Answer:
B) Method 2 will increase the standard deviation of the students' scores.
Step-by-step explanation:
Given that an instructor in a college class recently gave an exam that was worth a total of 100 points.
The average score for his students was 43 and the standard deviation of the scores was 5 points.
And now he is considering two different strategies for rescaling the exam results of which:
Method 1 = Add 17 points to everyone's score.
Method 2 = Multiply everyone's score by 1.7 .
And we have to check what will be the impact of these methods on the standard deviation of the students' scores.
For this let us consider a simple example to understand this:
Firstly, Formula for calculating Standard Deviation = [tex]\sqrt{\frac{\sum (X-Xbar)^{2}}{n-1}}[/tex]
Suppose,
X X - Xbar [tex](X - Xbar)^{2}[/tex]
3 3 - 6 = -3 -3 * -3 = 9
5 5 - 6 = -1 -1 * -1 = 1
10 10 - 6 = 4 4 * 4 = 16
Mean of above data, Xbar = [tex]\frac{3+ 5+10}{3}[/tex] = 6
Standard Deviation of data = [tex]\sqrt{\frac{26}{3-1} }[/tex] = 3.6055
Now let us suppose that we multiply each value of above data with 2 so the new data will be:
X X - Xbar [tex](X - Xbar)^{2}[/tex]
3*2 = 6 6 - 12 = -6 -6 * -6 = 36
5*2 = 10 10 - 12 = -2 -2 * -2 = 4
10*2 =20 20 - 12 = 8 8 * 8 = 64
Mean of new data, Xbar = [tex]\frac{6+ 10+20}{3}[/tex] = 12
Standard Deviation of new data = [tex]\sqrt{\frac{104}{3-1} }[/tex] = 7.2111
Hence, we see that when we multiply any value to the data the standard deviation will increase and in other words it will multiplied by that value which value we multiplied with each data value i.e. when we multiply each data value with 2 the standard deviation also get multiplied by as
3.6055 * 2 = 7.2111
Therefore option B is correct that Method 2 will increase the standard deviation of the students' scores.
And on the other hand Similarly by adding any constant to the data the Standard Deviation will remain same. Therefore Method 1 will have no impact on standard deviation of the students' scores.
A company reports the following: Sales $4,400,000 Average total assets (excluding long-term investments) 2,000,000 Determine the asset turnover ratio. Round your answer to one decimal place.
Answer:
2.2 times
Step-by-step explanation:
Given that,
Sales = $4,400,000
Average total assets (excluding long-term investments) = 2,000,000
Therefore, it is as follows;
Asset turnover ratio:
= Sales ÷ Average total assets (excluding long-term investments)
= $4,400,000 ÷ 2,000,000
= 2.2 times
Hence, the asset turnover ratio of this company is 2.2 times.
For a certain casino slot machine comma the odds in favor of a win are given as 27 to 73. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is (round to two decimal places as needed).
Answer:
The probability is 0.27
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, we have that:
Odds of a win are 27 to 73.
This means that for each 27 games that you are expcted to win, you are also expected to lose 73.
So
Desired outcomes:
27 wins
Total outcomes:
27 + 73 = 100 games
Probability
[tex]P = \frac{27}{100} = 0.27[/tex]
Answer:
The probability is 0.27
The University of Michigan's business school claims it has the highest average GPA in the Big 10 among its business students. The business school claims that the business student average GPA is 3.5. Your friend believes that Michigan's claims are falsely inflated. In an effort to prove whether the grades are falsely inflated, your friend collects a random sample of 100 business students from Michigan and gets an average GPA of 3.31 with a standard deviation of 0.3.
Interpret a 5% chance of a type I error occurring:
A. an alpha level of .05 means that 5% of the time, the null hypothesis is rejected when it is actually correct.
B. an alpha level of .05 means that 5% of the time, the null hypothesis is rejected when it is actually incorrect.
C. an alpha level of .05 means that 5% of the time, the null hypothesis is not rejected when it is actually correct.
D. an alpha level of .05 means that 5% of the time, the null hypothesis is not rejected when it is actually incorrect.
Answer:
A
Step-by-step explanation:
The type I error arises when we wrongfully reject the null hypothesis. The probability of occurrence of type I error is denoted as α. Thus, α=0.05 means that there is 5% probability that we reject the null hypothesis when it is true. So, we can say that the α=0.05, means that 5% of the time, we reject the null hypothesis when it is correct.
Answer:
A
Step-by-step explanation:
Consider a room that is 20 ft long, 15 ft wide, and 8 ft high. For standard sea level conditions, calculate the mass of air in the room in slugs. Calculate the weight in pounds.
Answer:
5.70456 slug
Step-by-step explanation:
Data provided in the question:
Dimensions of the room = 20 ft long, 15 ft wide, and 8 ft high
Now,
Volume of the room = 20 × 15 × 8
or
Volume of the room = 2400 ft³
we know,
Density of air = 0.0023769 slug/ft³
Therefore,
Mass of air in the room = Volume × Density
= 0.0023769 × 2400
= 5.70456 slug
The mass of air in the room is approximately 1268 slugs and the weight is approximately 40825.6 pounds.
Explanation:To calculate the mass of air in a room, we first need to find the volume of the room. The volume of a rectangular room can be calculated by multiplying its length, width, and height. So, the volume of the room is 20 ft x 15 ft x 8 ft = 2400 ft³.
Next, we need to convert the volume from cubic feet to cubic meters. Since 1 ft³ is approximately equal to 0.0283 m³, we can multiply the volume in cubic feet by 0.0283 to get the volume in cubic meters. Therefore, the volume of the room is 2400 ft³ x 0.0283 m³/ft³ = 67.92 m³.
