A homogeneous system in parametric vector form:
(x1,x2,x3) = (s,s,-0.25s)
Parametric vector Form:
Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.
So the set of parametric equations is x = t and y=t²+5.
According to the Question:
We are to solve them in parametric form.
X₁ + 2X₂ + 12X₃ = 0 ----------------------- (1)
2X₁ + X₂ + 12X₃ = 0 ----------------------- (2)
-X₁ + X₂ = 0 ----------------------- (3)
From equation 3 we get
x₁ = x₂
Substitute in 1 and 2 to get
3x₁ + 12x₃ = 0 and
3x₁ + 12x₃ = 0
Thus, we find these two equations are dependent. So we can have infinite solutions in parametric form only.
No unique solution is possible
Let x₁ = x₂ = s
Since 3x₁ +12x₃ = 0
x₁ = -4x₃
Or x₃ = -0.25s
So solution in parametric form is
(x1,x2,x3) = (s,s,-0.25s) for all real values.
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the probability that a discrete random variable equals any of its values is
A discrete distribution is used to calculate the probability that a random variable will be exactly equal to some value which is 0 ≤ P(X = x) ≤ 1 and ∑P(X = x) =1.
We can say that a discrete distribution is a probability distribution that depicts the occurrence of discrete or individually countable outcomes.
We know that the discrete probability distribution is counting of the occurrences that have countable or finite outcomes. We also know that discrete distributions contrast with continuous distributions, where outcomes can fall anywhere on a continuum, common examples of discrete distribution include the binomial, Poisson, and Bernoulli distributions.
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A company orders 22 boxed lunches from a deli for $226.60. If each boxed
lunch costs the same amount, how much do 13 boxed lunches cost?
Answer:
$2945.8
Step-by-step explanation:
226.60 multiplied by 13 is 2945.8.
To check the answer you divide 2945.8
and 13 to get 226.60 or 226.6
A sofa regularly sells for $550. The sale price is $456.50. Find the percent decrease of the sale price from the regular price.
Answer:
The percent decrease of the sale price of the sofa from the regular price is 17%.
Step-by-step explanation:
Sure! Here are the steps to find the percent decrease:
Find the difference between the regular price and the sale price: $550 - $456.50 = $93.50Divide the difference by the regular price: $93.50 ÷ $550 = 0.17Multiply by 100 to convert to a percentage: 0.17 × 100 = 17%The percent decrease of the sale price from the regular price is 17%.
Answer:
17% is the percen
Please I need help as soon as possible thanks to anyone who answers
Formula:
(A+B/2)H
A=base
B=Base
H=height
A. 100 cm (i think not to sure about this one)
B. 174 cm
C. 240cm
Answer:
Step-by-step explanation:Formula:
(A+B/2)H
A=base
B=Base
H=height
A. 100 cm (i think not to sure about this one)
B. 174 cm
C. 240cm
in general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect _____ .
In general, if the sample size is large, adding an extremely large outlier to a data set will not substantially affect the mean (average) of the data set.
This is because the mean is calculated by summing all the values in the data set and dividing by the total number of values. As the sample size increases, the influence of any individual value on the mean becomes smaller. An extremely large outlier may have a significant impact on the sum of the data set, but if the sample size is large enough, the impact on the mean will be relatively small.
However, adding an extremely large outlier to a data set can substantially affect other measures of central tendency and dispersion, such as the median and standard deviation. These measures are based on the order and spread of the data, rather than the sum of the data, and may be more sensitive to extreme values.
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how to find the derivative
We utilize the differentiation method to obtain the derivative of a function. This entails calculating the limit of the ratio of the change in output (y value) to the change in input (x value). The formula then yields the function's derivative. f'(x) = [tex]\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}[/tex].
Determining the derivative of a function is a simple process. Initially, you must establish the sort of function you are dealing with.
Once the kind of function has been decided, the variables of the function must be identified.
The power rule is then used to determine the derivative of each of the terms.
Lastly, you must combine all of the terms to obtain the overall derivative.
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What is the measure of an exterior angle of a twelve sided polygon?
The measure of an exterior angle of a twelve sided polygon is 30 degrees
The measure of an exterior angle of a polygon is the angle formed between one side of the polygon and the extension of an adjacent side.
