ALGEBRA 2
There were 350 tickets sold for the spring concert at the local high school. Adult tickets cost $4.00 each, student tickets cost $2.50 each, and senior tickets cost $2.00 each. There were 40 fewer senior tickets sold than student tickets. If a total of$1,095 was collected from tickets, write the linear systems that could be used to find the number of each type of ticket sold
Answers
Answer:
\(\left\{ \begin{array}{ll} a+s+r=350 \\ 4a+2.5s+2r=1095\\r=s-40 \end{array} \right.\)
Step-by-step explanation:
Let's define our variables. Let a represent the number of adult tickets sold, s represent the number of senior tickets sold, and r represent the number of senior tickets sold.
We know that a total of 350 tickets were sold. So, the number of adult, student, and senior tickets sold must total 350. Therefore, we can write the following equation:
\(a+s+r=350\)
We know that each adult ticket costs $4, each student ticket costs $2.50, and each senior ticket costs $2. We are given that a total of $1095 was collected. Therefore, the number of tickets multiplied by their respective price must equal $1095. So, we can write the following equation:
\(4a+2.5s+2r=1095\)
Finally, we know that 40 fewer senior tickets were sold than student tickets. So, however many students tickets were sold, we can subtract 40 to get the number of senior tickets sold. Therefore:
\(r=s-40\)
So, our system of equations is:
\(\left\{ \begin{array}{ll} a+s+r=350 \\ 4a+2.5s+2r=1095\\r=s-40 \end{array} \right.\)
And we're done!
Related Questions
Simplify
-15p+23p
Pls help
Answers
8p
Step-by-step explanation:
-15p + 23p
Combine like terms
8p
What is the measure of angle AED?
Answers
Answer:
Step by step explanation:
well this is simble you just do it
A group of 25 people are going to run a race. The top 8 finishers advance to the finals.
Answers
You pick a card at random.
5
6
7
8
What is P(not less than 6)?
Answers
Answer:
3/4
Step-by-step explanation:
You can see that there are 4 cards with numbers 5, 6, 7 and 8 on them. They make the sample space. Total outcomes, n(S) = 4
Let the event E is picking a card not less than 6.
The outcomes of the event 'not less than 6' are 6, 7 and 8. So n(E) = 3
So, the required probability, P(not less than 6) = n(E) / n(S) = 3/4
Answer:
3/4
Step-by-step explanation:
There are 4 cards total
The card not less than 6 are 6,7,8 = 3 cards
P( not less than 6) = number of cards not less than 6 / total
= 3/4
help please quick 100 points quick tell me what to write please if you now how to do this
Answers
Answer:
8 footballs
18 basketballs
36 baseballs
24 softballs
Step-by-step explanation:
Let f = footballs
f = 8
Let b = basketballs
b = 2+2f = 2 +2(8) = 2 +16 = 18
Let B = baseballs
B = 5f -4 = 5(8) -4 = 40-4 = 36
Let s = softballs
s = 6+1/2B = 6+1/2(36) = 6+18 = 24
The total is 86
f+b+B +s = 86
8+18+36+24 = 86
86=86
There are 8 footballs.
Two more than twice the number of footballs are basketballs:
2f + 2 = b
f = number of footballs
b = number of basketballs
In the first statement, there are 8 footballs. So, f = 8
2(8) + 2 = b
16 + 2 = b
18 = b
Therefore, there are 18 basketballs.
Four less than 5 times the number of footballs are baseballs:
5f - 4 = a
f = number of footballs
a = number of baseballs
In the first statement, there are 8 footballs. So, f = 8
5(8) - 4 = a
40 - 4 = a
36 = a
Therefore, there are 36 baseballs.
Six more than half of the baseballs are softballs:
a/2 + 6 = s
a = number of baseballs
s = number of softballs
In the third statement, there are 36 baseballs. So, a = 36
(36)/2 + 6 = s
18 + 6 = s
24 = s
Therefore, there are 24 softballs.
Best of Luck!
