The probability that a randomly selected subject in this is Male or answered 'No' is A: 0.18.
The probability that a randomly selected subject in the study is Male or answered "No" is the sum of the probability that the subject is Male and the probability that the subject answered "No", which is a measure of the overlap between these two events.
To find the probability that a subject is Male, we take the number of Male subjects (50) and divide it by the total number of subjects (100):
P(Male) = 50/100 = 0.5
To find the probability that a subject answered "No", we take the number of subjects who answered "No" (48) and divide it by the total number of subjects (100):
P(No) = 48/100 = 0.48
We can use the formula P(A or B) = P(A) + P(B) - P(A and B) to find the probability that a randomly selected subject is Male or answered "No"
P(Male or No) = P(Male) + P(No) - P(Male and No)
We know that 18 out of 50 Male subjects answered No and 16 out of 50 Female subjects answered no, so the probability that a Male subject answered No is 18/50 = 0.36, and the probability that a Female subject answered No is 16/50 = 0.32
P(Male and No) = P(Male) * P(No|Male) = 0.5 * 0.36 = 0.18
P(Female and No) = P(Female) * P(No|Female) = 0
Hence, the probability that a randomly chosen subject in this is male or answered 'no' is A: 0.18.
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A fair coin is tossed four times, and the sequence of heads and tails is observed. (a) List each of the 16 sequences in the sample space S. (b) Let events A, B, C, and D be given by A = {at least 3 heads}, B = {at most 2 heads}, C = {heads on the third toss}, and D = {1 head and 3 tails}. If the probability set function assigns 1/16 to each outcome in the sample space, find (i). P(A), (ii) P(A n B), (iii) P(B), (iv) P(A n C), (v) P(D), (vi) P(A U C), (vii) P(B n D).
The probability of getting at least two heads is there for 11/16. There are six ways to get two heads and two tales
There are 24 = 16 outcomes in all.
The phrase "at least two heads" is defined as "all outcomes" minus "at most 1 tails": tttt, or httt, thtt, ttht, ttth; that is, 5 ways; the probability of at least two heads is therefore (16-5)/16=11/16.
For instance, two heads: hhtt. How many different ways are there to arrange two h's and two t's? One may naively say 4! (4*3*2*1) However, this treats H and H, T and T as distinct when they are actually one and the same. To make up for this, we divide twice by 2: Probability is 6/16=3/8 since 24/(2*2)=6 ways.
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The question is wrong, the correct question:
A fair coin is tossed 4 times. What is the probability of getting at least 2 heads, two heads, or two tails?
what is the solution to the system of equations pictured below? (the solution to the system is where the graphs of the two equations intersect.)
The solution of the system of equations plotted is (x,y) = (4,7).
When a system of linear equations is given, then there exist 3 cases:
Case 1: Unique single solution:
In this case, the lines of the system of equations intersect at one point. That point is the solution of both equations.
The reason we consider intersection as the solution since that the intersection point tells us that it can satisfy both of the given equations simultaneously.
Case 2: No solution:
Then there is no such point that can satisfy both equations simultaneously. Thus, there is no solution to the given system of equations.
Case 3: Infinite number of solutions:
Well, in that case, both the lines are overlapping each other. Thus, all of the points of one line lie on another line too.
And since the given lines are made up of an infinite number of points, thus we will get infinite solutions.
In your case, the lines intersect at points where x=4 and y=7, or say they intersect at coordinate (4,7). Thus, the solution of a given system of equations is x=4 and y=7.
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1.39 × 102 in standard form.
Answer: 141.78
Step-by-step explanation: 1.39 x 102 = 141.78
Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
The probability that she will make a basket on or before her last attempt within her average waiting time are 1/8 and 2/8
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment;
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively);
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%;
Given:
Hannah makes 5 out of 8 attempted free-throws.
