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Rufina [12.5K]
1 year ago
10

Please help I’ll mark you as brainliest if correct!

Mathematics
2 answers:
Anna11 [10]1 year ago
6 0

Answer: 1, 8, 3

Step-by-step explanation: +7 jumps.

2 + 7 = 9

9 + 7 = 16 ..... In traditional clock 16 is 4 O'clock.

4 + 7 = 11

11 + 7 = 18 ..... In traditional clock 18 is 6 O'clock.

6 + 7 = 13 ..... In traditional clock 13 is 1 O'clock.

now: next three terms in order are

1 + 7 = 8

8 + 7 = 15 ..... In traditional clock 15 is 3 O'clock.

3 + 7 = 10

The next three terms are: 1,8,3.

2, 9, 4, 11, 6, 1, 8, 3.

kakasveta [241]1 year ago
4 0

Answer:

  ..., 1, 8, 3

Step-by-step explanation:

You want the sequence of clock face numbers that starts 2, 9, 4, 11, 6, ....

<h3>Clock face sequence</h3>

The numbers in the given sequence are each 7 hours after the one before. 7 hours after a given hour is the same as 5 hours before on a 12-hour clock.

Continuing the sequence by adding 7 or -5 to the previous value to keep within the range [1, 12], we get ...

  2, 9, 4, 11, 6, 1, 8, 3, 10, 5, 12, 7, 2 (and repeats from here)

The next three numbers in the sequence are 1, 8, 3.

__

<em>Additional comment</em>

We have described the sequence as the function ...

  f(1)=2\\\\f(n)=\begin{cases}f(n-1)+7&\text{for }f(n-1) < 6\\f(n-1)-5&\text{for }f(n-1)\ge 6\end{cases}

The sequence can also be described by the explicit function ...

  f(n)=1+\!\!\!\mod\!(7n+6,12)

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Of the entering class at a​ college, ​% attended public high​ school, ​% attended private high​ school, and ​% were home schoole
Veronika [31]

Answer:

(a) The probability that the student made the​ Dean's list is 0.1655.

(b) The probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c) The probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

Step-by-step explanation:

The complete question is:

Of the entering class at a college, 71% attended public high school, 21% attended private high school, and 8% were home schooled. Of those who attended public high school, 16% made the Dean's list, 19% of those who attended private high school made the Dean's list, and 15% of those who were home schooled made the Dean's list.

a) Find the probability that the student made the Dean's list.

b) Find the probability that the student came from a private high school, given that the student made the Dean's list.

c) Find the probability that the student was not home schooled, given that the student did not make the Dean's list.

Solution:

Denote the events as follows:

<em>A</em> = a student attended public high school

<em>B</em> = a student attended private high school

<em>C</em> = a student was home schooled

<em>D</em> = a student made the Dean's list

The provided information is as follows:

P (A) = 0.71

P (B) = 0.21

P (C) = 0.08

P (D|A) = 0.16

P (D|B) = 0.19

P (D|C) = 0.15

(a)

The law of total probability states that:

P(X)=\sum\limits_{i} P(X|Y_{i})\cdot P(Y_{i})

Compute the probability that the student made the​ Dean's list as follows:

P(D)=P(D|A)P(A)+P(D|B)P(B)+P(D|C)P(C)

         =(0.16\times 0.71)+(0.19\times 0.21)+(0.15\times 0.08)\\=0.1136+0.0399+0.012\\=0.1655

Thus, the probability that the student made the​ Dean's list is 0.1655.

(b)

Compute the probability that the student came from a private high school, given that the student made the Dean's list as follows:

P(B|D)=\frac{P(D|B)P(B)}{P(D)}

             =\frac{0.21\times 0.19}{0.1655}\\\\=0.2410876\\\\\approx 0.2411

Thus, the probability that the student came from a private high school, given that the student made the Dean's list is 0.2411.

(c)

Compute the probability that the student was not home schooled, given that the student did not make the Dean's list as follows:

P(C^{c}|D^{c})=1-P(C|D^{c})

               =1-\frac{P(D^{c}|C)P(C)}{P(D^{c})}\\\\=1-\frac{(1-P(D|C))\times P(C)}{1-P(D)}\\\\=1-\frac{(1-0.15)\times 0.08}{(1-0.1655)}\\\\=1-0.0815\\\\=0.9185

Thus, the probability that the student was not home schooled, given that the student did not make the Dean's list is 0.9185.

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