A community would like to add a brick paver border around their swimming pool. They created the following image to represent the pool with the border. A large rectangle with a length of 48 feet and a width of 28 feet. Inside of it is another rectangle with a length of 32 feet and a width of 12 feet. Part A: Find the total area of the brick paver border that surrounds the 12 ft by 32 ft pool. Show your work. (2 points) Part B: If brick pavers cost $8 per square foot, what is the total cost of the brick pavers needed for this project? Explain. (2 points)
Answers
Part A: The total area of the brick paver border is \(960\) square feet.
Part B: The total cost of the brick pavers needed for this project is $\(7,680\).
Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.
The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.
Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).
Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).
Note: The calculations provided assume that the border consists of a single layer of brick pavers.
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The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean μ = $633 and standard deviation σ = $45.
(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)
(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.09? (Round your answer to the nearest dollar.)
$
Answers
Answer:
(a) 0.3863
(b) $693
Step-by-step explanation:
Mean μ = $633
Standard deviation σ = $45.
(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.)
We solve this question using the z score formula
z = (x-μ)/σ
where:
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x > $646
z = $646 - $633/$45
z = 0.28889
Probability value from Z-Table:
P(x<646) = 0.61367
P(x>646) = 1 - P(x<646) = 0.38633
Approximately = 0.3863
The probability that the actual costs will exceed the budgeted amount is 0.3863
(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.09? (Round your answer to the nearest dollar.
Let the budgeted amount = x
Converting 0.09 to percentage = 0.09× 100% = 9%
100 - 9% = 91%
We find the z score of 91%
= 1.341
We are to find x
Using z score formula
z = (x-μ)/σ
1.341 = x - 633/45
Cross Multiply
1.341 × 45 = x - 633
60.345 = x - 633
x = 60.345 + 633
x = $693.345
Approximately to the nearest dollar is $693
Is this table proportional?
Answers
No, this table is not proportional
You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values. If those ratios are, all the same, the table shows a proportional relationship.
Let us understand this by looking at the table provided
1st value is 1/5
2nd value is 3/10
We have to check whether the table is proportional or not
If the 1st value will be equal to the 2nd value then we can say that the table is proportional, otherwise, the table is not proportional
1/5 ≠ 3/10
We can say that table is not proportional. There is no need to check for other values as the condition becomes unsatisfied for the first two values.
Final answer: No, this table is not proportional
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Please help me on this question: Divided and write each answer in simplest form!
Answers
Answer:
use scientific calculator
11. 21/16
12. 6/5
13. 1/12
14. 7/9
15. 25/9
16. 10/9
17. 25/24
18. 3/4
Two parallel lines are crossed by a transversal. What is the value of x? x = 40 x = 70 x = 110 x = 130.
Answers
If two parallel lines are crossed by a transversal, the value of x is option (b) x = 70 degrees
When two parallel lines are intersected by a transversal, eight angles are formed. Two of these angles are vertical angles, which are opposite angles that share the same vertex and are formed by the intersection of two lines.
Vertical angles are always congruent, meaning they have the same measure. This is a geometric property that is true regardless of the angle's degree measurement.
In this problem, one of the vertical angles is given to be 70 degrees. Therefore, the other vertical angle must also have a measure of 70 degrees. This means that the value of x, which is the measure of one of the vertical angles, is also 70 degrees.
So, correct option is (b) x = 70 degrees.
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The given question is incomplete, the complete question is:
Two parallel lines are crossed by a transversal. What is the value of x? a) x = 40 b) x = 70 c) x = 110 d) x = 130.
Q15
A football manager needs to prepare an end of season report about his team's goal
scoring performance last season.
He wants to put this information into groups and display it in a suitable chart for the report.
0
2
3
2
2
2
1
0
3
1
Goals scored in each match last season.
3
2
4
2
4
2
3
0
3
3
3
1
2
4
1
4
2
2
3
0
2
3
4
2
2
Draw a chart to show this information.
Make a comment about what your chart shows about the team's performance.
2
1
3
0
2
Answers
According to the information of the chart we can infer that the team had 10 goals and 40 matches in total.
