The variance for the number of voters who favor the ballot measure in groups of 21 is calculated using the formula for a binomial distribution, which yields an answer of 3.78. The closest option to this value is 3.6, answer option d.
Explanation:In the question about a town where 22% of voters favor a given ballot measure, we are asked to find the variance for the number of voters who favor the measure in groups of 21 voters. To calculate the variance, we use the formula for the variance of a binomial distribution, which is np(1-p), where 'n' is the number of trials (voters in this case), 'p' is the probability of a voter favoring the measure, and '1-p' is the probability of a voter not favoring the measure.
Using the information provided:
n = 21 (the number of voters in a group)p = 0.22 (the probability of a voter favoring the measure)Thus, the variance (Var) is:
Var = np(1-p) = 21 × 0.22 × (1 - 0.22) = 21 × 0.22 × 0.78 = 3.78
The closest answer to 3.78 is 3.6, which is option d.
Variance formula: [tex]\(npq\)[/tex]. Substitute [tex]\(n = 21\), \(p = 0.22\), \(q = 0.78\)[/tex]. Calculate to get variance. Answer: d. 3.6
To find the variance for the number who favor the measure in groups of 21 voters, we can use the binomial distribution formula.
The variance of a binomial distribution is given by [tex]\(npq\)[/tex], where:
- [tex]\(n\)[/tex] is the number of trials (number of voters in each group),
- [tex]\(p\)[/tex] is the probability of success (proportion of voters favoring the measure), and
- [tex]\(q\)[/tex] is the probability of failure (proportion of voters not favoring the measure).
Given:
- [tex]\(n = 21\)[/tex],
- [tex]\(p = 0.22\)[/tex] (22% favor the measure), and
- [tex]\(q = 1 - p = 1 - 0.22 = 0.78\)[/tex],
Let's calculate the variance:
[tex]\[ \text{Variance} = npq = 21 \times 0.22 \times 0.78 \][/tex]
[tex]\[ \text{Variance} = 21 \times 0.1716 \][/tex]
[tex]\[ \text{Variance} = 3.5976 \][/tex]
Rounded to one decimal place, the variance is approximately [tex]\(3.6\)[/tex].
So, the correct answer is d. 3.6.
If cosθ =1/3 , then sinθ = _____.
Answer:
I'm pretty sure the answer for this is ±[tex]\frac{2\sqrt{2} }{3}[/tex]
Step-by-step explanation:
I did the assignment.
Is 1,000,000 rational?
What are 3 ratio equivalents to 14:2, also how would I get the answer
Need help with this math problem
On a 24 question math test, Nuno got 6 questions wrong. Nuno's score decreased by 30 points.
Drag the numbers to form the equation that represents how much Nuno's score changed by each incorrect answer.
( )( )= ( )
4, -4, 5, -5, 24, -24, 30, -30, 1/6, -1/6
Show work
A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture worth $0.54 a pound, how much of each bean is used? Model the scenario then solve it. Then, in two or more sentences explain whether your solution is or is not reasonable.
35 pounds of $0.20 coffee beans and 85 pounds of $0.68 coffee beans create a 120-pound mixture valued at $0.54 per pound when mixed. Solving the system of linear equations confirms these amounts as reasonable and correct.
To solve the problem of determining how much of each type of coffee bean is used in a mixture, we can use a system of equations to model the scenario. Let's define x as the number of pounds of the $0.20 coffee beans and y as the number of pounds of the $0.68 coffee beans. Given the total weight of the mixture is 120 pounds, we can formulate our first equation:
x + y = 120
The total value of the coffee mixture is $0.54 per pound, hence the second equation representing the total value of the mixture is:
0.20x + 0.68y = 0.54(120)
By solving this system of equations, we can find the precise quantities of each type of bean used in the mixture.
