What is the area enclosed by the curves y = x∧3 - 8x∧2 + 18x -5 and y = x + 5? a. 10.667 b. 11.833 c. 14.583 d. 21.333 e. 32
Answers
The area enclosed by the curves is approximately 21.333, which corresponds to option d.
To find the area enclosed by the curves y = x³ - 8x² + 18x - 5 and y = x + 5, follow these steps:
1. Set the two functions equal to each other to find the points of intersection: x³ - 8x² + 18x - 5 = x + 5.
2. Simplify the equation by subtracting x and 5 from both sides: x³ - 8x² + 18x - 10 = 0.
3. Solve the cubic equation for x to find the points of intersection. You can use a calculator or an online solver. The solutions are approximately x = 1, x = 2, and x = 5.
4. To find the area enclosed by the curves, integrate the difference of the two functions with respect to x between the points of intersection: ∫[x³ - 8x² + 18x - 10 - (x + 5)] dx from x = 1 to x = 5.
5. Simplify the expression inside the integral: ∫[x³ - 8x² + 18x - 15] dx from x = 1 to x = 5.
6. Evaluate the integral: [1/4 × 4x - (8/3) × x³ + 9 × x² - 15 × x] from x = 1 to x = 5.
7. Calculate the area by subtracting the values of the integral at the limits: A = F(5) - F(1), where F(x) represents the antiderivative.
8. A = (1/4 × 625 - (8/3) × 125 + 9 × 25 - 15 × 5) - (1/4 × 1 - (8/3) × 1 + 9 × 1 - 15 × 1) ≈ 21.333.
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Related Questions
The equation y = 700x + 800 models the typical annual cost, y, in dollars, of medical expenses x years after a person’s 20th birthday. What does 800 represent?
Answers
Answer:the annual medical expenses for a typical 20 yr old
Step-by-step explanation:
The speed of light in a vacuum is 29,980,000,000
centimeters per second. In scientific notation, this
number is written as
A. 2.998 x 10⁹.
B. 2.998 x10¹0.
C.
29.98 x 10⁹.
D. 29.98 x10¹0.
Answers
Answer:
\(\huge\boxed{\sf 2.998 \times 10^{10}}\)
Step-by-step explanation:
Given number:
29,980,000,000
Rules:
Move the decimal point after the first non-zero digit. (after 2)Here, we will move the decimal point 10 places to the left to move it after the first non-zero digit.Since we move the decimal point 10 places, we will write the number as a multiple of 10¹⁰ (10 being the exponent).The number will become:
2.998 × 10¹⁰
\(\rule[225]{225}{2}\)
Answer:
B. 2.998 x 10¹⁰
Step-by-step explanation:
Given :
29,980,000,000Steps in solving :
Take the zeros after the last non-zero digit as a power of 10.Take the non-zero part (in the part) and put a decimal point after between the thousands and hundreds place, and shift the remaining powers of 10 to the previously grouped part.Adjust further if needed to match an answer.Solving :
29,980,000,0002,998 x 10⁷2.998 x 10³ x 10⁷2.998 x 10¹⁰Organizational culture is set by a. the manager b. the ethics committee c. the engineer d. none of the given options
Answers
Organizational culture is defined as the common beliefs, values, attitudes, customs, behaviors, and traditions that characterize a specific organization and determine the manner in which it functions. Organizational culture is set by the manager.
In a corporate or business environment, organizational culture can influence the daily operations of employees. It is the responsibility of managers to create a positive culture that emphasizes teamwork, respect, integrity, and accountability. The manager is an essential individual responsible for establishing and maintaining the organization's culture, which will ultimately define the employee's attitudes, behaviors, and productivity levels. He or she sets the tone for the workplace by creating an environment that fosters collaboration, innovation, and success. Employees need to feel connected to their workplace and colleagues to be motivated to do their best work. If a manager promotes a culture of fear, competition, or dishonesty, employees may become unmotivated or unproductive. An effective manager understands the importance of creating a positive workplace culture and works hard to establish and maintain it. Managers can establish a positive culture by encouraging open communication, providing regular feedback and recognition, fostering a sense of teamwork, creating opportunities for professional development, and setting high standards for performance. Managers must lead by example and demonstrate the behaviors and attitudes that they expect from their employees. They must hold themselves and others accountable for their actions, communicate expectations clearly, and provide support when needed. A positive organizational culture will enable an organization to attract and retain top talent, increase employee engagement, and promote collaboration and innovation.