Lastly, we need to find the mass of air in the room. The average molar weight of air is approximately 28.8 g/mol. Since the mass of one cubic meter of air is 1.28 kg, the mass of air in the room is 67.92 m³ x 1.28 kg/m³ = 86.86 kg. To convert the mass from kg to slugs, we divide it by the conversion factor of 0.0685218 slugs/kg. Therefore, the mass of air in the room is 86.86 kg / 0.0685218 slugs/kg ≈ 1268 slugs.
To calculate the weight in pounds, we multiply the mass in slugs by the acceleration due to gravity. The acceleration due to gravity is approximately 32.2 ft/s². Therefore, the weight of the air in the room is 1268 slugs x 32.2 ft/s² = 40825.6 lb.
A random number generator on a computer selects two integers from 1 through 40. What is the probability that (a) both numbers are even, (b) one number is even and one number is odd, (c) both numbers are less than 30, and (d) the same number is selected twice?
Answer:
(a) 0.25
(b) 0.5
(c) 0.5256
(d) 0.025
Step-by-step explanation:
(a) There are 20 even numbers out of 40 the probability that both numbers are even is:
[tex]P=\frac{20}{40} *\frac{20}{40} =\frac{1}{4}=0.25[/tex]
(b) The events for which one number is even and one number is odd are:
- First is odd, second is even
- First is even, second is odd.
The probability is:
[tex]P = \frac{20}{40}*\frac{20}{40}+\frac{20}{40}*\frac{20}{40}=\frac{1}{2}=0.5[/tex]
(c) There are 29 numbers that are less than 30, the probability that both numbers are less than 30 is:
[tex]P=\frac{29}{40}*\frac{29}{40}=\frac{841}{1600}=0.5256[/tex]
(d) If any number from 1 to 40 is selected in the first pick, the probability that the same number is selected again is:
[tex]P=\frac{1}{40} =0.025[/tex]
Solar-heat installations successfully reduce the utility bill 60% of the time. What is the probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill?
Answer:
4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.
Step-by-step explanation:
For each installation, there are only two possible outcomes. Either it reduces the utility bill, or it does not. The probabilities for each installation reducing the utility bill are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem we have that:
Solar-heat installations successfully reduce the utility bill 60% of the time, which means that [tex]p = 0.6[/tex]
What is the probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill?
This is [tex]P(X \geq 9)[/tex] when [tex]n = 10[/tex]. So
[tex]P(X \geq 9) = P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 9) = C_{10,9}.(0.6)^{9}.(0.4)^{1} = 0.0363[/tex]
[tex]P(X = 10) = C_{10,10}.(0.6)^{10}.(0.4)^{0} = 0.0060[/tex]
So
[tex]P(X \geq 9) = P(X = 9) + P(X = 10) = 0.0363 + 0.0060 = 0.0423[/tex]
4.23% probability that at least 9/10 solar-heat installations are successful and will reduce the utility bill.
The probability of at least 90% success in solar-heat installations is found by using the binomial probability formula to calculate and add together the probabilities of exactly 9 and 10 successful installations out of 10.
Explanation:The problem in question is a classic scenario of binomial probability. Here, each solar-heat installation attempt is independent and each attempt is a success (reduces the utility bill) 60% of the time. We are interested in the probability of having 90% or more success in ten attempts.
In a binomial distribution, the formula for calculating the probability of k successes in n attempts is:
P(X=k) = C(n, k) * (p^k) * (1-p)^(n-k)
where C(n, k) is the binomial coefficient ('n choose k'), p is the probability of success on an individual trial, n is the number of trials, and k is the number of successes.
To calculate the probability that at least 9 out of 10 solar-heat installations are successful, we need to calculate P(X=9) and P(X=10) and add these probabilities together.
Calculations like these help inform decisions in a range of fields - from individual choices about energy saving at homes to policy and planning decisions at the level of energy utilization for entire nations.
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(3 points) In class we described the anti-malarial drug artemisinin (structure given below). What is the active functional group on the drug that is most responsible for its potency?
Answer: QINGHAOSU
Step-by-step explanation:Artemisinin is an antimalarial (Drug used to cure Malaria) drug whose active ingredient QINGHAOSU was isolated in the 1970s from the Plant called Artemisia annua by a Chinese Physician.
Artemisinin has been in use in ancient Chinese communities since the 4th century to cure Diseases. Artemisinin is potent in killing several forms of the Plasmodium specie and has been used to derive other antimalarial Drugs in use today like Artemeter and Artesunate.
A bacteria population starts with 400 bacteria and grows at a rate of r(t) = (450.263)e1.12567t bacteria per hour. How many bacteria will there be after three hours?
Answer:
11,713 bacteria
Step-by-step explanation:
Integrating the growth rate function gives us the population of bacteria at any given moment 't', in hours:
[tex]r(t) = (450.263)e^{1.12567t} \\\int\ {r(t)} \, dt =P(t) = \frac{450.263}{1.12567}*e^{1.12567t} +C[/tex]
Since at t=0, P(t) = 400, the value of C is:
[tex]P(0) = \frac{450.263}{1.12567}*e^{1.12567*0} +C\\400 = 400*1+C\\C=0[/tex]
The number of bacteria after 3 hours is:
[tex]P(3) = 400*e^{1.12567*3}\\P(3) =11,713[/tex]
A manufacturer can produce digital recorders at a cost of 50 dollars each. It is estimated that if the recorders are sold for p dollars apiece, consumers will buy q=120p recorders each month. a) Express the manufacturer's profit P as a function of q.
b)What is the average rate of profit obtained as the level of production increases from q=0 to q=15? (at dollars per unit)
c) At what rate is profit changing when q=15 recorders are produced? (at dollars per unit)
The manufacturer's profit is P(p) = 120p^2 - 6000p. The average profit for producing 0 to 15 recorders is 15 * 120. At 15 units, the rate of profit change is -3000.
