Adam needs both small and large cones to set up for a soccer practice. He knows there are fewer than 30 cones in the storage roo
m. He needs at least a dozen large cones. Let x represent the number of small cones and y represent the number of large cones. Select all inequalities that model this situation. x>0 y≥12 x+y≤30 y>12 x≥0 x+y<30
X: <span>the number of small cones y: </span><span> the number of large cones
a "dozen" means 12.
"</span>Adam needs both small and large cones to set up for a soccer practice<span>" mean that x must not be 0, and y must not be 0.
"</span>there are fewer than 30 cones in the storage room." mean that : x+y<30
"He needs at least a dozen large cones." means that y≥12
so we have:
i) x≠0, y≠0, that is x>0, y>0
ii) x+y<30
iii) y≥12
now let's check all choices we have:
<span> x>0 True by i y≥12 True by iii x+y≤30 Not True by ii (x+y is smaller than 30, the sum cannot be 30) y>12 Not true by iii (y may be = 12) x≥0 Not true by i, Adam needs small cones to (so we are assuming there are some in the storage room. Though this is open to interpretation) x+y<30 True</span>
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.