The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.
To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:
a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]
If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.
Let's form a matrix with these vectors as columns:
|-5 2 -17|
| 4 -1 16|
| 5 5 45|
Now, we can row reduce this matrix to its reduced row echelon form (RREF):
| 1 -2 5|
| 0 1 -3|
| 0 0 0|
From the RREF, we can write the system of linear equations:
x - 2y + 5z = 0
y - 3z = 0
Solving this system, we get:
y = 3z
x = 2y - 5z = 6z - 5z = z
Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.
Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.
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in how many ways can people sit around a round table if pierre and thomas want to sit together, but rosa doesn't want to sit next to either of them? (treat rotations as not distinct but reflections as distinct.)
There are 72 ways for people to sit around a round table if Pierre and Thomas want to sit together, but Rosa doesn't want to sit next to either of them.
First, we can seat Pierre and Thomas next to each other as a block. There are 2 ways to arrange them (PT or TP).
Next, we can seat Rosa in one of the 6 available seats that are not next to the block. There are 6 ways to do this.
Then, we can seat the remaining 4 people in the 4 available seats. There are 4! ways to do this.
Finally, we need to account for the fact that rotations are not distinct but reflections are distinct. Since there are 8 people seated around the table, there are 8 possible rotations. However, if we reflect the table (i.e., flip it over), we get a different seating arrangement. Therefore, there are 16 distinct arrangements.
Putting it all together, we have:
2 (arrangements for Pierre and Thomas) x 6 (arrangements for Rosa) x 4! (arrangements for the remaining 4 people) x 16 (accounting for distinct reflections) = 72
Therefore, there are 72 ways for people to sit around a round table if Pierre and Thomas want to sit together, but Rosa doesn't want to sit next to either of them.
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Use the order of operations to simplify the statement (-+) × (-8) + (-3)³. Show all your work please help me!!
Answer:
Step-by-step explanation:
(-+) × (-8) + (-3)³=32
Find the sum of \sqrt{25}
25
and 4\sqrt{2}4
2
in simplest form. Also, determine whether the result is rational or irrational and explain your answer.
Answer:
The answer to your problem is:
The sum of those given numbers in the simplest form is written as 11
The result is rational.
Difference between irrational and rational:
Irrational: Those numbers that cannot be written as a ratio of integers.
Rational: Those numbers that can be written as a ratio of integers.
[tex]\sqrt[]{4} = \sqrt{2^{2} } = 2[/tex] ( We know that )
[tex]3\sqrt{9} = 3 * \sqrt{3^{2} } = 3*3 = 9[/tex] ( Ok )
Thus: \/
[tex]\sqrt[]{4} + 3\sqrt{9} = 2+9 = 11[/tex]
Thus, the answer to your problem is,
The sum of those given numbers in the simplest form is written as 11
The result is rational.
two americans, two canadians, two mexicans, and two jamaicans are seated around a round table. in how many ways can all eight people be seated such that at least two pairs of people from the same country are seated together?
There are 4320 ways in which at least two pairs of people from the same country are seated together.
This is question of 'permutation and combination'.
The total number of ways in which all 8 people can be seated
= (8-1)! = 7! = 5040
Let's calculate the number of ways in which no two people from the same country are seated together.
First, we will fix the position of one of the Americans (let's call him A1) in the first seat. We can do this in one way.
In the next seat, we can seat any one of the six remaining people (2nd American, 1st Canadian, 2nd Canadian, 1st Mexican, 2nd Mexican, or 1st Jamaican).
Let's say we seat the 1st Canadian in the second seat. We can do this in six ways. The seventh seat can be occupied by the remaining person. We can do this in one way.So, the number of ways in which no two people from the same country are seated together is
6! = 720.
Now, let's calculate the number of ways in which at least two pairs of people from the same country are seated together.We can do this by finding the total number of ways in which all eight people can be seated and then subtracting the number of ways in which no two people from the same country are seated together.
So, the number of ways in which at least two pairs of people from the same country are seated together is:
5040 - 720 = 4320.
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1-3 answers the questions
The solution of the given problem of equation comes out to be the quadratic function's expression is [tex]y = -2x² + 8x + 3[/tex]
What is an equation?Variable words are commonly used in complex algorithms to show uniformity between two incompatible claims.