Explanation:The function for the manufacturer's profit P is given by P(p) = pq - 50q where q=120p. Thus, P(p) = 120p * p - 50 * 120p, simplifying to P(p) = 120p^2 - 6000p.
To express the average rate of profit from q = 0 to q=15, we need to calculate P(15)-P(0) and divide it by 15 - 0. Thus, ((120 * 15^2 - 6000 * 15) - (120 * 0^2 - 6000 * 0)) / (15 - 0) = 15*120.
The rate at which profit is changing when q = 15 is the derivative of the profit function evaluated at q = 15. We obtain P'(q) = 240p - 6000, and by inserting 15 for p, we obtain -3000 (at dollars per unit).
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a) The manufacturer's profit can be expressed as P = (p - 50)q. b) The average rate of profit obtained as the level of production increases from q=0 to q=15 is p - 50 dollars per unit. c) When q=15 recorders are produced, the rate at which profit is changing is p - 50 dollars per unit.
Explanation:a) To express the manufacturer's profit P as a function of q, we can use the equation: P = (p - 50)q. This equation represents the total revenue minus the total cost, where the total revenue is the selling price p multiplied by the quantity q, and the total cost is the cost of production per unit (50 dollars) multiplied by the quantity q.
b) The average rate of profit obtained as the level of production increases from q=0 to q=15 can be found by calculating the change in profit divided by the change in quantity. In this case, the change in profit is (p - 50)(15) - (p - 50)(0) = 15(p - 50) dollars, and the change in quantity is 15 units. Therefore, the average rate of profit is (15(p - 50))/15 = p - 50 dollars per unit.
c) To find the rate at which profit is changing when q=15 recorders are produced, we can calculate the derivative of the profit function with respect to q. Taking the derivative of P = (p - 50)q with respect to q gives us dP/dq = p - 50 dollars per unit. So, when q=15, the rate at which profit is changing is p - 50 dollars per unit.
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The number of hours sixth grade students took to complete a research project was recorded with the following results. Hours Number of students (f) 4 15 5 11 6 19 7 6 8 9 9 16 10 2 A student is selected at random. The events A and B are defined as follows. A = event the student took at most 9 hours B = event the student took at least 9 hours Are the events A and B disjoint? Yes No
Answer:
[tex] P(A \cap B) = P(X=9) =\frac{16}{78} \neq 0[/tex]
The correct answer would be:
NO
Step-by-step explanation:
For this case we have the following dataset given
Hours Number of students (f)
_______________________________
4 15
5 11
6 19
7 6
8 9
9 16
10 2
______________________________
Total 78
For this case we have defined the following events:
A = event the student took at most 9 hours
B = event the student took at least 9 hours
And we can find the empirical probability for both elements like this:
[tex] P(A) = \frac{78-2}{78}= \frac{76}{78}[/tex]
[tex] P(B) = \frac{16+2}{78}= \frac{18}{78}[/tex]
And for this case we want to see if A and B are disjoint
From definition two events X and Y are disjoint if the two sets not have a common elements, and we satisfy that:
[tex] P(X \cap Y) =0[/tex]
So this case the intersection for the events A and B is X=9, because at most 9 means [tex] X \leq 9[/tex] and at least 9 means [tex] X \geq 9[/tex] and the intersection between [tex] X \leq 9[/tex] and [tex] X \geq 9[/tex] is X=9
So then the probability:
[tex] P(A \cap B) = P(X=9) =\frac{16}{78} \neq 0[/tex]
So then we can conclude that the two events not are disjoint
The correct answer would be:
NO
No, the events A and B are not disjoint.
If two events have no outcomes in common, then they are called disjoint.
We have data of the number of hours sixth grade students took to complete a research project as:
For this case we have the following dataset given
Hours Number of students (f)
4 15
5 11
6 19
7 6
8 9
9 16
10 2
Total 78
Two events are:
A = event the student took at most 9 hours
B = event the student took at least 9 hours
Now, the number of students who took at most 9 hours
= 78 - 2
= 76
So, [tex]P(A)=\frac{76}{78}[/tex]
The number of students who took at least 9 hours
=16 +2
=18
So, [tex]P(B)=\frac{16}{78}[/tex]
Number of students who read exactly 9 hours
P(A n B)[tex]=\frac{16}{78}[/tex][tex]\neq 0[/tex]
Therefore the events A and B disjoint are not disjoint.
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An urn contains 6 red balls and 3 blue balls. One ball is selected at random and is replaced by a ball of the other color. A second ball is then chosen. What is the conditional probability that the first ball selected is red, given that the second ball was red?
Answer:
0.5882 or 58.82%
Step-by-step explanation:
The probability that both balls were red (A) is:
[tex]P(A)=\frac{6}{9}*\frac{5}{9}=0.3704[/tex]
The probability that the first ball was blue and the second ball was red (B) is:
[tex]P(B) = \frac{3}{9}*\frac{7}{9}=0.2593[/tex]
The conditional probability that the first ball selected is red, given that the second ball was red is:
[tex]P = \frac{P(A)}{P(A)+P(B)}=\frac{0.3704}{0.3704+0.2593} =0.5882[/tex]
Shankar has decided to train to be a Carbucks Barrista. Being young and inexperienced, for every order he makes a mistake in making that order with probability 1/3 and makes the order correctly with probability 2/3, with the probabilities of making an error independent across different orders.
a. Shankar comes into work Monday morning. What is the probability that he makes no mistakes on his first 10 orders but the 11th order is a mistake?
b. Another Employee (Fran) and Shankar decide to have a competition: Every customer that comes in, both Fran and Shankar would make the order for that person (so each person would get 2 of the same item!). The first amongst either Fran or Shankar that makes a mistake quits Carbucks and goes to grad school to learn probability.
