There are 40 children in a classroom and n of them do not wear spectacles. (4)/(5) of the boys and (2)/(3) of the girls wear spectacles. Express the number of boys who wear spectacles in terms of n.

9514 1404 393

  b = 80 -6n . . . . boys who wear spectacles

Step-by-step explanation:

We know the ratio of boys who wear spectacles to those who don't is ...

  (4/5) : (1 -4/5) = 4 : 1

If we let b represent the number of boys who wear spectacles, then the number who don't is b/4. Then total number of boys is then b +b/4 = 5b/4. The number of girls in the classroom is this number less than 40.

Let's define a few groups:

Then the total of children who do not wear spectacles is ...

  n = b/4 +(1/3)(40 -5b/4)

  12n = 3b +(160 -5b) = 160 -2b . . . . multiply by 12

  2b = 160 -12n . . . . . . . . . . . . . add 2b-12n

  b = 80 -6n . . . . the desired relation, b = boys who wear spectacles

Additional comment

The only values of n that make sense in this context are {8, 10, 12}, corresponding to {0, 15, 30} total girls and {40, 25, 10} total boys.

x -

median = 1.25

range = 12-14.5

interquartile = q12-q14.5

y -

median = 1

range = 15-17

interquartile = q15-q17

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.