The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.
Given that,
From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.
Whether the claim is true or false must be determined.
The statement is true.
An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.
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9.
3/5
+
3
20
please answer
Answer:9/10
Step-by-step explanation:
make 3/4 equal to 3/20 by multiplying by 5
15/20 + 3/20 = 18/20
18/20 = 9/10
Examine the graph of the function.
What is the rate of change of the function?
The rate of change of the function is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the function are 3 and 5
The inputs of the function are 1 and 2.
We have,
We will find two points on the graph.
The points on the graph are:
(0, 5), (1, 3), and (2, 1)
We can choose any two points.
(0, 5) and (1, 3)
The rate of change of the function.
= (3 - 5) / (1 - 0)
= -2/1
= -2
Thus,
The rate of change of the function is -2.
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Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts.
distinct x-intercepts of which one has a multiplicity of
x-intercepts and imaginary roots
distinct x-intercepts of which one has a multiplicity of
distinct x-intercepts
x-intercept with multiplicity
x-intercept with imaginary roots
distinct x-intercepts and imaginary root
distinct x-intercepts each with multiplicity
The all the possibilities and combination for the x - intercepts , of the roots of the polynomial with degree 4 are :
0 x-intercepts and 4 imaginary roots ,
4 distinct x-intercepts ,
1 x-intercept with multiplicity 4 and
2 distinct x-intercepts each with multiplicity 2 .
In the question ,
it is given that ,
there is polynomial of degree 4 ,
and some statements about the roots of the polynomial is given ,
we have to find the suitable options that are for the roots .
We know that the fourth degree polynomial will have theoretically four roots .
So , the possible situations for the roots are
it can have ,
0 x intercepts and 4 imaginary roots ( where imaginary roots must occur in pairs ) OR
it can have 4 distinct x intercepts . OR
1 x intercept that have multiplicity 4 , OR
2 distinct x intercepts that have multiplicity 2 .
Therefore , the possibilities options are (b) , (d) , (e) and (h) .
The given question is incomplete , the complete question is
Below are several options for the roots of a polynomial with degree 4. Consider all possibilities and combinations for the x- intercepts .
(a) 2 distinct x-intercepts of which one has a multiplicity of 3 ,
(b) 0 x-intercepts and 4 imaginary roots
(c) 3 distinct x-intercepts of which one has a multiplicity of 2
(d) 4 distinct x-intercepts
(e) 1 x-intercept with multiplicity 4
(f) 1 x-intercept with 3 imaginary roots
(g) 3 distinct x-intercepts and 1 imaginary root
(h) 2 distinct x-intercepts each with multiplicity 2
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➤ Solve the inequalities.
T -3 is less than or equal to 2
-3 is less than 2
< is the symbol
Dilate rectangle ABCD by
a scale factor of ½ using E
as the center.
As we dilate rectangle ABCD by a scale factor of 1/2 and use E as the center, the coordinates of the point D' = (2, -1).
What is meant by rectangle?A rectangle is a quadrilateral in Euclidean plane geometry with four right angles.
The coordinates of the rectangle's points A'B'C'D' are as follows:
A' = the point's coordinates (-2, -1)
B' = the coordinates of the point (-2, 1)
C' = the coordinates of the point (2, 1)
D' = the coordinates of the point (2, -1)
Using the point P as the chart's origin, we get;
The coordinates of point B are (-4, 2), and the coordinates of point C are (4, 2).
Given that the sides are parallel to each other, the coordinates of point A = (-4, -2) The coordinates of point D = (4, -2)
We have; given that the sides are parallel to the axis.