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plots are used to detect some of the common violations to the regression model assumptions. These graphical plots are easy to use and provide informal analysis of the estimated regression models.ResidualResponsePerfect multicollinearity
Answers
Answer:
Plots that can detect violations in regression assumptions, while response plots help analyse the relationship between the response variable and predictors are Residual plots and scatterplot matrix.
Step-by-step explanation:
There are several graphical plots commonly used to detect violations of regression model assumptions and analyze estimated regression models. Here are a few examples:
Residual plot: A residual plot shows the difference between the observed values of the response variable and the predicted values from the regression model. Patterns in the residuals, such as nonlinearity, heteroscedasticity (unequal variances), or outliers, can indicate violations of assumptions.
Response plot: This plot examines the relationship between the response variable and one of the predictor variables while holding other predictors constant. It helps identify nonlinearity or other issues in the relationship between the response and predictors.
Scatterplot matrix: A scatterplot matrix displays scatterplots between pairs of predictor variables. It can help detect issues like perfect multicollinearity, which occurs when two or more predictors are highly correlated, leading to problems in estimating the regression coefficients.
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You can get 672 calories from eating 8 apples. How many calories can you get from eating 1 apple?
Answers
Step-by-step explanation:
672 divides by 8
=8.375
Identify the mystery number. Explain your process for figuring it out.
Answers
We know that the value x we are looking for is even, and is greater than 6 and less than 10.
We start with the condition of being even.
Then x can be 2, 4, 6, 8, 10, 12, 14...
If we know that is greater than 6, we can eliminate 2, 4 and 6 from the list.
x can be: 8, 10, 12, 14...
If we know that x is less than 10, we can eliminate 10 and all the values above 10.
Then, x is 8, as it is the only value left in the list of possible values.
Answer: the number is 8.
find the value of x in the figure
Answers
To rent a midsize car for one day, Speedy charges a flat rate of $41 plus an additional fee of $0.10 per mile driven. Write an equation that relates the total cost of the car rental for one day as a function of the number of miles driven .
Answers
Answer:
C(m) = 41(flat rate) + .10m(rate per mile)
Step-by-step explanation:
Denisha has already read 42 pages
novel for her English class. For the rest of
the month, she plans to read 24 pages
every 3 days. What is the constant rate of
change in this situation?
A.
page per day
B. 6 pages per day
C. 8 pages per day
D. 24 pages per day
Answers
Answer:
B.6 pages per day
Order the number from least to greatest -12, 3/25, -0.41
Answers
Answer:
-12, -0.41, 3/25
Step-by-step explanation:
Answer:
the answer is -12, -0.41, 3/25.
Kristen's financial advisor has given her a list of 8 potential investments and has asked her to select and rank her favorite four. In how many different ways can she do this?
Answers
The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.
If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:
nPr = n!/{(n - r)!}.
In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.
Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.
Substituting n = 8, and r = 4 in the formula, we get:
8P4 = 8!/{(8 - 4)!}
= 8!/4!
= 5 * 6 * 7 * 8
= 1680.
Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.
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Jala has an aquarium in the shape of a rectangular prism with the dimensions shown. What is the height of the aquarium? Round your answer to the nearest tenths place.
Answers
height = 24.4in
hope it helps...!!!
Answer:
24.4in.
Step-by-step explanation:
31.25 x 15.5 = 484.375
11818.75 / 484.375 = 24.4in.
consider the following definition. a single-line code that reads as follows: int, open square bracket, close square bracket, open square bracket, close square bracket, numbers equals, open brace, open brace, 1 comma 2 comma 3, close brace, open brace, 4 comma 5 comma 6, close brace, close brace, semicolon. which of the following code segments produces the output 123456 ?
