Answers
Answer:
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Step-by-step explanation:
The last column is the solution
The rest of the columns are the coefficients of the variables
x +0y+0z = 400
-x +y+0z = 150
-8x +0y +z = 250
Related Questions
Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?
Answers
Answer:
4h - 6 = 70.
Step-by-step explanation:
Jahill's height is 70 inches. That is 6 inches shorter than 4 times his sister's height, h. That is the same thing as 4 times h minus 6.
70 = 4 * h - 6
4 * h - 6 = 70
4h - 6 = 70
4h = 76
h = 19.
His sister is 19 inches tall.
Hope this helps!
Answer:
Hello! The answer will be below! :3
Step-by-step explanation:
Question: Jahlil is 6 inches shorter than 4 times his sister’s height. Jahlil’s height is 70 inches. Which equation represents h, his sister’s height in inches?
Answer:The answer is 4h - 6 =70
(His sister is 19 inches tall)
Steps:
4 * h - 6 = 70
So, 4h - 6 = 70......
And 4h will be 76 which means h will equal to 19
His sisters hight is about 19in. tall.....
Hope this helps! :)
⭐️Have a wonderful day!⭐️
PLEASE EXPLAIN IN DETAILS HOW TO SOLVE LINEAR INEQUALITIES. Heres an example problem. Please solve and show your steps/explain.
6(x+8) ≥ ‒43+4x
Answers
Answer:
[tex]x \geq -91/2[/tex]
Step-by-step explanation:
[tex]6(x+8) \geq -43 + 4x[/tex]
Resolving Parenthesis
[tex]6x+48 \geq -43 + 4x[/tex]
Collecting like terms
[tex]6x - 4 x \geq -43-48[/tex]
[tex]2x \geq -91[/tex]
Dividing both sides by 2
[tex]x \geq -91/2[/tex]
Answer:
x ≥ - 91 / 2
Step-by-step explanation:
In this sample problem, the first thing we want to do is expand the part in parenthesis through the distributive property. This will make the simplification process easier. Another approach would be to divide either side by x + 8, but let's try the first.
Approach 1 : [tex]6(x+8) = 6x + 6 8 = 6x + 48[/tex]
[tex]6x + 48 \geq - 43+4x[/tex] - so we have this simplified expression. We now want to isolate x, so let's combine common terms here. Start by subtracting 6x from either side,
[tex]48 \geq - 43-2x[/tex] - now add 43 to either side,
[tex]91\geq -2x[/tex] - remember that dividing or multiplying a negative value changed the inequality sign. Dividing - 2 on either side, the sign changes to greater than or equal to, with respect to x,
[tex]- 91 / 2 \leq x[/tex], or in other words [tex]x \geq - 91 / 2[/tex]. This is our solution.
The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology. In
how many ways can she select 7 workshops if more than 4 must be about anthropology?
Answers
Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Step-by-step explanation:
Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.
If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), ( 6 anthropology, 1 psychology), (7 anthropology, 0 psychology)
Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]
[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex] [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answers
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
Which of the following is a rational function?
F(x)=8x^2-21x+45
F(x)= 3 root of X +17
F(x)= 16x
F(x)= 5x/x^2-25
Answers
For each of the finite geometric series given below, indicate the number of terms in the sum and find the sum. For the value of the sum, enter an expression that gives the exact value, rather than entering an approximation.
3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}
(1) Number of terms
(2) Value of Sum
Answers
Answer:
Number of term N = 9
Value of Sum = 0.186
Step-by-step explanation:
From the given information:
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} + \cdots + 3 (0.5)^{13}[/tex]
Number of term N = [tex]3 (0.5)^{5} + 3 (0.5)^{6} + 3 (0.5)^{7} +3 (0.5)^{8}+3 (0.5)^{9} +3 (0.5)^{10} +3 (0.5)^{11}+3 (0.5)^{12}+ 3 (0.5)^{13}[/tex]
Number of term N = 9
The Value of the sum can be determined by using the expression for geometric series:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{a(r^m-r^{n+1})}{1-r}[/tex]
here;
m = 5
n = 9
r = 0.5
Then:
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.5^5-0.5^{9+1})}{1-0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{3(0.03125-0.5^{10})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =\dfrac{(0.09375-9.765625*10^{-4})}{0.5}[/tex]
[tex]\sum \limits ^n_{k=m}ar^k =0.186[/tex]
For the given the geometric series, 3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³,
the responses are;
(1) The number of terms are 9
(2) The value of the sum is approximately 0.374
How can the geometric series be evaluated?The given geometric series is presented as follows;
3·0.5⁵ + 3·0.5⁶ + 3·0.5⁷ + ...+ 3·(0.5)¹³
(1) The number of terms in the series = 13 - 4 = 9
Therefore;
The number of terms in the series = 9 terms(2) The value of the sum can be found as follows;
The common ratio, r = 0.5
The sum of the first n terms of a geometric progression is presented as follows;
[tex]S_n = \mathbf{\dfrac{a \cdot (r^n - 1)}{r - 1}}[/tex]
The sum of the first 4 terms are therefore;
[tex]S_4 = \dfrac{3 \times (0.5^4 - 1)}{0.5 - 1} = \mathbf{ 5.625}[/tex]
The sum of the first 13 terms is found as follows;
[tex]S_{13} = \dfrac{3 \times (0.5^{13} - 1)}{0.5 - 1} = \mathbf{ \dfrac{24573}{4096}}[/tex]
Which gives;
The sum of the 5th to the 13th term = S₁₃ - S₄
Therefore;
[tex]The \ sum \ of \ the \ 5th \ to \ the \ 13th \ term =\dfrac{24573}{4096} - \dfrac{45}{3} = \dfrac{1533}{4096} \approx \mathbf{0.374}[/tex]
The value of the sum of the terms of the series is approximately 0.374Learn more about geometric series here:
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According to genetic theory, there is a very close to even chance that both children in a two child family will be of the same gender. Here are two possibilities.