The segment length AB = 2 - (-2) = 4
The segment length BC = 4 - (-4) = 8
The segment length CD = 2 - (-2) = 4
The segment length AD = 4 - (-4) = 8
As a result, a 1/2 dilation yields;
The segment length A'B' = AB/2 = 4/2 = 2
The segment length B'C' = BC/2 = 8/2 = 4
The segment length C'D' = CD/2 = 4/2 = 2
The segment length A'D' = AD/2 = 8/2 = 4
Point A' coordinates = Point A/2 coordinates = (-4, -2)/2 = (-2, -1)
= (-4, 2)/2 = (-2, 1) (-2, 1)
The coordinates of the point B' = (-2, 1) The coordinates of the point C' = (4, 2)/2 = (2, 1)
C' = the coordinates of the point (2, 1)
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Find the ratio a:b, please look at image below!
The ratio of a:b is 3:16
What is Ratio?
Ratio ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division. That is, a:b = a/b
To find the ratio a:b
[tex]\frac{a+3b}{5}[/tex] = [tex]\frac{a-2b}{2}[/tex]
Cross multiply
2(a+3b) = 5(a-2b)
Open bracket
2a + 6b = 5a - 10b
Collect like terms
2a - 5a = -10b - 6b
-3a = -16b
Divides through by -1
-3a/-1 = -16b/-1
3a = 16b
The Ratio a:b is 3:16
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Solve the system. Explain your answer using words, symbols, or both. please show your work thank you.
x+3y=8
x+y=2
The value of x and y is 3
What is meant by mathematical equation ?In mathematics, an equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. [2] [3] In other languages, the word equation and its cognates may have slightly different meanings; for example, in French, an équation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions linked by an equals sign.
Let the equations be
x + 3y = 8 ..............(1)
x + y = 2 ..............(2)
substracting equation 1 from 2
(x + 3y) - (x + y ) = 8 - 2
x + 3y - x + y = 6
3y - y = 6
2y =6
y = 6/2
y = 3
multiply the equation 2 with value of 3
x + y=2*3
x+y =6
x+3 = 6
x = 6 - 3
x = 3
Therefore the value of x and y is both are 3
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A candidate for office claims that "there is a correlation between television watching and crime."
Criticize this statement on statistical grounds.
The correct option regarding the statement is given as follows:
A. There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.
What are qualitative and quantitative variables?The variables are classified as qualitative or quantitative as follows:
Qualitative variables assume labels as values.Quantitative variables assume numbers as values.The relevance of the variables according to association and correlation are given as follows:
Qualitative variables can have association.Quantitative variables can have correlation.The variables in this problem are given as follows:
Television watching -> yes/no -> qualitative.Crimes committed -> yes/no -> qualitative.As they are qualitative variables, they can have association, and thus option A is correct.
Missing InformationThe options are given by the image presented at the end of the answer.
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What is the equation of a vertical ellipse with a major axis = 14, a minor axis = 12,
and a center of (3,5) ?
The equation (x - 3)² / 144 + (y - 5)² / 196 = 1 is the standard form of the ellipse.
How to determine the standard form of the equation of the ellipse
Herein we know the main features of a vertical ellipse, that is, the center and the lengths of its axes. The standard form of the equation of the ellipse:
(x - h)² / a² + (y - k)² / b² = 1, b > a
Where:
(h, k) - Center of the ellipse.a, b - Length of the semiaxes.If we know that (h, k) = (3, 5), a = 12, b = 14, then the standard form of the equation of the ellipse is:
(x - 3)² / 12² + (y - 5)² / 14² = 1
(x - 3)² / 144 + (y - 5)² / 196 = 1
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help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
Pls helppppppppppppp quick
Answer: (0, -3)
Step-by-step explanation:
You start from the x axis which is zero and then u go to the y axis and look for -3
For every point on the graph of F(x), there is a point on the graph of F1(x)
with exactly the same coordinates.
A. True
B. False
Which trigonometric functions have the same maximum value? y = arcsinx and y = arccosx y = arcsinx and y = arctanx y = arctanx and y = arcsecx y = arccosx and y = arcsecx.
Trigonometric functions have the same maximum value y = arcsinx and y = arccosx.
What is Trigonometric Function?
Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. It implies that these trig functions provide the relationship between a triangle's angles and sides.
Arcsin, Arccos, Arcsec, and similar symbols are used to represent inverse trigonometric functions.