Answers
The code segment `int[][] numbers = {{1, 2, 3}, {4, 5, 6}};` produces the output 123456.
The given code segment initializes a 2D integer array named `numbers` using the initialization syntax for multi-dimensional arrays in Java. The syntax consists of square brackets to represent dimensions and nested braces to specify the values.
In this case, `int[][] numbers` declares a 2D array of integers. The outer square brackets `[]` indicate that it is an array, and the inner square brackets `[]` denote that it is a 2D array. The numbers are assigned using the double brace initialization: `{{1, 2, 3}, {4, 5, 6}}`.
The outer braces represent the rows of the 2D array, and the inner braces represent the individual elements within each row. So, the first row of the `numbers` array is `{1, 2, 3}` and the second row is `{4, 5, 6}`.
Therefore, when accessing or printing the elements of `numbers` in order, it will produce the output 123456.
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can some help me
out with this problem please ?
Answers
Answer:
Step-by-step explanation:
If you are looking for the value of x, use the Pythagorean Theorem.
x² = 58² - 40² = 1764
x = √1764 = 42
Answer: 42cm
Step-by-step explanation:
Using the formula
(Hypotenuse^2)= (Opposite^2) + (Adjacent^2)
Hypotenuse= 58cm
Opposite= 40cm
Adjacent= x
Therefore
(58^2)= (40^2) + (x^2)
3364= 1600 + x^2
3364-1600= x^2
1764= x^2
x= 1764^1/2
x= 42
Adjacent= 42cm
What do you do in algebra
Answers
Basics of Algebra cover the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0. ...
Q 1: Find y, when, y + 15 = 30.
Solution: y = 30 – 15.
Q 2 : Find x, when, 9x = 63.
Q. 3: If x/7 = 21, then find x. Learning algebra helps to develop your critical thinking skills. That includes problem solving, logic, patterns, and reasoning. You need to know algebra for many professions, especially those in science and math.
Algebra is a system of manipulating numbers and operations to try to solve problems. When you learn algebra, you will learn the rules to follow for solving problems. But to help make that easier, you need to have a strong understanding of basic math facts. ... Being able to work with two-digit numbers is even more helpful. The Basic Laws of Algebra are the associative, commutative and distributive laws. They help explain the relationship between number operations and lend towards simplifying equations or solving them. Algebraic expressions include at least one variable and at least one operation (addition, subtraction, multiplication, division). For example, 2(x + 8y) is an algebraic expression. Algebra is thinking logically about numbers rather than computing with numbers. ... Paradoxically, or so it may seem, however, those better students may find it harder to learn algebra. Because to do algebra, for all but the most basic examples, you have to stop thinking arithmetically and learn to think algebraically. Algebra is an important life skill worth understanding well. It moves us beyond basic math and prepares us for statistics and calculus. It is useful for many jobs some of which a student may enter as a second career. Algebra is useful around the house and in analyzing information in the news.
find the value of 0 round to the nearest whole degree
Answers
Answer:
27°
Step-by-step explanation:
we have the 'opposite' as length 2 is opposite the angle θ
we have the adjacent (length 4) which is next to the angle θ
the hypotenuse is the longest side (we don't need)
Using SOHCAHTOA
we use TOA as O is opposite and A is adjacent
tanθ = opposite ÷ adjacent
tanθ = 2 ÷ 4
using the inverse sign to find θ
θ = tan⁻¹(2/4) = 27° (to the nearest whole degree)
Slope fields are not usually useful for ODEs of second order or higher, as we need to know the first derivative of our desired function in order to draw the slope field. True or false
Answers
Slope fields are not usually useful for ODEs of second order or higher, as we need to know the first derivative of our desired function in order to draw the slope field. This staetment is True
True.
Slope fields are a graphical tool that can be used to visualize the behavior of solutions to first-order ordinary differential equations (ODEs). They involve drawing short line segments at various points on the x-y plane to indicate the slope of the solution curve at those points, based on the value of the first derivative at each point.
