The eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
A typical element p of P4(R) is given by expression p(x)= a0 +a1x+a2x2 +a3x3 +a4x4,
where a0, .... , a4 ∈ R.
With that expression, the eigenvalue-eigenvector equation Tp = λp, which in
this case is xp′(x) = λp(x), becomes
a1x+2a2x2 +3a3x3 +4a4x4 = λ(a0 +a1x+a2x2 +a3x3 +a4x4)
Comparing coefficients in the equation above, we see that the eigenvalue-eigenvector equation is equivalent to the system of equations
0 = λa0 a1 = λa1 2a2 = λa2 3a3 = λa3
4a4 = λa4.
From the equations above, we can see that if j ∈ {0, 1, 2, 3, 4} and aj≠ 0, then we have λ = j and ak = 0 for any k≠ j. Thus the eigenvalue of T are 0,1,2,3,4 and the corresponding eigenvectors are of the form c, cx, cx2, cx3, cx4, where c ∈ R and c≠ 0.
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Find the difference between (1.5 × 108) and (7.4 × 107). Write the final answer in scientific notation.
7.6 × 10^8
7.6 × 10^7
5.9 × 10^−1
−5.9 × 10^1
Answer:
[tex]7.6 \times 10^7[/tex]
Step-by-step explanation:
[tex]1.5 \times 10^8-7.4 \times 10^7 \\ \\ =10^7 (15-7.4) \\ \\ =7.6 \times 10^7[/tex]
The difference between (1.5 x 10⁸) and (7.4 x 10⁷) is 7.6 x 10⁷.
What is subtraction?The mathematical operation is subtraction. It is employed to eliminate words or expression's objects.
To find the difference between (1.5 x 10⁸) and (7.4 x 10⁷) :
We subtract both the numbers,
(1.5 x 10⁸) - (7.4 x 10⁷)
To solve further, we take the common term outside the bracket.
(1.5 x 10⁸) - (7.4 x 10⁷)
= 10⁷ (15 - 7.4)
= 7.6 x 10⁷
Therefore, the difference is 7.6 x 10⁷.
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Aisha and David are reading a book that has 240 pages. Aisha has read
55% of the book, David has read 126 pages Which student has read
more pages so far? How many more pages has that student read?
Answer:
the answer that ur looking for is Aisha she has read more than David
Step-by-step explanation:
55% of 240=132
Answer:
Step-by-step explanation:
Ashia read more
Jose drove a total distance of 72,230.4 yd on a race track. He drove 12 laps where each lap was the same length. What was the length of each lap? Write your answer in miles.
Answer:6019.2
Step-by-step explanation: what you want to do is divide 72,230.4 by 12 and you'll get 6019.2
a positive radial velocity means the object is moving [x] the observer, while a negative velocity means the object is moving [y] the observer.
a positive radial velocity means the object is moving [x] the observer, while a negative velocity means the object is moving [y] the observer ,x away from, y towards
Radial velocity is the velocity of an object in the direction of an observer. A positive radial velocity means the object is moving away from the observer, while a negative velocity means the object is moving towards the observer.Radial velocity is the speed of an object in a particular direction, as observed from an observer. It is measured in the direction towards or away from the observer. A positive radial velocity means the object is moving away from the observer, in a direction radially outward from the observer. A negative radial velocity means the object is moving towards the observer, in a direction radially inward from the observer.
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in the diagram, the number line is marked at consecutive integers, but the numbers themselves are not shown. the four larger dots represent two numbers that are multiples of 3 and two numbers that are multiples of 5. which point represents a number which is a multiple of 15?A. AB. BC. CD. D
A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line.
What is number line
A number line is a visual representation of real numbers in elementary mathematics. It is an image of a magnitude line. It is assumed that each real number on the number line corresponds to a point on the number line, and vice versa.
What are 3 examples of a line?Pencil. Edges of a ruler Edges of a paper
Pencil.
Edges of a ruler.
Edges of a paper.
What are different types of lines?Horizontal Line, Vertical Line, Perpendicular line, Intersecting lines.
Oblique Lines, Divergent lines, Convergent Lines, and Parallel Lines.
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state the distinct ways the number 910 can be written as a product of two positive integer factors. (enter your answer as a comma-separated list of products.)
Here are different ways to express 910 as the product of two positive integer coefficients:
1 x 910, 2x455, 5x182, 10x91, 13x70, 15x61, 26x35, 30x31
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price was $80 yesterday and $104 today whats the percentage increase
Answer:
30%
Step-by-step explanation:
The price of the item increased by $24 from yesterday to today, which represents a 30% increase. To calculate this, divide the increase in price by the original price and multiply the result by 100%:
$24 / $80 x 100% = 30%
Therefore, the percentage increase in the price of the item from yesterday to today is 30%.
Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A ferret weighs 2.1 pounds and costs $3.40 per week to feed, while a Labrador Retriever weighs 70 pounds and costs $7.50 per week to feed. Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth.
$.06 / lb.
$16.56 / lb.
$1.73 / lb.
$1.62 / lb.
The slope of the line between these two points is $.06 / lb which is defined as the ratio of vertical extrade among points, the rise, to the horizontal extrade.
The slope is described because the ratio of the vertical extrade among points, the rise, to the horizontal extrade among the equal points, the run. . A slope with a extra absolute price shows a steeper line. The course of a line is both increasing, decreasing, horizontal or vertical. If a line is horizontal the slope is zero.
Let X1 = 2.1 pounds, Y1 = $3.4 and
X2 = 70 pounds, Y2 = $7.5
ΔX = 70 - 2.1 = 67.9
ΔY = 7.5 - 3.4 = 4.1
Slope (m) = ΔY / ΔX
= 4.1 / 67.9
= 0.060382916053019
= 0.06 (Rounded)
Therefore, answer is Option $.06 / lb.
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47. Find the value of x
400 mg is equal to how many grams
An airplane flying at a given altitude begins its descent directly above a ground marker that is 20.42 miles from the runway. If the glide angle of the airplane to the ground is 30 degrees, how far did the airliner travel in the air from the point of descent until the plane touched ground? Round your answer to the nearest tenth mile.
Answer:
40.8 miles.
Step-by-step explanation:
To solve this problem, we need to know the distance that the airplane traveled in the air from the point of descent until it touched the ground. This distance is determined by the glide angle and the altitude of the airplane.
In general, the distance traveled in the air is equal to the altitude of the airplane divided by the sine of the glide angle. In this case, we are given the altitude and the glide angle, so we can calculate the distance traveled in the air as follows:
Distance = Altitude / sin(glide angle)
Plugging in the values from the problem, we have:
Distance = 20.42 miles / sin(30 degrees)
The sine of 30 degrees is 0.5, so the distance traveled in the air is:
Distance = 20.42 miles / 0.5
This simplifies to:
Distance = 40.84 miles
Rounded to the nearest tenth mile, the distance traveled in the air is 40.8 miles. This is the answer to the problem.
12. Find the LCD: 27, 54, 9, 108
A. 6
B. 108
C. 27
D. 18
The LCD of the given number set is; B: 108
How to find the Lowest common denominator?
The least common denominator (LCD) is defined as the smallest number that is a common denominator for a given set of fractions or numbers.
Now, we are given the number set as;
27, 54, 9, 108
Let us break down these into their respective products in terms of the prime numbers to get;
27 = 3 * 3 * 3
54 = 2 * 3 * 3 * 3
9 = 3 * 3
108 = 3 * 3 * 3 * 2 * 2
Thus, the LCD = 3 * 3 * 3 * 2 * 2 = 108
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for which value(s) of x does f(x)=-10
Answer:
answer on the picture.........
Linda enrolls for 10 credit hours for each of two semesters at a cost of $550 per credit-hour (tuition and fees) in addition, textbooks cost $350 per semester. round your answer to the nearest dollar.
A) $488 B) $150 C) $1463 D) $975
Linda enrolls in two semesters for a total of 20 credits at a cost of $550 per credit hour (tuition and fees), plus $350 for each semester's textbooks. $488 is the total cost for one month. The right response in this case is option A.
In economics, the total cost is the total of all expenses a company incurs in order to produce a particular level of production.
The total cost is the sum of all the expenses a firm has expended to create a specific level of output. Product managers can assess their overall profit margin by adding together their fixed and variable costs. The sum of the fixed and variable expenses is the total cost.
The total cost for one semester = 10(550) + 350
= 5850
Total cost for one month = 5850/12
= 487.5 = $488
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28. The table below shows the comparison of the cost, in dollars, of a
life insurance policy for female non-smokers at certain
$100,000
ages.
Age, a
31
32
33
34
35
Cost, C
170
172
176
178
182
Model the data with a linear function using age 32 and 35. Then
predict the cost of life insurance for a female non-smoker of
age 40. Round to the nearest dollar.
