common multiple.
When we find the common multiple, we now know by which factor we have to break down the fraction in the numerator and the denominator
I have some examples attached below for help.
Answers
add t to s
raise the result to the 10th power
then double what you have
Answers
Well, 10% of 50 is 5.
so 5 times 7 (for the 70%) is 35.
A. 5x^3 + 6x
B. 6x^2 + 8x
C. 6x^3 + 4
D. 6x^3 + 8x
Answers
Answer:
D. 6x^3 + 8x
Step-by-step explanation:
2x(3x^2 + 4)
Distribute the 2x
2x(3x^2) +2x( 4)
6x^3 +8x
Answers
Answer:
x = - 7
Step-by-step explanation:
Given the 2 equations
y - x = 9 → (1)
10 + 2x = - 2y → (2)
Rearrange (1) expressing x in terms of y by adding x to both sides
y = x + 9
Substitute y = x + 9 into (2)
10 + 2x = - 2(x + 9) ← distribute
10 + 2x = - 2x - 18 ( add 2x to both sides )
10 + 4x = - 18 ( subtract 10 from both sides )
4x = - 28 ( divide both sides by 4 )
x = - 7