Answer:
C. If I lower my grades then I work alone
Step-by-step explanation:
In logic, the contrapositive of a conditional statement, [tex]P\to Q[/tex] is [tex]\neg Q\to \neg P[/tex].
In other words, the contrapositive of "If P then Q" is "If not Q, then not P".
The given conditional statement is:
"If I form a study group then I raise my grades."
We can break this conditional statement into the following propositional statements:
P : I form a study group
¬P : I work alone
Q : I raise my grades
¬Q : I lower my grades
The contrapositive of "If I form a study group then I raise my grades." becomes:
" If I lower my grades then I work alone"
The correct choice is C
To find the contrapositive of the given conditional statement "If I form a study group then I raise my grades," we have to negate both the hypothesis (the "if" or P part) and the conclusion (the "then" or Q part) and also reverse their order.
The original statement is in the form: If P then Q.
P: I form a study group.
Q: I raise my grades.
The contrapositive is: If not Q then not P.
Not Q: I do not raise my grades.
Not P: I do not form a study group.
So, the contrapositive of the original statement would be: "If I do not raise my grades then I do not form a study group."
Now let's match this to one of the choices given:
A. If I work alone then I lower my grades. (This is not the contrapositive; it introduces new concepts that weren't part of the original statement.)
B. If I raise my grades then I form a study group. (This is the converse, not the contrapositive.)
C. If I lower my grades then I work alone. (This is the contrapositive: "lower my grades" is equivalent to "do not raise my grades," and "work alone" is equivalent to "do not form a study group.")
D. If I form a study group then I lower my grades. (This is not the contrapositive; it's the inverse of the original statement.)
E. If I form a study group then I raise my grades. (This is the original statement.)
F. If I raise my grades then I work alone. (This is not the contrapositive; it introduces the concept of working alone.)
The correct choice that represents the contrapositive of the original statement is C. If I lower my grades then I work alone.
) For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. a) If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 125.
Answer:
0.2177Explanation:
The probability distribution of the standard normal variable, Z, is tabulated.
Z, the standard normal variable, is defined by:
Z = (X - μ) / σ, whereX is a normal variable (the systolic blood pressure,in mm Hg in this case)μ is the mean (114.8 mm Hg in this case), andσ is the standard deviation (13.1 mm Hg in this case).You want to find the probablity that the systolic pressure of a woman between the ages of 18 and 24 is greater than 125, which means P (X > 125).
Then, to use a table of Z-score, you have to convert X > 125 into Z and find the corresponding probabiiity.
These are the calculations:
X > 125 ⇒ Z > (125 - 114.8) / 13.1 ⇒ Z > 10.2 / 13.1 ⇒ Z > 0.7786Now use a table for the normal standard probabiity. Most tables use two decimals for Z, so you can round to Z > 0.78, which will yield P (Z > 0.78) = 0.2177.
U = {a, b, c, d, e, f, g} A = {a, c, e, g} B = {a, b, c, d} Find A ∩ B
[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]
[tex]\large\boxed{A\cap B=\{a,c\}}[/tex]
Provide a counterexample:
If a and b are integers where a is divisible by b and b is divisible by a, then a = b.
Answer:
[tex]a=2 \quad \text{and} \quad b=-2[/tex]
Step-by-step explanation:
Take [tex]a=2 \quad \text{and} \quad b=-2[/tex], note that
[tex]2=(-1)\cdot(-2)[/tex]
hence b divides a. On the other hand, we have that
[tex]-2=(-1)\cdot2[/tex]
which tells us that a divides b. Moreover, [tex]a=2 \neq -2=b[/tex].
Sophia has 16 plants and one window. Only five plants can be placed in the window at any given time. If each of the 16 plants spends the same amount of time in the window during an eight-hour period of sunlight, what is the greatest number of minutes in the sun that is possible per plant?
Answer:
120 minutes
Step-by-step explanation:
Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds ≅ 4 rounds
As there are four rounds to go in 8 hours, so the time for 1 round will be: 8/4 = 2 hours.
Therefore, 2 hours or 120 minutes of sunlight are possible for one plant ..
Answer:
The answer is actually 150 minutes.