To model the data with a linear function, we can use the two data points for ages 32 and 35 to find the slope and y-intercept of the line. Since the cost of life insurance for a female non-smoker at age 32 is $172 and the cost at age 35 is $182, the slope of the line is given by the formula:
$m = \frac{\text{cost at age 35} - \text{cost at age 32}}{\text{age 35} - \text{age 32}} = \frac{182 - 172}{35 - 32} = \frac{10}{3} = 3.33$
We can then use the point-slope formula to find the y-intercept of the line:
$y - y_1 = m(x - x_1)$
$y - 172 = 3.33(x - 32)$
To find the y-intercept, we can set $x = 0$ and solve for $y$:
$y - 172 = 3.33(0 - 32)$
$y - 172 = -105.76$
$y = 66.24$
Therefore, the equation of the line that models the data is given by:
$y = 3.33x + 66.24$
To predict the cost of life insurance for a female non-smoker of age 40, we can substitute 40 for $x$ in the equation above:
$y = 3.33(40) + 66.24$
$y = \boxed{239.44}$
Therefore, the predicted cost of life insurance for a female non-smoker of age 40 is $239.44.
question content area top part 1 write a differential formula that estimates the change in the surface area of a cube when the edge lengths change from x0 to x0dx
Differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]
As per the given data:
The surface area is given by
[tex]$$S = 6 x^2$$[/tex]
Differentiate both sides with respect to f(x)
[tex]$$S^{\prime}(x)=\frac{d}{d x}\left(6 x^2\right)\\\\=6(2) x^{2-1}$$[/tex]
= 12 x
The estimated change in surface area is given by
[tex]$$d S=S^{\prime}(x) d x= > d S\\\\$$[/tex]
= (12 x) dx
The change in surface area at [tex]$x=x_{0} $[/tex] is
[tex]$$d S=\left(12 x_0\right) d x$$[/tex]
Therefore the answer is [tex]$$d S=\left(12 x_0\right) d x$$[/tex]
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Write a differential formula that estimates the change in the surface area S=6x2 of a cube when the edge lengths change from [tex]x_{0}[/tex] to [tex]x_{0}[/tex] + dx
Atoms of element B from HCP lattice and those of the element A occupy 2/3 rd of tetrahedral voids. What is the formula of the compound formed by the elements A and B?
In a hexagonal-close-pack (HCP) unit cell, the ratio of lattice points to octahedral holes to tetrahedral holes = 1 : 1 : 2 is AB3
let the :
Number of lattice point = 1x.
Number of octahedral points = 1x
Number of tetrahedral points = 2x
If anions occupy the HCP lattice points and cations occupy half of the octahedral holes.
Number of anions occupying the HCP lattice points, A= 1x
Number of cations occupying the octahedral points, B = 1x
The formula of the compound will be =
If anions occupy the HCP lattice points and cations occupy all of the octahedral and the tetrahedral holes.
Number of anions occupying the HCP lattice points, A= 1x
Number of cations occupying the octahedral points, B = x
Number of cations occupying the tetrahedral points, B = 2x
total number of cations = x + 2x = 3x
The formula of the compound will be = AB3
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Two punches are made from steel bar stock 9-7/16 inches long. If one punch 4-1/64 inches long and the other is 4-3/32 inches long, how many inches of stock are wasted?
1-1 / 16''
1-21 / 64''
1-5 / 16''
After simplification of the given stock of steel bar , 1-21/64 inches of available stock are wasted.
As given in the question,
Length of the steel bar in stock = 9 7/16 inches
Length of one punch = 4 1/64 inches
Length of other punch = 4 3/32 inches
Simplification of the given data,
Length of steel bar - length of one punch
= 9 7/16 - 4 1/64
= 144/16 - 256/64
= (576 - 256)/64
= 320/64
=5 27/64 inches
Now,
subtract 4 3/32 from 5 27/64
= 5 27/64 - 4 3/32
= 347/64 - 131/32
=347/64 - 262/64
=(347-262)/64
=85/64
= 1 21/64inches
It means about "1 21/64" inches of the steel beam was wasted.
Therefore, after simplification the length of 1 21/64 inches of stock get wasted.
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1. A study explored the effect of ethanol on sleep time. Fifteen rats were randomized to one of three treatments. Treatment 1 was water (control). Treatment 2 waas 1g of ethanol per kg of body weight, and Treatment 3 was 2g/kg. The amount of REM sleep (in minutes) in a 24hr period was recorded: Treatment 1: 63, 54, 69, 50, 72 Treatment 2: 45, 60, 40, 56 Treatment 3: 31, 40, 45, 25, 23, 28
(a) Graph the data. Why did you choose the graph that you did and what does it tell you?
