The first showing of a new movie at the local movie theatre sold a total of 650 tickets. A ticket purchased at the door costs $11.50 and pre-purchased ticket costs $8.50. The total ticket sales for this movie were $6725. How many of each type of ticket were sold?

Total sales were $4659.1

Step-by-step explanation:

Given,

Commission = 11%

Amount of commission = $512.50

Let,

total sales = x

Therefore,

11% of x = 512.50

[tex]\frac{11}{100}x=512.50\\0.11x=512.50[/tex]

Dividing both sides by 0.11

[tex]\frac{0.11x}{0.11}=\frac{512.50}{0.11}\\x= $4659.1[/tex]

Total sales were $4659.1

Keywords: percentage, division

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Answer:

[tex]x= 28\°[/tex]

Step-by-step explanation:

We have labelled the given diagram and redrawn again in the attachment.

Also from the labelled diagram given below the given details are;

∠CPQ =[tex](5y-4)\°[/tex]

∠RQF =[tex]3y\°[/tex]

∠BRH =[tex](2x+13)\°[/tex]

∠CPQ = ∠PQF  (Alternate Interior Angle)

∠PQF + ∠RQF =180° (Straight angle property)

Now Substituting the values we get;

[tex]5y-4+3y=180\\8y=180+4\\8y=184\\y=\frac{184}{8}=23\°[/tex]

∠RQF =[tex]3y\° = 3\times23 = 69\°[/tex]

∠RQF = ∠BRH (corresponding angles)

[tex]69=2x+13\\2x = 69 -13\\2x=56\\x = \frac{56}{2} = 23\°[/tex]

Hence x = 23°

Answer:

1+3i

Step-by-step explanation:

(6+4i)-(5+i)

6+4i-5-i

1+4i-i

1+3i

Answer: 1+3i

Step-by-step explanation:

(6 + 4i) − (5 + i)

Before solving further, note that :

Minus × Minus = Plus

Plus × Minus = Minus

Plus × Plus = Plus

(6 + 4i) − (5 + i)

Open the bracket

= 6 + 4i - 5 - i

Collect like terms

= 6 - 5 + 4i - I

= 1 + 3i

Answer:

The difference between the given two expression as - 19 w - 3 .

Step-by-step explanation:

Given algebraic expression as

- 14 w - 3  and  5 w

Now, Let the difference between the given two expression = x

or, x = ( - 14 w - 3 ) - 5 w

or , x = - 14 w - 5 w -3

or,  x = w ( - 14 - 5 ) - 3

Or, x = -19 × w - 3

∴  x = -19 w -3

So, The difference is - 19 w - 3

Hence The difference between the given two expression as - 19 w - 3 . Answer

Answer:

[tex]\displaystyle -4 + c < -20[/tex]

Step-by-step explanation:

You could either do what I did in the above answer, or you could do this:

[tex]\displaystyle c - 4< -20[/tex]

It does not matter how you write it, as long as you understand the concept!

I am joyous to assist you anytime.

Answer:

-2/9

Step-by-step explanation:

Answer:

5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy.

Step-by-step explanation:

Alex wants to buy the same number of stamps and envelops.

Stamps are sold in packs of 14 and envelop are sold in the packs of 10.

Now, we have to find the least number of stamp packs and envelop packs that Alex should buy to get an equal number of stamps and envelops.

The least common multiple of 14 and 10 will give the result.

14 has multiples 14, 28, 42, 56, 70, .......

And 10 has multiples 10, 20, 30, 40, 50, 60, 70, ........

Therefore, 70 is the least common multiple.  

In that case 5 numbers of stamp packs and 7 number of envelop packs that Alex has to buy to get 70 stamps and 70 envelop. (Answer)

The least number of stamps and envelopes Alex can buy to have the same number is 70 of each, which he can get by purchasing five packs of each.

Alex wants to buy the same number of stamps and envelopes. To find the least number of each he could buy to have the same number, we need to find the least common multiple (LCM) of the two pack sizes, 14 (stamps) and 10 (envelopes).

The multiples of 14 are 14, 28, 42, 56, 70, etc., and the multiples of 10 are 10, 20, 30, 40, 50, 60, 70, etc. The first common multiple they share is 70.

Therefore, Alex can buy five packs of envelopes (5 x 10 = 50 envelopes) and five packs of stamps (5 x 14 = 70 stamps) to have the same number of each, which is 70.

Answer:

15p+15

Step-by-step explanation:

3(3p+5)-6p+3p(5-1)

9p+15-6p+3p(4)

9p-6p+15+12p

3p+12p+15

15p+15

Final answer:

The point (3,9) is the solution to the system of linear equations because it satisfies both inequalities y < 3x + 5 and y > -2/3x - 3 when the values of x and y are substituted into them.

Explanation:

To determine which of the given points is a solution to the system of linear equations:

y < 3x + 5
y > -2/3x - 3

We substitute the x and y values of each option into the inequalities to find a match.

For point (3,14): Substitute x = 3 and y = 14 into the inequalities.

