The members of the city cultural center have decided to put on a play once a night for a week. Their auditorium holds 500 people. By selling tickets, the members would like to raise $2,050 every night to cover all expenses. Letdrepresent the number of adult tickets sold at $6.50. Let's represent the number of student tickets sold at $3.50 each.

a.If all 500 seats are filled for a performance, how many of each type of ticket must have been sold for the members to raise exactly$2,050?

b.At one performance there were three times as many student tickets sold as adult tickets. If there were 480 tickets sold at that performance, how much below the goal of$2,050 did ticket sales fall?

Answer:

I think the first one is the correct answer!

Answer:

7 1/2

Step-by-step explanation:

2 1/2 times 3 is 7 1/2

Answer: 7 1/2 miles

Step-by-step explanation:

7 miles and a half

The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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The number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

The explanatory variable for this relationship is the number of seeds per square foot. The number of seeds per square foot is the variable that is being manipulated or changed by the farmers in order to observe the effect on the yield of the crop in pounds per square foot.

The farmers observed that the yields were the smallest when the number of seeds per square foot was either very small or very large, this means that there is an optimal number of seeds per square foot that yields the highest crop.

So, the number of seeds per square foot is the variable that explains the variation in the yield of the crop in pounds per square foot.

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Answer:

2 students said only fall

Step-by-step explanation:

Given:

Total number of students = 25

Number of students who like fall season (F) = 12

Number of students who like summer season (S) = 18

Number of students who like both fall and summer season \(\left ( F\cap S \right )\) = 10

To find:

Number of students who like only fall season

Solution:

A set is a well defined collection of objects. A universal set is the set of which all other sets are subsets. It is denoted by U.

According to the venn diagram,

n(only F) = \(=n(F)-n\left ( F\cap S \right )\)

\(=12-10=2\)

So, 2 students said only fall.

Answer:

x=8

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

4x+6−6=38−6

4x=32

Step 2: Divide both sides by 4.

Answer:

x=8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

f(-5) = 2|-5-5|

f(-5) = 2|-10|

f(-5) = 2 * 10

f(-5) = 20

f(0) = 2|0-5|

f(0) = 2|-5|

f(0) = 2 * 5

f(0) = 10

Answer: If your opponent is winning 3:1 then they are probably better then you if they are winning more then you are. (or you are just having a bad day)

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

Let's denote the three possibilities as follows:

A: Equally talented, each player has a 0.5 probability of winning a game.

B: You are slightly better, with a 0.6 probability of winning a game.

C: Your opponent is slightly better, with a 0.6 probability of winning a game.

Given that you won the second game but lost the first, third, and fourth games, we want to find the probability of scenario C given this outcome. Let P(C) represent the prior probability of scenario C being true.

According to the given information, each of the three scenarios (A, B, and C) is equally likely, so P(A) = P(B) = P(C) = 1/3.

Now, let's update the probabilities based on the outcome of the match:

In scenario A:

The probability of winning the second game is 0.5, and the probability of losing the first, third, and fourth games is 0.5 each. Therefore, the overall probability of the observed outcome in scenario A is (0.5 * 0.5 * 0.5 * 0.5) = 0.0625.

In scenario B:

The probability of winning all three games (assuming you are slightly better) is (0.6 * 0.6 * 0.6) = 0.216.

In scenario C:

The probability of winning the second game (assuming your opponent is slightly better) is 0.4, and the probability of losing the first, third, and fourth games is 0.6 each. Therefore, the overall probability of the observed outcome in scenario C is (0.4 * 0.6 * 0.6 * 0.6) = 0.05184.

Now, we can update the probabilities based on Bayes' theorem:

Posterior probability of scenario A: P(A|data) = (P(data|A) * P(A)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario B: P(B|data) = (P(data|B) * P(B)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

Posterior probability of scenario C: P(C|data) = (P(data|C) * P(C)) / (P(data|A) * P(A) + P(data|B) * P(B) + P(data|C) * P(C))

P(data|A) = 0.0625

P(data|B) = 0.216

P(data|C) = 0.05184

Plugging in the values, we get:

Posterior probability of scenario A: P(A|data) ≈ (0.0625 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.134

Posterior probability of scenario B: P(B|data) ≈ (0.216 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.466

Posterior probability of scenario C: P(C|data) ≈ (0.05184 * 1/3) / (0.0625 * 1/3 + 0.216 * 1/3 + 0.05184 * 1/3) ≈ 0.400

So, after the match, the posterior probability that your opponent is slightly better than you is approximately 0.400 or 40%.

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The assumptions necessary for confidence interval 90% with population mean salary  μ turns out to be (1000, 2100) this interval is based on sample size 25 is given by option C) The population must have an approximately normal distribution.

For a confidence interval to be valid, it is necessary to make certain assumptions about the population and the sample.

Here, the assumptions necessary for a valid 90% confidence interval based on a sample of size n = 25 are,

Random sampling,

The sample should be a random sample from the population.

That every member of the population has an equal chance of being selected.

Independence,

The sample observations should be independent of each other.