Now,
The average waiting time of hannah to make her first basket is 5/8
The probability of hannah making basket at her last attempt is 1/8
The probability of hannah making basket before her last attempt is 2/8
Hence, the probabilty will be 1/8 and 2/8;
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6-4 RectanglesQuadrilateral ABCDis a rectangle.1.IfAC= 2x+ 13 andDB= 4xâ 1, findDB.DB: 72.IfAC=x+ 3 andDB= 3xâ 19, findAC.AC= 143.IfAE= 3x+ 3 andEC= 5xâ 15, findAC.AC=604.IfDE= 6xâ 7 andAE= 4x+ 9, findDB.Db=825.Ifmâ DAC= 2x+ 4 andmâ BAC= 3x+ 1, findmâ BAC.6.Ifmâ BDC= 7x+ 1 andmâ ADB= 9xâ 7, findmâ BDC.7.Ifmâ ABD= 7xâ 31 andmâ CDB= 4x+ 5, findmâ ABD.8.Ifmâ BAC=x+ 3 andmâ CAD=x+ 15, findmâ BAC:39
Sides AC and DB of the rectangle ABCD are equal to 2x + 13 and 4x – 1, respectively. Angle BAC is measured by 3x + 1 and angle CAD by x + 15. Angles ABD and CDB are measured as 7x - 31 and 4x + 5, respectively. Angles BDC and ADB are measured as 7x + 1 and 9x – 7 respectively. Angles AEC and AE are measured as 5x - 15 and 3x + 3 respectively.
A rectangle is a polygon with four right angles and four sides. Two sides of the rectangle ABCD are AC and DB, with AC equal to 2x + 13 and DB to 4x - 1. Angle BAC is measured by 3x + 1 and angle CAD by x + 15. Angles ABD and CDB are measured as 7x - 31 and 4x + 5, respectively. Angles BDC and ADB are measured as 7x + 1 and 9x – 7 respectively. Angles AEC and AE are measured as 5x - 15 and 3x + 3 respectively.
You can find the missing sides and angles by looking at the rectangle's angles and sides. As an illustration, if AC = 2x + 13 and DB = 4x - 1, then DB = 72. Similar to this, if AC = x + 3 and DB = 3x - 19 then AC = 14. If AE = 3x + 3 and EC = 5x - 15, then AC = 6 is the result. If AE = 4x + 9 and DE = 6x - 7 then DB = 8 is the result.
The measures of the angles can be solved for using the supplied equations. As an illustration, if mDAC = 2x + 4 and mBAC = 3x + 1, then mBAC = 39. Similar to how mBDC = 7x + 1 if mADB = 9x - 7 and mBDC = 7x + 1 if mBDC = 7x + 1. Last but not least, mABD = 7x - 31 if mCDB = 4x + 5 and mABD = 7x - 31.
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for a study of tv shows, you obtain the rating, market share, and advertising revenue for 75 popular tv shows. which of these are statistical questions that could be answered from this data set? (select all that apply.)
Amongst the given options, we can conclude that the questions 'what is the distribution of ratings for the 75 shows in this sample' and 'is there a relationship between the rating and advertising revenue of the 75 shows in this sample' can be answered using this data set. Hence, options 3 and 4 are the correct options.
Statistics is a field of mathematics that is concerned with the collection, organization, study, understanding, and presentation of data. A data set is the collection of data aforementioned.
Here, we have been told that the data set includes the rating, market share, and advertising revenue for 75 popular tv shows. This means we will easily be able to find out the distribution of ratings for the 75 shows as well as the relationship between the rating and advertising revenue. Hence, options 3 and 4 are the correct answers.
The complete question that you have been looking for is given below -
For a study of TV shows, you obtain the rating, market share, and advertising revenue for 95 popular TV shows.
Which of these are statistical questions that could be answered from this data set? (Check all that apply.)
*Does the market share of TV shows differ based on the gender of viewers?*For all TV shows on network television, what percentage have ratings of 5.0 or lower?*What is the distribution of ratings for the 95 shows in this sample?*Is there a relationship between the rating and advertising revenue of the 95 shows in this sample?*Which of the 95 popular shows in this sample would you rate the highest?
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metric time is defined so that one day equals 10 hours, one hour equals 100 minutes, and one minute equals 100 seconds. convert 255 metric minutes into standard hours.
Converting 255 metric minutes as per the defined metric time into standard hours is equal to 2.55 hours.
Using defined metric time we have,
One day is equal to 10 hours
One hour is equal to 100 minutes
One minute is equal to 100 seconds
To convert 255 metric minutes into standard hours we have,
100 minutes = 1 hour
⇒ 1 minutes = ( 1 / 100 ) hour
⇒ 255 metric minutes = ( 255 ) × ( 1 / 100 ) hour
⇒ 255 metric minutes = ( 255/ 100 ) hour
⇒ 255 metric minutes = 2.55 hours
Therefore, the conversion of 255 metric minutes into standard hour using metric time is equal to 2.55 hours.
