Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues.
Explanation:Yes, it is possible for a 7 x 7 matrix to not be diagonalizable even if it has three eigenvalues. A matrix is diagonalizable if and only if it has n linearly independent eigenvectors, where n is the size of the matrix. In this case, since we have one eigenspace two-dimensional and one eigenspace three-dimensional, we have a total of 5 linearly independent eigenvectors. Since 5 is less than 7, the matrix is not diagonalizable.
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Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors.
Explanation:Yes, it is possible that matrix A is not diagonalizable. For a square matrix to be diagonalizable, it must have a complete set of eigenvectors. In this case, we have a 7 x 7 matrix with three eigenvalues, but only two eigenspaces are given (a two-dimensional eigenspace and a three-dimensional eigenspace). Since we don't have eigenvectors for all the eigenvalues, matrix A is not guaranteed to be diagonalizable.
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Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the first card is an ace, or the second a deuce, or the third a three, or, . . . , or the thirteenth a king, or the fourteenth an ace, and so on, we say that a match occurs. Note that we do not require that (13n + 1)th card be any particular ace for a match to occur but only that it be an ace. Compute the expected number of matches that occur.
Answer:
The expected number of matches that occur is 4.
Refer below for the explanation.
Step-by-step explanation:
Refer to the picture for complete steps.
On a very hot summer day, 5 percent of the production employees at Highlander Steel are dehydrated. The production employees are randomly selected for a special in-depth study on dehydration. What is the probability of randomly selecting 8 production employees on a hot summer day and finding that none of them are dehydrated
Answer:
P(X=0) = 0.0332
Step-by-step explanation:
5% of the employees are dehydrated. I.e. p = 5/100
p = 0.05
The percentage of employees that are not dehydrated = 100-5 = 95%
q = 1 - p = 1 - 0.05
q = 0.95
A total of 8 employees were randomly selected. n = 8
This is a binomial distribution question
P(X =r) = nCr (p^r)q^(n-r)
n = 8, r = 0
n -r = 8-0 = 8
P(X = 0) = 8C0 (0.05^0)(0.95^8)
8C0 = 1
P(X=0) = 1 * 1* 0.6634
P(X=0) = 0.6634
Answer:
The probability of picking 8 employee and none of them is dehydrated is 0.66
Step-by-step explanation:
P(employee is dehydrated) = 5%=5/100=1/20= 0.05
P(employee not dehydrated) = 1 - 0.05= 0.95
The probability of picking 8 employee and they are not dehydrated is:
= (0.95)^8
= 0.6634204312890625
= 0.66
What are the quotient and remainder of (3x^4+ 2x^2 - 6x + 1) = (x + 1)
Answer: Im 75% sure the answer is A. Its either A or B.
Step-by-step explanation:
Two components in a rocket operate independently, and the probability that for every component to fail on a launch is p. Let X denote the number of launches required to have a failure of the first component, and let Y denote the number of launches required to have a failure of the second component, X, Y
Answer: p = X/(1-X)X + Y/(1-Y)Y
Step-by-step explanation:
What are the functions of money?
Answer:
The functions of money are:
Function # 1. A Medium of Exchange: ...
Function # 2. A Measure of Value: ...
Function # 3. A Store of Value (Purchasing Power): ...
Function # 4. The Basis of Credit: ...
Function # 5. A Unit of Account: ...
Function # 6. A Standard of Postponed Payment:
Explanation:
My parents are bankers.
The ordered pairs in the table below represent a linear function.
What is the slope of the function?
One-fourth
One-half
2
4
Answer:
2Step-by-step explanation:
The ordered pairs are
x | y 2 | 3 5 | 9The slope is:
m = (y2 - y1)/(x2 - x1) m = (9 - 3)/(5 - 2)= 6/3 = 2Answer is 2
Answer:
4
Step-by-step explanation:
The graph is:
x y
1/4 2
1/2 4
Slope formula is (y2-y1/x2-x1)
4-2/0.5-0.25
2/0.25
4
Best of Luck!
Given that’s the measure of the angle is 109, what is the measure of angle k?
