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Gnom [1K]
3 years ago
13

The area of a rectangular garden is 6120 ft^2. If the width of the garden is 72 feets, what is its length?

Mathematics
2 answers:
lisabon 2012 [21]3 years ago
8 0
Area = width * length
6120/72 = 85 ft
krok68 [10]3 years ago
7 0
The length is 85, Because if you divide 6120 by 72 you will get 85. <span />
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898÷91,596 what is the answer
Dmitrij [34]

Answer:

For 100, your answer will be 102; For 898, your answer will be x; 100*x = 102*898 ... 102/x = 100/898 or x/102 = 898/100; x = 898*102/100 = 91596/100 = 915.96.

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7 0
2 years ago
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Let X be a set of size 20 and A CX be of size 10. (a) How many sets B are there that satisfy A Ç B Ç X? (b) How many sets B are
Svetlanka [38]

Answer:

(a) Number of sets B given that

  • A⊆B⊆C: 2¹⁰.  (That is: A is a subset of B, B is a subset of C. B might be equal to C)
  • A⊂B⊂C: 2¹⁰ - 2.  (That is: A is a proper subset of B, B is a proper subset of C. B≠C)

(b) Number of sets B given that set A and set B are disjoint, and that set B is a subset of set X: 2²⁰ - 2¹⁰.

Step-by-step explanation:

<h3>(a)</h3>

Let x_1, x_2, \cdots, x_{20} denote the 20 elements of set X.

Let x_1, x_2, \cdots, x_{10} denote elements of set X that are also part of set A.

For set A to be a subset of set B, each element in set A must also be present in set B. In other words, set B should also contain x_1, x_2, \cdots, x_{10}.

For set B to be a subset of set C, all elements of set B also need to be in set C. In other words, all the elements of set B should come from x_1, x_2, \cdots, x_{20}.

\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}&  \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{Maybe} & \cdots & \text{Maybe}\end{array}.

For each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus 2^{10} = 1024 possibilities for set B.

In case the question connected set A and B, and set B and C using the symbol ⊂ (proper subset of) instead of ⊆, A ≠ B and B ≠ C. Two possibilities will need to be eliminated: B contains all ten "maybe" elements or B contains none of the ten "maybe" elements. That leaves 2^{10} -2 = 1024 - 2 = 1022 possibilities.

<h3>(b)</h3>

Set A and set B are disjoint if none of the elements in set A are also in set B, and none of the elements in set B are in set A.

Start by considering the case when set A and set B are indeed disjoint.

\begin{array}{c|cccccccc}\text{Members of X} & x_1 & x_2 & \cdots & x_{10} & x_{11} & \cdots & x_{20}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set A?} & \text{Yes}&\text{Yes}&\cdots &\text{Yes}& \text{No} & \cdots & \text{No}\\[0.5em]\displaystyle\text{Member of}\atop\displaystyle\text{Set B?}&  \text{No}&\text{No}&\cdots &\text{No}& \text{Maybe} & \cdots & \text{Maybe}\end{array}.

Set B might be an empty set. Once again, for each element that might be in set B, there are two possibilities: either the element is in set B or it is not in set B. There are ten such elements. There are thus 2^{10} = 1024 possibilities for a set B that is disjoint with set A.

There are 20 elements in X so that's 2^{20} = 1048576 possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only 2^{20} - 2^{10} possibilities left.

5 0
2 years ago
What is the probability of rolling a 6 and then a 7 on a number cube?<br><br>NO LINKS PLEASE!​
tester [92]

Answer:

the probability of rolling 6 is 16 or 16.7%.

the probability of rolling 7 is 0.

Step-by-step explanation:

7 is 0 because its impossible to roll a 7 on one number cube.

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2 years ago
AD=<br> DC=<br> Angle a=<br> Angle b=<br> Angle c=
Nadya [2.5K]

9514 1404 393

Answer:

  AD= 8

  DC= 15

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Step-by-step explanation:

We have to assume the figure is a parallelogram.

Opposite sides of a parallelogram are congruent, so ...

  BC = AD = 8

  AB = DC = 15

Opposite angles are congruent, and adjacent angles are supplementary.

  180° - ∠D = Angle a = Angle c = 112°

  ∠D = Angle b = 68°

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2 years ago
A coat that usually costs $123 is marked 1/3 off. What is the sale price of the coat
svet-max [94.6K]
2/3 X 123 = $82
*2/3 of the original price
7 0
2 years ago
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