There are 268 cars, lorries and motorcycles in a car park.
There are 3 times as many cars as lorries.
There are 20 motorcycles.
(a) How many cars and lorries are there?
(b) How many lorries are there?

(a)

We know how many motorcycles are there, so the number of cars and lorries is the difference in the total number of cars, lorries, motorcycles and motorcycles

268-20=248.

So there are 248 cars and lorries

248 cars and lorries

(b)

Let the number of lorries be x, then the number of cars is 3x. There are 248 cars and lorries in total.

Now we can make an equation

So on the park there are 62 lorries. Then the number of cars is

There are 62 lorries and 186 cars

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.