At Jim's auto shop, it takes him minutes to do an oil change and minutes to do a tire change. Let be the number of oil changes he does. Let be the number of tire changes he does. Using the values and variables given, write an inequality describing how many oil changes and tire changes Jim can do in less than hours ( minutes).

The total time that Jim needs to change x oil changes and y tire changes is less than 180 min.

The time needed for x oil changes is 12 * x.

The time needed for y tire changes is 18 * y.

The total time is the sum of the above times and needs to be less than 180 that is

12 * x + 18 * y < 180 divide both sides of equation by 6

12/6 * x + 18/6*y < 180/6

2*x + 3*y < 30

2*x < 30 - 3*y divide both sides by 2 to get the inequality for x

x < 30/2 - 3/2*y = 15 - 1.5 y < 15 that is x < = 15

2*x + 3*y < 30

3*y < 30 - 2*x divide both sides by 3 to get the inequality for y

y < 30/3 - 2/3 *x = 10 - 2/3*x < 10 that is y < = 10

Also we can write x + y < x+ 3/2 * y < 15.

Explanation:

Jim's can do not more then 5 oil changes and not more then 10 tire changes or all together she can do not more then 15 total of oil and tire changes.

The question his incomplete, the complete question is;

Which of the following required Bohr's model of the atom to need modification

A. energies of electrons are quantized

b. electrons do not follow circular orbits around the nucleus

c. Quantized electrons energies are responsible for emission spectra lines

d. an electrons energy increases the farther it moves from the nucleus

electrons do not follow circular orbits around the nucleus

Explanation:

Neils Bohr's model of the atom closely follows the planetary model of Rutherford, hence is it sometimes referred to as the Bohr-Rutherford's model of the atom. Its main points are that;

Electrons are found in circular orbits

Electronic transition within the atom leads to spectral lines

The energy of an orbit is related to its size.

One major refinement of the Bohr's model of the atom is the Bohr-sommerfield model. Sommerfeld added that electrons are found in elliptical rather than circular orbits. This Bohr-sommerfield model was able to explain atomic spectral effects, such as the Stark effect in spectral line splitting.

Hence, the fact that electrons are found in elliptical rather than circular orbits was a major failure of Bohr's original proposition.