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While trying to decipher the madness that is Calc 2, you and your classmates Donald and Joe are discussing a problem. Donald has come up with the following work for the problem.
∫3xsin(x3)dx=x3 du=3x2 dx
=x/x∫3xsin(x3)dx
=x/1∫3x2sin(x3)dx
=x/1∫sin(u)du=x1⋅−cos(4)+C
=∫xcos(x)3)+C
Joe, on the other hand strongly believes Donald is wrong. A heated argument develops about who is correct and why. In your judgement, is Donald's work correct or not? Is there a way to double: check? Be sure to support your thinking.
Donald's work seems to be inaccurate. He substitutes u = x3 in the first step, however he does not correctly adjust the bounds of integration. He divides by x in the subsequent phase, which results in a division by zero at x = 0.
Additionally, it appears like Donald made a mistake while integrating sin(u)du in the final step. It should have been -cos(u) + C rather than x*cos(u) + C. One could try an alternative approach or use a calculator or computer to assess the integral to verify the work. Another option would be to look up the right answer in a book or internet resources.
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The dating web site oollama requires its users to create profiles based on a survey in which they rate their interest (on a scale from 0 to 3) in five categories: physical fitness, music, spirituality, education, and alcohol consumption. a new oollama customer, erin o'shaughnessy, has reviewed the profiles of 40 prospective dates and classified whether she is interested in learning more about them. based on erin's classification of these 40 profiles, oollama has applied a logistic regression to predict erin's interest in other profiles that she has not yet viewed. the resulting logistic regression model is as follows: for the 40 profiles (observations) on which erin classified her interest, this logistic regression model generates that following probability of interested. Probability of Probability ofObservation Interested Interested Observation Interested Interested35 1 1.000 13 1 0.41221 1 0.999 2 0 0.28529 1 0.999 3 0 0.21925 1 0.999 7 0 0.16839 1 0.999 9 0 0.16826 1 0.990 12 0 0.16823 1 0.981 18 0 0.16833 1 0.974 22 1 0.1681 0 0.882 31 1 0.16824 1 0.882 6 0 0.12828 1 0.882 20 0 0.12836 1 0.882 15 0 0.02916 0 0.791 5 0 0.02027 1 0.791 14 0 0.01530 1 0.791 19 0 0.01132 1 0.791 8 0 0.00834 1 0.791 10 0 0.00137 1 0.791 17 0 0.00140 1 0.791 4 0 0.00138 0 0.732 11 0 0.000(a) Using a cutoff value of 0.5 to classify a profile observation as Interested or not, construct the confusion matrix for this 40-observation training set.PredictedActual 0 10 1 Compute sensitivity, specificity, and precision measures and interpret them within the context of Erin's dating prospects.If required, round your answers to two decimal places. Do not round intermediate calculations.The sensitivity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 6 at identifying the profiles that Erin is interested in.The specificity of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 8 at avoiding recommending profiles to Erin that she will not be interested in.The precision of the model is . This suggests that the model is reasonably - Select your answer -goodbadItem 10 at suggesting profiles of interest to Erin.(b) Oollama understands that its clients have a limited amount of time for dating and therefore use decile-wise lift charts to evaluate their classification models. For the training data, what is the first decile lift resulting from the logistic regression model? Interpret this value.The first decile lift of this classification is . It means that the first decile of the logistic regression model - Select your answer -halvesdoublestriplesdoes not changeItem 12 the number of profiles that Erin is interested in versus random selection.(c) A recently posted profile has values of Fitness = 3, Music = 1, Education = 2, and Alcohol = 1. Use the estimated logistic regression equation to compute the probability of Erin's interest in this profile.If required, round your answers to three decimal places. Do not round intermediate calculations.Log odds =Probability of Interest =(d) Now that Oollama has trained a logistic regression model based on Erin's initial evaluations of 40 profiles, what should its next steps be in the modeling process?Oollama should use their model to suggest profiles - Select your answer -of interestwith lack of interestof interest and with lack of interestItem 15 to Erin in order to compute classification accuracy measures on a validation set.
The dating web site Oollama.com requires its users to create pro les based on a survey in which they rate their interest (on a scale from 0 to 3) in positive categories: physical fitness, music, spirituality, education, and alcohol consumption.