The value of one observation does not affect the value of another observation.

Normality,

The population of salaries must have an approximately normal distribution.

This assumption is necessary because the confidence interval is based on the Central Limit Theorem.

Which states that the sampling distribution of the sample mean is approximately normal.

Provided that the sample size is large enough and the population distribution is approximately normal.

Sample size,

The sample size should be large enough to ensure that the sampling distribution of the sample mean is approximately normal.

In general, a sample size of 25 is considered sufficient to meet this requirement.

Option A is incorrect because it describes an assumption necessary for the validity of a confidence interval based on the Central Limit Theorem.

Option B is incorrect because the population is assumed to have a normal distribution, not an approximate t-distribution.

Option D is incorrect because it describes a biased sample distribution.

Which would invalidate the results of any statistical analysis based on the sample.

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Answer:

A. is 2.

B. is 5.

C. is 1.

D. is 4.

E. is 6.

F. is 3.

Explaination for my answer

Its bascially just rearrange to make x =

The values from the evaluation of the quadratic function that shows the path of the ball are as follows;

a. The domain of the function that makes sense is; 0 ≤ x ≤ (3 + √(509))/5

b. The range in which the function makes sense is 0 ≤ y ≤ 101.8

c. The height of the ball after 3 seconds is 73 meters

d. The change in the situation of the new graph is the initial height changed from 100 meters 80 meters

e. The new function is g(x) = -5·x² + 6·x + 80

f. The domain and range will change because the maximum height and the x-intercept changes

The domain of a function is the set of the possible inputs of a function and the range is the set of the possible output values of the function.

a. The function is; f(x) = -5·x² + 6·x + 100

The positive factors of the above equation includes; (3 + √(509))/5

The domain where the function makes sense is 0 ≤ x ≤ (3 + √(509))/5

b. The range is the set of possible output values

The reasonable range of the function from the graph is found as follows;

At the maximum height;

x = -b/(2·a)

Therefore;

x = -6/(2×(-5)) = 0.6

f(0.6) = -5·(0.6)² + 6·(0.6) + 100 = 101.8

The range is 0 ≤ y ≤ 101.8

c. The height of the ball from the ground at time t = 3 seconds is found as follows;

f(3) = -5·3² + 6·3 + 100 = 73

The height of the ball at x = 3 seconds is 73-meters

d. The y-intercept of the new graph is 80

The difference between the two graphs is that the new graph is shifted 20 units downwards

The difference is indicated in the graph

e. The new function is found by subtracting 20 from the previous function to get;

g(x) = f(x) - 20 = -5·x² + 6·x + 100 - 20 = -5·x² + 6·x + 80

The type of transformation is a translation transformation

f. The maximum point and the x-intercept changes in the new function, therefore, a different domain and range is needed

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Answer:

175

Step-by-step explanation:

because you have 1.38 per pound and 241.50 divded by that = 175

The area between the singles and doubles sidelines in tennis is called the tramlines. Tramlines serve specific purposes and affect the rules and strategies of the game.

The tramlines, also known as alleyways or doubles alleys, are located on both sides of the tennis court, running parallel to the singles sidelines. They create additional playing areas for doubles matches, extending the width of the court. These tramlines are marked by lines that are typically one and a half feet wide.

During doubles play, each team member has their own respective tramline. The purpose of the tramlines is to define the legal hitting areas for players. When serving, the server must aim to hit the ball within the singles sideline and the tramline on their side of the court. After the serve, the ball is considered "in" if it lands within the tramlines and between the singles and doubles sidelines.

The presence of the tramlines influences the strategies and tactics used in doubles matches. Players can utilize the additional space to angle shots and create different angles for their opponents to cover. The tramlines also affect positioning and movement on the court, as players need to cover a wider area during rallies.

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Using percentage we can calculate that the team is expected to lose 4 matches.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.

By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.

Given in percentages the team will win 65% , team will draw =15%

Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %

Now calculating the total number of matches the team will lose :

20% of 20 matches = 4 matches

Hence the team is expected to lose 4 matches out of 20.

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Answer: the 3rd one

Step-by-step explanation:

Answer:

255,000

Step-by-step explanation:

if we look there is already 254,000 so now we look at the hundreds place.

In the hundreds place there is 920 witch is closer to 1,000

so 254,000 plus 1,000 is 255,000

Please Brainlylist :)

Answer:

x-int: (-5, 0), (7, 0)

vertex: (1, -36)

Step-by-step explanation:

Simply graph the equation and find what is asked (Fastest and easiest way).

Answer: 1/2

Step-by-step explanation:

Answer:

James finished studying at 5:35pm

Step-by-step explanation:

3:20+2:15=3:35

20+15=35

3+2=5

To answer 16-19, we need to determine the optimal quantities of goods 1 and 2 chosen by the consumer based on the given utility function (u(x1, x2) = min{x1, x2}), prices (p1 = $4, p2 = $2), and income (I = $18).