Step-by-step explanation:
What is the median for the set of data? Ages Stem Leaves
1 0, 3, 6
2 0, 1, 3, 7, 7, 8, 9
3 0, 2, 3, 3, 3, 3, 8, 9
4 6, 6, 6, 8 1|0 = 10 years old
30
31
32
33
Answer:
This is a stem leaf data, in which the stem generally stands for the "tens" place value while the leaf stands for the "ones" place value.
Expand the data, and find the median by finding the middle number:
10, 13, 16, 20, 21, 23, 27, 27, 28, 29, 30, 32, 33, 33, 33, 33, 38, 39, 46, 46, 46, 48
There are 22 numbers in all. To find the Median when there is a even amount of numbers, Find the two middle numbers, and find the mean of the two numbers:
(32 + 30)/2 = (62)/2 = 31
31 is your answer.
~
Find the standard deviation. Round to the nearest tenth. 1, 2, 11, 8, 16, 16,20, 16, 18 OA. 6.5 O B. 6.9 O C. 1.5 ? D. 7.4
Answer:
A. 6.5
Step-by-step explanation:
First we find the average [tex]\bar{x}[/tex] of the 9 data:
[tex]\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}[/tex]
Where n is the data number, that in this case is 9.
[tex]\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12\\[/tex]
The formula of the standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}[/tex]
We replace the data and find the value of the standard deviation:
[tex]\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}[/tex]
[tex]\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54[/tex]
We approximate the number and the solution is 6,5
Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through the three points ( 0 , 0 , 1 ) (0,0,1), ( 1 , 0 , 8 ) (1,0,8) and ( 0 , 1 , 9
The three vectors [tex]\langle0,0,1\rangle[/tex], [tex]\langle1,0,8\rangle[/tex], and [tex]\langle0,1,9\rangle[/tex] each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,
[tex]\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle[/tex]
[tex]\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle[/tex]
Then the cross product of these two results is normal to the plane:
[tex]\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle[/tex]
Let [tex](x,y,z)[/tex] be a point on the plane. Then the vector connecting [tex](x,y,z)[/tex] to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that
[tex]\langle-7,-8,1\rangle\cdot(\langle x,y,z\rangle-\langle0,0,1\rangle)=0[/tex]
which reduces to the equation of the plane,
[tex]-7x-8y+z-1=0\implies z=7x+8y+1[/tex]
Let [tex]z=f(x,y)[/tex]. Then the volume of the region above [tex]R[/tex] and below the plane is
[tex]\displaystyle\int_0^1\int_0^1(7x+8y+1)\,\mathrm dx\,\mathrm dy=\boxed{\frac{17}2}[/tex]
The problem involves finding the volume of a region under a plane defined by three points in a 3-dimensional space. Calculus and analytical geometry can be used to find the answer. Solution can only be provided if the equation of the plane is provided.
Explanation:The question involves finding the volume of a specific region defined within spatial coordinates in a three-dimensional Cartesian space. The three points provided (0,0,1), (1,0,8) and (0,1,9) define a plane. Unfortunately, the problem does not provide enough details to solve the problem. Having said this, the volume of a region R under a plane can usually be found by integrating over the area of R. This essentially involves setting up a double integral over the area R with the integrand being the height of the plane above each point in R. The solution, however, requires the equation of the plane, which can be found using the three points mentioned. This method relies on the understanding of the fundamentals of calculus and analytic geometry
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a slice of bread has 1.5 g of fat, 19 g carbohydrate and 4 g protein. how many kcal in the slice? please show all of you work in a dimensional analysis format.
Answer:
The answer is 105.5 kcal/slice of bread.
Step-by-step explanation:
The kcal per gram of:
protein = 4kcal/g.carbohydrate = 4kcal/g.fat = 9kcal/g.Now, you have:
1.5 g of fat + 19g of carbohydrate + 4g of protein = 1 slice of bread.If we multiply the amount of components by his kcal:
1.5g * 9kcal/g + 19g * 4kcal/g + 4g * 4kcal/g;Now gram/gram = 1, and we can cancel the grams in the equation:
1.5* 9kcal + 19 * 4kcal + 4 * 4kcal = 105.5kcal;Finally, the result of the kcal of the slice bread is:
105.5 kcal/slice of bread.catering service offers 8 appetizers, 11 main courses, and 7 desserts. A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts. How many ways can this be done?