Academic expressions called equations are used to show the equality of various academic numbers. Instead of a unique formula that splits 12 into two parts and can be used to analyse data received from [tex]y + 7[/tex] , normalization in this case yields b + 7.
Here,
A quadratic function's curve is shown in the provided illustration. The quadratic function's expression is
=> [tex]y = -2x² + 8x + 3[/tex]
We can use the knowledge that a quadratic function's standard form is
=> [tex]y = ax² + bx + c[/tex] , where a, b, and c are constants, to see this.
When y = [tex]-2x² + 8x + 3[/tex] is provided,
we can see that a = -2, b = 8, and c = 3 by comparing it to the standard form.
Therefore, the quadratic function's expression is [tex]y = -2x² + 8x + 3[/tex]
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which statistic is a measure of how data ardis prized in population and can be used to give context to large datasets
A statistic that is used to measure how data is distributed in a population is called a measure of dispersion. This statistic gives context to large datasets by providing an indication of how spread out the data is. This measure of dispersion is important because it helps to identify patterns and trends in the data.
For example, if the measure of dispersion is high, it indicates that the data is spread out and there is significant variation between data points. On the other hand, a low measure of dispersion suggests that the data is clustered together and there is little variation between data points.
This measure of dispersion is used to compare datasets, identify outliers, and make predictions about future trends. Ultimately, the measure of dispersion is an important tool for understanding the context of large datasets.
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R carries inversely as the cube S . If R=9 when S=3 , Find S when R= 243÷64.
R carries inversely as the cube S . If R=9 when S=3 , S= 4, when R= 243÷64.
Describe Inverse Proportionality?Inverse proportionality is a mathematical relationship between two variables, in which an increase in one variable leads to a decrease in the other variable in such a way that their product remains constant. In other words, if the value of one variable is multiplied by a certain factor, the value of the other variable will be divided by the same factor.
Mathematically, two variables x and y are said to be inversely proportional if their relationship can be expressed as:
x * y = k
where k is a constant, and the symbol * denotes multiplication.
For example, the distance travelled by a car is inversely proportional to the time taken to travel that distance, assuming the car maintains a constant speed. If we let d represent the distance travelled and t represent the time taken, then we can express their relationship as:
d * t = k
where k is a constant
If R varies inversely as the cube of S, then we know that:
R ∝ [tex]\frac{1}{S^{3} }[/tex]
We can express this relationship using a proportionality constant k:
R = [tex]\frac{k}{S^{3} }[/tex]
To find the value of k, we can use the given information that R = 9 when S = 3:
9 = [tex]\frac{k}{3^{3} }[/tex]
9 = [tex]\frac{k}{27 }[/tex]
k = 9 * 27
k = 243
Now we can use this value of k to find S when R = [tex]\frac{243}{64}[/tex]:
[tex]\frac{243}{64}=\frac{243}{S^{3} }[/tex]
Simplifying this equation, we get:
S³ = [tex]\frac{243*64}{243}[/tex]
S³ = 64
S = ∛64
S = 4
Therefore, when R = [tex]\frac{243}{64}[/tex], S = 4.
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a model for the world series two teams a and b play a series of games until one team wins four games. we assume that the games are played independently and that the probability that a wins any game is p. what is the probability that the series lasts exactly five games?
The probability that the series lasts exactly five games is 2p raise to the power 4(1-p).
How to find probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The higher the probability, the more likely it is that the event will occur.
To find the probability that the series lasts exactly five games, we need to consider all possible ways in which a team can win four games in five games played.
One possible scenario is that team A wins the first four games and team B wins the fifth game. The probability of this happening is:
P(A wins the first four games and B wins the fifth game) = p⁴ * (1-p)
Another possible scenario is that team B wins the first game, team A wins the next four games. The probability of this happening is:
P(B wins the first game and A wins the next four games) = p⁴* (1-p)
Therefore, the probability that the series lasts exactly five games is the sum of these two probabilities:
P(series lasts exactly five games) = p⁴* (1-p) + p⁴ * (1-p)
Simplifying the expression, we get:
P(series lasts exactly five games) = 2p⁴(1-p)
Therefore, the probability that the series lasts exactly five games is 2p⁴(1-p).
