Given,A school janitor has mopped 1/3 of a classroom in 5 minutes.We have to find the rate at which he is mopping.Using the concept of unitary method,Rate of mopping 1 classroom in 5 × 3 = 15 minutes= 1/15 of a classroom in 1 minute.Rate of mopping 1/3 classroom in 5 minutes = (1/3) ÷ 5= 1/15 classroom per minuteHence, the required rate at which he is mopping is 1/15 classroom per minute.
Answer: 1/15.
To determine the rate at which the janitor is mopping, we can calculate the fraction of the classroom mopped per minute.
Given that the janitor mopped 1/3 of the classroom in 5 minutes, we can express this as:
(1/3) classroom / 5 minutes
To simplify this fraction, we divide the numerator and denominator by the greatest common divisor, which is 1:
(1/3) classroom / (5/1) minutes = (1/3) classroom × (1/5) minutes
Multiplying the numerators and the denominators gives us:
1 classroom × 1 minute / 3 × 5
Simplifying further:
1 classroom × 1 minute / 15
Therefore, the rate at which the janitor is mopping is 1/15 classrooms per minute.
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The given information is that the janitor mopped 1/3 of a classroom in 5 minutes. We have to find out at what rate is he mopping.
The rate of mopping is 1/15 classrooms per minute.
Let's try to solve the problem below. The given fraction is 1/3 of a classroom that was mopped in 5 minutes. We need to find the rate of mopping which can be calculated by dividing the fraction of the classroom mopped by the time it took to mop it. The rate of mopping can be found by performing the following calculation:
Rate of mopping = Fraction of the classroom mopped/Time taken to mop
= 1/3/5
= 1/15
So the rate of mopping is 1/15 classrooms per minute. This is the simplified answer.
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Answer number two please please
Answer: 11
Step-by-step explanation:
Sooooo all I did was take the formula for the area of a triangle ( A= 1/2(b)(h) 0 and plug In the values. So 'b' would be 4 and 'h' would be 5.5. I assumed this rectangle had equal widths and equal heights.
Select the correct answer.
Which value in this data set is an outlier?
4,5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9,7
O A. 1
OB.
N
O C.
3
D. 9
Answer:
answer is 1
Step-by-step explanation:
Which scientist discovered DNA after experimenting with white blood cells?
What are the building blocks of proteins?
amino acids
ribosomes
tRNA molecules
chromosomes
What level of measurement is used in the operationalization of extracurricular participation?
Measures Extracurricular Participation Students listed the university-based clubs they participated in during the academic year. Based on these lists, we created a variable reflecting whether they were involved in at least one activity (37% were involved). Of the activities listed, 28% were sports/ recreation (i.e., intercollegiate athletics, club sports, intramural sports, or campus recreation), 18% fraternities/sororities, 15% cultural, 13% departmental/professional, 9% campus programs, 8% special interest, 7% service, and 3% religious.
The level of measurement used in the operationalization of extracurricular participation is categorical/nominal.
In the operationalization of extracurricular participation, the measurement of students' involvement in university-based clubs is done using categorical/nominal level of measurement.
This is evident from the variable created to reflect whether students were involved in at least one activity, indicating a binary (yes/no) response. The subsequent breakdown of the activities listed into different categories, such as sports/recreation, fraternities/sororities, cultural, departmental/professional, campus programs, special interest, service, and religious, further supports the use of categorical measurement.
Each activity falls into a distinct category, and the percentages represent the proportions of students engaged in each category. Categorical/nominal measurement allows for classifying and organizing data into mutually exclusive categories, without any inherent order or numerical value associated with the category.
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1. What type of angle am I?m<1=91 degrees, m<2=89 degrees
Complementary
supplementary
Other:
Answer:
Step-by-step explanation:
If they are added, they are supplementary. If anything else is done to them, there is no answer.
89 + 91 = 180 Supplementary angles add to 180.
At an electronics store, DVDs are on sale. Some DVDs cost $15.00 each and some cost $12.00 each. Bart purchased 8 DVDs and spent a total
of $105.00. Write a system of equations and solve by using substitution to determine how many $12.00 DVDs Bart purchased.
$105
15*3=45
12*5=60
60+45=105
(12*5)+(15*3)=105
Can i get brainliest
The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
At a hardware store, DVDs are at a bargain. A few DVDs cost $15.00 each and some expenses $12.00 each. Bart bought 8 DVDs and spent a sum of $105.00.
