$x-\ adults\\
y-\ students\\\\ \left \{ {{5x+3.50y=2517.5} \atop {x+100=y}} \right.\\\\
5x+3.5(x+100)=2517.5\\\\
5x+3.5x+350=2517.5\ \ \ | subtract\ 350\\\\
8.5x= 2167,5\ \ \ | divide\ by\ 8.5\\\\
x=255\\\\
y=355\\\\
There\ were\ 355\ student\ tickets\ and\ 255\ adult\ tickets.$

6 0

4 years ago

What is the mode for the set of data? 6,7,10,12,12,13 10 12 13 11

KonstantinChe [14]

12
because it is the only number that appears more than once which is basically the definition of mode.

4 0

3 years ago

A spinner with 6 equally sized slices is shown below. (2 slices are yellow, 1 is blue, and 3 are red.) The dial is spun and stop

Lady bird [3.3K]

Answer:

1/3

Step-by-step explanation:

We have 6 slices

2 are yellow

P ( yellow) = number of yellow / total

= 2/6

= 1/3

8 0

3 years ago

Read 2 more answers

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

3 years ago