Answer: The required number of ways is 46200.
Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.
A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.
We are to find the number of ways in which this can be done.
We know that
From n different things, we can choose r things at a time in [tex]^nC_r[/tex] ways.
So,
the number of ways in which 7 appetizers can be chosen from 8 appetizers is
[tex]n_1=^8C_7=\dfrac{8!}{7!(8-7)!}=\dfrac{8\times7!}{7!\times1}=8,[/tex]
the number of ways in which 8 main courses can be chosen from 11 main courses is
[tex]n_2=^{11}C_8=\dfrac{11!}{8!(11-8)!}=\dfrac{11\times10\times9\times8!}{8!\times3\times2\times1}=165[/tex]
and the number of ways in which 4 desserts can be chosen from 7 desserts is
[tex]n_3=^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!\times3\times2\times1}=35.[/tex]
Therefore, the number of ways in which the banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts is given by
[tex]n=n_1\times n_2\times n_3=8\times165\times35=46200.[/tex]
Thus, the required number of ways is 46200.
A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 4 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.
Answer: (16%, 24%)
Step-by-step explanation:
The confidence interval for proportion is given by :-
[tex]p\pm E[/tex]
Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]
The proportion of the respondents answered "crime and violence." : p=0.20
Margin of sampling error : [tex]E=\pm0.04[/tex]
Now, the 95% confidence interval for the proportion of the population that would respond "crime and violence" to the question asked by the pollsters is given by :-
[tex]0.20\pm 0.04\\\\=0.20-0.04,\ 0.20+0.04\approx(0.16,0.24)[/tex]
In percentage, [tex](16\%,24\%)[/tex]
Hence, the 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters =(16%, 24%)
The 95% confidence interval for the population that would answer "crime and violence" to the poll question, given a sample proportion of 20% and a margin of error of 4%, is between 16% and 24%.
Explanation:This question is about constructing a confidence interval based on poll data, a mathematical and statistical concept. The poll indicates that 20% of respondents believe the most pressing issue in the country today is "crime and violence", with a margin of error of ±4%. A 95% confidence interval for the population proportion can be constructed by adding and subtracting the margin of error from the sample proportion.
So in this case, we can calculate the low and high end of the interval as follows:
Low end = 20% - 4% = 16% High end = 20% + 4% = 24%So, we can be 95% confident that the true population proportion that would respond "crime and violence" to the question lies somewhere between 16% and 24% based on this poll.
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Fill in the blank. The number of _______ for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
The number of Degrees of Freedom is the answer.
The term 'degrees of freedom' refers to the number of sample values that can vary after specific restrictions have been placed on all data values. It is a critical concept in statistics, playing a role in areas such as hypothesis testing and confidence intervals.
Explanation:The blank should be filled with 'degrees of freedom'. The number of degrees of freedom for a collection of sample data is the number of sample values that can vary after certain restrictions have been imposed on all data values.
For instance, in a set of sample data with a fixed mean, if you know the values of all but one data point, you can calculate the value of the remaining one due to the restriction of the fixed mean. Therefore, in this case, the degrees of freedom would be n-1 (with 'n' representing the total number of sample data points).
The concept of degrees of freedom is an important aspect in various areas of statistics, including hypothesis testing and estimating confidence intervals.
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If possible, find the solution of y=x+2z
z=-1-2x
x=y-14
A. No solution
B.(11,-14,7)
C.(-4,10,7)
D.(3,4,0)
Answer:
C. (-4,10,7)
Step-by-step explanation:
Use the first equation to substitute for y in the last equation:
x = (x +2z) -14
14 = 2z . . . . . . add 14-x
7 = z . . . . . . . . divide by 2
Now, find x:
7 = -1 -2x . . . . substitute for z in the second equation
8/-2 = x = -4 . . . . . add 1, divide by -2
Finally, find y:
y = -4 +2(7) = 10 . . . . . substitute for x and z in the first equation
The solution is (x, y, z) = (-4, 10, 7).
Answer:
C
Step-by-step explanation:
EDGE
The student council at a college is made up of four freshmen, five sophomores, six juniors, and seven seniors. A yearbook photographer would like to line up two council members from each class for a picture. How many different pictures are possible if each group of classmates stands together?