Answer:
k is also 109 degrees bcoz they are corresponding angles
What is the surface area of this cylinder? Use 3.14 and round your answer to the nearest hundredth.
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a Normal distribution with mean that varies slightly from year to year and standard deviation 6.0. You plan to take an SRS of size n of the students who took the ACT exam this year and compute the mean score of the students in your sample. You will use this to estimate the mean score of all students this year. In order for the standard deviation of to be no more than 0.1, how large should n be
Answer:
The sample size must be atleast 3600
Step-by-step explanation:
We are given the following in the question:
The scores of individual students on the American College Testing (ACT) Program is a bell shaped distribution that is a normal distribution.
Population standard deviation = 6.0
We want that the sample standard deviation should not be more than 0.1.
Thus, the standard error should not be more than 0.1.
Standard error =
[tex]=\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting values, we get,
[tex]\dfrac{\sigma}{\sqrt{n}}\leq 0.1\\\\ \dfrac{6}{\sqrt{n}} \leq 0.1\\\\ \sqrt{n}\geq 60\\n\geq 3600[/tex]
Thus, the sample size must be atleast 3600
A waste management service attempts to design routes so that each of their trucks pick-up on average
four tons of garbage or less. A garbage collector believes, however, that he averages picking up more
than four tons of garbage per day and decides to perform a hypothesis test.
Identify a Type II error in the context of this hypothesis test.
a) Concluding that the garbage collector picks up on average more than 4 tons of garbage per day when,
in fact, he doesn’t.
b) Not concluding that the garbage collector picks up on average more than 4 tons of garbage per day
when, in fact, he does.
c) Concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact, he
picks up more.
d) Not concluding that the garbage collector picks up on average 4 tons of garbage per day when, in fact,
he does.
I'm confused with the wording but my guess is between B and C
Answer:
The correct option is (c).
Step-by-step explanation:
A type II error is a statistical word used within the circumstance of hypothesis testing that defines the error that take place when one is unsuccessful to discard a null hypothesis that is truly false. It is symbolized by β i.e.
β = Probability of accepting H₀ when H₀ is false.
In this case we need to test the hypothesis whether the garbage collector's belief is true or not.
The hypothesis can be defined as:
H₀: The garbage collector averages picking up four tons of garbage per day, i.e. μ = 4.
Hₐ: The garbage collector averages picking up more than four tons of garbage per day, i.e. μ > 4.
Consider that the garbage collector made a type II error while drawing the conclusions of the test.
This implies that the garbage collector failed to reject the null hypothesis incorrectly.
That is, he concluded that the he picks up on average four tons of garbage per day, when in fact he picks up more than four tons of garbage every day.
Thus, the correct option is (c).
Answer:4 tons
Step-by-step explanation:
just because ik;;;:)
2.
1. A small town's population is growing at
an exponential rate. In 2010, there were
700 residents in the town. In 2011 there
were 770 residents and in 2012, there
were 847 residents. What equation can
be used to determine p, the number of
residents in 2018?
Answer:
[tex]P(8)=700\cdot(1.1)^8\approx 1500[/tex], where t is the number of years since 2010.
Step-by-step explanation:
See my attached image for an explanation!
What is the area of the following shape?
Answer:
104 m^2
Step-by-step explanation:
We first find the area of the rectangle
A = l*w
A = 10*8
A = 80
Then we find the area of the triangle
A = 1/2 bh
A = 1/2 (8)(6)
= 24
Then we add the areas together to find the total area
80+24 = 104
At a large university a simple random sample of five female professors is selected and a simple random sample of 10 male professors is selected. The two samples are combined to give an overall sample of 15 professors. The overall sample is a A. simple random sample. B. biased due to imbalance. C. a stratified sample. D. All of the above
Answer:
D. All of the above
Step-by-step explanation:
Samples may be classified as:
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this problem:
Two random samples are selected and combined. The combination is a random sample. So A. is correct.
They are not balanced. More male professors than female are chosen. So B. is correct.
The teachers are divided into groups(male and female). And some members of each group are selected. So C. is correct.
