14. The maximum capacity for seating in a theater is 500 people. The theater sells two types of tickets, adult tickets for $7.25 each and child tickets for $4 each. If they sold out on a certain showtime and made a total of $3,157 in ticket sales, how many of each types of tickets was sold out that showtime?
Answers
Step-by-step explanation:
set x as the number of the adults in the show
500-x - number of children
(500-x)×4+7.25x=3157
2000-4x+7.25x=3157
3.25x=1157
3×1/4x=1157
13/4x=1157/×4
13x=4628/÷13
x=356
356 adult tickets was sold out.
500-356=144
144 child tickets was sold out.
Answer:
Adult tickets sold = 356
Child tickets sold = 144
Step-by-step explanation:
Given information:
Maximum number of seats = 500Cost of adult ticket = $7.25Cost of child ticket = $4Total revenue of sold-out show = $3,157Define the variables:
Let x = the number of adult tickets sold.Let y = the number of child tickets sold.Create two equations from the given information:
[tex]\textsf{Equation 1}: \quad x + y = 500[/tex]
[tex]\textsf{Equation 2}: \quad 7.25x+4y=3157[/tex]
Rewrite Equation 1 to make y the subject:
[tex]\implies y=500-x[/tex]
Substitute this into Equation 2 and solve for x:
[tex]\implies 7.25x+4(500-x)=3157[/tex]
[tex]\implies 7.25x+2000-4x=3157[/tex]
[tex]\implies 3.25x+2000=3157[/tex]
[tex]\implies 3.25x=1157[/tex]
[tex]\implies x=356[/tex]
Substitute the found value of x into the rewritten form of Equation 1 and solve for y:
[tex]\implies y=500-356[/tex]
[tex]\implies y=144[/tex]
Solution
Adult tickets sold = 356Child tickets sold = 144Learn more about systems of equations here:
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Related Questions
Public school per-student expenditures increased approximately linearly from $4.6 thousand in 1990 to $10.8 thousand in 2013. Predict the per-student expenditure in 2024.
In 2024 public school per-student expenditures will be about $thousand.
(Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places as needed.
Answers
per-student expenditures will be about $ 9.16.
Public school per-student expenditures in 1990 is $4.60
per-student expenditures in 2013 is $10.8
in 23 years per student expenditure has increase of 10.8-4.60 = $6.2
in 1 years per student expenditure has increase of $6.2/23.
in 34 years per student expenditure has increase of ($6.2/23)34 =$9.16
per-student expenditures will be about $ 9.16.
the act of spending (as money, time, or power) 2 : something this is spent hold a file of your costs. expenditure.
What are examples of costs?
Expenditure – this is the whole purchase fee of a great or service. for instance, a agency buys a $10 million piece of device that it estimates to have a useful life of five years. this will be labeled as a $10 million capital expenditure.
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square root of 72/98
Answers
Answer:√78= 8.9 √98= 9.9
Step-by-step explanation:
Answer:
6/7
Step-by-step explanation:
So first, we can simplify 72/98. If we divide both the numerator and denominator by 2, to get a simplified fraction. So we need to solve 72/2 and 98/2. 72/2 = 36 and 98/2 = 49 So now we have a simplified fraction. So now, we are left with the square root of 36/49, and we apply the radical rule. So now we have simplified radicals that make things easier. The square root of 36 is 6, while the square root of 49 is 7. This is because 36 can be broken down into factors of 6 and 6, so like 6^2 = 36. So square root of 36 is 6. While 49 can be broken down as 7 and 7, so like 7^2 = 49, so square root of 49 is 7. Therefore our answer is 6/7.
I hope this helps, have a blessed day!
find the area of the circle
Answers
Answer:
113.04 square feet
Step-by-step explanation:
A = π[tex]r^{2}[/tex]
A = π [tex](6[/tex][tex])^{2}[/tex]
A = 3.14 (36)
A = 113.04
Write 0.0000629 in scientific notation
Answers
Answer:
6.29 × 10^-5
Step-by-step explanation:
0.0000629
The number part of the answer is 6.29
To go from 0.0000629 to 6.29, the decimal point needs to move 5 places to the right, so the exponent on the 10 must be -5.
0.0000629 = 6.29 × 10^-5
Answer: 6.29*10^(-5)
Step-by-step explanation:
0.0000629=
0.629*10^(-4)= ==> there are 4 zeros before the decimal point.