Let 'x' be the number of $15 DVDs and 'y' be the number of $12 DVDs. Then the equations are given as,
x + y = 8 ...1
15x + 12y = 105 ...2
From equations 1 and 2, then we have
15x + 12(8 - x) = 105
15x + 96 - 12x = 105
3x = 9
x = 3
Then the value of y is given as,
y = 8 - 3
y = 5
The number of $15 DVDs and $12 DVDs at an electronics store will be 3 and 5, respectively.
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what are all possible values for x in the equation x^3=375?
Answer:
Select all possible values for x in the equation.
x cubed=375.
5*the cubed root of 3
the cubed root of 375
75*the cubed root of 5
125*the cubed root of 3
I am trying to do a practice test to prepare for my real test tomorrow and I don't understand the question. Can anyone help explain it plz any help would be great.
Step-by-step explanation:
Ops gets $140 per day and laborers get $100 per day. If 35 people were hired and payroll was $4820, how many ops were employed and how many laborers?
Answer:
2 laborers and 33 ops
Step-by-step explanation:
Given
Let:
L = Laborers
P = Ops
From the statements, we have:
[tex]L + P = 35[/tex] -- total people hired; and
[tex]140P + 100L = 4820[/tex] ---number of hirees
Required
Solve for L and P
Make L the subject in: [tex]L + P = 35[/tex]
[tex]L = 35 - P[/tex]
Substitute [tex]L = 35 - P[/tex] in [tex]140P + 100L = 4820[/tex]
[tex]140P + 100(35 - P) = 4820[/tex]
[tex]140P + 3500 - 100P = 4820[/tex]
Collect like terms
[tex]140P - 100P = 4820 - 3500[/tex]
[tex]40P = 1320[/tex]
Solve for P
[tex]P = 1320/40[/tex]
[tex]P = 33[/tex]
Substitute [tex]P = 33[/tex] in [tex]L = 35 - P[/tex]
[tex]L = 35 - 33[/tex]
[tex]L = 2[/tex]
Without using technical terms, state a final conclusion that addresses the original claim. Which of the following is the correct conclusion? A. The mean pulse rate (in beats per minute) of the group of adult males is bpm. B. The mean pulse rate (in beats per minute) of the group of adult males is not bpm. C. There sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is bpm. D. There sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is bpm.
Answer:
D. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate (in beats per minute) of the group of adult males is 69bpm.
Step-by-step explanation:
Hypothesis testing is used in statistics to confirm the validity of a statement or observation. Null hypothesis is the original observation for which the test is being conducted. Alternative hypothesis is set against the null hypothesis to reach a conclusion whether to accept or reject the null hypothesis. In the given scenario there is sufficient evidence to reject the null hypothesis.
Point P is located at (−2, 7), and point R is located at (1, 0). Find the y value for the point Q that is located two thirds the distance from point P to point R.
4.9
4.7
2.5
2.3
PLS HELP
Answer:
Step-by-step explanation:
2.3
I asked this question several times and not one person had helped me. Please im begging you. This is due today. Please answer all the questions and show your work! I will mark brainliest
Answer: a = 2^12 b= 2^12 c=2^20
d= 2^12 e= 2^64 f= 2^12 g= 2^22 h= 2^40
Step-by-step explanation:
Consider the following sentence and scheme of abbreviation: Only lunatics drive on the autobahn. Lx: x is a lunatic Dx: x drives on the autobahn Which of the following would be accurate translations of the above sentence into the language of PL? a. (x)(DxLx) b. (Ex)(DxLx) C. (x)(LxDx) d. (Ex)(LxDx)
Option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.
The accurate translation of the sentence "Only lunatics drive on the autobahn" into the language of PL (Propositional Logic) can be represented as:
b. (Ex)(DxLx)
Let's break down the translation scheme:
Lx: x is a lunatic (Lunatics)
Dx: x drives on the autobahn (Drive on the autobahn)
The sentence states "Only lunatics drive on the autobahn," which implies that there are some individuals who drive on the autobahn and they are lunatics. This can be expressed using existential quantification (Ex) to indicate that there exists at least one individual who satisfies the condition. Therefore, option b. (Ex)(DxLx) accurately translates the given sentence.
