Your local high school is putting on a musical. They have sold 1000 tickets. Adult tickets
were sold for $8. 50, while child tickets were sold for $4. 50. A total of $7100 was
collected from ticket sells. How many tickets of each kind were sold?
Answers
650 adult tickets were sold.
Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.
From the problem, we know that:
A + C = 1000 (the total number of tickets sold is 1000)
8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)
We can use the first equation to solve for A in terms of C:
A = 1000 - C
Substituting this expression for A into the second equation, we get:
8.50(1000 - C) + 4.50C = 7100
Expanding and simplifying:
8500 - 8.50C + 4.50C = 7100
4C = 1400
C = 350
So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:
A + 350 = 1000
A = 650
Therefore, 650 adult tickets were sold.
To know more about tickets sold refer here:
https://brainly.com/question/20954065
#SPJ11
Related Questions
(table: costs of birthday cakes) use table: costs of birthday cakes. assume that fixed costs are $10. the minimum average total cost occurs at output of:
Answers
If fixed costs are $10, the minimum average total cost occurs at output of value 4.
To find the minimum average total cost, we need to calculate the average cost for each level of output. The average cost is the sum of total costs (fixed cost plus variable cost) divided by the output level.
The variable cost can be calculated by finding the difference between the total cost of the previous level and the total cost of the current level.
Output level | Variable cost | Total cost | Average cost
0 | 0 | 10 | -
1 | 15 | 25 | 25
2 | 10 | 35 | 17.5
3 | 5 | 40 | 13.3
4 | 8 | 48 | 12
5 | 12 | 62 | 12.4
6 | 20 | 90 | 15
As we can see from the table, the minimum average total cost occurs at an output level of 4, which has an average cost of $12 per cake. Therefore, the answer is 4.
To learn more about cost click on,
https://brainly.com/question/29031823
#SPJ4
Complete question is:
Costs of birthday Cakes Variable Cost,
0 0
1 15
2 25
3 30
4 38
5 50
6 70
assume that fixed costs are $10. the minimum average total cost occurs at output of:
ompute det (B5) if B = 1 0 1 1 1 2 1 2 1 . 7. (5pts) Let A and B be 3 x 3 matrices, det(A) = 5, and det(B) = -4. Use the properties of determinants to compute: (a) det(AB) (b) det(3A) (e) det(B") (d) det (A-1) (e) det (A)
Answers
The determinants of the given matrices are -20, 135, 16, 0.2, and 5, respectively.
To compute the determinants of the given matrices, use the properties of determinants. The properties of determinants include:
1) det(AB) = det(A) * det(B)
2) det(kA) = k^n * det(A), where k is a scalar and n is the order of the matrix
3) det(A^T) = det(A)
4) det(A^-1) = 1 / det(A)
5) det(I) = 1, where I is the identity matrix
Using these properties, compute the determinants of the given matrices as follows:
(a) det(AB) = det(A) * det(B) = 5 * (-4) = -20
(b) det(3A) = 3^3 * det(A) = 27 * 5 = 135
(c) det(B^2) = det(B) * det(B) = (-4) * (-4) = 16
(d) det(A^-1) = 1 / det(A) = 1 / 5 = 0.2
(e) det(A) = 5
Therefore, the determinants of the given matrices are -20, 135, 16, 0.2, and 5, respectively.
To know more about the properties of determinants click here:
https://brainly.com/question/13320982
#SPJ11
I need answer Immediately!!!!!!
Answers
Answer:
Step-by-step explanation:
https://www.numerade.com/questions/write-the-equation-for-the-graph-that-is-shown-check-your-book-to-see-graph-3/
Hope it helps you
an investigator was interested in the relationship between color preference and number of siblings. a test of independence produced a c2 that allowed the null hypothesis to be rejected. the proper conclusion is
Answers
The proper conclusion when a test of independence produces a chi-square statistic (\(\chi^2\)) that allows the null hypothesis to be rejected is that there is evidence of a relationship between the variables being studied.