The optimal quantity of good 1 chosen by the consumer can be found by comparing the ratio of prices to the marginal utilities:

p1 / p2 = MU1 / MU2

Substituting the given prices and utility function, we have:

4 / 2 = 1 / MU2

Simplifying, we find MU2 = 2. This means the consumer equates the marginal utility of good 1 (MU1) to 1.

Since the utility function is u(x1, x2) = min{x1, x2}, the consumer will choose the smaller of the two quantities. In this case, the optimal quantity of good 1 chosen by the consumer is 1.

Using the same approach, we can determine the optimal quantity of good 2 chosen by the consumer. Comparing the ratio of prices to the marginal utilities:

4 / 2 = MU1 / MU2

Simplifying, we find MU1 = 8. This means the consumer equates the marginal utility of good 2 (MU2) to 2.

Since the utility function is u(x1, x2) = min{x1, x2}, the consumer will choose the smaller of the two quantities. In this case, the optimal quantity of good 2 chosen by the consumer is 2.

If p1 decreases to $1 while keeping p2 and income constant, the new ratio of prices to marginal utilities becomes:

1 / 2 = MU1 / MU2

Simplifying, we find MU2 = 2. This means the consumer still equates the marginal utility of good 1 (MU1) to 1.

Therefore, the optimal quantity of good 1 chosen by the consumer remains 1.

Similarly, if p1 decreases to $1 while keeping p2 and income constant, the new ratio of prices to marginal utilities becomes:

1 / 2 = MU1 / MU2

Simplifying, we find MU2 = 2. This means the consumer still equates the marginal utility of good 2 (MU2) to 2.

Therefore, the optimal quantity of good 2 chosen by the consumer remains 2.

To determine the size of the substitution effect for good 1 when p1 decreases from $4 to $1, we need to compare the quantities of good 1 chosen before and after the price change.

Before the price change, the consumer chose 1 unit of good 1. After the price change, the consumer still chooses 1 unit of good 1.

Since the quantity of good 1 chosen remains the same despite the price change, the substitution effect for good 1 is zero.

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Answer:

9

Solution:

BA=CA

and then 9^2=81

if you need an explaination message me :)

Answer:

y= 1/2x + 2

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

One thing is for certain. The final answer will be 1/r^12 or r^(-12)

When written as the given of (r^-4)^3, the powers are multiplied.

The first one is false. There are 4 factors of r^-4 If you get an answer that says it is true, then the question means that r^-4 is 3 equal factors of r^-12

B is true

C: not true. The exponents are multiplied, not added.

D is true

E: not true. This is the same thing as C.

The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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Answer:

(4, 4)

Step-by-step explanation:

If it is reflected on both axis, it will be (4, 4)

12! divided by 10! is not equivalent to 6! divided by 5!. Then the correct statement is 3.

Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

The statements are given below.

Statement 1 - The subtraction cannot be completed before the factorial of each number is calculated. This is the incorrect statement.

Statement 1 - 12! divided by 10! is not equivalent to 6! divided by 5!. This is the correct statement.

Statement 3 - The dividing out of common factors was performed incorrectly. There are sixty-six ways to choose ten items from twelve. This is the incorrect statement.

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Answer:

D and F

Step-by-step explanation:

(D) "In step 1, 12! divided by 10! is not equivalent to 6! divided by 5!."

(F) "There are sixty-six ways to choose ten items from twelve."

The two triangles are congruent, as the Pythagorean Theorem ensures that the hypotenuse of the two triangles will be equal.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

If two triangles have congruent side lengths, the hypotenuse for the two triangles will also be the same, hence the Pythagorean Theorem ensures the congruence of the two triangles.

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Once you have the probability and payout odds, you can use the above steps to determine the casino's expected gain/lose when 1000 people play the same bet throughout the day.

To accurately answer this question, more information is needed about the specific bet and the casino's odds for that bet.

However, I can help you determine the expected gain/lose once you provide the necessary information.
Step 1: Determine the probability of the bet outcome (win/lose) and the payout odds for each outcome.
Step 2: Calculate the expected gain/lose for a single bet by multiplying the probability of each outcome by its respective payout.
Step 3: Multiply the expected gain/lose per bet by the number of people (1000) to find the total expected gain/lose for the casino.

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The value of the given integral after the calculation is 54π/5.

here,

we consider the given data and try to simplify the integral

The integral is ∭Ey2 dV that is over the solid hemisphere x2+y2+z2≤9, y≥0x2+y2+z2≤9, y≥0.

The evaluation of the given integral can be possible using spherical coordinates. Furthermore, the solid hemisphere can also be described as 0≤θ≤π/2 and 0≤Ф≤2π.

therefore,

spherical coordinates are Ey² = (ρsinΦ)²= ρ²sin²φ

now, the Jacobian for the given spherical coordinate is r²sinθ

now,

∭Ey2 dV =∭ρ²sin³φr²sinθdρdθdφ

=∫\(0^{(\pi /2)}\) ∫\(0^{(\pi /2)}\) ∫\(0^{3}\)ρ⁴sin³φ sinθdρdθdφ

=(3⁵/5) x (1/2) x (2/3)

=54π/5

The value of the given integral after the calculation is 54π/5.

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