Asatellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. each unit contains the same number of non-upgraded sensors. if the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

a) 5/6
b) 1/5
c) 1/6
d) 1/7
e) 1/24

1/7 (option d) of the sensors on the satellite have been upgraded

Step-by-step explanation:

Each unit contains the same number of non-upgraded sensors

number of non-upgraded sensors for each module (nus)

total number of upgraded sensors on the satellite (tus)

satellite is composed of 30 modular units

total number of non-upgraded sensors on the satellite (tnus):

tnus=30*nus

total number of sensors on the satellite (ts):

ts=tnus+tus = 30*nus + tus (I)

The number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite

nus=(1/5)*tus

tus = 5 * nus (II)

Fraction of the sensors on the satellite have been upgraded (FU):

FU = tus/ts

Using I and II

FU= (5* nus)/(30*nus + tus)

FU = (5* nus)/(30*nus + 5 * nus)

FU = (5* nus)/(35*nus)

FU = 1/7

1/7 (option d) of the sensors on the satellite have been upgraded

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions