Answer:
The width of the garden is 100 feet.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2(L+W) where L = length and W = width.
Since we know the perimeter (the fence that surrounds the garden) is 820 feet and the length of the pen is 10 feet longer than 3 times its width, we can set an equation and solve for the width:
L = 10 + 3W
So substitute 10 + 3W for L in the equation:
2[(10 + 3W) + W) = 820
2(10 + 4W) = 820
10 + 4W = 410
4W = 400
W = 100
Therefore, the width of the garden is 100 feet.
Answer:
the number is 5
Step-by-step explanation:
6n + 3 = 33
6n = 30
n = 5
Answer:

Step-by-step explanation:
Given the following question:

In order to convert a mixed number into an improper fraction we have to divide the numerator (in this case; 22) by the denominator (in this case; 6) to find your answer.




Let three represent how many times 3 goes into 11, let 2 represent the remainder while of course keeping the denominator the same. Your answer is "3 2/3."
Hope this helps.
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Answer:
The probability of winning directly is, as you calculated, 8/36, and the probability of losing directly is (1+2+1)/36=4/36.
For the remaining cases, you need to sum over all remaining rolls. Let p be the probability of rolling your initial roll, and q=6/36=1/6 the probability of rolling a 7. Then the probability of rolling your initial roll before rolling a 7 is p/(p+q), and the probability of rolling a 7 before rolling your initial roll is q/(p+q). Thus, taking into account the probability of initially rolling that roll, each roll that doesn't win or lose directly yields a contribution p2/(p+q) to your winning probability.
For p=5/36, that's
(536)25+636=2511⋅36,
and likewise 16/(10⋅36) and 9/(9⋅36) for p=4/36 and p=3/36, respectively. Each of those cases occurs twice (once above 7 and once below), so your overall winning probability is
836+236(2511+1610+99)=244495=12−7990≈12−0.007.
Step-by-step explanation:
Suppose you throw a 4 and let p(4) your winning probability. At your next roll you have a probability 3/36 of winning (you throw a 4), a probability 6/36 of losing (you throw a 7) and a probability 27/36 of repeating the whole process anew (you throw any other number). Then:
p(4)=336+2736p(4),so thatp(4)=13.
Repeat this reasoning for the other outcomes and then compute the total probability of winning as:
ptot=836+336p(4)+436p(5)+…