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2 years ago

Write down all the subsets of {q,r,s}.

Mathematics

1 answer:

MrRissso [65]2 years ago

3 0

{q, r, s} consists of 3 elements, so there are 2³ = 8 possible subsets.

• empty set: { }

• every possible singleton set: {q}, {r}, {s}

• every possible pair: {q, r}, {q, s}, {r, s}

• the set itself: {q, r, s}

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Find the 13th term of the arithmetic sequence -3x – 1,42 + 4,112 + 9, ...

Strike441 [17]

Answer:

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

$\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots$

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

$\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}$

Find the common difference by subtracting the first term from the second:

$d = (4x+4) - (-3x - 1)$

Distribute:

$d = (4x + 4) + (3x + 1)$

Combine like terms. Hence:

$d = 7x + 5$

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

$\displaystyle x_n = a + d(n-1)$

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

$\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)$

To find the 13th term, let n = 13. Hence:

$\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)$

Simplify:

$\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}$

The 13th term is 81x + 59.

3 0

2 years ago

When the outliers are removed, how does the mean change? dot plot with 1 on 50, 1 on 76, 1 on 78, 2 on 79, 1 on 80, 1 on 81, 2 o

sveticcg [70]

We can plot this data on MS Excel and determine the distribution of these data reflected on the graph. Among these numbers, 50 is the outlier since it is very far from the other numbers ranging from 76 to 83. We can perform interquartile range to determine or verify the outliers in the data set. In this respect, we can see that there is not much distribution seen. The average of all data sets is equal to 96.25. When the outlier (50) is removed, we expect the mean to become higher since a low number was ommitted including high numbers only. Outliers are obtained from special causations such as human errors.

5 0

2 years ago

Read 2 more answers

2. The table shows the probabilities of winning or losing when the team is playing away or is playing at home.

tekilochka [14]

The total will be 08.99 because that’s how you divide and he is winning

5 0

2 years ago

Plzzzz help !!!! 15 points

ArbitrLikvidat [17]

Answer:

1. 17,20

2. 40,80

Step-by-step explanation:

1. 5+3=8

8+3=11

11+3=14

14+3=17

17+3=20

pattern is +3

2. 2.5*2=5

5*2=10

10*2=20

20*2=40

40*2=80

pattern is *2

6 0

3 years ago

Read 2 more answers

In a recent telephone survey, 5,000 randomly selected teenagers were asked to cite their primary social network sites. Six of 10

aleksklad [387]

Answer:

b. There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).

Step-by-step explanation:

Hello!

In general, a 95% confidence interval for the population proportion can be interpreted as: There is a 95% chance (or confidence) that the interval will contain the true value of the proportion.

(Remember the confidence level of 95% means that if you were to make 100 intervals for the population proportion, 95 of them will contain its true value)

The estimated parameter is the population proportion of teenagers that use Mybook as their primary social network site.

With this in mind then you can say that there is a 95% probability that the interval (0.2964, 0.9036) will contain the true value of the proportion of teenagers that use Mybook as their primary social network site.

The correct answer is: b

I hope this helps!

8 0

2 years ago