In statistical hypothesis testing, the chi-square test of independence is used to determine whether there is a significant association between two categorical variables.
The null hypothesis assumes that there is no relationship between the variables, while the alternative hypothesis suggests that there is a relationship.
When the test of independence yields a chi-square statistic that is large enough to reject the null hypothesis, it means that the observed data provides evidence against the assumption of independence.
In other words, the results suggest that there is a relationship between the variables being studied.
The rejection of the null hypothesis does not provide information about the nature or strength of the relationship.
It simply indicates that the observed data is unlikely to occur if the variables were truly independent.
Therefore, the proper conclusion in this case is that there is evidence of a relationship between color preference and the number of siblings based on the results of the test of independence.
Further analysis may be needed to explore the nature and significance of this relationship.
Learn more about chi-square test here:
https://brainly.com/question/30760432
#SPJ11
what is the radius of the circle
Answers
Answer:
The radius is probably 5 units
Answer:
Radius: 5
Center is (3, -1)
Step-by-step explanation:
4. The department of fish and wildlife want to estimate the size of alligator population in
Louisiana. The department issued 937 tags to hunters in 2018. The average length of the
alligators was 11.2 ft with a standard deviation of 2.06 feet. What is the mean and
standard deviation of the population?
Answers
Let's start by using the formula for the standard error of the mean:
SE = s / sqrt(n)
where s is the sample standard deviation, n is the sample size, and SE is the standard error of the mean. The standard error of the mean estimates the standard deviation of the population based on the sample data.
Substituting the values given, we get:
SE = 2.06 / sqrt(937)
SE ≈ 0.067
Next, we can use the formula for the confidence interval of the mean:
CI = X ± (Z * SE)
where X is the sample mean, Z is the z-score associated with the desired level of confidence, and SE is the standard error of the mean. The confidence interval estimates the range within which the population mean is likely to fall based on the sample data.
Assuming a 95% level of confidence (which corresponds to a z-score of 1.96), we get:
CI = 11.2 ± (1.96 * 0.067)
CI ≈ (11.07, 11.33)
Therefore, we can estimate that the mean length of the alligator population in Louisiana is between 11.07 and 11.33 feet.
To estimate the standard deviation of the population, we can use the formula:
s = sqrt(((n-1) * s^2) / n)
where s is the sample standard deviation, n is the sample size, and s is the population standard deviation. This formula estimates the population standard deviation based on the sample data.
Substituting the values given, we get:
s = sqrt(((937-1) * 2.06^2) / 937)
s ≈ 2.03
Therefore, we can estimate that the standard deviation of the alligator population in Louisiana is approximately 2.03 feet.
a random sample x1,x2 ...,xn of size n is taken from a poisson distribution with a mean of λ, 0 < λ < [infinity]. (a) show that the maximum likelihood estimator for λ is bλ
Answers
To find the maximum likelihood estimator (MLE) for λ, we need to maximize the likelihood function L(λ) with respect to λ of the Poisson distribution
First, let's write the probability density function (PDF) of the Poisson distribution:
P(X = k) = (e^(-λ) * λ^k) / k!
The likelihood function can be defined as the product of the probabilities for each observation in the random sample. Since the sample is independent and identically distributed, we can write the likelihood function as:
L(λ) = P(x1, x2, ..., xn | λ) = P(x1 | λ) * P(x2 | λ) * ... * P(xn | λ)
Taking the logarithm of the likelihood function (log-likelihood) will simplify the calculations. The log-likelihood function is:
log(L(λ)) = log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ))
Now, let's calculate the derivative of the log-likelihood function with respect to λ:
d/dλ log(L(λ)) = d/dλ (log(P(x1 | λ)) + log(P(x2 | λ)) + ... + log(P(xn | λ)))
= d/dλ (log(P(x1 | λ))) + d/dλ (log(P(x2 | λ))) + ... + d/dλ (log(P(xn | λ)))
To find the MLE, we set the derivative equal to zero and solve for λ:
d/dλ log(L(λ)) = 0
The derivative of log(P(x | λ)) with respect to λ can be calculated using the logarithmic differentiation technique. After taking the derivative, we equate it to zero and solve for λ.