If Fran is more experienced and makes mistakes on an order with probability 1/6 independent across orders and independent of what Shankar is doing on an order, what is the probability that Shankar quits and goes to grad school?
Answer:
Step-by-step explanation:
Since each trial is independent of the other
no of mistakes he does is binomial with p = 1/3
a) the probability that he makes no mistakes on his first 10 orders but the 11th order is a mistake
= [tex](\frac{2}{3}) ^{10} *\frac{1}{3}\\=\frac{2^{10} }{3^{11} }[/tex]
b) Prob that shanker quits = P(Shankar does I one mistake and Fran does not do the first one)+Prob (Shanker does mistake in the II one while Fran does both right)
= [tex]\frac{1*5}{3*6} +\frac{2}{3} \frac{1}{3}(\frac{5}{6})^2 =\frac{5}{18} +\frac{50}{216} \\=\frac{55}{108}[/tex]
Final answer:
Calculating probabilities in scenarios involving making mistakes in orders in a coffee shop setting. he probability that Shankar quits and goes to grad school before Fran is approximately 0.651.
Explanation:
a. For Shankar to make no mistakes on his first 10 orders but the 11th order is a mistake, the probability of making no mistakes on the first 10 orders and then making a mistake on the 11th order can be calculated as follows:
[tex]\[ P(\text{No mistakes on first 10 orders}) \times P(\text{Mistake on 11th order}) \][/tex]
[tex]\[ = \left(\frac{2}{3}\right)^{10} \times \frac{1}{3} \][/tex]
[tex]\[ = \left(\frac{1024}{59049}\right) \times \frac{1}{3} \][/tex]
[tex]\[ \approx 0.0173 \][/tex]
b. For Shankar to quit and go to grad school before Fran, Shankar must make a mistake before Fran does. The probability of Shankar quitting and going to grad school can be calculated as follows:
[tex]\[ P(\text{Shankar quits}) = 1 - P(\text{Fran quits first}) \][/tex]
Since Fran's probability of making a mistake on an order is [tex]\( \frac{1}{6} \)[/tex], the probability of Fran making no mistakes on an order is [tex]\( \frac{5}{6} \).[/tex] Thus, the probability of Fran not making a mistake before Shankar is:
[tex]\[ P(\text{Fran makes no mistakes before Shankar}) = \left(\frac{5}{6}\right)^{10} \][/tex]
Therefore,
[tex]\[ P(\text{Shankar quits}) = 1 - \left(\frac{5}{6}\right)^{10} \][/tex]
[tex]\[ \approx 0.651 \][/tex]
So, the probability that Shankar quits and goes to grad school before Fran is approximately \(0.651\).
A total of 584 tickets were sold for the school play. They were adult tickets or student tickets. The number of student tickets sold was three times the number of adult tickets sold. How many adult tickets were sold
Answer:
The answer to your question is 146 adult tickets
Step-by-step explanation:
Data
Total number of tickets = 584
student ticket = s
adult ticket = a
Condition
3a = s
Equation
s + a = 584
Substitution
3a + a = 584
Simplification
4a = 584
Solve for a
a = 584/4
a = 146
Find s
s = 3(146)
s = 438
Answer:146 adult tickets were sold.
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of student tickets that were sold.
A total of 584 tickets were sold for the school play. This means that
x + y = 584 - - - - - - - - - - - - - - 1
The number of student tickets sold was three times the number of adult tickets sold. This means that
y = 3x
Substituting y = 3x into equation 1, it becomes
x + 3x = 584
4x = 584
x = 584/4 = 146
y = 3x = 3 × 146
y = 438
In an area of the Midwest, records were kept on the relationship between the rainfall (in inches) and the yield of wheat (bushels per acre). Which is the best predicted value for y given x = 7.3? Assume that the variables x and y have a significant correlation. 36.5 36.0 36.7 36.2
Answer:
The correct answer is 36.2
Step-by-step explanation:
Hello!
Given the data:
Rainfall(inch) x: 10.5, 8.8, 13.4, 12.5, 18.8, 10.3, 7.0, 15.6, 16.0
Yield (bushels per acre) y: 50.5, 46.2, 58.8, 59.0, 82.4, 49.2, 31.9, 76.0, 78.8
The response variable is
Y: Yield of wheat (bushels per acre)
Explanatory variable:
X: Rainfall in a certain period (inch)
I've calculated the equation of regression using a statistics software, the estimated equation is:
^Y= 4.27 + 4.38X
To calculate the value that will take the response variable for a given value of X:
^Y= 4.27 + 4.38*7.3= 36.24 bushels per acre.
I hope it helps!
Without the necessary data such as a regression equation or the correlation coefficient, we are unable to predict the yield of wheat when rainfall is 7.3 inches. A regression equation is a statistical tool that helps understand the relationship between predictor and response variables, in this case, rainfall and yield of wheat.
Explanation:In order to predict the value of yield of wheat (y) given the rainfall (x = 7.3), we would need to understand the relationship between x and y, typically via a regression equation. A regression equation is a statistical tool used to understand the relationship between predictor variables (in this case, rainfall) and response variables (in this case, yield of wheat).
However, from the details provided, it seems we do not have the necessary data to conduct a regression analysis or connect x and y values in a meaningful way. Therefore, we're unable to directly predict the specific yield of wheat when rainfall is 7.3 inches over this data gap.