How to make a chart with the information of goals?To make a chart with the information of goals we have to consider the number of matches and goals that the team did. In this case the chart would be like the attached image.
According to the chart we can infer that this season the team had 40 matches and made 10 goals in total. So, this team have to improve because is very low the rate of goals in comparison with the number of matches.
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What is the greatest value? *
Summarize Data
Use the number of text messages Henry sent each day: 6, 12, 2, 6, 3, 4, 2, 5, 6.
Your answer
Answers
Answer:
12
Step-by-step explanation:
Woah that's a lot of points! Well in the list 12 is the largest! I think it may be wrong because it's pretty simple but yeah!
Consider the difference below.
x-3/x^2-x-5 - 5/8x
Place the steps require to simplify the given difference of two expressions into one, simplified rational expression in the correct order.
Answers
Answer: x-3/(x-3)(x+2) - 5/8x ➡️ 1/x+2 - 5/8x ➡️ 8x-5(x+2)/(x+2)(8x) ➡️ 3x-10/8x^2+16x
Just did this the other day...
The steps to simplify the expression (x - 3) / (x² - x - 5) - (5 / 8x) are,
Find the common denominator: LCM of (x² - x - 5) and 8x is 8x(x² - x - 5).
Rewrite the first fraction with the common denominator: [(x - 3)× 8x] / [8x(x² - x - 5)] - (5 / 8x).
Combine the fractions: [(8x² - 24x) - 5(x² - x - 5)] / [8x(x² - x - 5)].
Factor the denominator: 8x(x² - x - 5).
Simplify the expression: (8x² - 5x²) + (-24x + 5x) + 25 / [8x(x² - x - 5)].
Further simplify the numerator: 3x² - 19x + 25.
Final result: (3x² - 19x + 25) / [8x(x² - x - 5)].
To simplify the given difference of two expressions into one, simplified rational expression, follow these steps in the correct order:
Find a common denominator for the two fractions.
The common denominator for the fractions is the least common multiple (LCM) of the individual denominators, which are (x² - x - 5) and 8x. The LCM is 8x(x² - x - 5).
Rewrite the first fraction with the common denominator.
(x - 3) / (x² - x - 5) - (5 / 8x) = [(x - 3) × 8x] / [8x(x² - x - 5)] - (5 / 8x)
Combine the fractions by subtracting them.
= [(8x² - 24x) - 5(x² - x - 5)] / [8x(x² - x - 5)]
Factor the denominator of the resulting expression (if possible).
The denominator 8x(x² - x - 5) is already factored.
Simplify the expression, if possible.
= [8x² - 24x - 5x² + 5x + 25] / [8x(x² - x - 5)]
Combine like terms in the numerator.
= (8x² - 5x²) + (-24x + 5x) + 25 / [8x(x² - x - 5)]
Simplify the numerator further.
= 3x² - 19x + 25 / [8x(x² - x - 5)]
Therefore , the final simplified rational expression is equal to (3x² - 19x + 25) / [8x(x² - x - 5)].
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8x-2y
10 xy
(if x = 4 and y=-7) what is this evaluation
Answers
Answer: 2xy • (4x - 5y)
Step-by-step explanation:
STEP 1:
Equation at the end of step 1
((8 • (x2)) • y) - (2•5xy2)
STEP 2:
Equation at the end of step 2:
(23x2 • y) - (2•5xy2)
STEP 3:
STEP 4:
Pulling out like terms
4.1 Pull out like factors :
8x2y - 10xy2 = 2xy • (4x - 5y)
Final result :
2xy • (4x - 5y)
Histogram i would like someone to look it over for me please and thank you!
Answers
To complete the grouped frequency distribution for the data with a class width of 4, you can start by first obtaining the range of the data, determining the lower limit of the first class interval, and the upper limit of each class interval.
How to complete the grpuped frequency distributionAfter you have determined the upper limit of each class interval, the next thing to do will be constructing a table that shows the columns for the class intervals, the frequency of each interval, and the cumulative frequency.