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you may need to use the appropriate technology to answer this question. management decision systems (mds) is a consulting company that specializes in the development of decision support systems. mds has a four-person team working on a current project with a small company to set up a system that scrapes data from a collection of websites and then automatically generates a report for management on a daily basis. time (weeks) activity description immediate predecessor optimistic most probable pessimistic a report generation 2 8 12 b web scraping 4 9 11 c testing a, b 1 1 1 (a) construct the project network. (submit a file with a maximum size of 1 mb.) this answer has not been graded yet. (b) based solely on the critical path, estimate the probability that the project will be complete within 11 weeks. (round your answer to four decimal places.) (c) using all paths through the project network, estimate the probability that the project will be complete within 11 weeks. (round your answer to four decimal places.) (d) should you use the estimate in (b) or (c)? the probability estimate from (b) based on the critical path is more accurate.the probability estimate from (c) based on both paths is more accurate. the probability estimates from (b) and (c) are equal.
The mean and standard deviatiοn fοr the entire prοject can be calculated by adding the means and variances οf the paths: Prοject: mean = 15.33
What is Prοbability ?Prοbability can be defined as ratiο οf number οf favοurable οutcοmes and tοtal number οutcοmes.
Tο cοnstruct the prοject netwοrk, we can use the activity-οn-nοde (AON) apprοach, where nοdes represent activities and edges represent the lοgical relatiοnships between activities.
Here, activity A represents repοrt generatiοn, activity B represents web scraping, and activity C represents testing. The numbers οn the edges indicate the time estimates (οptimistic, mοst prοbable, and pessimistic) fοr each activity. The immediate predecessοrs fοr activity B and activity C are shοwn by the vertical lines cοnnecting them tο the nοdes representing their predecessοrs.
Tο estimate the critical path, we need tο find the lοngest path thrοugh the netwοrk, which is the path that takes the mοst time tο cοmplete. In this case, the critical path is A-B-C, with a duratiοn οf 8+9+1=18 weeks.
(b) Tο estimate the prοbability that the prοject will be cοmplete within 11 weeks based sοlely οn the critical path, we can use the critical path methοd (CPM) and the nοrmal distributiοn. The mean duratiοn οf the critical path is (8+9+1)/3=6 weeks, and the standard deviatiοn is[tex][(8-2)/6+(9-2)/6+(1-2)/6]^0.5=1.15[/tex] weeks.
The prοbability that the critical path will be cοmpleted within 11 weeks can be calculated using the standard nοrmal distributiοn as fοllοws:
P(Z <= (11-6)/1.15) = P(Z <= 4.35) = 1
Therefοre, the prοbability estimate is 1 οr 100%.
(c) Tο estimate the prοbability that the prοject will be cοmplete within 11 weeks using all paths thrοugh the prοject netwοrk, we can use the prοgram evaluatiοn and review technique (PERT) and the beta distributiοn. The mean duratiοn and standard deviatiοn fοr each activity can be calculated using the PERT fοrmula:
mean = (οptimistic + 4*mοst prοbable + pessimistic)/6
standard deviatiοn = (pessimistic - οptimistic)/6
The mean and standard deviatiοn fοr each activity are shοwn belοw:
Activity A: mean = (2+8+12)/6 = 7, stdev = (12-2)/6 = 1.67
Activity B: mean = (4+9+11)/6 = 8, stdev = (11-4)/6 = 0.83
Activity C: mean = (1+1+1)/6 = 0.33, stdev = (1-1)/6 = 0
Using the mean and standard deviatiοn fοr each activity, we can calculate the mean and standard deviatiοn fοr each path and fοr the entire prοject. The mean and standard deviatiοn fοr each path are shοwn belοw:
Path 1 (A-B-C): mean = 7+8+0.33 = 15.33, stdev [tex]= (1.67^2+0.83^2+0^2)^0.5 = 1.87[/tex]
Path 2 (A-C): mean = 7+0.33 = 7.33, stdev [tex]= (1.67^2+0^2)^0.5 = 1.67[/tex]
Therefοre, The mean and standard deviatiοn fοr the entire prοject can be calculated by adding the means and variances οf the paths: Prοject: mean = 15.33
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Brad is selling cups of lemonade at a stand outside his house. He has enough supplies on hand to make a maximum of 251 ounces of lemonade. A regular cup holds 11 ounces of lemonade and a small cup can hold 7 ounces of lemonade. Write the inequality in standard form that describes this situation. Use the given numbers and the following variables.
11x + 7y ≤ 251 this is the inequality's standard form, where the constant is on the right and the variables are on the left.