For ODEs of second order or higher, we need to know the values of higher-order derivatives of the solution function in order to draw a slope field. However, slope fields are not typically used for these types of ODEs, since the solutions can become more complicated and difficult to visualize in higher dimensions. Other methods, such as numerical methods or phase portraits, may be more appropriate for analyzing and visualizing solutions to ODEs of higher order.
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The test to detect the presence of strep throat is 98% accurate for a person who has the disease and 97% accurate for a person who does not have the disease. If 3. 5% of the people in a given population actually have strep throat, what is the probability that a randomly chosen person tests positive? A. 0. 0343 B. 0. 035 C. 0. 06325 D. 0. 2895.
Answers
Using the given percentages, it is found that the probability that a randomly chosen person tests positive is:
C. 0. 06325
Th percentage associated with a positive test are:
98% of 3.5%(person has the disease).3% of 96.5%(person does not have the disease).Hence:
\(p = 0.98(0.035) + 0.03(0.965) = 0.06325\)
Thus, option C is correct.
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suppose a survey of 979 business owners found that more than % bought . which part of the survey represents the descriptive branch of statistics? make an inference based on the results of the survey.
Answers
In this problem, descriptive statistics is used because the survey percentage is used to make inference for all business owners.
What is descriptive statistics?
Descriptive statistics is used when data from a sample, which is a sub-set of a population, is used to make inferences about the entire population.
In this problem, the data 979 business owners sampled is used to make inference about the population, which is composed by all business owners, hence descriptive statistics is used.
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The diagram shows a regular polygon. Work out the value of x.
Answers
Answer:
x = 67.5 degrees
Step-by-step explanation:
this is an octagon which has 8 sides
the sum of all interior angles can be found by taking the number of sides, reducing it by 2, and then multiplying by 180
(8-2)*180 = 6(180) = 1080
the 1080° must be split equally among all 8 angles because it is a 'regular' polygon
1080/8 = 135
however, 'x' represents half of each regular angle so it is 67.5 degrees
Solve: 6-x =4(5+x)-4
Answers
Answer:
option A , x=-2
Step-by-step explanation:
6-x =4(5+x)-4
6 - x = 4 × 5 + 4 × x - 4
6 - x = 20 + 4x - 4
6 - x = 4x + 16
-x - 4x = 16 - 6
-5x = 10
x = 10/-5
x = -2
therefore, option A is the correct option
hope it helps you
Answer:
First, finish the brackets
6-x=20+4x-4
Collect like terms
-x-4x=20-4-6
Solve
-3x=10
x=-10/3
x=-3.33333333333 Or x≅3.34
Step-by-step explanation:
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Foundation mathematics Final Exam-A22(main) < Question 12 of 19 > Find the absolute maximum and minimum values of each function over the indicated interval, and indicate the x-values at which they occur. f(x) = 2x³ - 2x² - 2x + 5; [− 1,0] 1 The absolute maximum value is 145 at x = 27 3 (Use a comma to separate answers as needed. Type an integer or a fraction.) The absolute minimum value is - 1 at x = 3. (Use a comma to separate answers as needed. Type an integer or a fraction.) Submit test
Answers
The task is to find the absolute maximum and minimum values of the function f(x) = 2x³ - 2x² - 2x + 5 over the interval [-1, 0]. The absolute maximum value is 145 at x = 27/3, and the absolute minimum value is -1 at x = 3.
To find the absolute maximum and minimum values of a function over a given interval, we need to evaluate the function at critical points and endpoints within that interval. In this case, the function is f(x) = 2x³ - 2x² - 2x + 5, and the interval is [-1, 0].
To begin, we calculate the derivative of the function f'(x) using the power rule of differentiation. The derivative of f(x) is f'(x) = 6x² - 4x - 2. Next, we find the critical points by setting f'(x) equal to zero and solving for x. In this case, there is only one critical point, which is x = 3. Now, we evaluate the function f(x) at the critical point x = 3 and the endpoints x = -1 and x = 0. This gives us f(-1), f(0), and f(3). Evaluating these values, we find that f(-1) = 6, f(0) = 5, and f(3) = -1.