Step 1: Multiply the second equation by 100 to clear the decimals for easier calculation:
20x + 68y = 54 times 120
Step 2: Solve for one of the variables, let's say x:
x = 120 - y
Step 3: Substitute x in the second equation:
20(120 - y) + 68y = 54 times 120
This simplifies to:
2400 - 20y + 68y = 6480
48y = 4080
Step 4: Solve for y:
y = 4080 / 48
y = 85
Step 5: Substitute y back into the first equation to find x:
x = 120 - 85
x = 35
If 35 pounds of the $0.20 beans and 85 pounds of the $0.68 beans are mixed together, we achieve the desired mixture weighing 120 pounds valued at $0.54 per pound. This solution is reasonable because the sum of the weights equals the total weight of the mixture, and the calculated total value per pound matches the desired value.
how do you write the number 7.04 in expanded form?
what is pie
i am am confused i need
help
A group of people have the number 12345.6789 written on a piece of paper. Then the group decides to play a game. The winner of the game is the person who can round the given number and get a number higher than any other person. Alice rounds to the nearest ten-thousand, Bob to the nearest thousand, Carol to the nearest hundred, Devon to the nearest ten, and Eugene to the nearest whole number. In addition, Felicity rounds the number to the nearest tenth, Gerald to the nearest hundredth, Harry to the nearest thousandth, and Irene rounds to the nearest ten-thousandth. Who wins the game?
Answer:
its devon
Step-by-step explanation:
can someone help me with this please !!!!
What is 19c+26=41+14c (Steps included please)
A weightlifter holds a 1,700 N barbell 1 meter above the ground. One end of a 2-meter-long chain hangs from the center of the barbell. The chain has a total weight of 500 N. How much work (in J) is required to lift the barbell to a height of 2 m?
The work done by the weightlifter to lift a barbell and a chain with a total weight of 2,200 N through a vertical distance of 1 meter is 2,200 joules.
The question involves calculating the work done when a weightlifter lifts a barbell from one height to a higher height. To find the work done, we can use the formula W = F imes d imes ext{cos}(\theta), where W is the work, F is the force, d is the distance through which the force acts, and \theta is the angle between the force and the direction of motion. Since the weightlifter is lifting vertically, the angle \theta is 0 degrees, and cos(0) is 1, simplifying the formula to W = F imes d.
The total weight of the barbell and the chain is the sum of both weights, which is 1,700 N + 500 N = 2,200 N. The barbell is initially 1 meter above the ground and needs to be lifted to a height of 2 meters, so the distance d is 2 m - 1 m = 1 m. Therefore, the work done to lift the barbell and chain is W = 2,200 N imes 1 m = 2,200 J.
Suppose there are 30 people at a party. do you think any two share the same birthday? let's use the random-number table to simulate the birthdays of the 30 people at the party. ignoring leap year, let's assume that the year has 365 days. number the days, with 1 representing january 1, 2 representing january 2, and so forth, with 365 representing december 31. draw a random sample of 30 days (with replacement). these days represent the birthdays of the people at the party. would you expect any two of the birthdays to be the same?
The probability that at least 2 people have the same birthday is 29.37%
Further explanationProbability is the likelihood of an event occurring. Probability is the number of ways of achieving success. Probability is also the total number of possible outcomes.
Suppose there are 30 people at a party. Do you think any two share the same birthday?
Let's use the random-number table to simulate the birthdays of the 30 people at the party, ignoring leap year.
Let's assume that the year has 365 days. number the days, with 1 representing January 1, 2 representing January 2, and so forth, with 365 representing December 31.
Draw a random sample of 30 days (with replacement). These days represent the birthdays of the people at the party. Would you expect any two of the birthdays to be the same?
[tex]1^{st} people = \frac{365}{365} \\ 2^{nd} people = \frac{364}{365} \\ 3^{rd} people = \frac{363}{365}[/tex]
For 30 people
365! = 365*364*363*...336
So
[tex]= \frac{365*364*363*...336}{(365^{30})} = \frac{365!}{(365^{30})}[/tex]
[tex]\frac{365!}{(365^{30})}[/tex] [tex]= \frac{365!/(365-30)!}{365^{30}}[/tex]
[tex]= \frac{365!/335!}{365^{30}} \\ = 0.2937 = 29.37%[/tex]
The probability that at least 2 people have the same birthday is 29.37%
Learn moreLearn more about the same birthday https://brainly.com/question/4538530Learn more about probability https://brainly.com/question/12448653Learn more about random sample https://brainly.com/question/12384344Answer details
Grade: 9
Subject: mathematics
Chapter: probability
Keywords: the same birthday, probability, random sample, party, simulate
how many different ways can you use the digit 3 and 5 to write expressions in exponential form? What are expression?