In any polygon, the sum of exterior angles is always 360 degrees. This is because if you start at one vertex of the polygon and walk all the way around the outside of the polygon, you will make a full 360-degree turn. Each time you make a turn at a vertex, you create an exterior angle, and the sum of these exterior angles is equal to 360 degrees.
In a twelve-sided polygon (a dodecagon), the measure of each exterior angle can be calculated using the formula:
measure of each exterior angle = 360 degrees ÷ number of sides
So for a dodecagon:
measure of each exterior angle = 360 degrees ÷ 12 = 30 degrees
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Activity 9
Directions: The scrambled words in the sentences that follow have to do with money
management. Unscramble the words and write the letters in the correct order.
1. Babysitting and yard work are two potential sources of MICOEN for teens.
2. A BETDI RCDA can be used to purchase groceries without using cash.
3. If you want to set-up a GUDETB, you need to know how much money you spend.
4. Your budget should include a VGISSAN plan.
5. Begin your budget by setting aside enough money to cover your PNEESSXE.
6. A(n) AAYWYAL plan allows you to put a small amount of money down and make regular
payments until you have paid for an item.
7. When you buy now and pay later, you use a method of payment called DERITC.
Babysitting and yard work are two potential sources of INCOME for teens.
A DEBIT CARD can be used to purchase groceries without using cash.
If you want to set-up a BUDGET, you need to know how much money you spend.
Your budget should include a SAVINGS plan.
Begin your budget by setting aside enough money to cover your EXPENSES.
A(n) LAYAWAY plan allows you to put a small amount of money down and make regular
payments until you have paid for an item.
When you buy now and pay later, you use a method of payment called CREDIT.
5r²+3
4r²-6r+1
7r-8
What is the perimeter of the triangle of the triangle shown
Answer: First Choice. 9r² + r -4
Step-by-step explanation:
Given information
Side 1 = 5r²+3
Side 2 = 4r²-6r+1
Side 3 = 7r-8
Formula for the perimeter of the triangle
Perimeter = Side 1 + Side 2 + Side 3
Substitute values into the formula
Perimeter = (5r² + 3) + (4r² - 6r + 1) + (7r - 8)
Simplify the expression
Perimeter = 5r² + 4r² + 7r - 6r + 3 + 1 - 8
Perimeter = 9r² + r + 4 - 8
Perimeter = [tex]\Large\boxed{9r^2+r-4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
5 functions each of 10 consumer project agencies
Generally, the main five functions of consumer protection agencies includes:
Educate consumers: One of the primary functions of consumer protection agencies is to educate consumers about their rights and responsibilitiesInvestigate complaints: Consumer protection agencies receive and investigate complaints from consumersEnforce consumer protection laws: Consumer protection agencies work to enforce laws and regulations that protect consumers from unfair and deceptive business practices. Set and enforce standards: Consumer protection agencies may set and enforce industry standards for products and services to ensure that they are safe and effective.Work with businesses: Consumer protection agencies may work with businesses to promote best practices and encourage ethical behavior.What are the 10 consumer protection agencies?Consumer protection agencies are organizations that work to protect consumers from unfair and deceptive business practices. These agencies perform a variety of functions to promote fair and ethical business practices and ensure that consumers are able to make informed decisions when purchasing goods and services.
The list of the consumer protection agencies we have in U.S. are:
Consumer Financial Protection BureauConsumer Product Safety CommissionFederal Trade CommissionFood and Drug AdministrationNational Highway Traffic Safety AdministrationRead more about consumer protection
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another name for the regression line is the _______ line.
Another name for the regression line is the least squares line.
A regression line is an estimate of the line that describes the true, but unknown, linear relationship between the two variables. The equation of the regression line is used to predict (or estimate) the value of the response variable from a given value of the explanatory variable.
Another name given to regression line is the least squares line because it is chosen so that the sum of the squares of the differences between the observed y-value and the value predicted by the line is as small as possible.
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∠1 and ∠2 are supplementary. m∠1=124°m∠2=(2x+4)° What is the value of x? Select from the drop-down menu to correctly answer the question. x = Choose...