So the correct answer is:
D. All of the above
A polynomial of degree at least 3 where all the zeros are positive whole numbers
We can build a polynomial given it's degree and zeros. Below I am going to show how we do that, and then I will solve the question, finding that one example of a desired polynomial is:
[tex]f(x) = x^3 - 15x^2 + 54x - 40[/tex]
Zeros of a function:
Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.
In this question:
Polynomial of degree 3, so 3 roots.
All positive, I will choose:
[tex]x_1 = 1, x_2 = 4, x_3 = 10[/tex]
I will choose the leading coefficient as a = 1.
Thus
[tex]f(x) = a(x - x_1)(x - x_2)(x - x_3)[/tex]
[tex]f(x) = (x-1)(x-4)(x-10)[/tex]
[tex]f(x) = (x^2-5x+4)(x-10)[/tex]
[tex]f(x) = x^3 - 15x^2 + 54x - 40[/tex]
The image shown in the end of this question shows that this polynomial has three positive roots, also all whole numbers.
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The University of Montana ski team has nine entrants in a men's downhill ski event. The coach would like the first, second, and third places to go to the team members. In how many ways can the nine team entrants achieve first, second, and third places
Answer:
504 ways
Step-by-step explanation:
The first position can go in 9 ways
The second position can go to the team in 8 ways
The third position can go to the team in 7 ways
Therefore, the first,second and third position can go to the team in:
9 X 8 X 7=504 ways
or Simply, we can use Permutation.
[tex]^9P_3=504[/tex] ways
A charge q1 = 5 μC, is at the origin. A second charge q2 = -3 μC is on the x-axis 0.8 m from the origin. The electric field at a point on the y-axis 0.5 m from the origin is:
Answer:
[tex]\vec{E}=\vec{E_1}+\vec{E_2}=[25856\hat{i}+163443.2\hat{j}]N/C[/tex]
Step-by-step explanation:
The electric field is given by:
[tex]E=k\frac{q_1q_2}{r^2}[/tex]
k: Coulomb's constant = 8.98*10^9 Nm^2/C^2
at the point P(0,0.5m) you have both x ad y component of the electric field. For the particle q1 you have:
[tex]\vec{E_1}=Ex\hat{i}+Ey\hat{j}\\\\\vec{E_1}=0\hat{i}+(8.89*10^9Nm^2/C^2)\frac{(5*10^{-6}C)}{(0.5m)^2}\hat{j}=179600N/C\hat{j}[/tex]
for the particle q2, it is necessary to compute the angle between the E vector and the axis, by using the distance y and x. Furthermore it is necessary to know the distance from q2 to the point P.
[tex]\vec{E_2}=Excos\theta \hat{i}-Eysin\theta \hat{j}\\\\\theta=tan^{-1}(\frac{0.5}{0.8})=32\°\\\\r=\sqrt{0.5^2+0.8^2}=0.94m\\\\\vec{E_2}=(8.89*10^9Nm^2/C^2)\frac{(-3*10^{-6C})}{(0.94m)^2}[cos(32)\hat{i}-sin(32)\hat{j}]\\\\=[25856.06\hat{i}-16156.71\hat{j}]N/C[/tex]
Finally, by adding E1 and E2 you obtain:
[tex]\vec{E}=\vec{E_1}+\vec{E_2}=[25856\hat{i}+163443.2\hat{j}]N/C[/tex]
What type of triangle, if any can be formed with angle measures of 32 degrees, 126 degrees, and 32 degrees?
Answer 1 only an obtuse triangle
Answer 2 either an acute isosceles triangle or an obtuse isosceles triangle
Answer 3 only an acute isosceles triangle
Answer 4 no triangle
No triangle can be formed.(answer 4)
What is triangle?In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees
We have,
Angles of triangle= 32 degrees, 126 degrees , 32 degrees
We know,
All triangles must have angles that measure up to 180 degrees.
[tex]32^{o} +126^{o} + 32^{o}[/tex]
=[tex]190^{o}[/tex] > [tex]180^{0}[/tex]
Hence ,That means that is no triangle can be formed.
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The sum of the given angles exceeds 180 degrees, which violates the basic rule of triangles, so no triangle can be formed with these measures.
