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nikklg [1K]
2 years ago
11

The Tabletop Games club, a student-led campus group, hosted a virtual concert last week to raise awareness about their club and

bring community members together. They sold full-price tickets for
$7.00, tickets for senior citizens were $5.25
and student tickets cost $5.50.

After the concert, they counted up the totals. There were a total of 215 tickets sold, and ticket sales brought in $1,214.00
. It was noted that there were 3 times as many senior citizen tickets sold as there were full-price tickets.

Write and solve a linear system to determine how many of each type of ticket were sold.



There were _____
full-price tickets.

There were ____
senior citizen tickets.

There were ____
student tickets.
Mathematics
1 answer:
yarga [219]2 years ago
3 0

Answer:

um i don't know this (i do im just lazy as heck)

Step-by-step explanation:

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Find the volume of the solid.
dmitriy555 [2]

In Cartesian coordinates, the region (call it R) is the set

R = \left\{(x,y,z) ~:~ x\ge0 \text{ and } y\ge0 \text{ and } 2 \le z \le 4-x^2-y^2\right\}

In the plane z=2, we have

2 = 4 - x^2 - y^2 \implies x^2 + y^2 = 2 = \left(\sqrt2\right)^2

which is a circle with radius \sqrt2. Then we can better describe the solid by

R = \left\{(x,y,z) ~:~ 0 \le x \le \sqrt2 \text{ and } 0 \le y \le \sqrt{2 - x^2} \text{ and } 2 \le z \le 4 - x^2 - y^2 \right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\sqrt2} \int_0^{\sqrt{2-x^2}} \int_2^{4-x^2-y^2} dz \, dy \, dx

While doable, it's easier to compute the volume in cylindrical coordinates.

\begin{cases} x = r \cos(\theta) \\ y = r\sin(\theta) \\ z = \zeta \end{cases} \implies \begin{cases}x^2 + y^2 = r^2 \\ dV = r\,dr\,d\theta\,d\zeta\end{cases}

Then we can describe R in cylindrical coordinates by

R = \left\{(r,\theta,\zeta) ~:~ 0 \le r \le \sqrt2 \text{ and } 0 \le \theta \le\dfrac\pi2 \text{ and } 2 \le \zeta \le 4 - r^2\right\}

so that the volume is

\displaystyle \iiint_R dV = \int_0^{\pi/2} \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta \, dr \, d\theta \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} \int_2^{4-r^2} r \, d\zeta\,dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} r((4 - r^2) - 2) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \int_0^{\sqrt2} (2r-r^3) \, dr \\\\ ~~~~~~~~ = \frac\pi2 \left(\left(\sqrt2\right)^2 - \frac{\left(\sqrt2\right)^4}4\right) = \boxed{\frac\pi2}

3 0
1 year ago
A blue Jay wanted to store some acorns for the winter. If she hides 18 acorns per tree, she will be left with four acorns; if sh
Semenov [28]

Answer:

4 trees and 76 acorns.

Step-by-step explanation:

Let the amount of trees be x.

18x+4=20x-4\\\\\implies2x=8\\\\\implies x=4

There are 4 trees, and there are 18x+4 acorns or 76 acorns.

Hope you have a nice day, and also you should mark brainliest :)

8 0
1 year ago
Read 2 more answers
Need the correct answer to this question please and thank you
Mashutka [201]

Answer:

C

Step-by-step explanation:

twice a number less three=2x-3

is one half of three times the number=3x/2

2x-3=3x/2

5 0
2 years ago
Jason and Shawn both begin riding their bikes from different points away from the ranger station. They both ride their bikes in
Nataly [62]

Answer:

The answer to the question is

Shawn has to wait for  3 minutes for Jason to meet him at 2 miles away from the station

Step-by-step explanation:

To solve the question, we note the variables

Bike speed = 20 mph

Start point of Jason = 1 mile away from the station

Starting point of Shawn = 2 mile away from the station

Total miles away from station = y

Direction of biking = away from the station

Therefore if they both start biking at the same time, Shawn is ahead of Jason

Riding speed of Shawn = Riding speed of Jason = 20 mph

That is Shawn has to wait for 1/20 hr or 3 minutes for Jason to meet him at 2 miles away from the station

3 0
3 years ago
Tara was making cakes to sell for a fundraiser for her school. Each cake requires 1 and 3/4 cups of sugar. She plans to make 5 c
BARSIC [14]
D
Just multiply 5 times 1 and 3/4!
3 0
3 years ago
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