Inverse functions refer to the trigonometric operations that are used to determine an angle from any of the angle's trigonometric ratios.
When solving inverse trigonometric equations, the following formula is used:
Arcsinx = Arcsinx -
arccosx = pi-arccosx.
Arctan = Arctan - Arctan
arsecx = pi - arsecx
The maximum values we obtain from the following equations are:
arcsinx = -1 to 1
arccosx = -1 to 1
arctanx = -pi/2 to pi/2
arcsecx = ∞
So the trigonometric functions which have the same maximum value is arcsinx and arccosx.
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A candidate for office claims that "there is a correlation between television watching and crime." Criticize this statement on statistical grounds.
There may be an association, but not a correlation unless the variables are quantitative. There could be a correlation between the average number of hours of TV watched per person and number of crimes committed per year. Even if there is a relationship, one does not cause the other.
What is correlation?Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).
What are qualitative and quantitative variables?
The variables are classified as qualitative or quantitative as follows:
Qualitative variables assume labels as values.
Quantitative variables assume numbers as values.
The relevance of the variables according to association and correlation are given as follows:
Qualitative variables can have association.
Quantitative variables can have correlation.
The variables in this problem are given as follows:
Television watching -> yes/no -> qualitative.
Crimes committed -> yes/no -> qualitative.
As they are qualitative variables, they can have association, and thus there is no correlation between the two variables
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What is the y-intercept, b, of the additive relationship represented by this table?
Enter your answer as an integer in the box.
b = ?
Answer:
3
Step-by-step explanation:
A grocery store sells a bag of 4 oranges for $1. 4. If have spent $2. 34 on oranges, how many did he buy?.
If he has $2.34 to spent on oranges, then he can buy 6 oranges
Total number of oranges in a bag = 4 oranges
The cost of 4 oranges = $1.4
The total amount that he spent = $2.34
Here we have to use the unitary method
The cost of 1 orange = The cost of 4 oranges / 4
Substitute the values in the equation
= 1.4/4
= $0.35
Then the number of oranges that he bought = The total amount that he spent / The cost of 1 orange
Substitute the values in the equation
= 2.34 / 0.35
Divide the terms
= 6.68
≈ 6
Hence, he can buy 6 oranges with $2.34
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Boden's account has a principal of $600 and a simple interest rate of 3.3%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$600\\ r=rate\to 3.3\%\to \frac{3.3}{100}\dotfill &0.033\\ t=years\dotfill &4 \end{cases} \\\\\\ A=600[1+(0.033)(4)] \implies A=600(1.132)\implies A = 679.2[/tex]
Answer: photo
Step-by-step explanation: picture
One of the brightest stars in the sky is Sirius , which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. How far, in miles, is Sirius ?
If one of the brightest stars in the sky is Sirius , which is part of the constellation Canis Major Sirius is 9 light years from the Earth. One light year=5.88 x 10^12 miles. The distance is 5.29 x 10^13 miles.
What is distance?Distance can be defined as the length of an object or how far an object is from another object.
Given data:
9 light years
5.88 x 10^12 miles
Now let find the how far, in miles, is Sirius
Distance = 5.88 x 10^ 12 miles× 9 light year
Distance = 52,920,000,000,000
Distance = 5.29 x 10^13 miles
Therefore we can conclude that the distance is 5.29 x 10^13 miles.
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What is the value of x? Show your work.
Out of a group of 360 students, exactly 18 are on the track team. What percent of the students are on the track team?
if we take 360 to be the 100%, what's 18 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 360 & 100\\ 18& x \end{array} \implies \cfrac{360}{18}~~=~~\cfrac{100}{x}\implies 20=\cfrac{100}{x} \\\\\\ 20x=100\implies x=\cfrac{100}{20}\implies x=5[/tex]
If (x+r)(x+s)=x² +3x-10 for all x, then what is the value for (r+s)?
The value of (r + s) in the given equation, (x+r)(x+s) = x² + 3x - 10, is (r + s) = 3
Determining the value of an expression from an equationFrom the question, we are to determine the value of the given expression.