Answer:
7257600
Step-by-step explanation:
Number of freshmen in the student council= 4
Number of sophomores in the student council= 5
Number of juniors in the student council= 6
Number of seniors in the student council= 7
Ways of choosing council members
⁴C₂×⁵C₂×⁶C₂×⁷C₂
[tex]^4C_2=\frac{4!}{(4-2)!2!}\\=\frac{24}{4}=6\\\\^5C_2=\frac{5!}{(5-2)!2!}\\=\frac{120}{12}=10\\\\^6C_2=\frac{6!}{(6-2)!2!}\\=\frac{720}{48}=15\\\\^7C_2=\frac{7!}{(7-2)!2!}\\=\frac{5040}{240}=21[/tex]
⁴C₂×⁵C₂×⁶C₂×⁷C₂=6×10×15×21=18900
Ways of lining up the four classes=4!=1×2×3×4=24
Ways of lining up members of each class=2⁴=2×2×2×2=16
Pictures are possible if each group of classmates stands together
⁴C₂×⁵C₂×⁶C₂×⁷C₂×4!×2⁴
=18900×24×16
=7257600
There are 453600 possible different pictures
How to determine the number of different pictures?
The given parameters are:
Freshmen = 4
Sophomores = 5
Juniors = 6
Seniors = 7
Two council members are to be selected from each group.
So, the number of ways this can be done is:
n = ⁴C₂×⁵C₂×⁶C₂×⁷C₂
Apply combination formula, and evaluate the product
n = 18900
Each group are to stand together.
There are 4! ways to arrange the 4 groups.
So, the total number of pictures is:
Total = 4! * 18900
Evaluate the product
Total = 453600
Hence, there are 453600 possible different pictures
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A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95% confident that his estimate is in error by no more than four percentage points question marks? Assume that nothing is known about the percentage of computers with new operating systems.
Answer:
n = 601
Step-by-step explanation:
Since we know nothing about the percentage of computers with new operating system, we assume than 50% of the computers have new operating system.
So, p = 50% = 0.5
q = 1 - p = 1 - 0.5 = 0.5
Margin of error = E = 4 percentage points = 0.04
Confidence Level = 95%
z value associated with this confidence level = z = 1.96
We need to find the minimum sample size i.e. n
The formula for margin of error for the population proportion is:
[tex]E=z\sqrt{\frac{pq}{n}}[/tex]
Re-arranging the equation for n, and using the values we get:
[tex]n=(\frac{z}{E} )^{2} \times pq\\\\ n=(\frac{1.96}{0.04})^{2} \times 0.5 \times 0.5\\\\ n = 601[/tex]
Thus, the minimum number of computers that must be surveyed is 601
Jerry spent ¾ of his allowance on baseball cards. If he was given S20, how mch did he spend on baseball cards.
Answer:
$15
Step-by-step explanation:
He had $20 and he spent [tex]\frac{3}{4}[/tex] of that in baseball cards, that is
[tex]20*\frac{3}{4}= \frac{20*3}{4} = \frac{60}{4} = 15.[/tex]
So, he spent $15 in baseball cards.
A real estate firm owns the Kasumba Garden Apartments which consists of 90 apartments. At $350 per month every apartment can be rented. However, for each $10 per month increase there will be two vacancies with no possibility of filling them. The firm wants to receive $31 980 per month from rents. What rent should be charged for each apartment?
Answer:
The rent should be $ 390 or $ 410.
Step-by-step explanation:
Given,
The original monthly rent of an apartment = $350,
Also, the original number of apartment that could be filled = 90,
Let the rent is increased by x times of $ 10,
That is, the new monthly rent of an apartment =( 350 + 10x ) dollars
Since, for each $10 per month increase there will be two vacancies with no possibility of filling them.