Exponential notation is used to express very large and very small numbers as a product of two numbers. We can cube the digit term in the usual way and multiply the exponent of the exponential term by 3 to write expressions in exponential form using the digit 3 and 5.
Explanation:Exponential notation is used to express very large and very small numbers as a product of two numbers. In the case of writing expressions in exponential form using the digit 3 and 5, we can cube the digit term in the usual way and multiply the exponent of the exponential term by 3. For example, if we want to write 3 to the power of 5 in exponential form, it can be written as 3³ x 5³ = 243 x 125. Therefore, there are multiple different ways to use the digits 3 and 5 to write expressions in exponential form.
Final answer:
To write expressions in exponential form using the digits 3 and 5, follow the rules of exponential arithmetic.
Explanation:
To write expressions in exponential form using the digits 3 and 5, we can follow the rules of exponential arithmetic. In exponential form, a number is written as the digit term multiplied by 10 raised to the power of the exponential term.
For example, if we want to write 35 in exponential form, we can write it as 3×105. If we want to write 53 in exponential form, it would be 5×103.
By using these rules, you can create different expressions by combining the digits 3 and 5 with different exponential terms.
If 1 meter = 3.28 feet, what is the height of the washington monument in meters?
the Washington monument is 555 feet
555/3.28 = 169.21 meters
Answer:
169.164
Step-by-step explanation:
555 / 3.28 = 169.164
Find the average rate of change of f on the interval [10, 60]. (round your answer to the nearest integer.)
The average rate of change for the function is 6 on the interval [10, 60].
What is Lagrange mean value theorem?Lagrange mean value theorem states that, if a function f is continuous over the closed interval [a, b] and differentiable over the open interval (a, b), then there must be at least one point c in the interval (a, b) where the slope of the tangent at the point c is equal to the slope of the tangent through the curve's endpoints, resulting in the expression f'(c) = {F(b) -F(a)}/(b-a)
According to the attached function graph,
At point x = 10,
F(10) = 400
At point x = 60,
F(60) = 700
Since the formula for the average rate of change of the function between x = a and x = b is,
The average rate of change = {F(b) -F(a)}/(b-a)
Here a = 10, b = 60 and F(10) = 400, F(60) = 700
Substitute the values in the formula,
So the average rate of change = (700 - 400)/(60 - 10)
The average rate of change = 300/50.
The average rate of change = 6
Hence, the average rate of change for the function is 6 on the interval [10, 60].
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Your question is incomplete, probably the missing graph is:
To find the average rate of change of f on the interval [10, 60], calculate the difference between the values of f at these two points and divide it by the difference between the two points.
Explanation:To find the average rate of change of f on the interval [10, 60], we need to calculate the difference between the values of f at these two points and divide it by the difference between the two points. Let's assume that f(10) = a and f(60) = b. The average rate of change of f on the interval [10, 60] is then given by (b-a)/(60-10). To round the answer to the nearest integer, we can use the nearest neighbor rounding method.
brad built 1/4 of a model airplane on monday and 2/3 of it on tuesday. he finished building the airplane on wednesday. what fraction of the airplane did he build on wednesday?
ms.blankenship had $80 to purchase school supplies for her class.She bought 32 glue sticks and 32 boxes of crayons.Each glue stick cost 1.40 and each box of crayons cost 0.59.How much money did ms.blankenship have left after these purchases
I have the same hundreds digit as ones digit. The value of my tens digit is 50. The value of my ones digit is 4. the number is.
Hundreds digit as ones digit. The value of my tens digit is 50. The value of my ones digit is 4,then the number is 454.
What is Number system?The system which deals with numbers and decimals is called number system.
The digit at ones place=4
The digit at tens place=50
hundreds digit as ones digit=400
Therefore the number is 400+50+4
=454
Therefore if same hundreds digit as ones digit. The value of my tens digit is 50. The value of my ones digit is 4. Then 454 is the Number.