Therefore, the value of x is 26.
What is angle ?in geometry, an angle is a measure of the amount of rotation between two intersecting lines, or between a line and a plane. It is typically measured in degrees, with a full rotation equal to 360 degrees. Angles can also be measured in radians, which is another unit of angular measurement .Since ∠1 and ∠2 are supplementary, their sum is equal to 180 degrees. That is:
m∠1 + m∠2 = 180
Substituting the given values, we have:
124° + (2x+4)° = 180°
Simplifying this equation, we get:
2x + 128 = 180
Subtracting 128 from both sides, we have:
2x = 52
Dividing both sides by 2, we get:
x = 26
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50 is what percent of 1000
Answer:500
explanchion: 1000/50=500
There is a 20% chance of snow on Tuesday and a 30% chance of snow on Wednesday. What is the probability that it willnotsnow on either day? Express your answer as a percent.
Answer:
56%
Step-by-step explanation:
The probability of snow on Tuesday is 20%, which means the probability of no snow on Tuesday is 100% - 20% = 80%.
Similarly, the probability of snow on Wednesday is 30%, which means the probability of no snow on Wednesday is 100% - 30% = 70%.
The probability that it will not snow on either day is the product of the probabilities of no snow on Tuesday and no snow on Wednesday:
(80%)(70%) = 56%
So the probability that it will not snow on either day is 56%.
What is the conversion of 63 f to c?
The conversion of 63 f to c is equivalent to approximately 17.22°C .
For 63 (degrees) Fahrenheit we write 63 °F, and (degrees) Celsius or centigrades are denoted with the symbol °C.
As a side note: the unit of temperature Fahrenheit is named after the German physicist Daniel Gabriel Fahrenheit.
So if you have been looking for 63 °F to °C, then you are right here, too.
To convert a temperature from Fahrenheit (°F) to Celsius (°C), you can use the formula:
°C = (°F - 32) * 5/9
So, to convert 63°F to °C, you can substitute 63 for °F in the formula:
°C = (63 - 32) * 5/9
= 31 * 5/9
= 155/9
≈ 17.22°C
Therefore, 63°F is equivalent to approximately 17.22°C (rounded to two decimal places).
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The histogram below summaries a ‘happiness’ score for a group of people. Estimate the fraction of the group who had a score of 35 or more.
The fraction of the group who had a score of 35 or more is 20%.
What is histogram?A histogram is a graphical representation of the distribution of numerical data. It consists of a series of bars (or rectangles) that are aligned along an axis, typically the x-axis, with the area of each bar proportional to the frequency or count of data points that fall within a specific interval or bin on that axis. Histograms are commonly used in statistics and data analysis to show the frequency distribution of a dataset. They allow you to visualize the shape of the distribution, including the central tendency (mean, median, mode) and the spread (variance, standard deviation). Histograms can also be used to identify outliers, gaps, and patterns in the data. They are often used in quality control to identify defects, in finance to analyze stock prices, in biology to analyze population distribution, and in many other fields where numerical data needs to be analyzed and understood visually.
Here,
First, you need to determine the range of scores represented in the histogram. This should be indicated by the x-axis of the histogram. Next, you need to identify the bin or bins in the histogram that correspond to scores of 35 or more. A bin is a group or interval of scores. The height of each bin represents the frequency or count of scores in that interval. Once you have identified the bin(s) that correspond to scores of 35 or more, you need to sum the heights of those bins to get the total count or frequency of scores that are 35 or higher. Finally, you can divide the total count or frequency of scores that are 35 or higher by the total count or frequency of scores in the entire histogram to get the estimated fraction of the group who had a score of 35 or more.
For example, if the histogram represents the happiness scores of 100 people and the bin or bins that correspond to scores of 35 or more have a total count of 20, then the estimated fraction of the group who had a score of 35 or more is 20/100 = 0.2 or 20%.
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2) Lou plans to go to a beauty salon. She sees this special offer. treatments (£31. facial) (£29 leg wax) (£35 massage) (£27. manicure) (£13 eyelash tint) book any 3 treatments get 25% off the total cost Lou wants to book a massage and 2 other different treatments. She has £60 to spend on the treatments. Work out the total cost of the 3 treatments using the special offer for Lou. Remember to write down the 3 treatments.
