Jack bought 4 rulers and 5 compasses for $18.92 altogether. If Jacks brother bought 2 rulers and 4 compasses for $14.98, what was the price of each compass?

Price of each compass = $3.68

Price of each ruler = $0.13

Step-by-step explanation:

Let R denote rulers and C denotes compasses

Jack bought 4 rulers and 5 compasses for $18.92

which algebraically translates to

4R + 5C = 18.92   eq. 1

Jack's brother bought 2 rulers and 4 compasses for $14.98

which algebraically translates to

2R + 4C = 14.98   eq. 2

Now we have two equations and two unknowns R and C

Choose any of the above equation and make any of the unknown the subject of the equation.

Choosing eq. 1

4R + 5C = 18.92

4R = 18.92 - 5C

R = (18.92 - 5C)/4    eq. 3

Now put this value of R into eq. 2

2R + 4C = 14.98

2((18.92 - 5C)/4) +4C = 14.98

9.46 - 2.5C + 4C = 14.98

1.5C = 5.52

C = 5.52/1.5

C = 3.68

So the price of each compass is $3.68

We can verify whether our answer is right or not. First we have to find the cost of R

Put this value of C into eq. 3

R = (18.92 - 5C)/4

R = (18.92 - 5*3.68)/4

R = (18.92 - 18.4)/4

R = 0.52/4

R = 0.13

So the price of each ruler is $0.13

Now let us verify:

from eq. 1

4R + 5C = 18.92

4(0.13) + 5(3.68) = 18.92

0.52 + 18.4 = 18.92

18.92 = 18.92  (hence proved)

from eq. 2

2R + 4C = 14.98

2(0.13) + 4(3.68) = 14.98

0.26 + 14.72 = 14.98

14.98 = 14.98  (hence proved)

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

54 kilometers per hour

step-by-step explanation:

according to rules:

1 km = 1000 meter

which means that 1 meter = 1/1000 km

1 hour = 3600 second [ as 1 hour = 60 min = 60 *60 seconds ]

which means that 1 second = 1/3600 hour

therefore, 1 kilometer/hour =

thus to convert 15 meter per second to kilometer per hour, we multiply 15 to 3.6 kilometer/hour.

15 meter/second=   which is the required answer.