For every 4,240 strings of decorative lights manufactured at a lighting factory, about
480 are considered deficient before the time of packaging and are disposed of.
if 162 strings of lights were disposed of last week because they were deficient, how
many strings of lights were manufactured?

1431 total strings of lights.

Step-by-step explanation:

First, we need to set up a proportion for this problem.

    480 deficient             =             162 deficient  

      4,240 total                                 x total

use the "butterfly" method: multiply each diagonal of the proportion and set them equal to each other.

162 * 4,240  =   480x

686880 =   480x

686880/480 =  x

x = 1431 total strings of lights.

answer: 12   they all have at least 28 days

step-by-step explanation: haha

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

the factor is 2

step-by-step explanation:

let f(x)=8(3^(x−2)+2)

to stretch a graph by 3, it would be 3f(x)

g(x) =3f(x)

g(x) = 3*(8(3^(x−2))+2)

g(x) = 24 (3^(x-2) )+6

x     −2     0     2     4     6

f(x) 1/64 1/16   1/4     1     4

1/64 * z * z = 1/16

i multiplies by z twice because it its 2 steps from -2 to 0

1/64 z^2 = 1/16

multiply by 64 to clear the fraction on the left side

1/4 * 64 z^2 =1/16 *64

z^2 = 4

take the square root of each side

sqrt(z^2) = ±sqrt(4)

z = ±2  

we are multiplying by 2 each time.