Thus, the new number of filled apartments = 90 - 2x,
Hence, the total revenue of the firm = ( 90 - 2x )(350 + 10x ) dollars,
According to the question,
( 90 - 2x )(350 + 10x ) = 31,980
[tex]90(350)+90(10x)-2x(350)-2x(10x)=31980[/tex]
[tex]31500+900x-700x-20x^2=31980[/tex]
[tex]-20x^2+200x+31500-31980=0[/tex]
[tex]20x^2-200x+480=0[/tex]
By the quadratic formula,
[tex]x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}[/tex]
[tex]x=\frac{200\pm \sqrt{1600}}{40}[/tex]
[tex]x=\frac{200\pm 40}{40}[/tex]
[tex]\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}[/tex]
[tex]\implies x=6\text{ or } x =4[/tex]
Hence, the new rent of each apartment, if x = 6, is $ 410,
While, if x = 4, is $ 390
Inâ 2001, the population in a town was 11% more than it was in 2000. If the population was 25,570 in 2002 which was 10% more than 2001 find the population in 2000
write the number (Round to the nearest wholeâ number.)
Answer: There was population of 22808 in 2000.
Step-by-step explanation:
Since we have given that
Population was in 2002 = 25,570
According to question, the population in 2002 was 10% more than 2001.
So, the population in 2001 was
[tex]25570=P_1(1+\dfrac{r}{100})\\\\25570=P_1(1+\dfrac{10}{100})\\\\25570=P_1(1+0.1)\\\\25570=P_1(1.01)\\\\\dfrac{25570}{1.01}=P_1\\\\25316.8\approx 25317=P_1[/tex]
Now, we have given that
In 2001, the population in a town was 11% more than it was in 2000.
So, population in 2000 was
[tex]25317=P_0(1+\dfrac{r}{100})\\\\25317=P_0(1+\dfrac{11}{100})\\\\\25317=P_0(1+0.11)\\\\25317=P_0(1.11)\\\\P_0=\dfrac{25317}{1.11}\\\\P_0=22808[/tex]
Hence, there was population of 22808 in 2000.
Scor Question Help 4.D.49 You can afford monthly payments of $500. If current mortgage rates are 2.83% for a 15-year fixed rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.) How much can you afford to borrow? S(Round to the nearest dollar as needed.) orary cess esources 6ew
Answer:
No down payment = $73 267; 10 % down payment = $81 408
Step-by-step explanation:
1. With no down payment
The formula for a maximum affordable loan (A) is
A = (P/i)[1 − (1 + i)^-N]
where
P = the amount of each equal payment
i = the interest rate per period
N = the total number of payments
Data:
P = 500
APR = 2.83 % = 0.0283
t = 15 yr
Calculations:
You are making monthly payments, so
i = 0.0283/12 = 0.002 358 333
The term of the loan is 15 yr, so
N = 15 × 12 = 180
A = (500/0.002 3583)[1 − (1 + 0.002 3583)^-180]
= 212 014(1 - 1.002 3583^-180)
= 212 014(1 - 0.654 424)
= 212 014 × 0.345 576
= 73 267
You can afford to spend $73 267 on a home.
2. With a 10 % down payment
Without down payment, loan = 73 267
With 10 % down payment, you pay 0.90 × new loan
0.90 × new loan = 73 267
New loan = 73267/0.90 = 81 408
With a 10 % down payment, you can afford to borrow $81 408 .
Here’s how it works:
Purchase price = $81 408
Less 10 % down = -8 141
Loan = $73 267
And that's just what you can afford.
An insurance company found that 9% of drivers were involved in a car accident last year. If seven drivers are randomly selected, find the probability that exactly two of them were involved in a car accident last year.
Answer: 0.1061
Step-by-step explanation:
Given : An insurance company found that 9% of drivers were involved in a car accident last year.
Thus, the probability of drivers involved in car accident last year = 0.09
The formula of binomial distribution :-
[tex]P(X=x)^nC_xp^x(1-p)^{n-x}[/tex]
If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-
[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]
Hence, the required probability :-0.1061
Draw a Hasse diagram of the partial order << of the set {2,3,4,6,8,9,10,12} where a << b iff b is divisible by a.
do not use horizontal line
Step-by-step explanation:
Consider the provided set {2,3,4,6,8,9,10,12}
Let the set is A.
[tex]A={(2 \prec 4), (2 \prec 6), (2 \prec 8), (2 \prec 10), (2 \prec 12), (3 \prec 6), (3 \prec 9), (4 \prec 8), (4 \prec 12), (6 \prec 12)}[/tex]
Hence the required Hasse diagram is shown in figure 1:
In the Hasse diagram 2 and 3 are on the same level as they are not related.