By solving the equation, we will obtain the MLE for λ.
Learn more about Poisson distribution: https://brainly.com/question/9123296
#SPJ11
You have two upcoming work trip. For the firt trip, you will cover 846 mile in 3. 5 day. For the econd trip, you will cover 322. 5 mile in 6 day. How many mile will you travel on average during each trip?
Answers
You have two upcoming work trip. For the firt trip, you will cover 846 mile in 3. 5 day. 147.73 mile will you travel on average during each trip.
What is ratio?Ratio is defined as compares quantities, that means it represents the value of each quantity with respect to the another quantity.
If a and b are two values, their ratio will be a:b,
According to given data,
first trip will cover 846 mile in 3.5 days.
so, total travel mile(per day) = 846/3.5 = 241.71 mile
also, second trip will cover 322.5 mile in 6 days.
so, total travel mile(per day) = 322.5/6 = 53.75 mile.
average of mile each trip = (241.71 + 53.71)/2
average of mile each trip = 295.46/2 = 147.73.
so, The answer is 147.73.
Learn more about the travel on average
https://brainly.com/question/29452079
#SPJ4
The expression 36 * 6 • 2 + 1 ls equal to
4
18
2.
13
Answers
Answer:
13
Step-by-step explanation:
36/6*2+1=?
First, do 36/6, which equals 6.
Then do 6 times 2 which equals 12.
12+1= 13
Suppose that an individual has a body fat percentage of 12.1% and weighs 139 pounds. How many pounds of his weight is made up of fat? Round your answer to the nearest tenth.
Answers
Answer:
16.8 pounds
Step-by-step explanation:
Given the following :
Body fat percentage = 12.1%
Weight = 139 pounds
How may pounds of the person's weight is made up of fat:
That is 12.1% of the person's entire body weight
Pound of person's weight composed of fat:
12.1% of 139
(12.1 / 100) × 139
0.121 × 139
= 16.819 pounds.
= 16.8 pounds
-20 = -4x - 6x
I need help solving it
Answers
Answer:
the answer is 2
Step-by-step explanation:
add -4x and -6x and the answer is -10x bc they are both negative x. then divide both -10x and -20 by -10 so that it is x by itself on one side and 2 on the other so its 2=x :)
Consider the first order differential equation t et y'+ = , y' + t2 – 25 y t-99 For each of the initial conditions below, determine the largest interval a
Answers
For the given first-order differential equation, we need to determine the largest interval on which a unique solution exists for each initial condition. The interval will depend on the specific initial condition and the behavior of the differential equation.
The first-order differential equation is given as:
t^et y' + y' + t^2 – 25yt - 99
To determine the largest interval on which a unique solution exists for each initial condition, we need to consider the behavior of the equation and any possible singularities or discontinuities.
For each initial condition, we can use standard techniques such as separation of variables or integrating factors to solve the differential equation and find the solution. The solution will depend on the initial condition and may have different behaviors based on the values of t and y.
It's important to note that the existence and uniqueness of solutions are generally guaranteed within a certain interval as long as the equation and initial condition satisfy certain conditions, such as Lipschitz continuity. However, without specific initial conditions, it is not possible to determine the exact intervals on which a unique solution exists.
Therefore, to determine the largest interval on which a unique solution exists for each initial condition, further analysis and specific initial conditions are required to assess the behavior of the equation and identify any constraints or limitations on the solution.
Learn more about first-order differential equation here:
https://brainly.com/question/30645878
#SPJ11
State the leading coefficient of -9x^5+3x^2+3-7x+10x^3
Answers
Answer:
-9
Step-by-step explanation:
We need to write the terms from highest power to smallest power
-9x^5+10x^3+3x^2-7x+3
The leading coefficient is the number in front of the highest power
-9
Answer:
-9
Step-by-step explanation:
In a polynomial, the leading coefficient is the coefficient to the variable with the largest exponent.