The total cost for each combination with the special offer would be:
Massage, leg wax, and manicure: £68.25
Massage, facial, and eyelash tint: £59.25
Massage, leg wax, and eyelash tint: £57.75
How to find the total cost?We can try out the different possibilities and calculate the total cost of each.
Let's start by listing the prices of the treatments she's interested in:
Massage: £35
Facial: £31
Leg wax: £29
Manicure: £27
Eyelash tint: £13
Now, we can try out the different combinations of 3 treatments and calculate their total cost:
Massage, facial, and leg wax:
Total cost = £35 + £31 + £29 = £95
With 25% off, the cost would be £71.25, which is over Lou's budget of £60, so this combination is not possible.
Massage, facial, and manicure:
Total cost = £35 + £31 + £27 = £93
With 25% off, the cost would be £69.75, which is still over Lou's budget of £60, so this combination is also not possible.
Massage, leg wax, and manicure:
Total cost = £35 + £29 + £27 = £91
With 25% off, the cost would be £68.25, which is within Lou's budget of £60. Therefore, this combination is possible.
Massage, facial, and eyelash tint:
Total cost = £35 + £31 + £13 = £79
With 25% off, the cost would be £59.25, which is within Lou's budget of £60. Therefore, this combination is also possible.
Massage, leg wax, and eyelash tint:
Total cost = £35 + £29 + £13 = £77
With 25% off, the cost would be £57.75, which is within Lou's budget of £60. Therefore, this combination is also possible.
From the above calculations, we can see that Lou can choose from three possible combinations of treatments that fit within her budget and qualify for the special offer:
Massage, leg wax, and manicure
Massage, facial, and eyelash tint
Massage, leg wax, and eyelash tint
The total cost for each combination with the special offer would be:
Massage, leg wax, and manicure: £68.25
Massage, facial, and eyelash tint: £59.25
Massage, leg wax, and eyelash tint: £57.75
Therefore, Lou can choose any of the above combinations and pay the corresponding total cost to enjoy the special offer.
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what is calculator of simplifying fractions
A calculator for simplifying fractions is a tool that can be used to reduce a fraction to its simplest form or lowest terms.
The process of simplifying a fraction involves finding the greatest common factor of the numerator and the denominator and then dividing both by that factor. This results in a fraction that has been simplified as much as possible. A calculator of simplifying fractions can perform this calculation automatically, making it a quick and easy way to simplify fractions.
This tool can be especially helpful for those who struggle with math, or for those who need to perform a large number of calculations quickly and accurately. Many online calculators are available for free and can simplify fractions in seconds.
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Please Help ASAP 10 POINTS
The amount of wrapping paper use to wrap the rectangular gift box is 292 ft².
What is the surface area of the rectangular prism?The surface area of a rectangular prism is expressed as;
S.A = 2( wl + hl + hw )
Given the data in the diagram;
Length l = 8ftWidth w = 6 ftHeight h = 7 ftPlug the values into the above formula and find the surface area.
S.A = 2( wl + hl + hw )
S.A = 2( (6×8) + (7×8) + (7×6) )
S.A = 2( 48 + 56 + 42 )
S.A = 2( 146 )
S.A = 292 ft²
Therefore, the surface area of the right rectangular prism is 292 ft².
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How many combinations of 4 can we make?
The different possibilities of combinations of 4 are combinations of 4 distinct items, combinations of 4 items with replacement, combinations of 4 items without replacement and combinations of 4 items without replacement
It depends on what exactly you mean by "combinations of 4." Here are a few possibilities and the corresponding answers:
Combinations of 4 distinct items: If you have 4 distinct items and you want to know how many different ways there are to choose a group of 4 from among them, the answer is 4 choose 4, which is equal to 1.
Combinations of 4 items with replacement: If you have a set of items and you want to know how many different groups of 4 you can make if you're allowed to repeat items, the answer is the number of items raised to the 4th power
Combinations of 4 items without replacement: If you have a set of items and you want to know how many different groups of 4 you can make if you're not allowed to repeat items
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If iq scores are normally distributed, having a mean of 100 and a standard deviation of 15, approximately what percentage of people have iq scores somewhere between 70 and 130?
