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saul85 [17]
3 years ago
6

At a parade, 1/4 of the participants have red hair, 1/6 of them have brown hair, and the rest have black hair. What fraction of

the participants have black hair
Mathematics
2 answers:
4vir4ik [10]3 years ago
6 0
Ok so first we need to find out how many have either red or brown hair, which is 1/4+1/6. here, we need to find a common denominator, which is 12. so we are going to multiply 1/4 by 3/3 and 1/6 by 2/2. this yields, 3/12+2/12=5/12. since the rest have black hair, we do 1-5/12 which is 7/12
AlekseyPX3 years ago
5 0
First we need to make the fractions have the same denominator. the smallest common multiple of 4 and 6 is 12, and 1x3= 3, and 4x3= 12, so 3/12 of the participants have red hair. 1x2= 2, and 6x2=12, so 2/12 of the participants have brown hair. 3+2=5, so 5/12 of the participants have red OR brown hair, and there's 7 left. therefore 7/12 of the participants have black hair.
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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
3 years ago
A regular assignment has 15 sides.Calculate the size of each interior angle
MariettaO [177]

Answer:

The measure of an interior angle of a regular 15-gon is 120°.

Step-by-step explanation:

We need to determine the measure of the size of an interior angle of a regular 15-gon having 15 sides.

Thus,

The number of sides n = 15

Hence,

Using the formula to determine the measure of an interior angle of a regular 15-gon is given by

(n - 2) × 180° = n × interior angle

substitute n = 15

(15 - 2) × 180 = 15 × interior angle

13 × 180 = 15 × interior angle

Interior angle = (10 × 180) / 15

                      = 1800 / 15

                      = 120°

Therefore, the measure of an interior angle of a regular 15-gon is 120°.

6 0
3 years ago
A full load for a small truck to haul is 2/3 ton of gravel. The truck is hauling 1/2 ton of gravel. Write a division sentence th
Romashka [77]

Answer:

The truck is hauling 3/4 of a full load

Step-by-step explanation:

we know that

2/3 ton of gravel represent the 100% of a full load

Find out how much of a full load the truck is hauling with 1/2 ton of gravel, using proportion

Let

x ----> the percentage of a full load

\frac{(2/3)}{100\%}=\frac{(1/2)}{x}\\\\x=100\%(1/2)/(2/3)\\\\x=100\%(3/4)\\\\x=75\%

Convert to fraction number

75\%=\frac{75}{100}=\frac{3}{4}

therefore

The truck is hauling 3/4 of a full load

6 0
3 years ago
Find 24% of 165. Need explanation
Irina-Kira [14]

Answer:

39.6

Step-by-step explanation:

i would give explanation but im bad at doing that

4 0
3 years ago
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Line Q??? You don't really have an image of it
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3 years ago
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