In this polynomial, the variable with the largest exponent is x^5.
The leading coefficient is the number in front of the variable. In this case, the leading coefficient is -9.
So, the leading coefficient is -9.
Which function has an inverse that is a function?
b(x)=x^2+3
d(x)=-9
m(x)=-7x
p(x)= |x|
Answers
Graph y+3=5(x-4) please quickly
Answers
Answer:
It crosses through 0,-23) and (4.6,0)
Step-by-step explanation:
A garden designer designed a square decorative pool. The pool is surrounded by a walkway.On two opposite sides of the pool, the walkway is 8 ft. On the opposite sides, the walkway is 10 ft. The final design for the pool and walkway covers a total area of 1400 square ft.
Answers
Note that the pool is in the shape of square with each of its four sides measuring 'x' units.
(a)
So the total length of the rectangular system is given by,
\(\begin{gathered} L=x+10+10 \\ L=x+20 \end{gathered}\)Thus, the total length of the rectangle is (x+20) units.
(b)
Similarly the total width of the rectangular system is given by,
\(\begin{gathered} W=x+8+8 \\ W=x+16 \end{gathered}\)Thus, the total width of the rectangle is (x+16) units.
(c)
Consider that the area of the rectangular area is calculated as,
\(\text{Area}=\text{Length}\times\text{ Width}\)Substitute the values,
\(\begin{gathered} A=(x+20)(x+16) \\ A=x(x+16)+20(x+16) \\ A=x^2+16x+20x+20\times16 \\ A=x^2+36x+320 \end{gathered}\)Thus, the above expression gives the area of the given rectangle.
2. Your recipe for making 12 chocolate chip cookies calls for 1.5 cups of chips. How many cups of chips
do you need to make 4 Dozen cookies?
Answers
Answer:
You need 6 cups of chips
Step-by-step explanation:
Which system of linear inequalities is graphed?
S x < -2
ly≤-x+2
O
J x ≤-2
y≤-x-3
S. x < -2
y≤ x 2
-
{
√ x < −3
С
Answers
According to the question, to graph the linear inequality expressions then the given expressions should be equal to the respective number.
In the first equation that is: x<-2 or x = -2
The given expression can be drawn in the second quadrant when the value of the x-axis is negative and it is a straight line which tends to infinity.
In the second equation that is: y ≤ x+2 or y = x+2
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
Similarly, in the third equation that is: y ≤ x-3 or y = x-3
The given expression can be drawn in the first as well as in the second quadrant when the value of the x-axis is negative as well as positive and it is a straight line which tends to infinity.
What is linear inequality?
Linear inequalities are those expressions in which comparison between the variables is performed. And the comparison can be done between two values or between the two expressions. It uses the symbols of the inequality like greater than, equal to, etc.
To learn more about the linear inequality from the given link:
https://brainly.com/question/21819032
#SPJ9
Which of these equations are consistent and possibly true? 1. A−B−C=0 2. C=−7.15m 3. ∣A∣−∣B∣=−2.9m 4. (42.1m)x^=(3.2m)y^ 5. Ay<0
Answers
equations 1, 2, 4, and 5 are consistent and possibly true, while equation 3 is not consistent.
Let's analyze each equation to determine if they are consistent and possibly true:
1. A - B - C = 0
This equation states that the difference between A, B, and C is zero. It is consistent and possibly true if A = B + C.
2. C = -7.15m
This equation states that the value of C is equal to -7.15m. It is consistent and possibly true if C is indeed equal to -7.15m.
3. |A| - |B| = -2.9m
This equation states that the absolute value of A minus the absolute value of B is equal to -2.9m. It is not consistent because the absolute value of a number is always non-negative, so the left-hand side of the equation can never be negative.