Comparing these values, we determine that the absolute maximum value is 6 at x = -1, and the absolute minimum value is -1 at x = 3. However, it seems there might be a mistake in the given solution. Upon evaluating the function at x = 27/3 (which simplifies to x = 9), we find that f(9) = 145, not 27/3 as stated in the given solution. Therefore, the correct absolute maximum value is 145 at x = 9. In conclusion, the absolute maximum value of the function f(x) = 2x³ - 2x² - 2x + 5 over the interval [-1, 0] is 6 at x = -1, and the absolute minimum value is -1 at x = 3.
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What type of angles are the following?
1. Smoothie Shack and Bed and Breakfast
Alternate interior angles
Corresponding Angles
Vertical Angles
Alternate Exterior Angles
Same-Side Interior Angles
2. Gas Station and Bank
3. Shoe Store and restaurant
4. Music shop and fire station
5. Arcade and Restaurant
6. Boutique and the Doctor's Office
7. Courthouse and Dentist
8. Bed & Breakfast and Restaurant
9. Hospital and Park
10. Coffee Shop and Doctor
11. Smoothie Shack and Pizza Bell
12. Library and Gas Station
13. Dance Studio and Shoe Store
14. Hospital and Gas Station
15. Optical and Coffee Shop
16. City Hall and Daycare
Answers
Smoothie Shack and Bed and Breakfast: Vertical Angles. Gas Station and Bank: Vertical Angles. Shoe Store and Restaurant: Same-Side Interior Angles. Music Shop and Fire Station: Same-Side Interior Angles.
Arcade and Restaurant: Same-Side Interior Angles. Boutique and Doctor's Office: No specific type of angles mentioned. Courthouse and Dentist: No specific type of angles mentioned. Bed & Breakfast and Restaurant: Alternate Interior Angles. Hospital and Park: No specific type of angles mentioned. Coffee Shop and Doctor: No specific type of angles mentioned. Smoothie Shack and Pizza Bell: No specific type of angles mentioned. Library and Gas Station: No specific type of angles mentioned. Dance Studio and Shoe Store: No specific type of angles mentioned. Hospital and Gas Station: No specific type of angles mentioned. Optical and Coffee Shop: No specific type of angles mentioned. City Hall and Daycare: No specific type of angles mentioned.
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A car uses 3.75 gallons of gasoline to travel 100.5 miles. How many miles per gallon does the car use in gasoline? Calculate the unit rate as a decimal.
Answers
Answer:Thus our answer is 60 miles per hour.
Step-by-step explanation:
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To calculate the miles per gallon, or the unit rate, you divide the total distance by the total fuel used. In this example, the car uses an average of 26.8 miles per gallon of gasoline.
Explanation:The unit rate represents the amount of miles a car can travel per one gallon of gasoline. To find this, we need to divide the total distance driven by the gallons of gasoline used.
Step 1: Identify the total distance and the total gallons used. Here, the total distance driven is 100.5 miles, and the gallons of gasoline used is 3.75.
Step 2: To find how many miles per gallon the car uses, divide the total miles by the total gallons used:
100.5 miles / 3.75 gallons = 26.8 miles per gallon.
So, the car uses an average of 26.8 miles per gallon of gasoline. In terms of decimals, 26.8 is the unit rate.
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which method would you use to round 2.6 to the closest whole number?
Answers
Answer:
Step 1: Locate and underline the whole numbers place (2) then look at the digit to the right (6):
2.6
Step 2: In this case, the digit to the right (6) is 5 or above. So, we add 1 to the whole numbers place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 3 as the answer.
In short: 2.6 rounded to the nearest whole number is 3.
5, 6 5/12, 6.45, 11/2 from least to greatest
Answers
Answer:
the answer is 5, 11/2, 6 5/12, 6.45
what is the maximum number of real zeros a polynomial function of degree three can have?