The next numbers are 4, 6, 9, and 10. 4, 6 and 10 are divisible by both 2. 6 and 9 are divisible by 3. Then 8 and 12 are divisible by 4 also 12 is divisible by 6.
Hence, the required diagram of the partial order of the set {2,3,4,6,8,9,10,12} is shown in figure 1.
Suppose that the pairwise comparison method is used to determine the winner in an election. If there are 13 candidates, how many comparisons must be made? comparisons (Type an integer.)
Answer:78
Step-by-step explanation:
For N=13 candidates
For pairwise comparison to determine the winner in an election we need to use combination
a pair of distinct candidates can be chosen in [tex]^NC_{2}=\frac{N\left ( N-1 \right )}{2}[/tex]
Therefore no of comparison to be made =[tex]^{13}C_{2}=frac{13\left ( 13-1 \right )}{2}=78[/tex]
Thus a total of 78 comparison is needed
To determine the number of comparisons needed using the pairwise comparison method when there are 13 candidates, we can use the formula (n-1) + (n-2) + ... + 1, where n represents the number of candidates. By substituting n = 13 into the formula, we find that a total of 78 comparisons must be made.
Explanation:To determine the number of comparisons needed using the pairwise comparison method, we can use the formula:
(n-1) + (n-2) + ... + 1
where n represents the number of candidates. Substituting n = 13, we get:
(13-1) + (13-2) + ... + 1
Simplifying the equation, we find:
12 + 11 + ... + 1 = 78
Therefore, a total of 78 comparisons must be made when there are 13 candidates.
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The graph of which function will have a maximum and a y-intercept of 4? f(x) = 4x2 + 6x – 1 f(x) = –4x2 + 8x + 5 f(x) = –x2 + 2x + 4 f(x) = x2 + 4x – 4
Answer:
Option C (f(x) = [tex]-x^2 + 2x + 4[/tex])
Step-by-step explanation:
In this question, the first step is to write the general form of the quadratic equation, which is f(x) = [tex]ax^2 + bx + c[/tex], where a, b, and c are the arbitrary constants. There are certain characteristics of the values of a, b, and c which determine the nature of the function. If a is a positive coefficient (i.e. if a>0), then the quadratic function is a minimizing function. On the other hand, a is negative (i.e. if a<0), then the quadratic function is a maximizing function. Since the latter condition is required, therefore, the first option (f(x) = [tex]4x^2 + 6x - 1[/tex]) and the last option (f(x) = [tex]x^2 + 4x - 4 [/tex]) are incorrect. The features of the values of b are irrelevant in this question, so that will not be discussed here. The value of c is actually the y-intercept of the quadratic equation. Since the y-intercept is 4, the correct choice for this question will be Option C (f(x) = [tex]-x^2 + 2x + 4[/tex]). In short, Option C fulfills both the criteria of the function which has a maximum and a y-intercept of 4!!!
Answer:
it is c: f(x) = –x2 + 2x + 4
The lifetime of an alkaline battery is exponentially distributed with a mean of 20 a) What is the probability that the battery will last between 10 and 15 hours?
Answer: 0.1342
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
[tex]P(x)=1-e^{\frac{-x}{\lambda}}[/tex], where [tex]\lambda [/tex] is the mean of the distribution.
Given : [tex]\lambda =20[/tex]
Then , the probability that the battery will last between 10 and 15 hours is given by :-
[tex]P(10<x<15)=P(15)-P(10)\\\\=1-e^{\frac{-15}{20}}-(1-e^{\frac{-10}{20}})\\\\=-e^{-0.75}+e^{-0.5}=0.13416410697\approx0.1342[/tex]
Hence, the probability that the battery will last between 10 and 15 hours = 0.1342
The probability that the battery will last between 10 and 15 hours is 18.13%.
Explanation:In order to find the probability that the battery will last between 10 and 15 hours, we need to use the exponential distribution. The exponential distribution is defined by the formula P(X
For this problem, the mean is 20, so λ = 1/20. Plugging in the values, we get P(10
Therefore, the probability that the battery will last between 10 and 15 hours is 18.13%.
