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3 years ago

Use inductive reasoning to describe the pattern of each sequence. Then find the next two terms. 1, 2, 5, 6, 9,

Mathematics

2 answers:

sladkih [1.3K]3 years ago

6 0

Answer:

continued: 10, 13, 14, 17, 18, 21....and so on

Step-by-step explanation:

The pattern for the sequence is it's counting by 1's then 3's then 1's and 3's again. It starts 1, count by one, you get 2, then the sequence changes. 2, count by three's, you get 5. This is the sequence but shown 1, 2 3 4 5, 6 7 8 9.

juin [17]3 years ago

5 0

It looks like the first 1 is the first problem, problem #1. (because of the period)
If this is the case, then the second sequence is 1, 0, -1, ...
1-1=0
0-1=-1
-1-1=-2
-2-1=-3
-3-1=-4
The sequence would then be 1, 0, -1, -2, -3, -4, ...

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On a coordinate plane, a line has points (negative 2, negative 4) and (4, 2). Point P is at (0, 4). Which points lie on the line

NikAS [45]

Answer:

the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

Step-by-step explanation:

Given that a line passes through two points

A(-2, -4) and B(4, 2)

Another point P(0, 4)

To find:

Which points lie on the line that passes through P and is parallel to line AB ?

Solution:

First of all, let us the find the equation of the line which is parallel to AB and passes through point P.

Parallel lines have the same slope.

Slope of a line is given as:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{2-(-4)}{4-(-2)} = 1$

Now, using slope intercept form ( $y = mx+c$ ) of a line, we can write the equation of line parallel to AB:

$y =(1)x+c \Rightarrow y = x+c$

Now, putting the point P(0,4) to find c:

$4 = 0 +c \Rightarrow c = 4$

So, the equation is $\bold{y=x+4}$

So, the coordinates given in the options which have value of y coordinate equal to 4 greater than x coordinate will be true.

So, the correct options are:

(–1, 3), (–2, 2) and (–5, –1)

8 0

3 years ago

Read 2 more answers

What is the least common multiple of 4, 27, 12.

ryzh [129]

The lease common multiple of the set of numbers is 108.

108/4=27.
108/27=4.
108/12=9.

7 0

3 years ago

2\%2%2, percent of the students at Hamilton Middle School have red hair. There are 700700700 students at Hamilton Middle School.

Andrew [12]

Answer:

<u>14 students</u> at Hamilton Middle School have red hair.

Step-by-step explanation:

Given:

2%, percent of the students at Hamilton Middle School have red hair.

There are 700 students at Hamilton Middle School.

Now, to find the number of students at Hamilton Middle School having red hair.

Total number of students = 700.

Percent of the students at Hamilton Middle School have red hair = 2%.

Now, to get the number of students at Hamilton Middle School having red hair:

$2\%\ of\ 700\\\\=\frac{2}{100} \times 700\\\\=0.02\times 700\\\\=14.$

Therefore, 14 students at Hamilton Middle School have red hair.

3 0

3 years ago

Read 2 more answers

How do you solve this absolute value equatuon? 4|x - 1| - 7 = -3

MatroZZZ [7]

4|x - 1| - 7 = -3 |add 7 to both sides

4|x - 1| = 4 |divide both sides by 4

|x - 1| = 1 ⇔ x - 1 = 1 or x - 1 = -1 |add 1 to both sides

x = 2 or x = 0

Answer: B.

3 0

3 years ago

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% of the time when t

garik1379 [7]

Answer:

a) P[A/B] = 0,019 or P[A/B] = 1,9 %

b) P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %

Step-by-step explanation:

Bayes Theorem :

P[A/B] = P(A) * P[B/A] / P(B)

The branches of events are as follows

Condition 1 real infection 1/300 and not infection 299/300

Then

1.- 1/300 299/300

When the test is done (virus present) 0,9 (+) 0,15 (-)

2.- 299/300

When the test is done ( no virus ) 0,15 (+) 0,85 (-)

Then:

P(A) = event person infected P(B) = person test positive

a) P[A/B] = P(A) * P[B/A] / P(B)

where P(A) = 1/300 = 0,0033 P[B/A] = 0,9

Then P(A) * P[B/A] = 0,0033*0,9 = 0,00297

P(B) is ( 1/300 )*0,9 + (299/300)*0,15

P(B) = 0,0033*0,9 + 0,9966*0,15 ⇒ P(B) = 0,1524

Finally

P[A/B] = 0,00297 /0,1524

P[A/B] = 0,019 or P[A/B] = 1,9 %

b) Following sames steps:

P[A- /B-] = (299/300) * 0,85 / (299/300) * 0,85 + (1/300 * 0,1)

P[A- /B-] = 0,8471 /0,8474

P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %

6 0

3 years ago