(b) Create an ANOVA table for the data using the formulas provided in class. Show your work. You may use R to check your answers.
(c) Evaluate the ANOVA assumptions graphically. Was ANOVA appropriate here?
(d) Based on the ANOVA table, make a conclusion in the context of the problem.
(e) Create 95% CIs for all pairwise comparisons of means using the Tukey method. Do this without R show your work. (You may use R to check your work). Summarize your results using letter codes. What do you conclude?
We have to find a problem at the 5% significance level.
Sample size = 10.
If the Significant value is between five and ten, we lose one till the test. W. C. has a critical value of 44. We must perform a one-tailed analysis of the test. What tail is that?
If one is more efficient than the other, we are asked.
Here, almost everything is positive, and we discover what our values are. Mhm. The following data set, High bromide, was employed to get more sleep for 10 patients who used love level high school.
That's the control group minus the other one.
The control group is made up of people. I'm not sure if it's a left or right tail, so we'll just calculate the two ends.
The right tail will be 44, the other tail will be divided by two, and 55 minutes will equal 44. It's extremely useful. Okay. It won't reject if it's less than 11, and it will if it's more than 44. Is the music good? There were 10 pupils in our class, and their scores were 1.9 plus 0.8 plus 1.1 plus 0.1. The value of our nut is 23.4. Okay. Critical value takes us directly to the center. This was only a right tail test because we were unable to rule out the null hypothesis. The results would change to 50 if we ran it again at the 1% significance threshold. ten tons and eleven
We failed to reject the hypothesis again.
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An actuary is studying hurricane models. A year is classified as a high, medium, or low hurricane year with probabilities 0.1, 0.3, and 0.6, respectively. The numbers of hurricanes in high, medium, and low years follow Poisson distributions with means 20, 15, and 10, respectively. Calculate the variance of the number of hurricanes in a randomly selected year
The variance of the number of hurricanes in a randomly selected year is 12.5 .
Mean number of hurricanes in a randomly selected year =
0.1 × 20 + 0.3 × 15 + 0.6 × 10 = 12.5
Now, since the sum of independent Poisson random variables also follows Poisson distribution.
Thus, the variance of the number of hurricanes in a randomly selected year = Mean = 12.5
In both statistics and probability theory, variance is the predicted squared deviation of a binomial distribution from its sample proportion or sample mean.
Dispersion, or how far apart from the mean a set of data are from one another, is measured by variance. A few ideas that involve variance are descriptive research, statistical inference, testing hypotheses, goodness of fit, and Monte Carlo sampling.
The variance of a set of uncorrelated explanatory variables is equal to the sum of their variances, making it easier to manipulate mathematically than other measures of dispersion like anticipated absolute deviation.
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g use the gas prices data set below to calculate a 3-month weighted moving average (wma) forecast for the average gas prices and predict the average retail gasoline price for june 2020. use the weights of 0.6, 0.3, and 0.1 for the 3-month wma, where the first weight is used for the most recent month and the last weight is used for the least recent month. round your answer to two decimal places, if necessary.
We calculated 3-month weight moving average forecast = 0.417
What is weight moving average?It is a statistical expression of calculating average forecast that allows to keep heavier weight with the most recent data.
How to calculate weight moving average?Given, weights for the 3 months are 0.6, 0.3 and 0.1 where the first weight is used for the most recent month and the last weight is used for the least recent month.
the weighing factor will be n, n-1 and n-2
n is the number of periods and n=3
now, weight moving average = [W1 × n +W2 × (n-1) × W3 × (n-2)]/ [n+(n-1)+(n-2)]
[0.6 x 3 +0.3 x 2 + 0.1 x 1]/ [3+2+1] = 0.417
hence, weight moving average is 0.417
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If it snows on a given day, the probability that it snows the next day is 7/10 If it does not snow on a given day, the probability that it snows the next day is 2/10 It is snowing today. By first drawing a tree diagram, work out the probability that it will snow on exactly one of the next two days. Give your answer as a fraction in its simplest form
Answer: 27/100
Step-by-step explanation:
Calculate and then write the reciprocal of your answer.
2/43 of the difference of 3 2/15 and 2 5/12
Step-by-step explanation:
3 2/15 - 2 5/12
4 - 25
1____________ = (60+4) - 25/60
39/60
60
2/43 * 39/60
=78/2580
The value of the reciprocal fraction is A = 30/1 = 30
What is Reciprocal Fraction?The fraction obtained by swapping or interchanging Numerator and Denominator with each other is known as the Reciprocal of the given fraction. The product of reciprocals is 1.