2. Use the binomial theorem to expand the expression. (а — 2b)^5
Answer:
[tex](a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]
Step-by-step explanation:
The binomial expansion is given by:
[tex](x+y)^{n}=_{0}^{n}\textrm{C}x^{^{0}}y^{n}+_{1}^{n-1}\textrm{C}x^{1}y^{n-1}+...+_{n}^{n}\textrm{C}x^{n}y^{0}[/tex]
In our case we have
[tex]x=a\\y=-2b\\n=5[/tex]
Thus using the given terms in the binomial expansion we get
[tex](a-2b)^{5}=_{0}^{5}\textrm{C}a^{0}(-2b)^{5}+_{1}^{5}\textrm{C}a^{^{1}}(-2b)^{4}+{_{2}^{5}\textrm{C}}a^{2}(-2b)^{3}+_{3}^{5}\textrm{C}a^{3}(-2b)^{2}+_{4}^{5}\textrm{C}a^{4}(-2b)^{1}+_{5}^{5}\textrm{C}a^{5}(-2b)^{0}[/tex]
Upon solving we get
[tex](a-2b)^{5}=-32b^{5}+5\times a\times16b^{4}+10\times a^{2} \times (-8b^{3})+10\times a^{3}\times 4b^{2}+5\times a^{4}\times (-2b)+a^{5}\\\\(a-2b)^{5}=-32b^{5}+80ab^{4}-80a^{2}b^{3}+40a^{3}b^{2}-10a^{4}b+a^{5}[/tex]
what is minimum spanning tree
Answer:
Given an unguided connected graph, an extension tree of this graph is a subgraph which is a tree that connects all vertices. A single graph may have different extension trees. We can mark a weight at each edge, which is a number that represents how unfavorable it is, and assign a weight to the extension tree calculated by the sum of the weights of the edges that compose it. A minimum spanning tree is then an extension tree with a weight less than or equal to each of the other possible spanning trees. Generalizing more, any non-directional graph (not necessarily connected) has a minimal forest of trees, which is a union of minimal extension trees of each of its related components.
The trace of a square matrix A is the sum of the diagonal entries in A and is denoted by tr A. It can be verified that tr(FG)equalstr(GF) for any two n times n matrices F and G. Show that if A and B are similar, then tr Upper A equals tr Upper B.
Answer with Step-by-step explanation:
We are given that tr(FG)=tr(GF) for any two matrix of order [tex]n\times n[/tex]
We have to show that if A and B are similar then
tr upper A=tr upper B
Trace of a square matrix A is the sum of diagonal entries in A and denoted by tr A
We are given that A and B are similar matrix then there exist a inverse matrix P such that
Then [tex]B=P^{-1}AP[/tex]
Let [tex] G=P^{-1} [/tex] and F=AP
Then[tex] FG= APP^{-1}[/tex]=A
GF=[tex]P^{-1}AP=B[/tex]
We are given that tr(FG)=tr(GF)
Therefore, tr upper A=trB
Hence, proved
Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. Your calculator answer would be 11.76 cm2. Now suppose you are asked to enter the answer to two significant figures. (Note that if you do not round your answer to two significant figures, your answer will fall outside of the grading tolerance and be graded as incorrect
Answer:
12 cm²
Step-by-step explanation:
Length of rectangle = 5.6 cm
Width of rectangle = 2.1 cm
Area of rectangle = Length of rectangle×Width of rectangle
⇒Area of rectangle = 5.6×2.1
⇒Area of rectangle = 11.76 cm²
11.76 has 4 significant figures in order to write this term in 2 significant terms we round of the term
The last digit in the decimal place is 6. Now, 6≥5 so we round the next digit to 8 we get
11.8
Now the last digit in the decimal place is 8. Now, 8≥5 so we round the next digit to 2 we get
12
∴ Hence the area of the rectangle when rounded to 2 significant figures is 12 cm²
find the value of solid cylinder figure not including cut out: cylinder is 9.7 ft in height, 7 feet in base length, with 4 ft hole cut out.
Answer:
251.28 cubic feet
Step-by-step explanation:
The height of the cylinder is 9.7 ft.