The expression we are to determine its value is
(r + s)
To do this, we will compare the terms of the given equation.
From the given equation
(x+r)(x+s) = x² + 3x - 10
First, we will expand the left-hand side of the equation
Expanding the left-hand side of the equation
(x+r)(x+s)
x(x + s) + r(x + s)
x² + xs + xr + rs
Factor the middle expressions
x² + x(s + r) + rs
x² + x(r + s) + rs
x² + (r + s)x + rs
Now, compare the resulting expression to the expression on the right-hand side
x² + 3x - 10
By comparison,
r + s = 3
Hence, the value is 3
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help meeeeeeeeeeeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
[tex]A=5300(1+\frac{.08}{12} )^{12\times6[/tex]
[tex]A=5300(1.00666666667)^{72}[/tex]
[tex]A=5300\times1.613502[/tex]
[tex]A=8551.561489[/tex]
Now, it is up to you to round to the nearest cent.
Thanks,
Eddie
David's iPod has about 10,000 songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of 225 seconds and a standard deviation of 60 seconds. Suppose we choose an SRS of 10 songs from this population and calculate the mean play time
x
of these songs. What are the mean and the standard deviation of the sampling distribution of
x?
Explain.
The mean and the standard deviation of the sampling distribution of x are given as follows:
Mean: 225 seconds.Standard deviation: 19 seconds.How to obtain the mean and the standard deviation of the sampling distribution of x?The mean and the standard deviation of the sampling distribution of x are defined according to the Central Limit Theorem, which states that:
The mean is the same as the population mean.The standard deviation is the division of the population standard deviation by the square root of the sample size.The parameters for this problem are given as follows:
Population mean of 225 seconds.Population standard deviation of 60 seconds.Sample size of 10 seconds.Hence the standard deviation for the sampling distribution of x is given as follows:
s = 60/sqrt(10) = 19 seconds.
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Express the formula d=rt in terms of the time,t. Use your formula to find the time when the distance is 40 and the rate is 8.
The expression for d=rt in terms of the time is t = d/r; t = 5.
What is time? Time can be defined as a continuous and ongoing sequence of events that occur consecutively from the past to the present to the future. Time is used to measure, measure or compare the duration of events or the intervals between them, and even the sequence of events. Time is a useful concept that we use in our daily life. We have to watch when we cook, play, study, go to school, meet someone, etc. So knowing the right time is very important. Time is usually the answer to when an event happens or happened. The concept of time determines when a certain event occurs, has occurred or will occur. Time is a measurable quantity and is also infinite. The time is calculated in seconds, minutes, hours, days, months and years.Therefore,
In the equation d=rt
t = d/r
when distance is 40 and the rate is 8
t = d/r
Replace d with 40 and rate with 8
t = 40/8
t = 5
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The area of a triangle is always one half the base b times the height h.
If the base is represented by the expression 4x + 2 and the height is represented by 3x, which expression gives the area of the triangle?
9x
9x2
12x2 + 6x
6x2+ 3x
The correct option is [tex]6x^2+3x[/tex] which is the area of triangle. It can be obtained by the formula of area of triangle and algebriac multiplication.
What is the are formula of area of a triangle?
Area of any shape is the measure of the 2 dimentional space occupied by that shape. Its SI unit is [tex]m^2[/tex]. Area of the triangle is given by the following formula:
[tex]A=\frac{1}{2}bh[/tex]
Here, A is the area, b is the base, and h is the height.
Substitute 4x+2 for b and 3x for h in the above equation.
[tex]A=\frac{1}{2}(4x+2)(3x)[/tex]
Now, multiply using algebriac multiplication as follows:
Initially, use distributive property as follows:
[tex]A=\frac{1}{2}[(4x)(3x)+(2)(3x)][/tex]
Now, multipliy and again open brackets as follows
[tex]A=\frac{1}{2}(12x^2+6x)\\=6x^2+3x[/tex]
This gives the area of the triangle is [tex]6x^2+3x[/tex]. Hence, the correct option is the last option.