6.29*10^(-(4+1))=6.29*10^(-5)
The coordinates of the endpoints of GH are G(2,7) and H(11,16). Point I is on GH and divides it such that GI:HI is 4:5. What are the coordinates of I?
Answers
The coordinates of I ( x, y) = ( 6, 11 )
What is coordinate in math?
A pair of numbers that use the horizontal and vertical separations from the two reference axes to define a point's location on a coordinate plane. typically expressed by the x-value and y-value pair (x,y).
The coordinates of the G = (2,7)
The coordinates of the H = (11,16)
Point I is on GH and divides it such that GI:HI is 4:5.
the coordinates of I ( x, y)
[tex]x = \frac{m_{1}x_{2} + m_{2} x_{1} }{m_{1} + m_{2} }[/tex]
[tex]x = \frac{4 * 11 + 5 * 2}{ 4 + 5}[/tex]
x = 6
[tex]y = \frac{m_{1}y_{2}+ m_{2}y_{1} }{m_{1} + m_{2} }[/tex]
[tex]y = \frac{4 * 16 + 5 * 7}{9}[/tex]
y = 11
the coordinates of I ( x, y) = ( 6, 11 )
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Write 53/16 as a decimal.
Answers
Answer:
3.3125
Step-by-step explanation:
53/16 is the same as 53 ÷ 16 =3.3125
What is the range of function represented by this graph?
Answers
f(x)=-(x+4)(x+2)
So the range is (-oo,1]
Consider oo as infinity sign
On January 1, Year 1, Jana started a small flower merchandising business that she named Jana’s Flowers. The company experienced the following events during the first year of operation: Started the business by issuing common stock for $43,000 cash. Paid $28,000 cash to purchase inventory. Sold merchandise that cost $20,000 for $42,000 on account. Collected $37,000 cash from accounts receivable. Paid $9,800 for operating expenses. Required a. Organize ledger accounts under an accounting equation and record the events in the accounts. In the last column of the table, provide appropriate account titles for the Retained Earnings amounts. b-1. Prepare an income statement. b-2. Prepare a balance sheet. b-3. Prepare a statement of cash flows. c. Since Jana sold inventory for $42,000, she will be able to recover more than half of the $43,000 she invested in the stock. Do you agree with this statement?
Answers
a) The organization of ledger accounts under an accounting equation and journal entries are as follows:
Accounting Equation:Assets = Liabilities + Equity
Cash + Inventory + A/Receivable C.Stock R/Earnings
1. $43,000 $43,000
2. -28,000 $28,000
3. $42,000 42,000 S/Revenue
4. -20,000 -20,000 COGS
5. 37,000 -37,000
6. -9,800 -9,800 Op Exp.
Bal. $42,200 $8,000 $5,000 $43,000 $12,200
Journal Entries:Debit Cash $43,000
Credit Common Stock $43,000
Debit Inventory $28,000
Credit Cash $28,000
Debit Accounts Receivable $42,000
Credit Sales Revenue $42,000
Debit Cost of goods sold $20,000
Credit Inventory $20,000
Debit Cash $37,000
Credit Accounts Receivable $37,000
Debit Operating expenses $9,800
Credit Cash $9,800
b1)
Jana's Flowers
Income StatementFor the year ended December 31, Year 1
Sales Revenue $42,000
Cost of goods sold $20,000
Gross profit $22,000
Operating expenses $9,800
Net income $12,200
b2) Jana's Flowers
Balance SheetDecember 31, Year 1
Cash $42,200
Accounts Receivable $5,000
Inventory $8,000
Total assets $55,200
Common Stock $43,000
Retained Earnings 12,200
Total equity $55,200
b3) Jana's Flowers
Statement of Cash FlowsFor the year ended December 31, Year 1
Net income $12,200
Changes in working capital:
Accounts Receivable (5,000)
Inventory (8,000)
Operating cash flow ($800)
Financing activities:
Common Stock $43,000
Cash flows $42,200
c) I do not agree with this statement. It does not necessarily flow that Jana selling $42,000 in goods will be able to recover more than half of the $43,000 she invested in her business. So far, she has made $12,200 from her investment.
Data Analysis:Cash $43,000 Common Stock $43,000
Inventory $28,000 cash $28,000
Accounts Receivable $42,000 Sales Revenue $42,000
Cost of goods sold $20,000 Inventory $20,000
Cash $37,000 Accounts Receivable $37,000
Operating expenses $9,800 Cash $9,800
Thus, it will take time for Jana to recover her investment in the business.