An accurate value can only be predicted if we are provided with more data or the specific correlation coefficient between the two variables and the regression equation (y = ax + b).
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The Bay of Fundy in Canada has the largest tides in the world. The difference between low and high water levels is 20 meters. At a particular point the depth of the water, y meters, is given as a function of time, t, in hours since midnight by y = D + A cos(B(t ? C)).
a) What is the value of B? Assume the time between successive high tides is 12.7 hours. Give an exact answer.
b) What is the physical meaning of C?
The value of B is determined by the equation 2π / 12.7, which corresponds to the tide's period. The variable C represents the time delay from midnight to the first high tide, which is a phase shift in the function.
Explanation:The Bay of Fundy tidal pattern can be modeled using a cosine function. Since tides go through a complete cycle (360 degrees or 2π radians) every 12.7 hours, the value of B, the frequency, can be determined by dividing 2π by the period of the tide in hours.
Therefore, B = 2π / 12.7.
The variable C in the equation represents a phase shift. In this context, a phase shift refers to a horizontal shift of the cosine function, which corresponds to a time delay or advance of the tides. The meaning of C is the time delay between midnight and the first high tide of the day.
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What is the strength of an electric field that will balance the weight of a 9.0 gg plastic sphere that has been charged to -1.6 nCnC ? Express your answer to two significant figures and include the appropriate units.
Answer: The strength of an electric field is E = - 0,05.10⁹ N/C.
Step-by-step explanation: According to the question, the plastic sphere is in equilibrium in an electric field. This sugests that the forces acting on the sphere, which are Gravitational Force (Fg) and Electric Force (Fe) are also in equilibrium, denotating Fg=Fe.
As Fg = m . g, with m = 0,009kg and g= 9,8m/s², we have Fg = 0,0882N.
Knowing the value of Fe, the strength of the electric field can be calculated as
E = Fe/Q, in which Q is the electric charge.
E = (0,0882) / (-1,6·10⁻⁹)
E = - 0,05·10⁹N/C
Classify each of the narratives below based on whether the mean or median provides a better description of the center of its distribution. global population.a. Age of first marriage for the population of a major city. b. Age of natural death for the population of a major city. c. Hours of sleep per day for an American adult. d. Caloric intake per day for an American adult. e. IQ scores for the population of a major city. f. Commute time per day for an American adult.
Answer:
Mean ;
Age of natural death for the population of a major cityHours of sleep for an American adultIQ scores for the population of a major city.Median;
Age of first marriage for the population of a major cityCaloric intake per day for an American adultCommute time per day for an American adultStep-by-step explanation:
The mean is used when the data under consideration is more of quantitative and in which the data is devoid of outliers as such the values are assumed to follow a normal distribution.
The median on the other hand is considered when the data are more of qualitative and usually contain outliers. Median on the other hand is best used when there is a skewed symmetry in the values given.
Mean ;
Age of natural death for the population of a major cityHours of sleep for an American adultIQ scores for the population of a major city.Median;
Age of first marriage for the population of a major cityCaloric intake per day for an American adultCommute time per day for an American adultWhether mean or median provides a better description of a data set depends on the skewness and outliers in the data. Generally, the mean is more sensitive to outliers whereas the median can better represent the central tendency of skewed distributions.
Explanation:In statistics, mean and median are two measures of central tendency. The mean is the average of the data points, while the median is the middle value. Whether the mean or median provides a better description depends on the distribution of the data.
A. Age of first marriage for the population of a major city: Here, mean may be a better metric as this data is likely normally distributed.B. Age of natural death for the population of a major city: Median can provide a better description, as the age of death might have outlying values which could skew the mean.C. Hours of sleep per day for an American adult: Mean can provide a better understanding since sleep hours are typically normally distributed.D. Caloric intake per day for an American adult: This may be more skewed with outliers, so the median might be more appropriate.E. IQ scores for the population of a major city: Here, the distribution is likely to be normal, so mean would be a good measure.F. Commute time per day for an American adult: Given potential outliers (long commutes), the median might be more appropriate.Learn more about Statistics here:https://brainly.com/question/31538429
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Suppose that the data for analysis includes the attributeage. Theagevalues for the datatuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.(a) What is themeanof the data? What is themedian?(b) What is themodeof the data? Comment on the data’s modality (i.e., bimodal,trimodal, etc.).(c) What is themidrangeof the data?(d) Can you find (roughly) the first quartile (Q1) and the third quartile (Q3) of the data?(e) Give thefive-number summaryof the data.(f ) Show aboxplotof the data.(g) How is aquantile–quantile plotdifferent from aquantile plot? g
Answer:
a) [tex]\bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96[/tex]
[tex] Median = 25[/tex]
b) [tex] Mode = 25, 35[/tex]
Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.
c) [tex] Midrange = \frac{70+13}{3}=41.5[/tex]
d) [tex] Q_1 = \frac{20+21}{2} =20.5[/tex]
[tex] Q_3 =\frac{35+35}{2}=35[/tex]
e) Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70
f) Figura attached.
g) When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.
By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.
Step-by-step explanation:
For this case w ehave the following dataset given:
13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70.
Part a
The mean is calculated with the following formula:
[tex]\bar X = \frac{\sum_{i=1}^{27} X_i }{27}= \frac{809}{27}=29.96[/tex]
The median on this case since we have 27 observations and that represent an even number would be the 14 position in the dataset ordered and we got:
[tex] Median = 25[/tex]
Part b
The mode is the most repeated value on the dataset on this case would be:
[tex] Mode = 25, 35[/tex]
Since 25 and 35 are repeated 4 times, so then the distribution would be bimodal.