(i). 24 couples have two children. In 16 or more of these families, it will turn out that both children are of the same gender.
(ii). 12 couples have two children. In 8 or more of these families, it will turn out that both children are of the same gender. Which possibility is more likely and why?
Answers
Answer:
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Step-by-step explanation:
(i) probability with 16 success out of 24 = 16/24 = 2/3
(ii) (i) probability with 8 success out of 12 = 8/12 = 2/3
Since the two experiments have the same probability, the observed probabilities are the same.
HOWEVER, since the theoretically probability is 1/2, 16.7% less than the experimental results, the number N of trials comes into play.
Using the binomial distribution,
(i)
p = 1/2
N = 24
x = 16 (number of successes)
P(16,24) = C(24,16) p^16* (1-p)^8
= 735471* (1/65536)*(1/256)
= 0.0438
(ii)
p = 1/2
N = 12
x = 8 (number of successes)
P(8,12) = C(12,8) p^8* (1-p)^4
= 495*1/256*1/16
= 0.1208
Therefore scenario (ii) is more likely to occur than scenario (i), and by almost 3 times.
Note: It would help to mention the topic you're on so answers will correspond to what is expected. Here we cover probability and binomial distribution.
Which of the following is the standard form of y =3/7 x-1 a)3/7x-y=1 b) y-3/7x= - 1 c) 7y-3x= -7 d) 3x - 7y= 7
Answers
Answer:
d)
Step-by-step explanation:
the general form is ax + by = c
help plsssssssssssss
Answers
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
Both the red and blue line segments stretch from the center of the circle to a
point on the circle. The length of the blue line segment is 5. How long is the
red line segment?
5
Center
O A. 10
O B. 2.5
O c. 5
O D. 7.5
Answers
Answer:
C. 5
Step-by-step explanation:
The circle has point in the center from where two line blue and red are stretched to the point on the circle. The blue line is 5 in length and the red line length is not known. The circumference of the circle is equal on all the area around the origin. Therefore the red line must also be 5 in length as of blue line.
Look at this triangle work out length AB
Answers
Answer:
2√137
Step-by-step explanation:
To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:
22² + 8² = c²
484 + 64 = c²
548 = c²
c = ± √548 = ± 2√137
c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.
please answer asap. there are two pics :)
Answers
Answer:
[tex]\boxed{\sf A. \ 0.34}[/tex]
Step-by-step explanation:
The first triangle is a right triangle and it has one acute angle of 70 degrees.
We can approximate [tex]\sf \frac{WY}{WX}[/tex] from right triangle 1.
The side adjacent to 70 degrees is WY. The side or hypotenuse is WX.
The side adjacent to 70 degrees in right triangle 1 is 3.4. The side or hypotenuse is 10.
[tex]\sf \frac{3.4}{10} =0.34[/tex]
Consider the statemen P. P.X=5 which of the following is an equivalent statement
Answers
Answer:
(D)R: x+2=7
Step-by-step explanation:
Given the statement P:x=5
An equivalent statement will be a statement whose result is exactly x=5.
From the given options:
R: x+2=7
R: x=7-2
R: x=5
Therefore, R is an equivalent statement.
The correct option is D.
The same bedroom furniture set costs $1,500 in both Florida and Alabama. The table gives a breakdown of the taxes someone would pay when purchasing the furniture set in either state. Alabama Florida State of Alabama: 4.225% County Tax: 1.375% City Tax: 3.0% State of Florida: 6.5% County Tax: 1% City Tax: 1.625% Which statement is true? A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations.