Count the number of data points that fall into each class interval, and record these frequencies in the frequency column of the table. Add up the frequencies to get the cumulative frequencies. Finally, use the figures obtained to determine the mean, median and mode.
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A bakery is making whole-wheat bread and apple bran muffins. For each batch of break they make $35 profit. For each batch of muffins, they make $10 profit. The break takes 4 hours to prepare and 1 hour to back. The muffins take 0.5 hours to prepare and 0.5 hours to bake. The maximum preparation time available is 16 hours. The maximum bake time available is 10 hours. Let x = # of the batches of bread and y = # of batches of muffins. How many batches of bread and muffins should be made to maximize profits?
4 batches of bread and 0 batches of muffins
4 batches of bread and 0 batches of muffins
2 batches of bread and 16 batches of muffins
2 batches of bread and 16 batches of muffins
4 batches of bread and 10 batches of muffins
4 batches of bread and 10 batches of muffins
1 batch of bread and 12 batches of muffins
Answers
The batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins
How many batches of bread and muffins should be made to maximize profits?The given parameters can be represented on the following table
Bread (x) Muffins (y)
Prepare 4 1 16
Bake 0.5 0.5 10
Profit 35 10
The parameters from the above table are
Max P = 35x + 10y
Subject to
4x + y <= 16
0.5x + 0.5y <=10
x, y > 0
Solving the above constraints using a graphing calculator, we have the following points
(x, y) = (4, 0) and (0, 16)
Substitute these values in Max P = 35x + 10y
So, we have
P = 35 x 4 + 10 x 0 = 140
P = 35 x 0 + 10 x 16 = 160
160 is greater than 140
Hence, the batches of bread and muffins should be made to maximize profits are 0 batches of bread and 16 batches of muffins
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i will give brainliest
Answers
Answer:
c=30
Step-by-step explanation:
Inverse: 22 + 8 = 30
c = 30
Answer:
c = 30
Step-by-step explanation:
Step 1: Add 8 to both sides.
\(c-8+8=22+8\) \(c=30\)Step 2: Check if solution is correct.
\(30-8=22\) \(22=22\)Therefore, the answer is c = 30.
using the line of best fit
Answers
The monthly cell phone bill when shared data equals zero is given as follows:
$26.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The intercept of the line in this problem is given as follows:
b = 26.
Hence $26 is the monthly cell phone bill when shared data equals zero.
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Which value is equivalent to the expression 45?
Answers
Answer:
what value are you talking about
Step-by-step explanation:
Answer:
It's 1024
Step-by-step explanation:
Help with math problems
Answers
Answer:
1) option A
2) p > 34
Step-by-step explanation:
1) Inequality: 7 ≤ n + 5
Subtract 5 from both sides,
7 - 5 ≤ n +5 - 5
2 ≤ n
The value of n is all values greater than or equal to 2.
So, the answer is option A.
2) Inequality: 16 + p > 50
Solution:
Subtract 16 from both sides,
16 - 16 + p > 50 - 16
p > 34
Where we use division in real life?? Give Examples
Answers
Answer: You might want to know how many 24 apples are, individually, also being an accountant, mathematician, scientist, all require Math and math follows PEMDAS [Parenthesis, exponents, multiplication, division, addition, subtraction.] normally.
Step-by-step explanation:
Also, if you multiple something let's say 378x54 and get 20,412 and let's say you want to divide this huge number to a smaller number you can divide from 2 all the way up! Mathematics is not just something we have to learn, it's also something we can use!
What is the midpoint of WY?
Answers
Answer:
The mid point of XY should be -0.5
Step-by-step explanation:
I don't know if that's what you want
I hope I helped ¯\_(ツ)_/¯
Donna sliced several pizzas to serve at her party. Each slice represents
1
7
of each pizza. There are 49 slices of pizza. How many pizzas did Donna slice?
Answers
Answer:
She sliced 7 pizzas
Step-by-step explanation:
7 times 7 = 49
What is the intermediate step in the form (x+a)^2=b as a result of complementing the square for the following equations
Answers
The intermediate step in the form (x+a)²=b as a result of completing the square for the equation x² + 2x = 319 is (x+1)² = 320.