4. (42.1m) * \(\hat{x}\) = (3.2m) * \(\hat{y}\)
This equation states that the product of 42.1m and \(\hat{x}\) (unit vector in the x-direction) is equal to the product of 3.2m and \(\hat{y}\) (unit vector in the y-direction). It is consistent and possibly true if the magnitudes of \(\hat{x}\) and \(\hat{y}\) are appropriately related to satisfy this equation.
5. Ay < 0
This equation states that the y-component of vector A is less than zero. It is consistent and possibly true if the y-component of vector A is indeed negative.
In summary, equations 1, 2, 4, and 5 are consistent and possibly true, while equation 3 is not consistent.
Learn more about equations here
https://brainly.com/question/14686792
#SPJ4
Among the given equations, the consistent and possibly true equations are:
A - B - C = 0 (Equation 1)
C = -7.15m (Equation 2)
Ay < 0 (Equation 5)
Let's analyze each equation to determine which ones are consistent and possibly true:
1. A - B - C = 0:
This equation represents the sum of three variables, A, B, and C, equal to zero. Without any further information about the variables, we cannot determine its consistency or truth.
2. C = -7.15m:
This equation sets the variable C equal to -7.15m. It is consistent and true if the value of C is indeed -7.15m.
3. |A| - |B| = -2.9m:
This equation states the absolute value of A minus the absolute value of B equals -2.9m. However, the absolute value of a quantity is always positive, so it cannot be negative. Therefore, this equation is inconsistent and unlikely to be true.
4. (42.1m)x^ = (3.2m)y^:
This equation equates a scalar quantity, 42.1m, multiplied by the unit vector x^, with a scalar quantity, 3.2m, multiplied by the unit vector y^. Since x^ and y^ are perpendicular unit vectors, it is not possible for them to be equal. Therefore, this equation is inconsistent and unlikely to be true.
5. Ay < 0:
This equation states that the y-component of vector A is less than zero. It is consistent and possibly true if the y-component of A is indeed negative.
Based on the analysis above, the equations that are consistent and possibly true are equation 2 (C = -7.15m) and equation 5 (Ay < 0).
To know more about consistent, refer here:
https://brainly.com/question/12791933
#SPJ4
Which equation has exactly one solution in common with the equation y=6x-2?
A. 18x - 3y = 6
B. 1/2y = 3x - 2
C. 2y = 4x - 12
D. 18x - 12 = 3y
Answers
Answer:
A. 18x - 3y = 6
Step-by-step explanation:
By taking 3 common from the terms 18x and 3y we get,
3 (6x-3y) = 6
or, 6x - y = 6/3
or, 6x - y = 2
And,
The equation becomes,
y = 6x - 2
The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
By taking 3 commons from the terms 18x and 3y we get,
3 (6x-3y) = 6
6x - y = 6/3
6x - y = 2
The equation becomes,
y = 6x - 2
Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.
To know more about equations follow
https://brainly.com/question/2972832
#SPJ2
Which equations can be used to solve for y, the length of the room? Select three options.
y(y + 5) = 750
y2 – 5y = 750
750 – y(y – 5) = 0
y(y – 5) + 750 = 0
(y + 25)(y – 30) = 0
Answers
NEED HELP ASAP PLEASE CLICK ON PHOTO!!
Answers
Explanation:
Every triangle is equal to 180 degrees
We know that there is a right angle so
180-90=90
90/2=45
Hope this helps!!
write in simplest form
8 5/12 + 11 1/4
Answers
Answer:
19 2/3
Step-by-step explanation:
8+11=19, & 5/12+1/4=8/12
What do you put on the X axis of an ogive?
Answers
The X-axis (horizontal axis) often represents a "class boundaries" of such an ogive, whereas the Y-axis (vertical axis) typically shows the frequency count.
Explain about the ogive graph?A sort of frequency polygon that displays cumulative frequencies is an ogive, often known as a cumulative frequency polygon.
In other words, the graph adds the cumulative percents from left to right.On an ogive graph, "class boundaries" are shown along the x-axis while cumulative frequency is shown on the y-axis. Comparable to a histogram, an ogive features a single point that indicates in which the top right corner of the rectangular would be located in place of rectangles. This type of graph is typically simpler to make from such a frequency table.Thus, The X-axis (horizontal axis) often represents a class boundaries being measured of such an ogive.