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20 10 12 13 4 1 5 0 19
Place for min , med, mode etc
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Me deben el 20% de 18700 y me pagan el 15% de 900 cuánto me deben aún?
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Answer:
3
Step-by-step explanation:
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Answer:
Your answer is [tex]2x^{10}[/tex].
Step-by-step explanation:
How is it similar and how is it different?
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Using the intersection operation between two data-sets, it is found that the graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.
What is the result of the intersection operation between two data-set?The result of the intersection operation between two data-set is the set that contains elements that belong to both sets.
For this problem, we have that a is to the left of b, as a < b, hence:
a is plotted before b on the number line.The intersection between the operations x > a and x < b is the following interval: a < x < b.Hence:
The graph of x > a and x < b is similar to the graph of x > a for a < x < b and different for x > b.
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certain grocery store charges a fee of 3% of the total bill to have groceries delivered. What is the total price the store charges to deliver $140 worth of groceries?
Answers
The total price the store charges to deliver $140 worth of groceries will be $4.20.
How to calculate the percentage?It should be noted that the certain grocery store charges a fee of 3% of the total bill to have groceries delivered.
Therefore, the total price the store charges to deliver $140 worth of groceries will be:
= Percentage charged × Cost
= 3% × $140
= 0.03 × $140
= $4.20
The amount charged is $4.20.
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Find the sum: 1.23 + 4.99.
Answers
Answer: 4.113
Step-by-step explanation: so like 1 goes into 4 4 times and then 2 dont go inna 9 so you got 11 because if you cant go down u goin up and then da three go into nine evenly so like i hope you fail
Answer:
6.22
Step-by-step explanation:
1.23 + 4.99 is equal to 6.22.
(If adding decimals is a harder concept for you, just ignore the decimal point and add normally.)
Hope this helped!
(ratings and voting brainliest always help)
write a problem based on the information given c = regular cost of one airline ticket 0.2c = amount of 20% promotional discount 3(c - 0.2c) = 330
Answers
The question for this information:
The cost of buying 3 airline tickets at a promotional discount of 20% is 330 dollars. Find the regular cost of 1 ticket.
Discounts and allowances are price reductions from a product's or service's base price.
Discount is calculated by subtracting the sell price of an article from its Marked price.
The given conditions in the question are
C=regular cost of a ticketamount of promotional discount=20%=0.2cAnd the expression 3(c - 0.2c) = 330So from the above information we can see that if the price of a ticket is c dollars then the discounted price of 1 ticket will be (c - 0.2c).
Total price of 3 tickets =3(c - 0.2c)
but the total price is 330 dollars
Therefore:
3(c - 0.2c) =330
or, 2.4c=330
or, c=330÷2.4
or, c=137.5 dollars
Hence the regular price of each ticket is 137.50 dollars.
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how to increase the accuracy of simpson rule and maclaurin series expansion respectively?
Answers
Because it matches a parabola to the curve rather than a straight line, Simpson's rule is more precise.
The other approaches are only accurate for functions whose graphs are linear, whereas Simpson's rule yields the exact area beneath the graphs of functions of degree two or less (parabolas and straight lines).Why is trapezoidal less accurate than Simpson's rule?
When the underlying function is smooth, Simpson's Rule is more accurate than the trapezoidal rule because it employs quadratic approximations rather than linear ones. In cases where there are an odd number of evenly spaced points, the formula is typically provided.What are Simpson's rule's restrictions?
It is obviously incorrect because the actual integral will always differ from it (except in some cases, such as the area under straight lines). Integrals, unlike Simpson's technique, allow you to obtain precise results in terms of basic constants.Learn more about Simpson's Rule
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Han ran 1/4 the length of his road,which is 7 miles long how far did han run?
Answers
Han ran 1.75 miles
because 25% of 7 is 1.75
Please, I will mark brainliest.
Answers
Answer: RS=2.4
Step-by-step explanation:
QR=RS ==> R is the midpoint of QS, so the distance from point R and point Q is equal to the distance from point R and point S.
7x-6=2x
7x=2x+6
5x=6
x=6/5
x=1.2
RS=2x
RS=2(1.2)
RS=2.4
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pls i need anwer
Answers
-8x = -56
x=7
A 61 in. wood plank is cut into 3 pieces. The longest piece is 5 times the length of the smallest piece. The medium piece
less than 2 times the length of the smallest.