What is system of inequalities?A group of two or more inequalities that must be met concurrently constitute a system of inequalities. A collection of values for the variables that simultaneously fulfil all of the inequalities is the solution to the system. The variables in the inequalities indicate quantities that are connected to one another. Systems of inequalities are used to simulate real-world circumstances when a given task is subject to a number of restrictions or limits.
Let us suppose the number of regular cups = x.
The number of small cups = y.
Thus, the total for lemonades is:
11x + 7y ≤ 251
This is the inequality's standard form, where the constant is on the right and the variables are on the left.
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if the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
The probability that the 100 orders can be filled without reordering components, if the manufacturer stocks 105 components is 1, or 100%.
The probability of being able to fill 100 orders without reordering components depends on the total number of components stocked. If the manufacturer stocks 105 components, then the probability of being able to fill 100 orders without reordering components is 1. Since 105 is greater than or equal to 100, the probability of being able to fill the orders without reordering components is 1 (100%).
Mathematically, this can be expressed as P(Filling 100 orders) = 1, where P stands for probability, and Filling 100 orders stands for the event of being able to fill 100 orders without reordering components.
This is because, if the manufacturer stocks 105 components, then they have enough components to fulfill the 100 orders without reordering components. So, the probability of being able to fulfill the orders without reordering components is 100%, or 1.
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Suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 orlower. Which of the following describes the sampling distribution of p?A. Mean = 15; Standard deviation = 0.0648; non-Normal.B. Mean = 15; Standard deviation = 3.24; approximately NormalC. Mean = 0.3; Standard deviation = 3.24; approximately NormalD. Mean = 0.3; Standard deviation = 0.0648; non-NormalE. Mean = 0.3; Standard deviation = 0.0648; approximately Normal
approximately Normal.
In the given problem, suppose you are going to roll a 10-sided die 50 times and record p, the proportion of times that the roll is 3 or lower. The question is asking us to determine the sampling distribution of p.The mean of p is given by: [tex]μp = 50 × 0.3 = 15[/tex]And
the standard deviation of p is given by: σp = sqrt[tex](50 × 0.3 × 0.7) = 3.24[/tex]
Therefore, the correct option is: Mean = 0.3; Standard deviation = 3.24;
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what is the average period of the trials that were conducted with an amplitude of 10 degrees? answer in units of seconds.
The average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.
What is amplitude ?
In mathematics, amplitude refers to the maximum displacement or distance from the equilibrium position of a periodic function, such as a sine or cosine wave. In other words, if a periodic function oscillates back and forth between two extreme values, the amplitude is the maximum distance from the average value or midpoint of the oscillation to one of the extreme values.
To calculate the average period of the trials that were conducted with an amplitude of 10 degrees, we simply add up all the periods and divide by the total number of trials.
10 degrees: 1.66 s, 1.700 s, 1.71 s, 1.68 s, 1.72 s
Average period = (1.66 + 1.700 + 1.71 + 1.68 + 1.72) / 5 = 1.694 seconds
Therefore, the average period of the trials that were conducted with an amplitude of 10 degrees is 1.694 seconds.
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a state's license plates consist of 4 letters followed by 5 digits. how many possible license plates can be issued using this condition?
In the following question, among the conditions given, There are 26^4 x 10^5 possible license plates that can be issued using this condition.
Hence, This is because the license plates consist of 4 letters and 5 digits. There are 26 possible letters that can be used in the first four places, so the total possible combinations of 4 letters is 26^4. There are 10 possible digits that can be used in the last five places, so the total possible combinations of 5 digits is 10^5. Multiplying these two together gives the total number of possible license plates: 26^4 x 10^5.
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There are a total of $26^4 × 10^5$ possibilities, which simplifies to 26,000,000,000 (twenty-six billion) possibilities. Therefore, with this condition, twenty-six billion license plates can be issued.
A state's license plates consist of 4 letters followed by 5 digits.
How many possible license plates can be issued using this condition?
When designing a license plate, the condition provided in the question suggests that a license plate should consist of 4 letters followed by 5 digits.
Therefore, we can count the total number of license plates in two phases.
The number of choices for each segment must be taken into account separately for the letters and the numbers.
When considering the letter possibilities, there are 26 options for each position since there are 26 letters in the alphabet.
For the first 4 positions, there are a total of $26^4$ = 456,976 possibilities.
