This is real now! i need
brenton’s weekly pay, p(h) , in dollars, is a function of the number of hours he works, h. he gets paid $20 per hour for the first 40 hours he works in a week. for any hours above that, he is paid overtime at $30 per hour. he is not permitted to work more than 60 hours in a week.
which set describes the domain of p(h)?
a.{h| 0 ≤ h ≤ 40}
b.{h| 0 ≤ h ≤ 60}
c.{p(h)| 0 ≤ p(h) ≤ 1,400}
d.{p(h)| 0 ≤ p(h) ≤ 1,800}

B. {h| 0 ≤ h ≤ 60}

Step-by-step explanation: Here, h represents the number of hours he got paid and P(h) represents the amount he paid.

He gets paid $20 per hour for the first 40 hours he works in a week.

That is, P(h) = 20 for 0 ≤ h ≤ 40

And, For any hours above that, he is paid overtime at $30 per hour, while,  He is not permitted to work more than 60 hours in a week.

That is, P(h) = 30 for 40 < h ≤  60

⇒ The all possible values of h in the function P(h) are,

0 ≤ h ≤ 40 and 40 < h ≤  60 ⇒ 0 ≤ h ≤ 60,

Since, the domain is the set of all possible value of input,

Hence, the domain of P(h) = 0 ≤ h ≤ 60

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be