Answer:

A subordinate clause—also called a dependent clause—will begin with a subordinate conjunction or a relative pronoun and will contain both a subject and a verb. This combination of words will not form a complete sentence. It will instead make a reader want additional information to finish the thought.

Answer:

25.6

Step-by-step explanation:

$32.00 / 100 = $0.32

$0.32 x 20 = $6.40

So $32.00 - $6.40 = $25.60

Answer: $25.60

Step-by-step explanation: you just subtract 20% fro 30 on a calculator.

Answer:

Option A is correct.

Step-by-step explanation:

See the two graphs given in the diagram attached.

The first graph shows the function f(x) = x²

Hence, it passes through the points (1,1), (-1,1), (2,4) and (-2,4) points.

Now, from the plotted second graph we see the points (2,2), and (-2,2) are on the curve.

Hence, the y-value corresponding to the same x-value reduces by a factor [tex]\frac{1}{2}[/tex] in the second graph i.e. the graph of y = g(x) compared to the first graph.

So, we can conclude that the transformed graph has the equation [tex]g(x) = \frac{1}{2} x^{2}[/tex].

Hence, option A is correct. (Answer)

Answer:

The answer is g(x) = (1/2) x^2

Step-by-step explanation:

Answer: y=2x-20

Step-by-step explanation:

y+18=2(x-1)

y+18=2x-2

y=2x-20

Answer:

9 Miles

Step-by-step explanation:

6+(6/2)=9

Hope this helps!

Answer: 9 miles

Step-by-step explanation:

6 = 10

x = 15

x= 15* 6/ 10

X= 90/10

x= 9

Answer:

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The equation of the line in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

In this problem we have

[tex]m=0.5\\b=2[/tex]

substitute

[tex]y=0.5x+2[/tex]

The easiest way to graph a line is with a pair of points.

Find the intercepts

The y-intercept is given ----> point (0,2)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=0.5x+2[/tex]

[tex]x=-4[/tex]

so

The x-intercept is the point (-4,0)

Plot the intercepts and join the points to graph the line

using a graphing tool

The graph in the attached figure

Answer:  9

====================================

Explanation:

The intersection of the two sets is the list of all values that are in both sets at the same time.

Let's convert set A into roster notation. Roster notation means we just list out all the members (use ellipses if there are a lot of values you don't want to write out; luckily these sets are small). Plug n = 2 into x = 3n and you'll find that x = 6. Repeat for n = 3, and you get x = 9. Repeat for n = 4 and you get x = 12.

Set A looks like this: {6, 9, 12}

-------

Repeat the same basic steps for set B. We'll plug m = 1 into x = 4m-3 to get x = 1. Plug m = 2 into that same equation to get x = 5. Finally m = 3 leads to x = 9

Set B = {1, 5, 9}

-------

In summary,

A = {6, 9, 12}

B = {1, 5, 9}

We see that only 9 is in both sets at the same time.

Therefore, [tex]A \cap B = \left\{ 9 \right\}[/tex] which says "the intersection of set A and set B is the set { 9 } ".

The Venn Diagram shown below has the single element 9 in the overlapping region of the two circles. The other values are in their proper respective circles, but not inside the overlapping region. Set U is the universal set.

The area of the rectangle with dimensions (3x + 5) by (x - 2) is represented by the algebraic expression 3x² - x - 10.

The area of a rectangle is found by multiplying its length by its width. Given a rectangle with length (3x + 5) and width (x - 2), we can find its area by using the formula for the area of a rectangle, which is length × width.

Area = (3x + 5)(x - 2)
By expanding this, we use the distributive property:
Area = 3x(x) + 3x(-2) + 5(x) + 5(-2)
Area = 3x² - 6x + 5x - 10
By combining like terms, we get:
Area = 3x² - x - 10

You can't factor anything out of this. At least I don't think

The expression 25x + 14 cannot be traditionally factored as it does not have any common factors, nor does it follow any special binomial patterns. It is already in its simplest form.

Explanation:

The expression 25x + 14 cannot be factored in the traditional sense because it does not have common factors nor does it fit the pattern of a special binomial such as a difference of squares or a perfect square trinomial. The expression is already in its simplest form unless we have additional restrictions or information about variable x. If we were to consider factorization in terms of factoring out a greatest common factor (GCF), since the coefficients 25 and 14 have no common factors other than 1, we cannot factor anything out. Sometimes, in different contexts, we can apply transformations, such as multiplying an equation by a constant to simplify fractions or rearranging terms for clarity, but these strategies do not apply to the expression 25x + 14 as given.

Answer:

Triangle

The triangle has 3 sides but the other ones have 4 sides. A quadrilateral has 4 sides.