Part c
The midrange is defined as:
[tex] Midrange = \frac{Max+Min}{2}[/tex]
And if we replace we got:
[tex] Midrange = \frac{70+13}{3}=41.5[/tex]
Part d
For the first quartile we need to work with the first 14 observations
13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25
And the Q1 would be the average between the position 7 and 8 from these values, and we got:
[tex] Q_1 = \frac{20+21}{2} =20.5[/tex]
And for the third quartile Q3 we need to use the last 14 observations:
25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70
And the Q3 would be the average between the position 7 and 8 from these values, and we got:
[tex] Q_3 =\frac{35+35}{2}=35[/tex]
Part e
The five number summary for this case are:
Min = 13 , Q1 = 20.5, Median=25, Q3= 35, Max = 70
Part f
For this case we can use the following R code:
> x<-c(13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30,33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70)
> boxplot(x,main="boxplot for the Data")
And the result is on the figure attached. We see that the dsitribution seems to be assymetric. Right skewed with the Median<Mean
Part g
When we use a quantile plot is because we want to show the percentage or the fraction of values below or equal to an specified value for the distribution of the data.
By the other hand the quantile-quantile plot shows the quantiles of the distribution values against other selected distribution (specified, for example the normal distribution). If the points are on a straight line we assume that the data values fit very well to the hypothetical distribution selected.
HELP ASAP the answer is on one of the arrows shown find x please show work
Focus on the sub-triangle on the left. It is a right triangle with legs 9 and 6, so its hypothenuse is
[tex]\sqrt{9^2+6^2}=\sqrt{81+36}=\sqrt{117}[/tex]
Now focus on the sub-triangle on the right. It is a right triangle with legs 6 and x, so its hypothenuse is
[tex]\sqrt{6^2+x^2}=\sqrt{x^2+36}[/tex]
Now, the entire triangle has legs [tex]\sqrt{117}[/tex] and [tex]\sqrt{x^2+36}[/tex], and its hypothenuse is [tex]9+x[/tex]. Write the Pytagorean theorem one last time to get
[tex]117+(x^2+36)=(9+x)^2\iff x^2+153=81+18x+x^2 \iff 18x+81=153[/tex]
Subtract 81 from both sides to get
[tex]18x=72 \iff x=\dfrac{72}{18}=4[/tex]
Answer: x = 4
Step-by-step explanation:
The attached photo shows a clearer illustration of the given triangle.
Looking at the photo, assuming ∆BCD is a right angle triangle. To determine BC, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
BC² = 9² + 6²
BC² = 81 + 36 = 117
BC = √117
To determine θ, we would apply the tangent trigonometric ratio.
Tan θ opposite side/adjacent side
Tan θ = 6/9 = 0.6667
θ = 33.6914
Considering ∆ABC,
Hypotenuse = x + 9
Adjacent = √117
Cos θ = adjacent side/ hypotenuse
Cos 33.6914 = √117/(x + 9)
Cross multiplying, it becomes
0.8320 = √117/(x + 9)
x + 9 = √117/0.8320
x + 9 = 13
x = 13 - 9 = 4
Trying to find length and area from this triangle.
Answer:
24, 204
Step-by-step explanation:
to find the height
we would use the heron formula when all the sides are given
S which is equal to half of the perimeter of the triangle which is (a+b+c)/2.
S = (17+ 25+ 26)/2 = 68/2 = 34
Area = √S(S-A)(S-B)(S-C)
Area= (1/2)bh
we equate it back to the formula Area = √S(S-A)(S-B)(S-C)
it becomes
(1/2)bh = √S(S-A)(S-B)(S-C)
A = IABI= 25
B= IBCIM = 26
C= IACI = 17
b = base = IACI = 17
S = 34
(1/2)bh = √S(S-A)(S-B)(S-C)
(1/2)17h = √34(34-25)(34-26)(34-17)
(17/2)h = √34(9)(8)(17) = √34 x 9 x 8 x 17
(17/2)h = √41616 = 204
17h/2 = 204
17h = 204 x 2 = 408
h = 408/17 = 24 inch
height = h = IBDI = 24 in
Area = (1/2)bh
= (1/2) x 17 x 24
= 12 x 17 = 204 or we use the heron formula just like the above which we get 204 before multiplication by 2.
Suppose each of 12 players rolls a pair of dice 3 times. Find the probability that at least 4 of the players will roll doubles at least once. (Answer correct to four decimal places.)
Answer:
Our answer is 0.8172
Step-by-step explanation:
P(doubles on a single roll of pair of dice) =(6/36) =1/6
therefore P(in 3 rolls of pair of dice at least one doubles)=1-P(none of roll shows a double)
=1-(1-1/6)3 =91/216
for 12 players this follows binomial distribution with parameter n=12 and p=91/216
probability that at least 4 of the players will get “doubles” at least once =P(X>=4)
=1-(P(X<=3)
=1-((₁₂ C0)×(91/216)⁰(125/216)¹²+(₁₂ C1)×(91/216)¹(125/216)¹¹+(₁₂ C2)×(91/216)²(125/216)¹⁰+(₁₂ C3)×(91/216)³(125/216)⁹)
=1-0.1828
=0.8172
Describe the sets of points in space whose coordinates satisfy the given inequalities or combinations of equations and inequalities."x2 + y2 + 4, z = y
Answer:
Step-by-step explanation:
This is a circle with radius 2 and z = y
All points on or within the circle x2 + y2 +4 and in the plane z = y
A measurement of the circumference of a disk has an uncertainty of 1 . 5 mm. How many measurements must be made so that the diameter can be estimated with an uncertainty of only 0 . 5 mm
Answer:
How many measurements must be made = 9
Step-by-step explanation:
The steps are as shown in the attachment.
