What is the theoretical probability of rolling a 1 or a 5 on a standard six-sided die?

The functions q and r are defined as follows.<br> HELP PLEASE

dusya [7]

Answer:

-22

Step-by-step explanation:

First do r(3) by replacing x with 3 in r:

2*3^2 + 2 = 2*9 + 2 = 18 + 2 = 20

Then replace r(3) with 20 to do q(20):

-20-2 = -22

7 0

3 years ago

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

Lina20 [59]

Answer:

The differential equation for the amount of salt A(t) in the tank at a time t > 0 is $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

Step-by-step explanation:

We are given that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another brine solution is pumped into the tank at a rate of 3 gal/min, and when the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

The concentration of the solution entering is 4 lb/gal.

Firstly, as we know that the rate of change in the amount of salt with respect to time is given by;

$\frac{dA}{dt}= \text{R}_i_n - \text{R}_o_u_t$

where, $\text{R}_i_n$ = concentration of salt in the inflow $\times$ input rate of brine solution

and $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

So, $\text{R}_i_n$ = 4 lb/gal $\times$ 3 gal/min = 12 lb/gal

Now, the rate of accumulation = Rate of input of solution - Rate of output of solution

= 3 gal/min - 2 gal/min

= 1 gal/min.

It is stated that a large mixing tank initially holds 500 gallons of water, so after t minutes it will hold (500 + t) gallons in the tank.

So, $\text{R}_o_u_t$ = concentration of salt in the outflow $\times$ outflow rate of brine solution

= $\frac{A(t)}{500+t} \text{ lb/gal } \times 2 \text{ gal/min}$ = $\frac{2A(t)}{500+t} \text{ lb/min }$

Now, the differential equation for the amount of salt A(t) in the tank at a time t > 0 is given by;

= $\frac{dA}{dt}=12\text{ lb/min } - \frac{2A(t)}{500+t} \text{ lb/min }$

or $\frac{dA}{dt}=12 - \frac{2A(t)}{500+t}$ .

4 0

3 years ago

You have 60 CD cases that you would like to store on a shelf that is 24 inches long. if each CD case is 3/8 inch wide, is there

Jet001 [13]

Yes you do.

The shelf is 24 in. long, so to fit, the total width of all the cases must be < 24 in.

If each case is 3/8 inches:
60 * 3/8 = 22.5

22.5 < 24, therefore they will all fit.

5 0

3 years ago

Read 2 more answers

Jenny and Lester are running the 100 meter dash. Jenny completes it in 15.2 seconds and Lester completed it in 15.7 seconds. Wha

matrenka [14]

Jenny won the race as she finished the race much more quickly and has greater average speed than Lester.

$\sf \boxed{\sf speed:\frac{distance}{time \ taken} }$