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3 years ago

Find an explicit formula for the arithmetic sequence -5,13,31,49,...

Mathematics

1 answer:

nadezda [96]3 years ago

6 0

Step-by-step explanation:

b(n) = b(1) + (n-1) d, where d is the difference,

d = 13-(-5) = 18

b(n) = (-5) + (n-1)(18)

= -5 +18n -18

b(n) = 18n -23

You might be interested in

Which algebraic expression represents the word expression "three times the square of a number, n, subtracted from 54"?

sveta [45]

Answer:

54 - 3n²

Step-by-step explanation:

Square of a number n = n²

Three times the square of n = 3*n² = 3n²

Expression:

54 - 3n²

3 0

3 years ago

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction.

klemol [59]

Answer:

a) the expected number of tweets with no reaction is 71 tweets

b) the variance is 20.59 tweets² ( ≈ 21 tweets )and the standard deviation is

4.537 tweets (≈ 5 tweets)

Step-by-step explanation:

we can use the binomial probability distribution

P(x, N, p ) = N!/[(N-x)!x!] * p^x * (1-p)^(N-x)

where

x = number of successful events

N = population total

p = probability for success for every individual and independent event

P = probability for x successful events

in our case p = 71% = 71/100 (probability of a tweet without reaction) , N = 100 tweets

a) the expected number of tweets

E(x) = N* p = 100 tweets * 71/100 = 71 tweets

b) the variance is

V(x) = N * p * (1-p)

V = 100 * 71/100 * (1-71/100) = 71* 29/100 = 20.59 tweets² ( units of variance are [N²] )

the standard deviation is

s = √V = √20.59 tweets² = 4.537 tweets

6 0

3 years ago

What is the midpoint of the line segment with endpoints ( 3.5,2.2) and (1.5,-4.8)?

Fantom [35]

Answer:

Option A) (2.5,-1.3) is correct

The midpoint of the given line segment is M=(2.5,-1.3)

Step-by-step explanation:

Given that the line segment with end points (3.5, 2.2) and (1.5, -4.8)

To find the mid point of these endpoints midpoint formula is $M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

Let ( $x_1,y_1$ ) be the point (3.5, 2.2) and ( $x_2, y_2$ ) be the point (1.5, -4.8)

substituting the points in the formula

$M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$M=\left(\frac{3.5+1.5}{2}, \frac{2.2-4.8}{2}\right)$

$=\left(\frac{5}{2}, \frac{-2.6}{2}\right)$

$=\left(2.5,-1.3\right)$

Therefore M=(2.5,-1.3)

The midpoint of the given line segment is M=(2.5,-1.3)

8 0

3 years ago

on a recent hike through riverbend park antoinette traveled 2/3 mile in 1/3 hour . Which unit rate describes antoinettes speed i

My name is Ann [436]

Answer:

Her speed is of 2 miles per hour.

Step-by-step explanation:

Velocity:

The velocity is given by the following formula:

$v = \frac{d}{t}$

In which v is the velocity, d is the distance and t is the time.

2/3 mile in 1/3 hour .

This means that $d = \frac{2}{3}, t = \frac{1}{3}$

Which unit rate describes antoinettes speed in miles per hour?

This is v. So

$v = \frac{d}{t} = \frac{\frac{2}{3}}{\frac{1}{3}} = \frac{2}{3}*\frac{3}{1} = 2$

Her speed is of 2 miles per hour.

5 0

3 years ago

There are 3 cats in a room and no other creatures. Each cat has 2 ears, 4 paws, and 1 tail. Which of the following shows a ratio

Maru [420]

A. 1:2:4
None of the other ones fit correctly.

3 0

3 years ago

Read 2 more answers