Option a. (x)(DxLx) would mean "For all x, x drives on the autobahn implies x is a lunatic." This does not capture the meaning of the original sentence because it suggests that everyone who drives on the autobahn is a lunatic, which is not what the sentence implies.
Option c. (x)(LxDx) would mean "For all x, x is a lunatic implies x drives on the autobahn." Again, this does not capture the intended meaning of the original sentence as it suggests that all lunatics drive on the autobahn.
Option d. (Ex)(LxDx) would mean "There exists an x such that x is a lunatic and x drives on the autobahn." This translation does not capture the sense of the original sentence, which states that only lunatics drive on the autobahn, not that there exists at least one lunatic who drives on the autobahn.
Therefore, option b. (Ex)(DxLx) is the accurate translation of the given sentence into the language of PL.
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A beam of light in air strikes a slab of crown glass (n = 1.52) and is partially reflected and partially refracted. Find the angle of incidence if the angle of reflection is twice the angle of refraction.
The angle of incidence for a beam of light in air striking a slab of crown glass, where the angle of reflection is twice the angle of refraction, can be determined using the laws of reflection and refraction. The angle of incidence is approximately 39.2 degrees.
we can apply the laws of reflection and refraction to find the relationship between the angles. Let's denote the angle of incidence as θ, the angle of reflection as θ_r, and the angle of refraction as θ_t.
According to the law of reflection, the angle of reflection is equal to the angle of incidence: θ_r = θ.
According to Snell's law of refraction, the relationship between the angles of incidence and refraction is given by: n_1 × sin(θ) = n_2 × sin(θ_t), where n_1 and n_2 are the refractive indices of the two media.
In this case, the light travels from air (with a refractive index of approximately 1) to crown glass (with a refractive index of 1.52). Substituting the values, we have: sin(θ) = (1.52 / 1) × sin(θ_t).
Since the angle of reflection is twice the angle of refraction, we can write: θ = 2θ_t.
Substituting this relation into the previous equation, we get: sin(2θ_t) = (1.52 / 1) × sin(θ_t).
Using the double-angle trigonometric identity, sin(2θ_t) = 2sin(θ_t)cos(θ_t), we have: 2sin(θ_t)cos(θ_t) = 1.52sin(θ_t).
Dividing both sides by sin(θ_t), we obtain: 2cos(θ_t) = 1.52.
Solving for cos(θ_t), we have: cos(θ_t) = 1.52 / 2.
Taking the inverse cosine, we find: θ_t = cos^(-1)(1.52 / 2) ≈ 26.8 degrees.
Finally, substituting this value into θ = 2θ_t, we get: θ ≈ 2 × 26.8 degrees ≈ 53.6 degrees.
Hence, the angle of incidence is approximately 39.2 degrees.
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HELPPPPPPPPPP :(
If there are two doors, each 36 inches wide.
Door A opened to 86° angle. Door B opened to 82°
which door's outer edge is farther from its closed position? and please explain it ♡
Answer:
B its B
Step-by-step explanation:
You have 35 plants. You want to split them equally between 4 sections of your garden. You use as many as you can in each section. How many plants do you have left?
answer:
3 plants are left !
step-by-step explanation:
hi there!
first lets use our times table to see which number gets use closest to 35 when it is multiplied by 4
4, 8, 12, 16, 20, 24, 28, 32,
4 * 8
= 32
then you can just subtract 35 by 32 to get you final answer of
35 - 32
= 3 plants are left over
( i hope i did the problem right since the wording of it was kinda hard to understand it )
________________________________________________________
| | | | |
| 1 | 2 | 3 | 4 |
| | | | |
________________________________________________________
| | | | |
| 5 | 6 | 7 | 8 |
| | | | |
________________________________________________________
| | | | |
| 9 | 10 | 11 | 12 |
| | | | |
________________________________________________________
| | | | |
| 13 | 14 | 15 | 16 |
| | | | |
________________________________________________________
| | | | |
| 17 | 18 | 19 | 20 |
| | | | |
________________________________________________________
| | | | |
| 21 | 22 | 23 | 24 |
| | | | |
________________________________________________________
| | | | |
| 25 | 26 | 27 | 28 |
| | | | |
________________________________________________________
| | | | |
| 29 | 30 | 31 | 32 |
| | | | |
________________________________________________________
i made a table with each number being the plant! just in case your a visual learner like me!
but i hope this help you and if i made anything confusing or if i made a mistake please let me know! but other then that i hope you have a good rest of your day :)
There are 3 plants left.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
Total number of plants = 35
And, You want to split them equally between 4 sections of your garden.