A new Oollama customer, Erin O'Shaughnessy, has reviewed the pro les of 40 prospective dates and classi ed whether she is interested in learning more about them. Based on Erin's classi cation of these 40 pro les, Oollama has applied a logistic regression to predict Erin's interest in other pro les that she has not yet viewed. The resulting logistic regression model is as follows:
Log odds of Interested = −0.920 + 0.325 × Fitness − 3.611 × Music
+5.535 × Education − 2.927 × Alcohol
The detailed solution is attached below.
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How do I solve this math problem
The estimate of the integral by parts ∫₀³f(x)g'(x) = 62.1
What is integration?Integration is the process of reverse differentiation. It is the process of finding the anti-derivative of a function.
How to estimate the value of the integral?Since we have the integral [tex]\int\limits^3_0 {f(x)g'(x)} \, dx[/tex] and f(x) = x³. To evaluate the integral within the limits, we use integration by parts.
So, for any integral by parts
[tex]\int\limits^a_b {u(x)v'(x)} \, dx = [u(x)v(x)]^{a} _{b} - \int\limits^a_b {v(x)u'(x)} \, dx[/tex]
So, for the given integral [tex]\int\limits^3_0 {f(x)g'(x)} \, dx[/tex], we have that
[tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(x)g(x)]^{3} _{0} - \int\limits^3_0 {g(x)f'(x)} \, dx[/tex]
So, we have that
[tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(x)g(x)]^{3} _{0} - \int\limits^3_0 {g(x)f'(x)} \, dx\\= [f(x)g(x) - f(0)g(0)] - [{g(3)f'(3) - g(0)f'(0)}][/tex]
Now, we have that f(x) = x³. So,f'(x) = 3x².
So,
f(3) = 3³ = 27 and f'(3) = 3(3)² = 27.Also, form the table
g(0) = 2.3 and g(3) = 4.9Substituting these into the equation, we have that
[tex]\int\limits^3_0 {f(x)g'(x)} \, dx = [f(3)g(3) - f(0)g(0)] - [{g(3)f'(3) - g(0)f'(0)}]\\= [27 \times 4.9 - 0 \times 2.3] - [{4.9 \times 27 - 2.3\times 27}]\\= (132.3 - 0) - (132.3 - 62.1)\\= 132.3 - 132.3 + 62.1\\= 0 + 62.1\\= 62.1[/tex]
So, integral [tex]\int\limits^3_0 {f(x)g'(x)} \, dx = 62.1[/tex]
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solve for inequality
|x-1/2| + 4 ≤ 5/2
The solution set of the inequality |x - 1 / 2| + 4 ≤ 5 / 2 is x ≥ 2 and x ≤ - 1.
How to determine the solution set involving absolute values
In this problem we find an inequality including an absolute value, which requires some additional treatment by taking definition of absolute value into account, in order to determine the complete solution set:
For x < 1 / 2:
- x + 1 / 2 + 4 ≤ 5 / 2
- x + 9 / 2 ≤ 5 / 2
4 / 2 ≤ x
x ≥ 2
For x ≥ 1 / 2:
x - 1 / 2 + 4 ≤ 5 / 2
x + 7 / 2 ≤ 5 / 2
x ≤ - 2 / 2
x ≤ - 1
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9=1=1/1/0²
p= 13.6 correct to 3 significant figures.
By considering bounds, work out the value of q to a suitable degree of accuracy.
Give a reason for your answer.
Answer: I'm sorry but this equation is not valid, and it does not make any sense to me. There is no variable q and the equation is not a mathematical equation so I cannot give you a value of q. Also, the statement p = 13.6 is not related to the equation provided. Therefore, I cannot answer this question. Can you please provide more context or clarify what you are trying to ask?
Please answer this question for me
The area for the given quadrilateral will be 5400m^2, Perimeter=300m and no. of rabbits that van fit are 270.
what are quadrilaterals?
A quadrilateral is a polygon with four sides, four vertices, and four angles.
It is formed by joining four non-collinear points. The sum of the interior angles of quadrilaterals is always equal to 360 degrees. The word quadrilateral is derived from the Latin words ‘Quadra’ which means four and ‘Latus’ means ‘sides’. Not all the four sides of a quadrilateral need to be equal in length. Hence, we can have different types of quadrilaterals based on sides and angles.
Five special quadrilaterals are shown below in the image, along with their definitions and pictures, and points for them to get proven.