Given data ,
Let the value of the reciprocal fraction be represented as A
Now , the equation will be
Let the first fraction be represented as p
Now , the value of p = 3 2/15
On simplifying , p = 47/15
Let the second fraction be represented as q
Now , the value of q = 2 5/12
On simplifying , q = 29/12
Now , the equation is B = p - q
Substituting the values in the equation , we get
B = ( 47/15 - 29/12 )
B = 43/60
Now , ( 2/43 ) of the value of A is given as
C = ( 2/43 ) ( 43/60 )
On simplifying the equation , we get
C = ( 2/60 )
C = ( 1/30 )
Now , the reciprocal fraction is given as
A = 30/1
A = 30
Hence , the reciprocal fraction is A = 30/1
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which of the following initial values of the variable y would result in the variable z being set to 2 after the code segment is executed?
When the following code section runs, the value of the variable y will be -2.
Given that,
We have to find when the following code section runs, what value will the variable y have? Assume the following input values:
The code mentioned above is explained in the section below.
Here, x=5, n=0, and the input values are 1–6.
So, x>3 is true.
Control will go to second if block and input y and z.
Now y=1 and z=2 and n=1
Next control goes to if(x) since x>0 which is true.
Now z=3 and x=4 and y=0 and n=0
Her n==0 so r=z- ++x => 3- (5) =>-2.
Hence r=-2
Therefore, the variable r=-2 is the output for the code.
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which of the following is a correct factorization of -3x^2+10x-8
Answer:
Step-by-step explanation:
Find the value of x in the kite.
18
32
65.7
The value of x in the kite is 32 (option B)
Polygons are defined as plane (two-dimensional) and closed shapes that are formed by joining three or more line segments with each other.
A polygon can be categorized as regular and irregular polygon based on the length of its sides.
Given figure of kite is a polygon,
Three angles of kite are given as 100° , 101° and (4 + 3x)°
It is given that sides opposite sides are equal to each other
Therefore, opposite angles are also equal
=> 4 + 3x = 100
=> 3x = 96
=> x = 96 / 3
=> x = 32
Hence , Value of x in the kite is 32
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What activities in your municipality do you think produce these gases?
Some activities carried out in my municipality that produce greenhouse gases are:
The cattle industry Transport in specific contextsAnalysis of activities that produce greenhouse gasesThere are many activities that produce these types of gases, some are:
The cattle industry: methane is produced in this industry, which is a potent greenhouse gas.Transport: driving different types of vehicles produces greenhouse gases, for example, CO₂ (carbon dioxide).¡Hope this helped!
refers to meeting the needs of the present generation without compromising the ability of future generations to meet their own needs
The term that refers to meeting the needs of the present generation without compromising the ability of future generations has been sustainability.
¿What is sustainability?This has been a development that focuses on meeting the needs that arise today without compromising the resources of the following generations.
Sustainability is of paramount importance because:
It enables and contributes to economic growth. Contribute to environmental care and conservation.¡Hope this helped!
Please Help!
You are at a fundraising carnival. You want to play one game and you've narrowed it down to two options, as follows:
OPTION 1: Choose a face card (K, Q, J) from a deck of cards. Then, spin an odd number on an 11-part spinner. $5 per play. Grand prize is $150.
OPTION 2: Roll two dice with a product greater than 4 and less than 12. Then, choose a numbered card from a deck of cards. $15 per play. Grand prize is $200.
Which option will you choose and why? Show your work and explain your thinking.
a psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores. she uses this data to test the hypothesis that the mean dexterity score is different than 45.
A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores, then if she wants to improve her precision she should use a larger sample size.
Each sample has an equal chance of being chosen as part of the sampling procedure known as random sampling. A randomly selected sample is intended to be a fair reflection of the entire population. By increasing sample size, you can improve the accuracy of your estimates, which means that the result will be more "statistically significant" for any given estimate or size of effect. The accuracy of the average results will increase with sample quantity. Smaller error margins and the identification of outliers in the data are two further benefits of larger sample sizes.
If they observe an effect that is almost significant, some researchers decide to increase their sample size. This is done rather than concluding that there is no effect because the researcher believes he is short on samples. Because the standard error is reduced as sample size increases, confidence intervals are narrower. c) The statement "there is a 95% likelihood that the population mean is between 350 and 400" is similar to the statement "there is a 95% confidence interval for the population mean is (350, 400)".
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Correct Question:
A psychologist selects a random sample of 25 handicapped students and measures their manual dexterity scores. she uses this data to test the hypothesis that the mean dexterity score is different than 45. What would you advise her?