Now,
To find the left plants after splitting into 4 sections, we can divide and find the remainder as;
The number of left plants = 35 ÷ 4
4 ) 35 ( 8
- 32
-------
3
Clearly, The remainder = 3
Thus, There are 3 plants left.
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What is the probability of 3 people sharing the same birthdays? How many different pairs of people are there when there are three humans? (Think nPr or nCr)
The probability of three people sharing the same birthdays is approximately [tex]0.0000075[/tex] or [tex]0.00075[/tex]%, and there are three different pairs of people when there are three humans.
The probability of three people sharing the same birthday depends on the assumptions made about the distribution of birthdays. Assuming that birthdays are uniformly distributed throughout the year and that leap years are not considered, there are [tex]365[/tex] possible birthdays for each person. The first person can have any birthday, and the probability that the second person shares the same birthday is [tex]$\frac{1}{365}$[/tex]. Similarly, the probability that the third person shares the same birthday as the first two is also [tex]$\frac{1}{365}$[/tex]. Multiplying these probabilities together, we get [tex]$\left(\frac{1}{365}\right) \times \left(\frac{1}{365}\right) = \frac{1}{133,225}$[/tex], approximately [tex]0.0000075[/tex] or [tex]0.00075\%[/tex].When there are three humans, the number of different pairs of people can be calculated using the combination formula, also known as [tex]$\binom{n}{r}$[/tex]. In this case, [tex]$n$[/tex] represents the total number of people ([tex]3[/tex]), and [tex]$r$[/tex] represents the number of people chosen at a time ([tex]2[/tex] for pairs). Applying the formula, we have [tex]$\binom{3}{2} = 3$[/tex]. Therefore, there are three different pairs of people when there are three humans: ([tex]1,2[/tex]), ([tex]1,3[/tex]), and ([tex]2,3[/tex]).In conclusion, the probability of three people sharing the same birthdays is extremely low (approximately [tex]0.0000075 \ or \ 0.00075\%[/tex]), and when there are three humans, there exist three different pairs of people.
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What is the area of the triangle in square yards?
Answer:
DON'T LOOK AT THE PICTURE!!
Step-by-step explanation:
Find the measure of C to the nearest tenth of a degree
i need help with this i will mark you as brainliest
Answer:
The answer is 7 (A)
Step-by-step explanation:
Answer:
D. The length is the same as line MN.
Step-by-step explanation:
Even if the line is moved any one bit, the length of the line will not change. So as a result, A, B & C are already out. That leaves D as our answer.
3. Michael surveyed a random sample of students in his school about
the number of sports they play. There are 300 students in Michael's
school. Use the results of the survey to estimate the number of
students in Michael's school who play exactly one sport. Explain
your answer. PLEASE HELP ILL ALSO MARK IT THE MOST BRAINLY ANSWER I didn’t spell that right but oh well
Answer:
Micheal surveyed 60 students.
Answer: Look at the explanation please.
Step-by-step explanation:
Please note that I am using what is in the Mathematics textbook.
So we need to know for the students who play Exactly 1 sport.
So you have to make an equation. It will look like this...
15/60 = x/300
Note that we get the 15 from the table of the number of students. We get 60 from adding 13+15+32 which is all the students Michael has surveyed. Lastly we get 300 from the question There are 300 students in his school.
x = 75 when you do the math. Cross multiply and divide.
Hope this helps :)
2. A (simplified representation of) the 2019 British parliament was as a weighted voting system (326 : 316, 259, 35, 12, 12, 10,6). The Conservative party had 316 votes, the Labour party had 259 votes
a) the Shapley-Shubik Index of the Conservative party is 3360/5040.
b) the Shapley-Shubik Index of the Labour party is 82.142
To calculate the Shapley-Shubik index for a party in a weighted voting system, we need to consider all possible orderings of the parties and determine the party's contribution to the winning coalition in each ordering. The Shapley-Shubik index represents the average contribution across all possible orderings.
(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation:
To calculate the Shapley-Shubik Index of the Conservative party, we consider all possible orderings of the parties and determine the Conservative party's contribution to the winning coalition in each ordering.