Now
as given quadrilateral is rectangular in shape because opposite sides are equal and parallel.
and Length = 90m and breadth=60m
Therefore,
Area=L*B =90*60=5400m^2
Perimeter=2(L+B)=2*150=300m
one rabbit takes 20m^2 of area
No. of rabbits that can fit in 5400m^2 of area=5400/20=270
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What is 67% of 800? ,ms
Answer:
536
Step-by-step explanation:
Answer: 536
Step-by-step explanation:
Step 1: As we know, a whole of something is equal to 100%. In this case, we want to find what 67% of 800 is. We know that 100% of 800 is, well, just 800.Step 2: If 100% of 800 is 800, then we can get 1% of 800 by dividing it by 100. Let's do 800 / 100. This is equal to 8.0. Now we know that 1% is 8.0.Step 3: Now that we know what 1% of 800 is, we just need to multiply it by 67 to get our solution! 8.0 times 67 = 536. That's all there is to it!
Question 2 of 16
In a survey of the students' lunch preferences at a school, 523 said they prefer chicken, 295 said they prefer pasta, and 126 said they prefer salad.
How many more students prefer chicken than students combined who prefer pasta and salad?
Answer:
102
Step-by-step explanation:
523 said they prefer chicken,
295 said they prefer pasta,
and 126 said they prefer salad.
523-295-126 =102
i need help for studying for a test
Answer:
70
Step-by-step explanation:
1 3/5 divided by 2/5 in mixed number simplest form
Answer:4
Step-by-step explanation:
1 3/5 = 8/5
8/5 / 2/5 = 4
premise 1: if 901,223 is divisible by 6, then it is divisible by 3 premise 2: conclusion: 901,223 is not divisible by 6 supply the missing premise that would make this a valid argument. state what valid argument form you used.
Premise 3: 901,223 is not divisible by 6.
Valid argument form used: Modus Tollens.
Step 1: Divide 901,223 by 6.
901,223 ÷ 6 = 150,203.83333
Step 2: Round down the answer.
150,203.83333 rounded down = 150,203
Step 3: Check if the answer is divisible by 3.
150,203 ÷ 3 = 50,067.3333
Step 4: Round down the answer again.
50,067.3333 rounded down = 50,067
Step 5: Check if the answer is divisible by 3.
50,067 ÷ 3 = 16,689
Step 6: Round down the answer again.
16,689 rounded down = 16,689
Step 7: Check if the answer is divisible by 3.
16,689 ÷ 3 = 5,563
Step 8: Round down the answer again.
5,563 rounded down = 5,563
Step 9: Check if the answer is divisible by 3.
5,563 ÷ 3 = 1,854.3333
Step 10: Round down the answer again.
1,854.3333 rounded down = 1,854
Step 11: Check if the answer is divisible by 3.
1,854 ÷ 3 = 618
Step 12: Check if the answer is divisible by 3.
618 ÷ 3 = 206
Step 13: Check if the answer is divisible by 3.
206 ÷ 3 = 68.66666666
Step 14: Round down the answer again.
68.66666666 rounded down = 68
Step 15: Check if the answer is divisible by 3.
68 ÷ 3 = 22.66666666
Step 16: Round down the answer again.
22.66666666 rounded down = 22
Step 17: Check if the answer is divisible by 3.
22 ÷ 3 = 7.333333
Step 18: Round down the answer again.
7.333333 rounded down = 7
Step 19: Check if the answer is divisible by 3.
7 ÷ 3 = 2.333333
Step 20: Round down the answer again.
2.333333 rounded down = 2
Step 21: Check if the answer is divisible by 3.
2 ÷ 3 = 0.666666
Conclusion: 901,223 is not divisible by 6
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What is a perimeter of a rectangluar drive way measuring 20 feet long and 15 feet wide?
Answer:
Step-by-step explanation:
P = 2l+b)
P = 2(20 + 15)
P = 2(35)
P = 70 feet
Answer:
70 feet
Step-by-step explanation:
Perimeter of rectangle:length = 20 feet
width = 15 feet
[tex]\sf \boxed{\text{Perimeter of rectangle = 2* ( length * width)}}[/tex]
[tex]\sf = 2* (20 + 15)\\\\ = 2 * 35\\\\= 70 \ feet[/tex]
Show me how to shade decimal number 0.009 in a base- ten block
To shade decimal number 0.009 in a base-ten block, you would shade one 1/100th block and nine 1/1000th blocks. This can be seen in the image below.