To know more about the ogive, here
https://brainly.com/question/2500839
#SPJ4
A baby weighed 8 pounds at birth if she triples her weight by age 2 how much does she weight at age 2
Answers
Answer:
The answer is 24 pounds
Step-by-step explanation:
Tripling is another way of saying multiplying by 3, so when you multiply 8 and 3...you get 24
Solve the equation
The equation is -3 = 8x -4y for y
Answers
Answer:
\(y=\frac{3}{4}+2x\)
Step-by-step explanation:
5. Holly ran 3/5 mile on Saturday and 3/5 mile on Sunday. How many miles did Holly run in those 2 days?
Answers
Answer: He did not convert the fractions into the like fraction to add.
Step-by-step explanation:Given: The distance Jonah runs on Sunday= milesThe distance Jonah runs on Monday= milesThe total distance he ran = Since both the fractions are not like , thus multiply 2 to the numerator and the denominator of the first fraction [to add fractions first convert them into like fractions], we get The total distance he ran = The right answer is "The total distance he ran ="
scores on the sat verbal test in recent years follow approximately the n(515, 109) distribution. how high must a student score in order to place in the top 5% of all students taking the sat?
Answers
We need to determine the score a student must achieve to place in the top 5% of all students taking the SAT Verbal test with an N(\(515, 109\)) distribution, which came out to be \(695\) marks.
Identify the mean (μ) and standard deviation (σ) of the distribution: In this case, µ \(= 515\) and σ\(= 109\).
Determine the percentile rank: To place in the top \(5%\)% of students, we need to find the score corresponding to the \(95th\) percentile, as this represents the point where \(95\)% of students have a lower score.
Use a standard normal (Z) table or calculator to find the Z-score corresponding to the \(95th\) percentile: A Z-score represents the number of standard deviations a data point is from the mean.
For the \(95th\) percentile, the Z-score is approximate \(1.645\).
Apply the Z-score formula to find the required SAT score: \(X =\) µ \(+ Z*\) σ. In this case, \(X = 515 + (1.645 *109)\).Calculate the result: \(X = 515 + (1.645 *109)\)
\(=515 + 179.305 = 694.305\).
Round up to the nearest whole number: Since a student's SAT score must be a whole number, round up to \(695\). A student must score \(695\) or higher on the SAT Verbal test to place in the top \(5\)% of all students taking the test, given the N(\(515, 109\)) distribution.
Learn more about standard deviation:
https://brainly.com/question/29808998
#SPJ11
shang like some modern laws sculpture made of four identical solid right pyramid with square faces. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase. He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet. What is the volume of material he must purchase?
a. 2 ft.
b. 4 ft.
c. 6 ft.
d. 8 ft.
Answers
The correct answer is c. 6 ft³.To calculate the volume of the sculpture, we need to find the volume of one pyramid and then multiply it by four.
The volume of a pyramid can be calculated using the formula V = (1/3) * base area * height. In this case, the base area of the pyramid is a square with side length 2 feet, so the area is 2 * 2 = 4 square feet. The height of the pyramid is 6 feet. Plugging these values into the formula, we get V = (1/3) * 4 ft² * 6 ft = 8 ft³ for one pyramid. Since there are four identical pyramids, the total volume of the sculpture is 8 ft³ * 4 = 32 ft³.
However, the question asks for the volume of sculpting material needed, so we need to subtract the volume of the hollow space inside the sculpture if there is any. Without additional information, we assume the sculpture is solid, so the volume of material needed is equal to the volume of the sculpture, which is 32 ft³. Therefore, the correct answer is c. 6 ft³.
Learn more about sculpture here:
brainly.com/question/20758351
#SPJ11
Pleaseeeeee helpppppp
Answers
They are both factors of 15x-10 because 5(3x-2)=15x-10
factor x factor=product.
In this case 15x-10 is the product