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Answer:
d
Step-by-step explanation:
Select the statement below that is true about correlations.A. Correlations can only be negativeB. Correlations are a measure of how much one variable changes as the other variable changesC. Correlations are a measure used to determine the degree to which two variables are related.D. Correlations are a measure of causation between two variablesE. A negative correlation implies no relationship between variablesF. Correlations can only be positive
The statements that are True about the Correlations is , "Correlations are a measure used to determine the degree to which two variables are related" , the correct option is (c) .
In the question,
few statements about Correlation is given ,
we need to find the statement that is True .
we know that , Correlation is the term that is used to measure the degree of relationship between two variable ,
the correlation can be negative , positive or 0 ,
and the negative correlation implies that if one variable increases then other variable decreases and vice a versa .
So , from the above information about Correlation ,
we conclude that , the True statement is "Correlations are a measure used to determine the degree to which two variables are related. "
Therefore , the statement in option (c) is True .
The given question is incomplete , the complete question is
Select the statement below that is true about correlations.
(a) Correlations can only be negative
(b) Correlations are a measure of how much one variable changes as the other variable changes
(c) Correlations are a measure used to determine the degree to which two variables are related.
(d) Correlations are a measure of causation between two variables
(e) A negative correlation implies no relationship between variables
(f) Correlations can only be positive .
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In 8 day, a ample of vanadium-48 decay to 1/√2 of it original amount. Determine the half-life of vanadium-48
The half-life of vanadium-48 is 16 days.
What is half life?
The half-life formula is used to determine the half-life of a material whose quantity is degrading or decreasing. When a substance degrades, the rate of decay varies depending on the quantity present. It is exceedingly challenging to determine the life of a decaying substance since when the quantity of the chemical decreases, the pace of decay likewise slows down. In order to offer the appropriate metrics to quantify the life of decomposing material, the half-life formula is applied.
According to law of radio active decay, IN=N
N-- amount of sample present
N1--- initial amount of sample
Decay 0 constant
Half life = 16 days
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what algebraic expression represents a number increased by 5
Answer: x+5
Step-by-step explanation:
Because we don't have a number so we call it x. And to increase by 5 just need to +5. So x+5
T/F the proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the .
The proportion of the variation in the dependent variable y that is explained by the estimated regression equation is measured by the coefficient of determination.
What is coefficient of determination?
The effectiveness of a statistical model in forecasting a result is shown by the coefficient of determination (R²). The dependent variable in the model is a representation of the result.
R² can have a value of 0 or 1, with 1 being the maximum achievable. Simply said, a model's R² will be closer to 1 the more accurate its predictions are.
R² is a more precise measure of goodness of fit. The amount of volatility in the dependent variable that the model can account for.
You can typically tell whether your linear regression data's R² is high or low by graphing it. The graphs below, for instance, display two sets of simulated data:
Dots represent the observations.
The line of best fit, or predictions of the model, is displayed as a black line.
Purple lines represent the deviations (the residuals) between the data and their expected values.
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to construct a confidence interval using matched pairs, we must compute the standard deviation of the
We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated.
The complete question is:
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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We must calculate the standard deviation of the differences between the values in the matched pairs in order to build a confidence interval using those values.
What is the difference between standard deviation and confidence interval?
The 95% confidence interval is another frequently used measure of accuracy. In order to calculate it, a range of values that is 95% likely to contain the true population mean must be created using the standard deviation.
According to the 68-95-99.7 Rule, 95% of values are within two standard deviations of the mean, so to calculate the 95% confidence interval, one need only add and deduct two standard deviations from the mean.
Data dispersion in relation to the mean is quantified by a standard deviation, or σ. Data are said to be more closely clustered around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
The difference between the values in the matched pairs' standard deviation is calculated
To construct a confidence interval using matched pairs, we must compute the standard deviation of the ___ between the values in the matched pairs.
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