How to shade decimal number 0.009 in a base- ten block?Shading decimal numbers in a base-ten block is a great way to visualize numbers in a concrete way. To shade decimal number 0.009 in a base-ten block, start by breaking down the number into its place values. The number 0.009 is equivalent to 9 thousandths, or 0.001. Begin by drawing a base-ten block with four places on the left and one on the right. The four places on the left are labeled hundredths, tenths, ones, and tens respectively. The one place on the right is labeled tenths. Next, shade in the thousandths place, which is the rightmost place on the base-ten block. This will represent the 9 thousandths from 0.009. The thousandths place should be shaded in with a gray or light color. Finally, the remaining places should be left blank, since 0.009 does not have any values in the hundredths, tenths, or ones places. The tenths place should also be left blank. In this way, decimal number 0.009 can be easily visualized in a base-ten block. The thousandths place is shaded in, while the remaining places are left blank.1 tenth | 0 hundredths | 0 thousandths | 9 ten-thousandths
____ | ____ | ____ | ____
We can shade 0.009 in a base-ten block as follows:100th | 0
10th | 0
1st | 9
We can shade the 9 in the 1st place value to represent 0.009.To learn more about to shade decimal number refer to:
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Suppose you are assigned the number 1, and the other students in your statistics class call out consecutive numbers until each person in the class has his or her own number.
Explain how you could get a random sample of four students from your statistics class. (Select all that apply.)
A. Randomly choose four of the students that are sitting in the back row.
B. Use a computer or random-number table to randomly select four students after numbers are assigned.
C. Randomly choose four of the first students that walk into the classroom.
D. Randomly choose four of the tallest students in the classroom.
E. Randomly choose four of the last students that walk into the classroom.
The most suitable method to obtain a random sample of four students from the statistics class would be to use a computer or random-number table to randomly select four students after numbers are assigned.
This method ensures that every student has an equal chance of being selected and that the sample is truly random. This is the only method that guarantees that the sample is random and representative of the entire class.
The other methods listed (A, C, D, and E) do not ensure randomness, as they are based on non-random criteria (such as seating arrangement, height, or time of arrival). These methods might introduce bias into the sample and lead to incorrect conclusions about the population.
Hence, the correct answer is B.
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HELP PLEASEEEEE I GIVE WAT EVER
Answer:
Step 1
Step-by-step explanation:
I believe is correct pls report if wrong idc it is my fault
find a polynomial function with the leading coefficient one or negative 1 that has the given zeros multiplicity and degrees 01 multiplicity to 03 multiplicity to degree 4
The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).
Find a polynomial function ?The function is negative for since the leading coefficient is positive and the highest degree is odd (9) (-inf, -6).
It then crosses the -6 root to turn positive until it again crosses the -2 root.
(It crosses because the odd multiplicity of both roots)
The function remains negative from -2 until root 4, where it crosses into the positive, where it does not cross since there is an even multiplicity.
In light of the aforementioned, only the first option makes sense. because the leading coefficient is positive and the highest degree is odd (9) the function is negative for (-inf, -6).
Then it crosses the -6 root to become positive until it crosses again the root -2.
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Write a recursive rule for the sequences:
1,3,-2,5,-7,12,...
and 1,2,2,4,8,32,...
The recursive formula for each sequence is given as follows:
1,3,-2,5,-7,12: [tex]a_n = a_{n - 2} - a_{n - 1}, a_1 = 1, a_2 = 3[/tex]1,2,2,4,8,32: [tex]a_n = a_{n - 1} \times a_{n - 2}, a_1 = 1, a_2 = 2[/tex]How to define the recursive formulas?
The first sequence is given as follows:
1,3,-2,5,-7,12...
The pattern is that each term is the subtraction of the second to last term by the last term, hence the formula is given as follows:
1,3,-2,5,-7,12: [tex]a_n = a_{n - 2} - a_{n - 1}[/tex]
The second sequence is given as follows:
1,2,2,4,8,32,...
The pattern is that each term is obtained by the multiplication of the two previous terms, hence the formula is given as follows:
[tex]a_n = a_{n - 1} \times a_{n - 2}, a_1 = 1, a_2 = 2[/tex]
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It is reported that the wild tiger population has declined by 97%
over the last 20 years.
There are now 3200 tigers left in the wild.
To the nearest thousand, how many wild tigers were there 20 years ago?
The nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
Determine Percentage decrease theory.The percentage decrease theory suggests that a decrease in the price of a product or service will lead to an increase in demand for that product or service.
This theory is based on the idea that consumers are more likely to buy a product or service if its price is lower. This theory can be applied to both new and existing products or services.
For example, a retailer may decide to decrease the price of a product in order to attract more customers and increase sales. Similarly, a company may choose to reduce the cost of a service in order to make it more attractive to potential customers.
This question is using the percentage decrease theory. According to this theory,
you can calculate the percentage decrease by subtracting the current value from the original value and then dividing by the original value.
Step 1: Subtract the current number of wild tigers (3200) from the original number of wild tigers (20 years ago).
Original - Current = Change
120,000 - 3200 = 116,800
Step 2: Divide the change (116,800) by the original number of wild tigers (120,000)
Change / Original = Percentage Change
116,800 / 120,000 = 97%
Step 3: Multiply the percentage change (97%) by the original number of wild tigers (120,000)
Percentage Change x Original = Estimated Original
97% x 120,000 = 116,400
Therefore, to the nearest thousand, there were an estimated 116,000 wild tigers 20 years ago.
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A middle school took all of its 6th grade students on a field trip to see a symphony at a theater that has 4100 seats. The students filled 2296 of the seats in the theater. What percentage of the seats in the theater were filled by the 6th graders on the trip?
The percentage of the seats in the theater were filled by the 6th graders on the trip with expression is 56%.
What is a expression? What is a mathematical equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have a middle school that took all of its 6th grade students on a field trip to see a symphony at a theater that has 4100 seats. The students filled 2296 of the seats in the theater.
Assume that the theater filled up [x]% of seats at the theater. Then, we can write -
[x]% = (2296/4100) x 100
[x]% = 0.56 x 100
[x]% = 56%
Therefore, the theater filled up with 56% of seats with 6th grade students.
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The data set shows the numbers of hours that employees at a certain shop worked in one week. What is the mean number of hours they worked that week? 30 15 32 48 16 51
A. 32
B. 35
C. 31
D. 30
Answer:
Step-by-step explanation:
Find the domain of f(x) = √-6x - 7
Use two lower case o's for infinity. "oo" is how you type in infinity.
Answer: The domain of a function is the set of all possible input values (x-values) for which the function produces a valid output (y-value).
The square root function is defined for non-negative numbers, so the expression inside the square root must be non-negative.
In this case, -6x - 7 must be greater or equal to 0.
-6x - 7 ≥ 0
x ≥ (7 + 7)/6 = 14/6 = 7/3
So the domain of the function is x ≥ 7/3, or x ∈ [7/3, ∞)
In interval notation, the domain of f(x) = √-6x - 7 is x ∈ [7/3, oo)
Step-by-step explanation:
a group of students take hundreds of digital photos for a science project about weather patterns. each photo file contains data representing the level of red, green, and blue for each pixel in the photo. the file also contains metadata that describes the date, time, and geographic location where the photo was taken. for which of the following goals would analyzing the metadata be more appropriate than analyzing the data? select two answers.
The metadata be more appropriate than analyzing the data is a series of binary digits called bits.
The term called metadata can be defined as the data that provides information about one or more aspects of a given data and it also provide a structured reference that helps to sort and identify all of its attributes such as Author, created Date, modified date, type of the file and the size of the file.
Here we have given that a group of students take hundreds of digital photos for a science project about weather patterns.
And also each photo file contains data representing the level of red, green, and blue for each pixel in the photo.
Where the file also contains metadata that describes the date, time, and geographic location where the photo was taken.
In this scenario, we have to analyze the metadata would be more appropriate than analyzing the data when determining the likelihood that the photo was taken or created at a particular public event.
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Hannah makes 5 out of 8 attempted free-throws! What is the average waiting time for Hannah to make her first basket, and what is the probability that she will make a basket on or before her last attempt within her average waiting time?
42% of people are likely to see a movie today, or probability of 0.42.
Explain about the probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.
Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen.
The likelihood that a movie is being viewed right now is:
0.5 of 0.6(if it rains today) (if it rains today).
0.3 of 1 - 0.6 = 0.4(if it does not rain today) (if it does not rain today).
therefore adding them:
p =0.5 (0.6) +0.3(0.4)
=0.3 +0.12 = 0.42
42% of people are likely to see a movie today, or 0.42.
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