The total number of possible orderings of the parties is given by the factorial of the total number of parties: 7! = 5040.
In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Conservative party, with 316 votes, does not reach the threshold alone.
However, if we consider the cumulative votes of the Conservative party and the Labour party (316 + 259 = 575), we reach the winning threshold. Therefore, the Conservative party's contribution to the winning coalition is 575 votes.
Since there are 6 other parties, we need to distribute the remaining votes among them. We can do this in 6! = 720 different ways.
The Shapley-Shubik Index is calculated by summing the contributions of the Conservative party across all possible orderings and dividing by the total number of orderings:
Shapley-Shubik Index of the Conservative party = (575 * 720) / 5040 = 3360 / 5040
Therefore, the Shapley-Shubik Index of the Conservative party is 3360/5040.
(b) To compute the Shapley-Shubik Index of the Labour party, we follow a similar approach:
The Labour party has 259 votes. We consider all possible orderings of the parties and determine the Labour party's contribution to the winning coalition in each ordering.
In each ordering, we examine the cumulative votes of the parties in the order until the winning threshold of 326 votes is reached. The Labour party alone does not reach the threshold.
However, if we consider the cumulative votes of the Labour party and the Conservative party (259 + 316 = 575), we reach the winning threshold. Therefore, the Labour party's contribution to the winning coalition is 575 votes.
Similar to the previous calculation, we distribute the remaining votes among the 6 other parties in 6! = 720 different ways.
The Shapley-Shubik Index of the Labour party is calculated by summing the contributions of the Labour party across all possible orderings and dividing by the total number of orderings:
Shapley-Shubik Index of the Labour party = (575 * 720) / 5040
= 82.142
Therefore, the Shapley-Shubik Index of the Labour party is 82.142.
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Given question is incomplete, the complete question is below
A (simplified representation of) the 2019 British parliament was as a weighted voting system [326 : 316,259,35,12,12,10,6]. The Conservative party had 316 votes, the Labour party had 259 votes, and various other parties had the remaining votes.
(a) The Shapley-Shubik Index of the Conservative party is 3360/5040. Justify this calculation.
(b) Compute the Shapley-Shubik Index of the Labour party.
Consider the quadratic equation x2+8x+9=0. Which of the following is the correct form after substituting a, b, and c into the Quadratic Formula?
Answer:
x²+8x+9=0
Comparing above equation with ax²+bx +c
we get
a=1
b=8
c=9
quadratic equation is
[tex]x = \frac{ - 8± \sqrt{ {8}^{2} - 4×1×9} }{2*1} [/tex]
[tex]x = \frac{ -8± \sqrt{ 64-36} }{2} [/tex]
2x+8=±[tex] \sqrt{ {28}}[/tex]
taking + ve
2x=[tex] \sqrt{ {28}}[/tex]-8
x=[tex] 2\sqrt{ {7}}[/tex]-8/2
x=[tex] \sqrt{ {7}}[/tex]-4
taking -ve
2x=-[tex] \sqrt{ {28}}[/tex]-8
x=-[tex] 2\sqrt{ {7}}[/tex]-8/2
x=-[tex] \sqrt{ {7}}[/tex]-4
As given
x²+8x+9=0General equation
Ax²+Bx+COn comparing
A=1B=8C=9[5 points) At a certain rate of compound interest 100 will increase to 200 in x years, 200 will increase to 300 in years, and 300 will increase to 1,500 in z years. If 600 will increase to 1,000 in n years, find an expression for n in terms of x, y, and z.
At a certain compound interest rate, the amount of 100 will increase to 200 in x years, 200 will increase to 300 in y years, and 300 will increase to 1,500 in z years. We need to find an expression for n, the number of years it takes for 600 to increase to 1,000.
The given information implies that the ratio of the final amount to the initial amount after a certain number of years is constant. We can express this ratio as follows:
(200 / 100) = (300 / 200) = (1500 / 300)
Simplifying this equation, we get:
2 = 3/2 = 5
Now, let's calculate the value of n. We know that 600 will increase to 1,000 in n years. We can set up a ratio using the same constant ratio calculated above:
(1000 / 600) = (300 / 200)
Simplifying the equation, we have:
5/3 = 3/2
Cross-multiplying, we get:
(5 * 2) = (3 * 3)
10 = 9
Since the equation is not valid, it means there is no value of n that satisfies the given conditions. Therefore, we cannot express n in terms of x, y, and z.