The percentage of people have iq scores somewhere between 70 and 130 is 95.44%.
To solve this problem, we need to standardize the IQ scores and then use a standard normal distribution table or calculator to find the proportion of scores between 70 and 130.
First, we need to calculate the z-scores for IQ scores of 70 and 130, using the formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean (100), and σ is the standard deviation (15).
For an IQ score of 70:
z = (70 - 100) / 15 = -2
For an IQ score of 130:
z = (130 - 100) / 15 = 2
We can now look up the proportion of scores between -2 and 2 in a standard normal distribution table or calculator. This represents the proportion of scores within two standard deviations of the mean, which is approximately 95% according to the empirical rule of normal distribution.
However, we want to find the proportion of scores between 70 and 130, not between -2 and 2. To do this, we need to subtract the proportion of scores below 70 (which is the same as the proportion below -2) from the proportion of scores below 130 (which is the same as the proportion below 2). The result gives us the proportion of scores between 70 and 130.
Using a standard normal distribution table or calculator, we can find that the proportion of scores below -2 (or 70) is 0.0228, and the proportion of scores below 2 (or 130) is 0.9772. Therefore, the proportion of scores between 70 and 130 is:
0.9772 - 0.0228 = 0.9544
This means that approximately 95.44% of people have IQ scores between 70 and 130.
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How do I find the equivalent answer to the solution?
Answer: D.6
hope this helped
Find the length of side in simplest radical form with a rational denominator.
Answer:
x=2sqrt2
Step-by-step explanation:
The legs are equal, thus the sides are x, x, and hypotenuse is 4. This means that x^2+x^2=4^2. Thus, 2x^2=16 => x^2=8 => x= sqrt8 => x=2sqrt2
Solve the area of a triangle formula for the variable b: A= 1/2 bh
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Answer: I am not understanding what you want us to help you with. In long form is says Area= 1/2 base x height
Step-by-step explanation:
What is the area of the parallelogram?
396 ft2
four hundred ten and five-eights ft2
792 ft2
eight hundred twenty-one and one-fourth ft2
25 points. Please show working out!
Answer:
42 m
Step-by-step explanation:
Equilateral triangle means that all sides are the same thus if the perimeter is 12 m
12m/3 = 4m for each side
The length of the boom will then how many triangles make the length which looks to be about 10.5
So 10.5 x 4 = 42 m
Does the graph represent a function?
PLS HELP!
Answer: yes
Step-by-step explanation:
None of the points intercept eachother if we make a vertical line and there are no y-values with more than one x-value.
if 3x-4=-25, then x=?
Answer: x = -7
Step-by-step explanation:
3x-4=-25
add 4 on each side
3x=-21
both are divisible by 3
x=-7
Evaluate and simplify the expression when x=1 and y=2
3(x+2y)-2x+10
Please show your work
step by step so I will know how to solve this for my next problem.
Answer:
Therefore, when we put x=1 and y=2, the equation 3(x+2y)-2x+10 simplifies to 23.
Step-by-step explanation:
To evaluate and simplify the expression first we have to put x=1 and y=2 in the equation as given in the question,
3(x+2y)-2x+10 = 3(1+2(2))-2(1)+10
=3(1+2(2))-2+10
= 3(1+4)+8
= 3(5)+8
= 15+8
= 23
Therefore, when we put x=1 and y=2, the equation 3(x+2y)-2x+10 simplifies to 23.
Linda's Dog Walking Service
Cost ($)
5 8 8 8 8
50
30
20
0
20 40 60 80 100 120
# of minutes
According to the graph the value of the Dog Walking Service would be $0.75 per minute.
How to know the value per minute of Linda's service?To know the value per minute of the Dog Walking Service offered by Linda we must carry out the following mathematical procedure:
Rule of three.If every 20 minutes is worth $15, how much is each minute worth?
To do this we must follow the following rule of three:
20 minutes = $151 minute = ?1 * 15 / 20 = $0.75Additionally, we must take into account that according to the graph, the value per minute decreases if we contract more hours of service. For example, with 40 minutes of service it would be worth 0.5 each minute.
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