1. If z represents the length of the smallest piece, write the expression that represents the medium size piece.
2. Write an equation to show that length of all the pieces together equal to the total length of 61 inches.
3. What is the length of each piece of wood? Explain how you know you are correct.
Answers
The length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.
How to represent expressions?The wood is 61 inches and it is divide into 3 pieces.
The longest piece is 5 times the length of the smallest piece.
The medium piece less than 2 times the length of the smallest.
let
z = length of the smallest piece of wood
longest piece = 5z
medium piece = 2z
The equation to represent the total piece together is equal to 61 inches.
z + 5z + 2z = 61
Therefore, the length of each wood piece can be calculated as follows:
z + 5z + 2z = 61
8z = 61
z = 61 / 8
z = 7.625 inches
longest piece = 5(7.625) = 38.125 inches
medium piece = 2(7.625) = 15.25 inches
Therefore, the length of the smallest, medium and the longest piece of wood are 7.625, 15.25 and 38.125 inches.
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25 pts - 37.5 if brainliest
Find the equation of the trend line (line of best fit)
Answers
Based on the given points on the graph, the equation for the line of best fit or the trend line is y = 1.874x + 3.656
What is the trend line?Due to the fact that the points on the graph are not on a straight line, the least squares method can be used to find the line of best fit equation.
Using a linear regression calculator, you can find the equation of the trend line by inputting the values of y and x in the graph.
When run through a linear regression calculator, the result will be:
y = 1.874x + 3.656
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Can anybody help me with this
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Answer: is C y=-2x-2
jwndnknwdkwnkw
how to do universal math by hands
Answers
Answer:
find the profound of life by your ethernal soul
I need help with 19 please. I will give Brainly and bunch of extra points. Thank you .
Answers
What is the decimal equivalent of each rational number? a. ___9/11 b. __4/5 c. ___-17/5 d. __5/9
Answers
Classify each of the following statements as true or false. If false, tell why. a. 5 is a divisor of 20. b. 10 is a multiple of 20.
Answers
Answer:
Yes; no
Step-by-step explanation:
a. If we divide 20 by 5, we get 4. Meaning, both 4 and 5 are divisors of 20.
b. 10 is not a multiple of 20; The multiples of 20 are 20, 40, 60, 80, 100, 120, 140, etc. Multiples only go upwards not down. Nothing plus 20 is equal to 10 therefore 10 is not a multiple of 20. 20 is a multiple of 10 though.
Which of the following are solutions to the quadratic equation below? Check all that apply. X^2+16=2
Answers
Step-by-step explanation:
x²+16=2
x²+16-2=0
x²+14=0
x²=-14
x=√-14=7i
PLEASE SHOW YOUR WORK!!!!!!
Craig’s job pays him $18.75 per hour, plus overtime at
the usual rate. Last month, Craig worked the following
hours per week:
• Week 1 = 37 hours
• Week 2 = 47 hours
• Week 3 = 42 hours
• Week 4 = 39 hours
Answers
The monthly payment to Craig is $ 3093.75
Given,
The payment got by Craig for his job = $ 18.75 per hour
Weekly working hours of Claig:
Week 1 = 37 hours
Week 2 = 47 hours
Week 3 = 42 hours
Week 4 = 39 hours
We have to find the total monthly payment of Craig:
That is,
Week 1 + Week 2 + Week 3 + Week 4
For getting the weekly salary, we have to multiply hourly payment with hours worked:
So,
Week 1 = 37 × 18.75 = 693.75
Week 2 = 47 × 18.75 = 881.25
Week 3 = 42 × 18.75 = 787.5
Week 4 = 39 × 18.75 = 731.25
Now calculate the total monthly payment:
That is,
693.75 + 881.25 + 787.5 + 731.25 = 3093.75
Therefore,
The monthly payment to Craig is $ 3093.75
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A zoologist needs to dive into the shark exhibit to supervise its cleaning. The depth of the water in the exhibit is 40 feet, and the divers can safely descend at a rate of 2 feet per minute. Which number expresses how deep below the water the divers are after 15 minutes? − 30 feet − 15 feet − 40 feet − 2 feet
Answers
Answer:
30 feet
Step-by-step explanation:
1 minute = 2 feet
15 minute = ? Feet
15 x 2 = 30
? = 30 feet
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Answers
Answer:
A
Step-by-step explanation:
Range is on the y-axis, therefore, it would be from -1 to 5.