Answers
A polynomial can have as many real zeros as its degree, hence one with three degrees can have as many as three zeros.
What are the roots of an equation?The roots of an equation are the solution of that equation since an equation consists of hidden values of the variable to determine them by different processes and then the resultant is called roots.
A polynomial with n degrees can have as many variables as n in total.
For example, a quadratic equation ax² + bx + c = 0 is a two-degree equation so it has a maximum of two roots or zeros.
A polynomial with the given degree structure will have exactly 3 roots because it has 3 degrees.
Hence "The maximum number of real zeros in a polynomial will be same as its degree thus 3 degrees will have 3 zeros".
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What is the simplified form of the expression? 5 c squared d minus 4 c + 3 minus 3 + 2 c squared d minus 3 c + d minus 7 3 c squared d minus 7 c + 2 d minus 10 3 c squared d minus 7 c + 4 d minus 10 7 c squared d minus 7 c + 2 d minus 10 7 c squared d minus 7 c + 4 d minus 10
Answers
Answer:
7 c squared d minus 7 c + 4 d minus 10
Step-by-step explanation:
because thats the answer on edge 2020 I promise :)
Answer:
7c²d-7c+4d-10
Step-by-step explanation:
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Consider two independent binomial experiments. In the first one, 94 trials had 54 successes.In the second one, 63 trials had 40 successes. Answer the following questions. Use a confidence level of 96%. Use 4 decimal places for each answer. Do not round from one part to the next when performing the calculations, though. Find the point estimate. Find the critical value. Find the margin of error. Find the confidence interval. < p 1 − p 2
Answers
The 96% confidence interval for the difference in proportions is (−0.1127, 0.3191)
To compare the proportions of success in two binomial experiments, we can use the two-sample Z-test.
Let p1 be the proportion of success in the first experiment and p2 be the proportion of success in the second experiment. We want to test the null hypothesis H0: p1 = p2 against the alternative hypothesis Ha: p1 ≠ p2.
First, we calculate the point estimate of the difference in proportions:
\(pp1 - p2 = \frac{54}{94} - \frac{40}{63} = 0.1032\)
Next, we find the critical value of the test statistic. Since the confidence level is 96%, we have alpha = 0.04/2 = 0.02 on each tail of the distribution. Using a standard normal distribution table, we find that the critical values are ±2.0537.
The margin of error is given by:
\(ME= z \sqrt{\frac{p1(1-p1)}{n1} +\frac{p2(1-p2)}{n2} }\)
where z* is the critical value, n1 and n2 are the sample sizes of the two experiments. Plugging in the values, we get:
\(ME= z \sqrt{\frac{0.5769(1-0.5769)}{94} +\frac{0.6349(1-0.6349)}{63} }= 0.2159\)
Finally, we can construct the confidence interval for the difference in proportions as:
(p1 - p2) ± ME
which gives us:
0.1032 ± 0.2159
Thus, the 96% confidence interval for the difference in proportions is (−0.1127, 0.3191).
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2. 3. W Wha Expl 326 A 8 Skills Quiz 10. The school dance committee is choosing a location for the annual end-of-year dance. A random survey was given to 500 students. Their preferences are indicated in the table. Based upon this survey, how many of the 1,500 students would be expected to vote for the school gym? A. 320 students B. 960 students C. 390 students D. 150 students
Answers
We anticipate that roughly 480 of the school's 1,500 pupils will choose the gym as the venue for the annual end-of-year dance.
How many of the 1,500 students would be expected to vote for the school gym?According to the preferences table, 160 of the 500 pupils who participated in the poll picked the school gym as the venue for the yearly dance. We may use the percentage of students who favored the school gym in the sample to calculate the number of students out of 1,500 who would be expected to vote for the gym:
160/500 = 0.32
This indicates that 32% of the sample's students favored using the school gym. Using this ratio, we can determine how many of the 1,500 pupils favor the school gym:
1.5 times 0.32 equals 480 students.
As a result, we anticipate that roughly 480 of the school's 1,500 pupils will choose the gym as the venue for the annual end-of-year dance.
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