If there are 12 doctors and 42 nurses, what is the ratio of doctors to nurses reduced to lowest terms?

2/7

Step-by-step explanation: We can write a ratio using the word to, using a colon, or using a fraction bar. Here, since we want our answer in lowest terms, I would write the ratio using a fraction bar.

So we need to compare the number of doctors

to the number of nurses.

We know that there are 12 doctors so we write 12 in the numerator of our ratio and we also know there are 42 nurses so we write 42 in the denominator of our ratio and this gives us 12/42.

Notice however that 12/42 is not in lowest terms so we need to divide the numerator and the denominator

by their greatest common factor of 6 to get 2/7.

So the ratio of the number of doctors to the number of nurses is 2/7.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!