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 
denote the 20 elements of set X.
Let 
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 .
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 .
![\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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Ccccccccc%7D%5Ctext%7BMembers%20of%20X%7D%20%26%20x_1%20%26%20x_2%20%26%20%5Ccdots%20%26%20x_%7B10%7D%20%26%20x_%7B11%7D%20%26%20%5Ccdots%20%26%20x_%7B20%7D%5C%5C%5B0.5em%5D%5Cdisplaystyle%5Ctext%7BMember%20of%7D%5Catop%5Cdisplaystyle%5Ctext%7BSet%20A%3F%7D%20%26%20%5Ctext%7BYes%7D%26%5Ctext%7BYes%7D%26%5Ccdots%20%26%5Ctext%7BYes%7D%26%20%5Ctext%7BNo%7D%20%26%20%5Ccdots%20%26%20%5Ctext%7BNo%7D%5C%5C%5B0.5em%5D%5Cdisplaystyle%5Ctext%7BMember%20of%7D%5Catop%5Cdisplaystyle%5Ctext%7BSet%20B%3F%7D%26%20%20%5Ctext%7BYes%7D%26%5Ctext%7BYes%7D%26%5Ccdots%20%26%5Ctext%7BYes%7D%26%20%5Ctext%7BMaybe%7D%20%26%20%5Ccdots%20%26%20%5Ctext%7BMaybe%7D%5Cend%7Barray%7D)
.
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 
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 
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}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Bc%7Ccccccccc%7D%5Ctext%7BMembers%20of%20X%7D%20%26%20x_1%20%26%20x_2%20%26%20%5Ccdots%20%26%20x_%7B10%7D%20%26%20x_%7B11%7D%20%26%20%5Ccdots%20%26%20x_%7B20%7D%5C%5C%5B0.5em%5D%5Cdisplaystyle%5Ctext%7BMember%20of%7D%5Catop%5Cdisplaystyle%5Ctext%7BSet%20A%3F%7D%20%26%20%5Ctext%7BYes%7D%26%5Ctext%7BYes%7D%26%5Ccdots%20%26%5Ctext%7BYes%7D%26%20%5Ctext%7BNo%7D%20%26%20%5Ccdots%20%26%20%5Ctext%7BNo%7D%5C%5C%5B0.5em%5D%5Cdisplaystyle%5Ctext%7BMember%20of%7D%5Catop%5Cdisplaystyle%5Ctext%7BSet%20B%3F%7D%26%20%20%5Ctext%7BNo%7D%26%5Ctext%7BNo%7D%26%5Ccdots%20%26%5Ctext%7BNo%7D%26%20%5Ctext%7BMaybe%7D%20%26%20%5Ccdots%20%26%20%5Ctext%7BMaybe%7D%5Cend%7Barray%7D)
.
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 possibilities for a set B that is disjoint with set A.
There are 20 elements in X so that's 
possibilities for B ⊆ X if there's no restriction on B. However, since B cannot be disjoint with set A, there's only 
possibilities left.
She can plant 34 plants in all. If you multiply 34 and 2 you will get 34 and I think that is the answer.
Answer:
About 6 athletes.
Step-by-step explanation:
We are concerned only with the percent of athletes that are above one standard deviation.
Between one standard deviation and two standard deviations, there is 13.6% of the athletes.
From 2 to 3, there is 2.1%. Above 3, there is 0.2%.
The sum of those percentages is 15.9% of 40 = 0.159 · 40 = 6.36 or about 6 athletes.
Hope this helps.
All you have to do is change the whole number to a fraction. Say you have 4 divided by 1/2. All you have to do to make a whole number a fraction is put it over 1. So now you would have 4/1 (4 being the numerator) divided by 1/2. When you divide fractions always remember this; Keep, Switch, Flip. Keep 4/1, Flip the division sign to multiplication, and Flip 1/2 to make it 2/1. Then you multiply the numerators and the denominators. So 4/1 * 2/1 = 8/1. Hope this helped.
3. The correct answer is 2) 3m² - 6.
(2m² + 3m - 4) + (m² - 3m - 2) Given
2m² + m² These numbers are like terms, because they both end in m².
3m² Since m² can also be written as 1m², and 2 + 1 = 3, this is the sum of 2m² and m² (1m²).
3m + (-3m) These numbers are like terms, because they both end in m. -3m is negative because it was being subtracted.
0 Since we're adding a negative, it's the same as subtracting something. 3m - 3m is 0.
-4 + (-2) These numbers are like terms, because they are both simple integers with no variable. Once again, we're adding a negative because it was being subtracted.
-6 -4 + (-2) is the same as -4 - 2, which is -6. Remember that when you're subtracting from a negative, the number seems to become larger. For instance, 1 - 1 is 0, but -1 - 1 is -2.
3m² - 6 Put all of the terms together. We don't have to write out 0, because 0 is the same as nothing.
5. This one is a bit unclear, but I think that the correct answer is 2) II and IV. The slope formula can be written as y = mx + b, where m is the slope and b is the y-intercept, or the place where the line crosses the y-axis. In this equation, b is 2, which is a positive number, so the y-intercept shifts upward. This means that the answer is either 2 or 3. As for |x - 6|, the way this is written makes the equation somewhat confusing. I believe that the bars are meant as absolute value bars, which, put simply, turn negatives into positives. This means that this part is x + 6, so the line shifts to the right. However, if they were intended as parentheses, the line would shift to the left, because we're subtracting 6 from x. I'm almost certain those were intended as absolute value bars, though, so I think that the answer is 2.
Hope this helps!