Explanation:To determine what type of triangle can be formed with angle measures of 32 degrees, 126 degrees, and 32 degrees, we need to consider two rules: First, the sum of the angles in any triangle must be 180 degrees. Second, the classification of whether a triangle is acute, obtuse, or right is based on the measures of its angels.
Adding the given angles together (32 degrees + 126 degrees + 32 degrees), we get 190 degrees. Since this sum is greater than 180 degrees, it violates the first rule of triangles. Therefore, no triangle can be formed with these given angle measures.
What is the volume of the square pyramid with base edges 32 mm and slant height 34 mm?
9,920 mm3
10,010 mm3
7,680 mm3
10,240 mm3
Answer:
V = 10,240mm^3
Step-by-step explanation:
The volume of pyramid is given by the following formula:
[tex]V=\frac{1}{3}bh[/tex] (1)
b: base of the pyramid = (32mm)^2
h: height
Thus, it is necessary to find the value of h, by using the Pitagoras's theorem, one half of the base and the slant height (which forms a rectangle triangle with h):
[tex]h=\sqrt{(34)^2-(16)^2}=30mm[/tex]
by replacing in (1) you obtain:
[tex]V=\frac{1}{3}(32mm)^2(30mm)=10,240\ mm^3[/tex]
hence, the volume is 10240mm^3
i’ll mark brainlist the first personify gets it
I am going to assume 10.42 is 10 minutes 42 secons.
10 min * 60 seconds / per minute, = 600 seconds
600 + 42 = 642 seconds starting
-
8 min * 60 seconds / per minute, = 480 seconds objective
To solve for how long this will take set up an equation,
642 - 1.6t = 480
162 = 1.6t
t = 101.25 days
Since time has a decial, it needs to be rounded up in order for her to be fully below 8 minutes.
Therefore the answer is 102 days.
What’s the value of Y?
Answer:
44
Step-by-step explanation:
if 88 is the right angle degree, that means the acute angle would be half of 88.
88÷2=44
Find the arc length of the shaded region. Multiply through by #(3.14) Round solution to
tenth place. Ex. 1.2
90°
Given:
The radius of the circle is 12 units.
The central angle of the shaded region is 90°
We need to determine the arc length of the shaded region.
Arc length:
The arc length of the shaded region can be determined using the formula,
[tex]Arc \ length=(\frac{\theta}{360} ) 2 \pi r[/tex]
substituting [tex]\theta=90[/tex] and r = 12, we get;
[tex]Arc \ length=(\frac{90}{360} ) 2 (3.14)(12)[/tex]
Multiplying the terms, we have;
[tex]Arc \ length=\frac{6782.4}{360}[/tex]
Dividing, we get;
[tex]Arc \ length=18.84[/tex]
Rounding off to the nearest tenth, we get;
[tex]Arc \ length =18.8[/tex]
Thus, the arc length of the shaded region is 18.8 units.
A group of statistics students conducted a survey about smoking habits on campus to determine the proportion of students who believe that smoking hookah (a water pipe) is less harmful than smoking cigarettes. Of the 50 students surveyed, 45 think that smoking hookah is less harmful than smoking cigarettes.
Which of the following is a reason that this group of students should not calculate a confidence interval for the proportion of all students who believe that smoking hookah is less harmful than smoking cigarettes? Check all that apply.
a) The sample needs to be random but we don’t know if it is.
b) The actual count of students who believe that smoking hookah is less harmful than smoking cigarettes is too small.
c) The actual count of students who do not believe that smoking hookah is less harmful than smoking cigarettes is too small.
d) n(p^) is not greater than 10.
e) n(1 - p^) is not greater than 10.
Answer:
The answer is A, C and D
Step-by-step explanation:
a
c
d
The correct answer is a) The sample needs to be random but we don’t know if it is.
Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate.
Why is it necessary to satisfy the random condition?The situation at random we receive impartial population data from random sampling. It might be dangerous to draw conclusions about a community from data that was not randomly chosen samples since such data typically contains some type of bias.
Calculate success by multiplying the sample % by the sample size to make sure the sample size is adequate, and calculate failure by multiplying one less than the sample percentage by the sample size. The condition is satisfied if both of these items are larger than ten.