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Daily question: what is 5 to the 3rd power?
Answer:
125
Step-by-step explanation:
5 to the 3rd power means 5³
5³ = 5x5x5
= 125
10. Use the diagram below to find the value of x.
Answer:
x=20
Step-by-step explanation:
Hello There!
Remember the exterior angle of a triangle rule:
An exterior angle of a triangle is equal to the sum of the opposite interior angles
Knowing this, we can create an equation to solve for x
exterior angle (100) = sum of opposite interior angles (3x+2x)
100 = 2x+3x
now we solve for x
step 1 combine like terms
2x+3x=5x
now we have 100=5x
step 2 divide each side by 5
5x/5=x
100/5=20
we're left with x = 20
Answer:
With their steel hoofs, their long legs, their stag-like muscles, their thick skins, their powerful horns, they could walk the roughest ground, cross the widest deserts, climb the highest mountains, swim the widest rivers, fight off the fiercest bands of wolves, endure hunger, cold, thirst and punishment as few beasts of the earth have ever shown themselves capable of enduring.
What is the value of f?
[tex]f+44^{\circ}[/tex] and [tex]71^{\circ}[/tex] are opposite angles.
Therefore
[tex]f+44^{\circ}=71^{\circ}\\f=27^{\circ}[/tex]
27°
Step-by-step explanation:Using information about angles, we can create an equation to solve for f.
Verticle Angles
There is a special angle relationship known as vertical angles. Vertical angles are opposite angles made by interesting lines. The left angle (made up of f and 44°) and the right angle (71°) are vertical angles. We know this because they are opposite each other and formed by the same interesting lines. Verticle angles are always congruent. This means that their measurements are equal.
Solving for f
We can use the information above to create an equation. Since we know that the left and right angles are congruent, we can set the equal to each other.
f + 44 = 71Now, we can subtract 44 from both sides and solve for f.
f = 27So, angle f must equal 27°.
16. Suppose that 7₁, 72 are linear dependent in a vector space V. Show that V₁ + V2, V₂ - V₁ are also linearly dependent.
By supposing that 7₁, 72 are linearly dependent in a vector space V. The coefficient of 7₁ is 1 and the coefficient of 72 is 0, while in the second linear combination, the coefficient of 7₁ is 0 and the coefficient of 72 is 1. Therefore, we can conclude that V₁ + V2, V₂ - V₁ is also linearly dependent.
To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we will begin by using the given linear combination of vectors to determine whether they are linearly dependent or independent. Suppose that 7₁, and 72 are linearly dependent in a vector space V.
Let us recall that a set of vectors is linearly dependent if it can be represented as a linear combination of other vectors in the vector space. This implies that if 7₁, 72 are linearly dependent, then there exist scalars α and β, not all zero, such that α7₁ + β72 = 0. To show that V₁ + V2, V₂ - V₁ is also linearly dependent, we need to use the definitions of vector addition and subtraction to writing each of these vectors as a linear combination of 7₁ and 72. Let's begin with V₁ + V2.
Using the definition of vector addition, we have
V₁ + V2 = 1 · 7₁ + 1 · 72 = 7₁ + 72.
Similarly, using the definition of vector subtraction, we have
V₂ - V₁ = -1 · 7₁ + 1 · 72 = -7₁ + 72.
Now we can write V₁ + V2, V₂ - V₁ as linear combinations of 7₁ and 72:
V₁ + V2 = 1 · (7₁ + 72) + 0 · (-7₁ + 72)V₂ - V₁
= 0 · (7₁ + 72) + 1 · (-7₁ + 72)
Notice that the coefficients in each linear combination are not all zero. We can say that V₁ + V2, V₂ - V₁ is linearly dependent.
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The base angles of an
isosceles triangle
Measure (2x+40)° and
(5x+16)". find x and the
Measure of both angles.
Answer:
71
93.5
x=15.5
Step-by-step explanation:
(2x+40)+(5x+16)+(x)=180
you have to put all the measures together and equal it to 180. when it comes to triangles, all the angles added together are equal to 180.
now solve the equation and you should get this:
x=15.5
the next step is to solve the give equations separately:
2(15.5)+40=71
5(15.5)+16=93.5
(15.5)=15.5
now to check the work, you have to add all the measures that were just calculated:
71+93.5+15.5=180 so check!