Answers
Answer:
A: True
B, C and D: False
Step-by-step explanation:
We have a total sales tax for Alabama that is:
[tex]T_A=4.225+1.375+3=8.6[/tex]
The total sales tax for Florida is:
[tex]T_F=6.5+1+1.625=9.125[/tex]
The total sales tax is greater in Florida than in Alabama.
A. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by about $8. TRUE
The sales tax difference in this purchase can be calculated as:
[tex]1500(T_F-T_A)=1500\left(\dfrac{9.125-8.6}{100}\right)=1500\cdot 0.00525=7.875\approx 8[/tex]
B. The furniture set is cheaper in Florida, because the amount of sales tax will be lower by about $10. FALSE (it is cheaper in Alabama)
C. The furniture set is cheaper in Alabama, because the amount of sales tax will be lower by $10. FALSE (the sale tax in Alabama is $129)
The amount of sales tax in Alabama is:
[tex]ST_A=1500\cdot T_A=1500\cdot 0.086=129[/tex]
D. The furniture set costs the same in either state, because the amount of sales tax will be the same for the two locations. FALSE (it is not the same in both states).
What is the next term of the geometric sequence? 1, 2, 4, 8, 16,
Answers
Answer: 32
Step-by-step explanation:
When solving the equation, which is the best first step to begin to simplify the equation? Equation: -2 (x + 3) = -10 A: (-2)(-2)(x+3)= -10(-2) B: -1/2(-2)(x+3)= -10(-1/2) C: -2/2(x+3)= -10/2 D: -2/-10(x+3)= -10/-10
Answers
Answer:
Step-by-step explanation:
Given the shape of the equation -2(x+3) = -10. Since x is being multiplied by -2, the first step would be to divide by -2, which is equivalent to multiply by (-1/2) on both sides. Hence the answer is B
A deep-sea diver is in search of coral reefs.he finds a beautiful one at an elevation of -120 4/7feet. While taking pictures of the reef he catches sight of a manta ray. He swims up 25 3/7feet to check it out.what is the diver's new elevation?
Answers
Answer:-95 1/7 feet
Step-by-step explanation:
-120 4/7+25 3/7=-95 1/7 feet
Can someone solve this for me
Answers
Answer:
[tex]12 {y}^{9} - 6 {y}^{5} + 4 {y}^{2} + 21[/tex]
Step-by-step explanation:
divide each term by 2y^3
Multiply through by the least common denominator.
In a certain state, license plates each consist of 2 letters followed by either 3 or 4 digits. How many differen license plates are there that have no repeated letters or digits?
Answers
Answer:
26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities
Step-by-step explanation:
There is nothing stating that the letters and numbers can't be repeated, so all 26 letters of the alphabet and all 10
digits can be used again.
If the first is A, we have 26 possibilities:
AA, AB, AC,AD,AE ...................................... AW, AX, AY, AZ.
If the first is B, we have 26 possibilities:
BA, BB, BC, BD, BE .........................................BW, BX,BY,BZ
And so on for every letter of the alphabet. There are 26 choices for the first letter and 26 choices for the second letter. The number of different combinations of 2 letters is: 26 × 26 = 676
The same applies for the three digits. There are 10 choices for the first, 10
for the second and 10 for the third:
10 × 10 × 10 = 1000
So for a license plate which has 2 letters and 3 digits, there are: 26 × 26 × 10 × 10 × 10 = 676 , 000 possibilities.
Hope this helps.
Given that is both the median and altitude of , congruence postulate SAS is used to prove that is what type of triangle?
A.
equilateral
B.
scalene obtuse
C.
isosceles
D.
scalene acute
Answers
Answer:isosceles is the correct
Step-by-step explanation:
According to the given conditions the triangle ABC is an isosceles triangle.
What is an isosceles triangle?An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Given that, BD is median and altitude in the triangle ABC, and we are asked to find that what type of the triangle ABC will be if we prove triangles ADB and CBD congruent by SAS rule,
So, the proof is as follows,
AD = CD [definition of median]
∠ ADB = ∠ CDB [definition of altitude]
BD = BD [reflexive property]
∴ Δ ADB ≅ Δ CBD by SAS rule
AB = BC by CPCT
According to the definition of an isosceles triangle we can say that, ABC is an isosceles triangle.
Hence, according to the given conditions the triangle ABC is an isosceles triangle.
Learn more about isosceles triangles, click;
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What is the vertex of the graph of g(x) = |x – 8| + 6?