The base length is 7 feet. So, the radius(R) = [tex]\frac{7}{2} = 3.5 feet[/tex]
The length of 4 feet cylinder cut out. So, the radius of the cut cylinder (r) = [tex]\frac{4}{2} = 2 feet[/tex]
We have to find the volume of solid cylinder figure without cutting part.
= Volume of the whole cylinder - Volume of the hole cut
We know that volume of a cylinder is [tex]\pi *r^2*h[/tex]
Using this formula,
= [tex]\pi *R^2*h - \pi *r^2*h[/tex]
= [tex]\pi h [R^2 - r^2][/tex]
Here π = 3.14, R = 3.5, r = 2 and h = 9.7
Plug in these values in the above, we get
= [tex]3.14*9.7 [3.5^2 - 2^2]\\= 30.458[12.25 - 4]\\= 30.458[8.25]\\= 251.2785 ft^3[/tex]
When round of to the nearest hundredths place, we get
So, the volume of solid cylinder figure not including cut out= 251.28 cubic feet
1. A 20 kg object is thrown with an initial upward velocity of 2 m/s. If air resists motion of the object by 4 N for each m/s, what is the terminal velocity of this object? (Hint: use the model developed in Day 10 Lecture notes)
Answer:
49 m/s
Step-by-step explanation:
We don't know what your model is, so we'll solve this based on the balance of forces. Air resistance exerts an upward force of ...
(4 N/(m/s))v
Gravity exerts a downward force of ...
(20 kg)(9.8 m/s²) = 196 N
These are balanced (no net acceleration) when ...
(4 N/(m/s))v = 196 N
v = (196 N)/(4 N/(m/s)) = 49 m/s
The terminal velocity is expected to be 49 m/s.
The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts (a) and (b) below. Actress left parenthesis years right parenthesis 27 29 32 27 37 28 26 45 28 36 Actor left parenthesis years right parenthesis 62 37 38 37 30 36 48 41 39 42 a. Use the sample data with a 0.05 significance level to test the claim that for the population of ages of Best Actresses and Best Actors, the differences have a mean less than 0 (indicating that the Best Actresses are generally younger than Best Actors). In this example, mu Subscript d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the actress's age minus the actor's age. What are the null and alternative hypotheses for the hypothesis test?
Final answer:
The null hypothesis (H₀) for the test is μₖ = 0, meaning on average there is no age difference between Best Actresses and Best Actors, while the alternative hypothesis (Hᴏ) is μₖ < 0, suggesting that Best Actresses are, on average, younger than Best Actors.
Explanation:
To test the claim that the population of ages of Best Actresses is generally younger than Best Actors, we can set up the following null and alternative hypotheses:
The null hypothesis (H₀): μₖ = 0, which states that there is no difference in the mean age between Best Actresses and Best Actors.The alternative hypothesis (Hᴏ): μₖ < 0, which suggests that the mean age of Best Actresses is less than that of Best Actors, indicating that on average, Best Actresses are younger when they win the award.To conduct this hypothesis test at a 0.05 significance level, we calculate the differences (actress's age - actor's age) for each paired set of data and examine whether the mean difference is significantly less than 0 using the appropriate statistical methods (such as a t-test, if assumptions are met).
Final answer:
The null hypothesis (H0) is that there is no difference in mean age (mu Subscript d) between Best Actresses and Best Actors, represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that actresses are younger on average, represented as Ha: mu Subscript d < 0. A t-test at the 0.05 significance level is used to test these hypotheses.
Explanation:
To test the claim that the population of ages of Best Actresses and Best Actors have a mean difference of ages less than 0, we need to set up null and alternative hypotheses for a hypothesis test. The null hypothesis (H0) will claim that there is no difference in the mean age (mu Subscript d) between actresses and actors, which is mathematically represented as H0: mu Subscript d = 0. The alternative hypothesis (Ha) claims that the mean age of actresses is less than that of actors, which is represented as Ha: mu Subscript d < 0.
To conduct the hypothesis test, we compare the actual mean differences we calculate from the sample with the null hypothesis using a t-test at a 0.05 significance level. If our test statistic falls within the critical region, we will reject the null hypothesis in favor of the alternative hypothesis, suggesting that actresses, on average, are younger than actors when they win the awards.