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Katen [24]
2 years ago
9

125 tickets were sold for the jazz band concert for a total of $1,022. Student tickets cost $6 each, and general admission ticke

ts cost $10 each. How many of each kind of ticket were sold?
Mathematics
1 answer:
Phoenix [80]2 years ago
5 0

Answer:

The number of student tickets was 57

The number of general admission tickets was 68

Step-by-step explanation:

Let

x----> the number of student tickets

y---> the number of general admission tickets

we know that

x+y=125

x=125-y ---> equation A

6x+10y=1,022 ----> equation B

Substitute equation A in equation B and solve for y

6(125-y)+10y=1,022

750-6y+10y=1,022

4y=1,022-750

4y=272

y=68

Find the value of x

x=125-68=57

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Paintballs are $2.30 per pound.
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1 year ago
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The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V
aleksklad [387]

Answer:

The answer is explained below

Step-by-step explanation:

Given that The volume of air inside a rubber ball with radius r can be found using the function V(r) = \frac{4}{3}\pi r^3, this means that the volume of the air inside the rubber ball is a function of the radius of the rubber ball, that is as the radius of the rubber ball changes, also the volume of the ball changes.

As seen from the function, the radius is directly proportional to the volume of the ball, if the radius increases, the volume also increases.

V(\frac{5}{7} ) is equal to the volume of the ball when the radius of the ball is \frac{5}{7}. Therefore:

V(\frac{5}{7} )=\frac{4}{3} \pi *(\frac{5}{7} )^3=1.53\ unit^3

3 0
2 years ago
For a polygon to be convex means that all of its interior angles are less than 180 degrees. Prove that for all integers n ≥ 3, t
Alexeev081 [22]

Answer: check explanation

Step-by-step explanation:

Let K(n) be the sum of the interior angles in any n-sided convex polygon which is exactly 180(n −2)

degrees.

CASE: n = 3. A 3-sided polygon is a triangle, whose interior angles were shown always to sum to be 180 degree

INDUCTION HYPOTHESIS: Suppose that K(b) holds for some b ≥ 3. Which means that the interior angles in any b-sided convex

polygon is exactly 180(n −2) degrees.

INDUCTION STEP: We need to show that K(n is greater than or equals to 3) . That is, the interior angles of any b+1-sided convex polygon

is exactly 180(b−2) = 180(b −1) degrees,

Let X be any (b+1)-vertex convex polygon, say with successive vertices x1, x2,..., xb+

Now Y is also a convex polygon , so by the induction hypothesis K(b), the sum of the interior

angles of Y is 180(k −2).

Now let T be the triangle with vertices xk , xb+1, x1. The sum of the interior angles in X is the sum of those

in Y plus the sum of those in T .

So the sum of the interior angles in X is

180(b −2)+180 = 180((b +1)−2) = 180(b −1).

Since X was arbitrary, we conclude that the sum of the interior angles of any (b +1)-sided convex polygon

is 180((b−2)+1) = 180(b−1). That is, P(b +1) holds.

And which means that n is greater or equals to 3

8 0
1 year ago
The student to faculty ratio at a small college is 17:3 the total number of students and faculty is 740. How many faculty member
larisa86 [58]

Answer:

111

Step-by-step explanation:

It is given that the student to faculty ratio at a small college is 17:3.

Let number of students and faculty members are 17x and 3x respectively.

It is given that total number of students and faculty is 740.

17x+3x=740

20x=740

Divide both sides by 20.

x=37

Number of student =17\times 37=629

Number of faculty members =3\times 37=111

Therefore, there are 111 faculty members at the college.

3 0
2 years ago
Find the area of the unfolded box bottom.
Marysya12 [62]
The answer is 150 because 
5*30
shortcut: 5*3=15
add the zero from the 50
150 is your answer..
6 0
2 years ago
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