The Internal Revenue Service estimates that 8% of all taxpayers filling out forms make mistakes.
An IRS employee randomly selects and checks 10 forms for mistakes. What is the probability that exactly one has an error?
The same IRS employee announces at lunch one day that she is going to check 25 randomly selected forms after lunch.
Calculate the mean and the standard deviation of the number of forms with mistakes she should expect to find.
The IRS employee checked 25 randomly selected forms and didn't find any mistakes. Does this provide convincing evidence to cause her supervisor to believe that she is missing mistakes? Explain.
Probability of exactly one error in 10 forms: Use binomial distribution with n = 10 and p = 0.08..Mean and standard deviation of forms with mistakes: Calculate using expected value and standard deviation formulas for a binomial distribution.
To calculate the probability that exactly one form has an error out of 10 randomly selected forms, we use the binomial probability formula: P(X = k) = (n C k) * p^k * (1-p)^(n-k), where n is the number of trials, p is the probability of success, and k is the number of successes. In this case, n = 10, p = 0.08, and k = 1. Plugging in these values, we can calculate the probability as P(X = 1) = (10 C 1) * (0.08)^1 * (1-0.08)^(10-1).
The mean (expected value) of the number of forms with mistakes can be calculated as μ = n * p, where n is the number of trials and p is the probability of success. In this case, n = 25 and p = 0.08. The standard deviation can be calculated as σ = sqrt(n * p * (1-p)), where sqrt represents the square root. Plugging in the values, we can calculate the mean and standard deviation.
Finding no mistakes in 25 randomly selected forms does not provide strong evidence to conclude that the employee is missing mistakes. The probability of not finding any mistakes in 25 forms can be calculated using the binomial distribution with parameters n = 25 and p = 0.08. If the actual proportion of mistakes is 8%, it is possible to observe a sample without mistakes due to random chance. To draw a more reliable conclusion, a larger sample size or additional evidence would be needed.
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Calculate the following limits using the limit laws and limx→2f(x)=−3, limx→2g(x)=4, limx→2h(x)=7 (a) limx→2(f(x)−2g(x))= (b) limx→2(h(x)2)= (c) limx→2h(x)⋅g(x)f(x)=
The value of limits after using limit laws is [tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]
What are Limit Laws?
Limit laws, also known as limit properties or limit theorems, are a set of rules and principles that allow us to simplify and evaluate limits of functions. These laws provide a systematic approach to finding the limit of a more complex expression by breaking it down into simpler parts.
Given:
[tex]\lim_{x \to 2} f(x) &= -3 \\\lim_{x \to 2} g(x) &= 4 \\\lim_{x \to 2} h(x) &= 7\end{align*}\textbf{(a) Calculate} $\lim_{x \to 2} (f(x) - 2g(x))$:[/tex]
Using the limit laws, we can split the expression and apply the limit laws individually:
[tex]\lim_{x \to 2} (f(x) - 2g(x)) &= \lim_{x \to 2} f(x) - \lim_{x \to 2} (2g(x)) \\&= \lim_{x \to 2} f(x) - 2 \lim_{x \to 2} g(x) \\&= (-3) - 2(4) \\&= -3 - 8 \\&= -11[/tex]
Therefore,[tex]$\lim_{x \to 2} (f(x) - 2g(x)) = -11$.[/tex]
[tex]\textbf{(b) Calculate} $\lim_{x \to 2} (h(x))^2$:[/tex]
Again, using the limit laws, we can apply the limit to the expression:
[tex]\lim_{x \to 2} (h(x))^2 &= \left(\lim_{x \to 2} h(x)\right)^2 \\&= (7)^2 \\&= 49[/tex]
Therefore,
[tex]\lim_{x \to 2} (h(x))^2 = 49$.\textbf{\\\\(c) Calculate} $\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)}$:[/tex]
Applying the limit laws, we can evaluate the limit as follows:
[tex]\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} &= \frac{\lim_{x \to 2} h(x) \cdot \lim_{x \to 2} g(x)}{\lim_{x \to 2} f(x)} \\\\&= \frac{7 \cdot 4}{-3}\\ \\&= \frac{28}{-3}[/tex]
Therefore,[tex]$\lim_{x \to 2} \frac{h(x) \cdot g(x)}{f(x)} = -\frac{28}{3}$.[/tex]
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