To reduce the uncertainty in the diameter of a disk from 1.5mm to 0.5mm, three times more measurements of the circumference would need to be made. This is due to the relationship between the circumference and diameter, and how the uncertainty propagates through this relationship.
Explanation:This question pertains to the areas of accuracy, precision, and uncertainty in measurements. Understanding these concepts is vital in the field of physics. The circumference of a disk and its diameter are related by the constant π (Pi): Diameter = Circumference / π.
The question states that there is an uncertainty of 1.5 mm in measuring the circumference. Given that the diameter and circumference are directly connected, when you reduce the uncertainty in the measurement of the circumference (e.g., by taking more measurements), you also reduce the uncertainty in the diameter. However, the relationship is not linear. Through propagation of uncertainty principles, the uncertainty in diameter would be the uncertainty in the circumference divided by π. To reduce this to 0.5 mm, you would require three times more measurements.
The precision of a measurement system is closely linked to the size of its measurement increments. The smaller the measurement increment, the more precise the tool. Various factors can contribute to the uncertainty of a measurement, including the smallest division on a given tool, the ability of the person making the measurement, irregularities in the object being measured, and unforeseen circumstances that affect the outcome.
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Giorgio offers the person who purchases an 8-ounce bottle of Allure two free gifts, chosen from the following: an umbrella, a 1-ounce bottle of Midnight, a feminine shaving kit, a raincoat, or a pair of rain boots. If you purchased Allure, what is the probability you randomly selected an umbrella and a shaving kit in that order?a. 0.20 b. 0.00c. 0.05d. 1.00
Answer:
P(T) = 1/20 = 0.05
The probability of randomly selecting an umbrella and a shaving kit in that order is 0.05
Step-by-step explanation:
The probability of randomly selecting an umbrella and a shaving kit in that order.
P(T) = Probability of selecting umbrella first P(U) × probability of selecting shaving kit second P(S)
P(U) = 1/5 (1 umbrella out of five possible gifts)
P(S) = 1/4 (1 shaving kit out of four remaining possible gifts)
P(T) = 1/5 × 1/4
P(T) = 1/20 = 0.05
The probability that a person will select an umbrella and a shaving kit in that order is 1/20.
The following can be deduced from the information given:
P(U) = 1/5 (1 umbrella out of five possible gifts)
P(S) = 1/4 (1 shaving kit out of four remaining possible gifts)
Therefore, the probability that a person will select an umbrella and a shaving kit in that order will be:
P(T) = 1/5 × 1/4
P(T) = 1/20 = 0.05
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The employees of a company work in six departments: 31 are in sales, 54 are in research, 42 are in marketing, 20 are in engineering, 47 are in finance, and 58 are in production. The payroll department loses one employee's paycheck. What is the probability that the employee works in the research department?
Answer:
[tex]\frac{3}{14}[/tex]
Step-by-step explanation:
There are 252 (=31+54+42+20+47+58) employees in total. 54 of those are in research. So the chances that one check that gets lost belongs to a research employee can be calculated as follows:
[tex]P=\frac{54}{252}= \frac{3}{14}[/tex]
Two planes left the airport traveling in the same direction. The distance Plane A traveled is modeled by the function d(t)=290t where d represents distance in miles and t represents time in hours. Plane B traveled a total of 540 miles in 2 hours. How does the distance Plane A traveled in 1 hour compare to the distance Plane B traveled in 1 hour? The distance Plane A traveled in 1 h is greater than the distance Plane B traveled in 1 h. The distance Plane A traveled in 1 h is less than the distance Plane B traveled in 1 h. The distance Plane A traveled in 1 h is equal to the distance Plane B traveled in 1 h.
Answer:
The distance Plane A traveled in 1 h is greater than the distance Plane B traveled in 1 h.
Step-by-step explanation:
The equation of the distance traveled by Plane A is
[tex]d(t) = 290t[/tex]
The plane B traveled 540 miles in 2 hours.
So in 1 hour, plane B traveled 540/2 = 270 miles:
How does the distance Plane A traveled in 1 hour compare to the distance Plane B traveled in 1 hour?
Plane A:
d(1) = 290*1 = 290
Plane A traveled 290 miles in 1 hour.
Plane B travaled 270 miles in 1 hour.
So the correct answer is:
The distance Plane A traveled in 1 h is greater than the distance Plane B traveled in 1 h.
Answer:
The distance Plane A traveled in 1 h is greater than the distance Plane B traveled in 1 h.
Step-by-step explanation:
When no geometric tolerance is specified, the size tolerance controls the ______________ as well as the size
Answer:
...the size tolerance controls both the measurements or dimensions of a piece, and the size.
Step-by-step explanation:
However, dimensional tolerance controls neither the shape, nor the position, nor the orientation of the elements to which said tolerance applies. In manufacturing, geometric irregularities occur that can affect the shape, position or orientation of the different elements of the pieces. An applied dimensional tolerance, for example, has an effect on the parallelism and flatness of that piece.
Luna Company accepted credit cards in payment for $7,950 of services performed during July 2018. The credit card company charged Luna a 1.55 percent service fee; it paid Luna as soon as it received the invoices. Required Based on this information alone, what is the amount of net income earned during the month of July? (Do not round intermediate values. Round final answer to 2 decimal places.)
Answer:
$7826.78
Step-by-step explanation:
Total income = 7950
With a service fee charge of 1.55%, the service fee charge = [tex]1.55\%\times7950 = \dfrac{1.55}{100}\times7950 = 123.225[/tex]
Net income = 7950 - 123.225 = 7826.775 = $7826.78
An alternative solution:
Service charge = 1.55%
Net income = (100 - 1.55)% × 7950
= 98.45% × 7950 = [tex]\dfrac{98.45}{100}\times7950 = 7826.775=7826.78[/tex]
Answer:
Step-by-step explanation:
Accepted credit= $ 7950
Charges for services =1.55% of the total
7950 - 1.55% of 7950
7950 - (1.55/100)*7950
7950 - 123.225
7826.775
7826,78 two decimal places
This is the net income earned during the month of July
An electronics firm sells four models of stereo receivers, three CD decks, and six speaker brands. When the three types of components are sold together, they form a "system." How many different systems can the electronics firm offer?