Similarly, for the last 5 positions,
there are 10 options for each position since there are 10 digits.
There are $10^5$ = 100,000 possibilities for the last 5 positions.
The entire plate's total number of combinations is obtained by multiplying these numbers.
There are a total of $26^4 × 10^5$ possibilities
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how do i find x? I didn’t understand this problem
The correct length of the missing part of the triangle would be = 10. That is option A.
How to calculate the missing length of the triangle?The length of the smaller triangle = 20
The width of the smaller triangle = 16
The length of the bigger triangle = 20+X
The width of the bigger triangle = 24
But for similar triangles = 16/24 = 20/20+X
16(20+X) = 20×24
320+ 16x = 480
16x = 480-320
16x = 160
X = 160/16
X = 10
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Georgia surveyed some of her friends at Jones Middle School about their favorite type of music. The data she collected is shown below. Georgia concludes that the favorite type of music among the middle school students is rock music, followed by pop music.
Part A: Do you think Georgia’s conclusion is valid? Why or why not? Include a discussion about the sampling method Georgia used in your reasoning.
Part B: How would you recommend conducting the survey to get the most valid conclusion from the most representative sample?
It's difficult to determine the validity of Georgia's conclusion without more information about her sampling method. If Georgia used a random sampling method where each student at Jones Middle School had an equal chance of being selected to participate in the survey, then her conclusion could be considered more valid.
b. To conduct the survey to get the most valid conclusion from the most representative sample, she could use a random sample.
How to explain the samplingIn addition, the sample size and the margin of error of the survey are important factors to consider when evaluating the validity of the conclusion.
Georgia could consider using a random sampling method where each student at Jones Middle School has an equal chance of being selected to participate in the survey. She could also increase the sample size to get a more accurate representation of the entire student population. It would also be important to consider the margin of error and confidence level of the survey to ensure that the results are reliable. Finally, Georgia could also consider stratifying her sample by grade level or other relevant factors to ensure that the sample is representative of the entire student population at Jones Middle School.
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The shaded area in the decimal grid below represents the amount of money that Karla has. She plans on dividing the money evenly between her three younger brothers. Her brothers are planning to spend the money on pieces of candy that cost $0.10 each.
What will be the maximum number of pieces of candy that each brother can buy?
(The large square of the grid represents $1.00 and each small square represents $0.01.)
Answer:
4 pieces each
Step-by-step explanation:
You want to know the number of $0.10 candies each brother can buy with his equal share of Karla's $1.44.
DiagramEach column of the diagram represents $0.10, the cost of one piece of candy. Then 3 columns represent 3 pieces, or one for each brother.
We can divide the shaded area into four (4) groups of 3 columns, representing 4 pieces of candy that each brother can buy. The remaining $0.24 will be divided so that each brother will have $0.08 left over after buying 4 pieces of candy.
Select ALL the set of numbers that are possible values for x in the inequality, x<-3
The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)
To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.
{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.
{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.
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Complete Question:
Select all the sets of numbers that are possible values for x in the inequality, x<-3.
{5,7,9}{-9, -7, -5}{-33, -22, -11}{-5,0,5}PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP
Answer:
[tex]\textsf{The value of t is 14m. }[/tex]
Step-by-step explanation:
To find:-
The value of "t" .Answer:-
F I G U R E : -
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\multiput(3,.5)(0,4){2}{$\sf 13m $}\multiput(1,2.5)(5.5,0){2}{$\sf t $}\put(5,-2){$\boxed{\bf{-\ By }\ \bf " Tony Stark"}$}\end{picture}[/tex]
As we know that the perimeter of a parallelogram is the sum of all the side lengths of it . Also we know that the opposite sides are equal in a parallelogram. Therefore, here the two other sides AD and DC would be "t" and "13m" respectively.
Now also we are given that the perimeter of the parallelogram is 54m . So we can create a equation to find out "t" as ,
[tex]:\sf\implies Perimeter = 13m + t + 13c
m + t\\[/tex]
Since the perimeter is 54m , therefore;
[tex]:\sf\implies 54m = 26m + 2t \\[/tex]
Subtract 26m on both the sides,
[tex]:\sf\implies 54m - 26m = 2t\\[/tex]
Simplify,
[tex]:\sf\implies 28m = 2t \\[/tex]
Divide both the sides by "2" ,
[tex]:\sf\implies t = \dfrac{28m}{2} \\[/tex]
Simplify,
[tex]:\sf\implies \pink{ t = 14m } \\[/tex]
Hence the value of t is 14m .