For this case we have the following system of equations:

[tex]x-5y = 33\\5x-6y = 70[/tex]

We multiply the first equation by -5:

[tex]-5x + 25y = -165[/tex]

Thus, we have the equivalent system:

[tex]-5x + 25y = -165\\5x-6y = 70[/tex]

We add the equations:

[tex]-5x + 5x + 25y-6y = -165 + 70\\19y = -95\\y = - \frac {95} {19}\\y = -5[/tex]

We find the value of the variable "x":

[tex]x-5 (-5) = 33\\x + 25 = 33\\x = 33-25\\x = 8[/tex]

Thus, the solution of the system is:

[tex](x, y) :( 8, -5)[/tex]

Answer:

[tex](x, y) :( 8, -5)[/tex]

Answer:

The value of y is 14

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have the points

[tex](-2, y)\ and\ (4, 6)[/tex]

[tex]m=-\frac{4}{3}[/tex]

substitute in the formula the given values

[tex]-\frac{4}{3}=\frac{6-y}{4+2}[/tex]

solve for y

[tex]-\frac{4}{3}=\frac{6-y}{6}[/tex]

Multiply by 6 both sides

[tex]-8=6-y[/tex]

[tex]y=6+8=14[/tex]

Volume of sphere having radius of 3 inches is 113.04 cubic inches.

Solution:

Given that the radius of a sphere is 3 inches. Need to determine the volume of sphere

Formula for volume of sphere is as follows :

[tex]V=\frac{4}{3} \pi r^{3}[/tex]

Where V is volume of sphere , π is constant value = 3.14 and r = radius of a sphere.

In our case, r = 3 inches

On substituting the value of π as 3.14 and value of r as 3 inches in the formula of volume of sphere, we get

[tex]V=\frac{4}{3} \times 3.14 \times 3^{3}=4 \times 3.14 \times 9=113.04 \text { cubic inches }[/tex]

Hence volume of sphere having radius of 3 inches is 113.04 cubic inches.

Answer:

3/4

Step-by-step explanation:

21/28=3/4

Answer:

3/4

Step-by-step explanation:

Answer:

275

Step-by-step explanation:

h hamburgers

c cheeseburgers

(h + c) -total

(c + h) = 614

64 more cheeseburgers sold then hamburgers:

64 more cheeseburgers sold then hamburgers

(c - h) = 64

(c + h) = 614

+(c - h) = 64

2c = 678

c = 678/2 = 339

c + h = 614

339 + h =614

h = 614 - 339 = 275

To find the cost of 24 candy bars, calculate the cost per candy bar (found by dividing $20 by 16, equaling $1.25) and multiply it by 24. Therefore, 24 candy bars would cost $30.

The subject of the question involves unit pricing, a common concept in mathematics. To find the cost of 24 candy bars, first identify the cost per candy bar, then multiply this unit price by the number of candy bars in question.

From the question, we know that 16 candy bars cost $20. So the unit price, or cost per candy bar, is $20 divided by 16, which equals $1.25.

Therefore, the cost of 24 candy bars would be $1.25 (the cost per candy bar) multiplied by 24 (the number of candy bars), which equals $30. Hence, 24 candy bars would cost $30.

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Answer:

The Time taken by submarines to travel before the vessel is 11 hours

Step-by-step explanation:

Given as :

The average speed of aircraft carrier = 15 mph

The average speed of submarine = 15 mph

The distance between them = 300 mile

The time taken by aircraft = T hour

The time taken by submarine = T + 2  hour

Now, Speed = [tex]\dfrac{\textrm Distance}{\textrm Time}[/tex]

So, Distance =  Speed × Time

Now,

300 miles = 15 × T + 15 × ( T + 2)

Or, 300 = 15 T + 15 T + 30

or, 300 - 30 = 30 T

Or, 270 = 30 T

∴ T = [tex]\frac{270}{30}[/tex]

I,e T = 9 hours

So, T + 2 = 9 + 2 = 11 hours

Hence The Time taken by submarines to travel before the vessel is 11 hours Answer

Answer:

y = 5

Step-by-step explanation:

Divide each side by 8 to get (y-9) = -4.

Add 9 to each side to isolate the variable y. This leaves you with y = 5

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1:}[/tex]

[tex]8(y-9)=-32\qquad\text{divide both sides by 8}\\\\\dfrac{8\!\!\!\!\diagup(y-9)}{8\!\!\!\!\diagup}=\dfrac{-32\!\!\!\!\!\diagup^4}{8\!\!\!\!\diagup_1}\\\\y-9=-4\qquad\text{add 9 to both sides}\\\\y-9+9=-4+9\\\\y=5[/tex]

[tex]\bold{METHOD\ 2:}[/tex]

[tex]8(y-9)=-32\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\(8)(y)+(8)(-9)=-32\\\\8y-72=-32\qquad\text{add 72 to both sides}\\\\8y-72+72=-32+72\\\\8y=40\qquad\text{divide both sides by 8}\\\\\dfrac{8y}{8}=\dfrac{40}{8}\\\\y=5[/tex]

Answer:

x=11, now it's the right answer :/

Step-by-step explanation:

-3x+15=4-2x

-3x+11=-2x

11=x

Fixed

Answer:

The correct answer is D. 15 squared centimeters.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Base one = 10 centimeters

Base two = 5 centimeters

Height = 2 centimeters

2. Let's find out the area of the trapezoid, using the following formula:

Area = 1/2 (Base one + Base two) * Height

Replacing with real values:

Area = 1/2 (10 + 5) * 2

Area = 1/2 (15 * 2) = 1/2 (30)

Area = 15 centimeters ²

The correct answer is D. 15 squared centimeters.