A. 169
B. 72
C. 13
D. 36
Answer:
B. 72
Step-by-step explanation:
The total number of different systems that can be bundled together is the product of the possible number of ways to select 1 out of 4 stereo receivers, by 1 out of 3 CD decks and by 1 out of 6 speakers. Assuming that the order at which products are picked does not matter, the number of different systems is:
[tex]n=\frac{4!}{(4-1)!1!}*\frac{3!}{(3-1)!1!}*\frac{6!}{(6-1)!1!}\\n=4*3*6\\n=72\ systems[/tex]
The electronics firm can offer 72 different systems.
The electronics firm can offer 72 different systems by combining 4 models of stereo receivers, 3 CD decks, and 6 speaker brands together.
To find the number of different systems the electronics firm can offer, we use the combinations formula. Since there are 4 models of stereo receivers, 3 CD decks, and 6 speaker brands, the total number of different systems can be calculated as:
4 models * 3 CD decks * 6 speaker brands = 72 different systems
Therefore, the answer to the question is 72 different systems (option B).
Assume that T is a linear transformation. Find the standard matrix of T.
T: set of real numbers R^2 →R^2 first rotates points through ( -pi/6) radians (clockwise) and then reflects points through the horizontal x1-axis.
Answer:
The Matrix of T is
[tex]\left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\-sin(\pi/6)&-cos(\pi/6)\end{array}\right][/tex]
Step-by-step explanation:
Rotate -pi/6 Clockwise is the same as rotating pi/6 anticlockwise. The matrix of that rotation is
[tex]\left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\sin(\pi/6)&cos(\pi/6)\end{array}\right][/tex]
The matrix of the reflection through the x1-axis is
[tex]\left[\begin{array}{cc}1&0\\0&-1\end{array}\right][/tex]
Therefore, the composition is the product of both matrices is the matrix of T
[tex]MT = \left[\begin{array}{cc}1&0\\0&-1\end{array}\right] * \left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\sin(\pi/6)&cos(\pi/6)\end{array}\right] = \left[\begin{array}{cc}cos(\pi/6)&-sin(\pi/6)\\-sin(\pi/6)&-cos(\pi/6)\end{array}\right][/tex]
I hope that works for you!
To find the standard matrix of the linear transformation [tex]\( T \)[/tex], we need to perform two operations in sequence: a rotation through [tex]\( -\frac{\pi}{6} \)[/tex] radians (clockwise) and a reflection through the horizontal [tex]\( x_1 \)-axis[/tex]. We will find the matrices for each of these transformations and then multiply them to get the standard matrix for [tex]\( T \)[/tex].
1. Rotation Matrix [tex]\( R \)[/tex]:
The matrix that represents a rotation through an angle [tex]\( \theta \)[/tex] in the counterclockwise direction is given by:
[tex]\[ R(\theta) = \begin{bmatrix} \cos(\theta) -\sin(\theta) \\ \sin(\theta) \cos(\theta) \end{bmatrix} \][/tex]
For a clockwise rotation, we use a negative angle, so for [tex]\( -\frac{\pi}{6} \)[/tex] radians, the rotation matrix is:
[tex]\[ R\left(-\frac{\pi}{6}\right) = \begin{bmatrix} \cos\left(-\frac{\pi}{6}\right) -\sin\left(-\frac{\pi}{6}\right) \\ \sin\left(-\frac{\pi}{6}\right) \cos\left(-\frac{\pi}{6}\right) \end{bmatrix} = \begin{bmatrix} \frac{\sqrt{3}}{2} \frac{1}{2} \\ -\frac{1}{2} \frac{\sqrt{3}}{2} \end{bmatrix} \][/tex]
2. Reflection Matrix [tex]\( M \)[/tex]:
The matrix that represents a reflection through the horizontal[tex]\( x_1 \)[/tex]-axis is given by:
[tex]\[ M = \begin{bmatrix} 1 0 \\ 0 -1 \end{bmatrix} \][/tex]
3. Standard Matrix of [tex]\( T \)[/tex]
To find the standard matrix of[tex]\( T \)[/tex], we multiply the rotation matrix [tex]\( R \)[/tex] by the reflection matrix [tex]\( M \)[/tex]:
[tex]1 0 \\ 0 -1[/tex]
[tex]\end{bmatrix} \begin{bmatrix} \frac{\sqrt{3}}{2} \frac{1}{2} \\ -\frac{1}{2} \frac{\sqrt{3}}{2} \end{bmatrix} \] \[ T = \begin{bmatrix} \frac{\sqrt{3}}{2} \frac{1}{2} \\ \frac{1}{2} -\frac{\sqrt{3}}{2} \end{bmatrix} \][/tex]
Therefore, the standard matrix of the linear transformation [tex]\( T \)[/tex] is:
[tex]\[ \boxed{T = \begin{bmatrix} \frac{\sqrt{3}}{2} \frac{1}{2} \\ \frac{1}{2} -\frac{\sqrt{3}}{2} \end{bmatrix}} \][/tex]
This matrix represents the transformation that first rotates points through [tex]\( -\frac{\pi}{6} \)[/tex] radians (clockwise) and then reflects them through the horizontal [tex]\( x_1 \)-axis.[/tex]