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A mixture of pulverized fuel ash and Portland cement to be used for grouting should have an average compressive strength of more than 1300KN=m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture has standard deviation ? = 60. Let ? denote the true average compressive strength.
Answer:
Check the explanation
Step-by-step explanation:
Hypotheses are:
[tex]H_o[/tex] : μ 1300, [tex]H_a[/tex] : μ > 1300
The distribution of test statistics will be normal with mean
mean 1300
and standard deviation
[tex]sd=\frac{\sigma}{\sqrt{n}}=\frac{68}{\sqrt{11}}[/tex]=20.50277
Now z-score for T-1331.26 and μ 1300 is
-1300-1.52 1331.26 1300 68/V11
[tex]z=\frac{1331.26-1300}{68/\sqrt{11}}= 1.52[/tex]
So the probability distribution of the test statistic when H0 is true is
a = P(z > 1.5247) = 0.0643
Solve for 3x minus one equals 27
Answer:
the answer is 9.3
Step-by-step explanation:
Answer:
9.
Step-by-step explanation:
You would subtract the one to isolate the variable so 3x = 27 then divide by 3 so the answer is 9.
A relation is a special type of function.
A. True
B. False
(30) points
Lena is a college basketball player who has made 75%, percent of the free-throws she has attempted in her career. she decided to practice a new technique for shooting her free-throws. lena was curious if this new technique produced significantly better or worse results. she tried the new technique and made 70%, percent of 50 attempts. here's lena's alternative hypothesis: ha : the proportion of attempts made using this new technique is. what is an appropriate way for lena to finish her alternative hypothesis a.equal to 75% b.not equal to 75% c.not equal to 70% d.equal to 70%
Answer:
b
Step-by-step explanation:
Add a cell phone assembly plant, 80% of the cell phone keypad pass inspection. A random sample of 181 keypads is analyzed. Find the probability that less than 76 in the sample keypads pass inspection.
Answer:
0% probability that less than 76 in the sample keypads pass inspection.
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 181, p = 0.8[/tex]
So
[tex]\mu = E(X) = np = 181*0.8 = 144.8[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{181*0.8*0.2} = 5.38[/tex]
Find the probability that less than 76 in the sample keypads pass inspection.
Using continuity correction, this is [tex]P(X < 76 - 0.5) = P(X < 75.5)[/tex], which is the pvalue of Z when X = 75.5.
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75.5 - 144.8}{5.38}[/tex]
[tex]Z = -12.88[/tex]
[tex]Z = -12.88[/tex] has a pvalue of 0
0% probability that less than 76 in the sample keypads pass inspection.
If you double a number and then add 32, you get two ninths
of the original number. What is the original number?
Answer:
The number is -18
Step-by-step explanation:
Let x be the original number
2x +32 = 2/9x
Multiply each side by 9 to get rid of the fractions
9(2x +32) =9* 2/9x
18x +288 = 2x
Subtract 18x from each side
18x-18x+288 = 2x-18x
288 = -16x
Divide each side by -16
288/-16 = -16x/-16
-18 =x
Answer:
–18
Step-by-step explanation:
let the number is [tex]x[/tex], from the problem we know that
[tex]2x+32=\frac{2}{9}x
\\9x+144=x
\\x=-\frac{144}{8}=-18[/tex]
What is the surface area of this square pyramid
Answer 144 ft2
Step-by-step explanation:
Answer:
The surface area is 81 feet squared
Step-by-step explanation:
IM SO SORRY! the answer is 33 feet squared
Expression is equivalent 1/3+(3/4+2/3)?
The expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.
Explanation:The expression is equivalent to 1/3 + (3/4 + 2/3). To solve this expression, we need to simplify the inner parentheses first. Adding 3/4 and 2/3, we get a common denominator of 12:
3/4 + 2/3 = 9/12 + 8/12 = 17/12Now, we can substitute the simplified fraction back into the original expression:
1/3 + (3/4 + 2/3) = 1/3 + 17/12To add the fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 12:1/3 + 17/12 = 4/12 + 17/12 = 21/12Finally, we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 3:21/12 = (3 * 7) / (3 * 4) = 7/4Therefore, the expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.