To use completing the square to solve the equation x² + 2x = 319, we have to write the left-hand side of the equation as a perfect square.
Add the square of half of the coefficient of x to both sides of the equation:
x² + 2x + (2/2)² = 319 + (2/2)²
x² + 2x + 1 = 320
The left-hand side of the equation can now be factored as a perfect square:
(x+1)² = 320
This is the equation in the form (x+a)²=b, where a=1 and b=320.
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The complete question is as follows:
What is the intermediate step in the form (x+a)²=b as a result of complementing the square for the following equation?
x² + 2x = 319
What do numbers have a difference of 8
Answers
Answer:
20-12=8
here it is the difference is 8.
√10 Multiple √15 is equal to
(a) 5√6
(b) 6√5
(c) √30
(d) √25
step by step
Solve :-
Answers
Answer:
(a). 5√6
Step-by-step explanation:
\( \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = 5 \sqrt{6} \)
5 radical 6
hi i need help as i try with old answer and its wrong
Answers
SOLUTION
The exercise has no question
Review the simple interest rate based on FICO scores to answer the question:
FICO Score Simple Interest Rate
800–850 5.295%
740–799 6.597%
670–739 9.132%
580–669 10.358%
300–579 14.313%
Kamryn plans to borrow $13,250.00 with a simple interest rate loan. Determine the amount of interest Kamryn will save if she is able to raise her credit score from 665 to 680.
Answers
Kamryn would save $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
To determine the amount of interest Kamryn will save by raising her credit score from 665 to 680, we need to compare the interest rates associated with each credit score range.
According to the given information, a credit score of 665 falls within the range of 580-669, where the corresponding simple interest rate is 10.358%.
Let's calculate the interest Kamryn would pay on a loan of $13,250.00 at an interest rate of 10.358%.
Interest = Principal * Rate
= $13,250.00 * 0.10358
≈ $1,370.56
Therefore, if Kamryn were to borrow $13,250.00 with a credit score of 665, she would pay approximately $1,370.56 in interest.
Now, let's consider the scenario where Kamryn raises her credit score to 680. A credit score of 680 falls within the range of 670-739, where the corresponding simple interest rate is 9.132%.
Calculating the interest with a credit score of 680:
Interest = Principal * Rate
= $13,250.00 * 0.09132
≈ $1,210.57
Thus, if Kamryn were able to raise her credit score from 665 to 680, she would save approximately $1,370.56 - $1,210.57 = $159.99 in interest.
Therefore, Kamryn would save approximately $159.99 in interest by raising her credit score from 665 to 680 when borrowing $13,250.00 with a simple interest rate loan.
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Bike route A is 12 times as long as bike route B. The total length of the bike trails is 845 miles. What is the length of each bike trail?
Answers
Length of bike route A is 12(65)=780 and length of bike route B is 65.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that the Bike route A is 12 times as long as bike route B.
Let x be the length of the bike route B.
12x be the length of the bike route B.
The total length of the bike trails is 845 miles
12x+x=845
13x=845
Divide both sides by 13
x=65
Length of bike route A is 12(65)=780 and length of bike route B is 65.
Hence, Length of bike route A is 12(65)=780 and length of bike route B is 65.
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100 POINTS PLEASE HELPPP An entry of (100) in net income, reported on the income statement, would be entered as (100) where else?
A. In balance sheet liabilities
B. In balance sheet assets
C. In financing cash flow
D. In operating cash flow
Answers
Answer:
The entry of net income of (100) would be entered in option D, in the operating cash flow section of the cash flow statement.
Step-by-step explanation:
The operating cash flow section of the cash flow statement reports cash inflows and outflows that result from the company's operating activities, such as revenues and expenses. Net income is an important component of operating cash flow, as it represents the profit earned by the company during a period after deducting all the expenses. When net income is negative, it is referred to as a net loss and would be entered as a negative number in the operating cash flow section of the cash flow statement.