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What are the converse, inverse, and contrapositive of the following conditional statement? What are the truth values of each? If today is Sunday, then tomorrow is Monday.
If tomorrow is not Monday then today is not Sunday.
The given statement is "If today is Sunday, then tomorrow is Monday".
What is contrapositive statement?A contrapositive statement occurs when you switch the hypothesis and the conclusion in a statement, and negate both statements. In this example, when we switch the hypothesis and the conclusion, and negate both, the result is: If it is not a polygon, then it is not a triangle.
Here,
1. If tomorrow is Monday then, today is Sunday.
2. If today is not Sunday then tomorrow is not Monday.
3. If tomorrow is not Monday then today is not Sunday.
Therefore, if tomorrow is not Monday then today is not Sunday.
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chelsea has $45 to spend at the fair. she spends $20. on admissib and $15 on snacks. she wants to play a game that costs $0.65 per game. Write an inequality to find the maximum number of times, x, Chelsa can play games. Using this inequality, determine the maximum number of times she can play the game.
Answer: The required inequality is [tex]35+0.65x\leq 45[/tex] and teh maximum number of times that Chelsea can play the game is 15.
Step-by-step explanation: Given that Chelsea had $45 to spend at the fair. she spends $20 on admissible and $15 on snacks. She wants to play a game that costs $0.65 per game.
We are to write an inequality to find the maximum number of times, x, Chelsea can play games.
Also, to find the maximum number of times she can play he game.
According to the given information, the inequality can be written as follows :
[tex]20+15+0.65\times x\leq 45\\\\\Rightarrow 35+0.65x\leq 45.[/tex]
And, the solution of the above inequality is as follows :
[tex]35+0.65x\leq 45\\\\\Rightarrow 0.65x\leq 45-35\\\\\Rightarrow 0.65x\leq 10\\\\\Rightarrow x\leq \dfrac{10}{0.65}\\\\\Rightarrow x\leq 15.38.[/tex]
Thus, the maximum number of times Chelsea can play the game is 15.
John needs to make a scale drawing of his school building for art class. If the building is 256.25 meters long, and John scales it down using a ratio of 25 meters to 1 inch, how long will the building be in the sketch?
Answer:
10.25 inches in the sketch
Step-by-step explanation:
Since we are talking about scales drawing, we can solve this problem using proportions, the ratio John will use is 25:1. We will write the proportion using this information and then we will solve for x.
[tex]\frac{25}{1} =\frac{256.25}{x} \\x=256.25/25\\x=10.25[/tex]
Therefore, the building will be 10.25 inches in the sketch.
What is the probability of rolling two six-sided dice and obtaining at least one 3?
One day, the temperature started at 8 degrees at 6:00 a.m., then climbed 3 degrees by noon, and then dropped 7 degrees by midnight. What was the temperature at midnight?
12×6=(8×6)+(_×6)=answer this question
A test consists of 15 questions. 9 are true-false questions, and 6 are multiple-choice questions that have four choices each. a student must select an answer for each question. in how many ways can this be done?
Compute i^600+i^599+i^598+....+i+1, where i^2=-1
Quickly please
Andrew sold 45 tickets to the school play and Sara sold 40 tickets. What is the best ratio of the number of tickets Andrew sold to the number of tickets Sara sold?
it cost $5 plus $2 per ride at the county fair use the expression 5 + 2r to determine how much Shelia will spend if she goes on 7 rides.
What factor makes the number sentence true 7 x 4 equals blank x 7
and 2008 Classic Car Wash estimated its business would increase by 20% each year. if they washed 19,300 in 2008, how many cars can they expect to wash in 2010
Answer: The amount of cars they can expect to wash is 27, 792 in 2010.
Step-by-step explanation:
This problem asks us to calculate the potential growth of the business through a period. One of the ways to solve this problem is to use the formula for exponential growth to determine the number of cars they expect to wash in 2010.
[tex]f(x) = a(1 + r) ^x\\f(x) = 19, 300 (1+0.20)^2\\f(x) = 19, 300 (1.20)^2\\f(x) = 27, 792[/tex]
a = initial growth - 19, 300
r = growth rate - 0.20
x = time (years) - 2 years
We get 27, 792 as our final answer.