GIVING BRAINLIEST FOR RIGHT ANSWER (provide proof please i need to know how you got the answer)
Answer:
x<-8
Step-by-step explanation:
The arrow shows that x must be less than -8. We also know that the circle is not filled in. This means that x must be less than -8 and x≠-8. Hence, x<-8.
PLEASE MARK AS BRAINLIESTWhat is the nature of consciousness, and how do we know that other beings possess it?
We can infer that other beings possess consciousness based on their behavior and similarities to ourselves
The nature of consciousnessConsciousness refers to the subjective experience of awareness, self-awareness, and the ability to perceive, reason, and make decisions.
However, the question arises whether animals, plants, or even machines possess consciousness.
To answer this question, we must rely on behavioral, neuroscientific, and philosophical evidence.
Behavioral evidence involves observing animals and their actions to see if they exhibit behaviors that suggest they have consciousness. Neuroscientific evidence involves studying the brain structures and functions of animals and humans to identify the mechanisms underlying consciousness. Philosophical evidence involves considering the nature of consciousness and its role in the universe.Read more about consciousness at
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Combine like terms in the expression –5x + 2y + 5x – 8y.
Answer:
-6y
Step-by-step explanation:
-5x + 2y + 5x - 8y =
= -5x + 5x + 2y - 8y
= -6y
Answer:
10x-6y
Step-by-step explanation:
5x+5x=10x
and 2y-8y=-6y
Let me know if this helps
Help please refer to the image
Answer: What grade are you in? Because I had to do this for my 8th or 9th grade year as a homeschooler.... I never had help...I had the same brand laptop and my studies were done on T4L......
Step-by-step explanation:
x2 +3x--3x+5 I think give me a few minutes to check myself
If AB=7x-4 and CB=6x what’s length of chord AC
48 is length of chord AC.
How is a chord defined?
Three or more notes come together to form a chord. A single note, referred to as the root, serves as the foundation for chords. Triads will be covered in this lesson.
A root, third, and fifth are used to make them. A line segment connecting two locations on the circle's circumference is what is referred to as the chord of a circle. The diameter, which runs through the centre of the circle, is the lengthiest chord of the circle.
since OD intersects AB to form a right angle at point B, so it bisects the chord AC.
so AB = BC (1)
given AB = 7x - 4
and CB = 6x
from (1) we have
7x - 4 = 6x
x = 4
so AB = 7(4) - 4 = 24
CB = 6(4) = 24
length of chord AC = AB + BC = 24 + 24 = 48
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The complete question is -
Segment OD intersects AB to form a right angle at point B.
If AB = 7x - 4 and CB = 6x, what is the length of the chord AC?
three women earned a total of £36 they shared the £36 in a ratio 7:3:2 Donna receives the largest amount work out the amount Donna receives .
Answer:
£21
Step-by-step explanation:
We know
Three women earned a total of £36. They shared the £36 in a ratio of 7:3:2. Meaning for every £12, one receives £7, one receives £3, and one receives £2.
Donna receives the largest amount working out the amount Donna receives. Meaning Donna receives £7.
To get from 12 to 36, we time 3.
We take
7 x 3 = £21
So, Donna receives £21
jason is making a concrete driveway. he mixes dry cement and water in the correct ratio. the table shows how much dry cement to mix with different amounts of water. jason says a graph of the relationship includes the point (63, 140). is jason correct?
Jason is correct when he says that a graph of the relationship includes the point (63, 140).
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.
The relationship is defined according to the equation presented as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one, which is also the constant ratio of the relationship.
From the table given at the end of the answer, when x = 54, y = 120, hence the constant is given as follows:
k = 120/54
k = 2.2222.
Hence the equation is:
y = 2.2222x.
When x = 63, the output of the function is given as follows:
y = 2.2222 x 63
y = 140.
Hence Jason is correct when he says that a graph of the relationship includes the point (63, 140), as when x = 63, the output of the function is of y = 140.
Missing InformationThe table is given by the image presented at the end of the answer.
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x-2
A. 44 in
B. 48 in
C. 52 in
D. 64 in
X
X
x-2
The figure above consists of five congruent rectangles. If the total area of the figure is 75in¹, what
is its perimeter?
