All categories

2 years ago

The drama club was selling tickets

Mathematics

1 answer:

Lubov Fominskaja [6]2 years ago

5 0

Answer:

108 student tickets, and 176 adult tickets were sold

Step-by-step explanation:

Adult ticket $8 Call the number of adult tickets sold "a"

Student ticket $5 Call the number of student tickets sold "s"

Since we are talking about TWO consecutive days of sold out seats, the total number of seats sold were 2* 142 = 284

Then we create two different equations with the information given:

a + s = 284

8 * a + 5 * s = 1948

we can solve for s in the first equation as follows: s = 284 - a

and use it in the second equation

8 a + 5 (284 - a) = 1948

8 a + 1420 - 5 a = 1948

combining

3 a = 528

a = 528/3

a = 176

we find the number of student tickets using this answer in the substitution equation we used:

s - 284 - 176 = 108

Therefore 108 student tickets, and 176 adult tickets were sold.

You might be interested in

Choose the best coordinate system to find the volume of the portion of the solid sphere rho <_4 that lies between the cones φ

MrRissso [65]

Answer:

So, the volume is:

$\boxed{V=\frac{128\sqrt{2}\pi}{3}}$

Step-by-step explanation:

We get the limits of integration:

$R=\left\lbrace(\rho, \varphi, \theta):\, 0\leq \rho \leq 4,\, \frac{\pi}{4}\leq \varphi\leq \frac{3\pi}{4},\, 0\leq \theta \leq 2\pi\right\rbrace$

We use the spherical coordinates and we calculate a triple integral:

$V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}}\int_0^4 \rho^2 \sin \varphi \, d\rho\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \left[\frac{\rho^3}{3}\right]_0^4\, d\varphi\, d\theta\\\\V=\int_0^{2\pi}\int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \sin \varphi \cdot \frac{64}{3} \, d\varphi\, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} [-\cos \varphi]_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \, d\theta\\\\V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\$

we get:

$V=\frac{64}{3} \int_0^{2\pi} \sqrt{2} \, d\theta\\\\V=\frac{64\sqrt{2}}{3}\cdot[\theta]_0^{2\pi}\\\\V=\frac{128\sqrt{2}\pi}{3}$

So, the volume is:

$\boxed{V=\frac{128\sqrt{2}\pi}{3}}$

4 0

2 years ago

A normal distribution has a mean of 4 and a standard deviation of 1. What percent of values are from 4 to 7?

Igoryamba

Answer:

49.865%

Step-by-step explanation:

Given that:

μ = 4 ; σ = 1

For x = 4

P(x < 4) :

Z score (x - μ) / σ

P(x < 7) - P(x < 4)

((7 - 4) / 1) - ((4 - 4) / 1)

P(Z < 3) - P(Z < 0)

Usibg the Z probability calculator :

0.99865 - 0.5

= 0.49865

= 0.49865 * 100

= 49.865%

6 0

2 years ago

Number 28 ignore the bubbled in answer

Ghella [55]

Answer:

y = -7x+34

Step-by-step explanation:

We have 2 points, so we can find the slope

m = (y2-y1)/(x2-x1)

= (6--1)/(4-5)

= (6+1)/(4-5)

= 7/-1

= -7

We can use point slope form to make an equation

y-y1 = m(x-x1)

y--1 = -7(x-5)

y+1 = -7(x-5)

Distribute

y+1 = -7x+35

Subtract 1 from each side

y+1-1 = -7x+35-1

y = -7x+34

3 0

2 years ago

Use the Distributive Property and mental math to find the product. 9×76 =

Fed [463]

Answer:

684

Step-by-step explanation:

Trust

8 0

2 years ago

A square desk can seat four people, one on each side. If you push two desks together, you can fit six people. Three desks pushed

weeeeeb [17]

Answer:

Option c. 104 people

Step-by-step explanation:

For 1 desk : 4 people

For 2 desks: 6 people

For 3 desks: 8 people

For 51 desks:

We can see the pattern in the number of people that can be seated on the tables.

Using arithmetic series: 4,6,8,....

a(n) = a1 + (n-1)d

n = 51

d = a2 - a1 = 6 - 4 = 2

a(51) = 4 + (51 - 1) 2

= 4 + (50)2

= 4 + 100

= 104

3 0

2 years ago