The perimeter of the figure, given the rectangles and the total area, can be found to be 48 inches
How to find the perimeter ?The total area is 75 in² which means that the areas of all 5 rectangles add up to 75 in². We can use this to solve for x to be:
5 × ( x × ( x - 2 )) = 75 in²
5 × ( x² - 2x ) = 75 in²
x² - 2x = 15 in²
(x - 5)(x + 3) = 0
x - 5 = 0 or x + 3 = 0
x = 5 or x = -3
Dimensions of a rectangle cannot be negative so x is equal to 5.
The perimeter is then:
= ( x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x - 2 ) + x + (x - 2 ) + x + ( x -2 ) + x
= ( 5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 - 2 ) + 5 + (5 - 2 ) + 5 + ( 5 -2 ) + 5
= 48 inches
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a sample point refers to a(n) . a. numerical measure of the likelihood of the occurrence of an event b. set of all possible experimental outcomes c. individual outcome of an experiment d. initial estimate of the probabilities of an event
A sample point refers to an option (c) individual outcome of an experiment
In probability, a sample point is a specific outcome or event that can occur in an experiment or study. It represents a single instance or realization of the random process being studied. For example, if the experiment is flipping a coin, a sample point could be "heads" or "tails". The set of all possible sample points is called the sample space.
Sample points are important in probability theory because they help determine the probability of a particular event occurring. By calculating the number of sample points that satisfy a given condition, we can determine the likelihood of that condition being met, and make predictions about the behavior of random processes.
Therefore, the correct option is (c) individual outcome of an experiment
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Need help ASAP!!!!
Answer the question using a table of values.
The graphic at the end shows the graph of the absolute value function.
How is the function graphed?
The following is the function:
y=−2³√x−1+2
To graph this, we must first identify some points on the line, which requires evaluating the line in a variety of x values.
Replace the value 2 of x in f(x)=-8x-1+2
x is replaced with 2 f(2)=-8+2 f(2)=-6.
Evaluation in x = 3 results in:
y = -8√(3)-1+2
The vertex points (1,2), (2,-6), and (3,-9.31) can be used to graph the square root.
Once you have accumulated enough data points, you may plot them using absolute value functions to create the graph you see below in this case.
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Please use the information below for a geometric sequence to do the following:
a. sub 1 equals 640 r equals one half
A) List the first 6 terms of the sequence
B) Write the terms of this sequence as a series.
C) Provide a graph of the geometric sequence.
D) List the first 6 partial sums of the series.
SHOW ALL MATH WORK AND EXPLANATIONS FOR THIS FROM START TO FINISH! IT'S A 10 POINT PROBLEM!
Answer:
A) To find the terms of the geometric sequence, we use the formula:
a_n = a_1 * r^(n-1)
where a_n is the nth term of the sequence, a_1 is the first term, r is the common ratio, and n is the position of the term in the sequence.
Given that a_1 = 640 and r = 1/2, we can find the first 6 terms of the sequence:
a_1 = 640
a_2 = a_1 * r = 640 * (1/2) = 320
a_3 = a_2 * r = 320 * (1/2) = 160
a_4 = a_3 * r = 160 * (1/2) = 80
a_5 = a_4 * r = 80 * (1/2) = 40
a_6 = a_5 * r = 40 * (1/2) = 20
So the first 6 terms of the sequence are: 640, 320, 160, 80, 40, 20.
B) To write the terms of the sequence as a series, we simply add the terms together:
640 + 320 + 160 + 80 + 40 + 20 + ...
The series has an infinite number of terms.
C) Here is a graph of the geometric sequence:
|
640| o
| o
320| o
| o
160| o
|o
0|___________________
1 2 3 4 5 6
The horizontal axis represents the position of the term in the sequence (n), and the vertical axis represents the value of the term (a_n). Each dot on the graph represents a term in the sequence.
D) To find the partial sums of the series, we add up the terms up to a certain position in the sequence. For example, the first partial sum is simply the first term:
S_1 = 640
The second partial sum is the sum of the first two terms:
S_2 = 640 + 320 = 960
The third partial sum is the sum of the first three terms:
S_3 = 640 + 320 + 160 = 1120
Continuing this pattern, we can find the first 6 partial sums of the series:
S_1 = 640
S_2 = 960
S_3 = 1120
S_4 = 1200
S_5 = 1240
S_6 = 1260