Answers
Answer:
(8,6)Step-by-step explanation:
g(x) = |x – 8| + 6 was transformed from the parent function g(x) = |x|:
8 unit right
6 units up
a parent absolute value function has a vertex at (0,0)
if the function is moved so is the vertex:
(0+8,0+6)
(8,6)
So, the vertex of this function is at (8,6)
Answer: vertex = (8, 6)
Step-by-step explanation:
The Vertex form of an absolute value function is: y = a|x - h| + k where
a is the vertical stretch(h, k) is the vertexg(x) = |x - 8| + 6 is already in vertex form where
h = 8 and k = 6
so the vertex (h, k) = (8, 6)
differentiate with respect to X
[tex] \sqrt{ \frac{cos2x}{1 +sin2x } } [/tex]
Answers
Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):
[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]
Simplify the leading term as
[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]
Quotient rule:
[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]
Chain rule:
[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]
[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]
Put everything together and simplify:
[tex]\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2\sin^2(2x)-2\cos^2(2x)}{(1+\sin(2x))^2}[/tex]
[tex]=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{-2\sin(2x)-2}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac{\sin(2x)+1}{(1+\sin(2x))^2}[/tex]
[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]
[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]
[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]
Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answers
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = [tex]\sqrt{21}-1[/tex]
x = [tex]-\sqrt{21}-1[/tex]
Answer:
A) x = –1 ± square root 21
is the answer:)
In △ABC,a=11 , b=20 , and c=28 . Find m∠A .
Answers
Answer:
18.4°
Step-by-step explanation:
Use law of cosine.
a² = b² + c² − 2bc cos A
11² = 20² + 28² − 2(20)(28) cos A
121 = 1184 − 1120 cos A
cos A = 0.949
A = 18.4°
"A motorist wants to determine her gas mileage. At 23,352 miles (on the odometer) the tank is filled. At 23,695 miles the tank is filled again with 14 gal- lons. How many miles per gallon did the car average between the two fillings?"
Answers
Answer:
24.5 mpg
Step-by-step explanation:
(23,695 - 23,252) / 14 = 24.5mpg
Answer:
The car averaged a total of 24.5 miles per gallon between the two fillings
Step-by-step explanation:
Firstly, we calculate the difference between the mileages.
This will give us the total distance traveled.
That would be 23,695 - 23,352 = 343 miles
The tank capacity obviously is 14 gallons
So mathematically, miles per gallon averaged between the two fillings = distance traveled by the car/gallon of fuel used = 343/14 = 24.5 miles per gallon
Why should you find the least common denominator when adding or subtracting rational expressions?
Answers
Answer:
It is necessary to look for the least common denominator when one is trying to add or subtract rational expressions that do not have the same denominator.
Step-by-step explanation:
for example the denominator of the two addends are not the same. One has (x+2), the other (x-2).
Variables A and B have a covariance of 45, and variables C and D have a covariance of 627. How does the A and B relationship compare to the C and D relationship?
Answers
Answer:
variable A and Variable B are more negatively related than variable C and variable D.
Step-by-step explanation:
Variables A and B have a covariance = 45
Variables C and D have a covariance = 627
Comparing the relationship between variable A AND B with the relationship between variable C and D
variable A and Variable B are more negatively related than variable C and variable D. this is because the covariance between variable A and Variable B are less positive
The side length of the cube is s. Find the domain of the volume of the cube.
Answers
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
For the claim that is given symbolically below, determine whether it is part of a left-tailed, right-tailed, or two-tailed hypothesis test.
p > 0.50
a. a right-tailed hypothesis test
b. a two-tailed hypothesis test
c. impossible to determine from the information given
d. a left-tailed hypothesis test
Answers
Answer:
Option A a right tailed hypothesis test
Step-by-step explanation:
A claim given symbolically is most of the time derived from the alternative hypothesis usually tested against the null hypothesis.
A symbolic claim with the option of a less than indicates a left tailed test, while one with the option of greatest than indicate a right tail test and one with the option of both (not equal to; either less or greater) indicates a two tailed test.
In this case study, the sample proportion for the claim was greater than 0.50 thus, the test is a right tailed hypothesis test
A square matrix N is called nilpotent if there exists some positive integer k such that Nk = 0. Prove that if N is a nilpotent matrix, then the system Nx = 0 has nontrivial solutions.
Answers
Answer:
Nx = λx
Nx = 0, with x≠0
if N is nilpotent matrix, then the system Nx = 0 has non-trivial solutions
Step-by-step explanation:
given that
let N be a square matrix in order of n
note: N is nilpotent matrix with [tex]N^{k} = 0[/tex], k ∈ N
let λ be eigenvalue of N and let x be eigenvector corresponding to eigenvalue λ
Nx = λx (x≠0)
N²x = λNx = λ²x
∴[tex]N^{k}x[/tex] = (λ^k)x
[tex]N^{k}[/tex] = 0, (λ^k)x = [tex]0_{n}[/tex], where n is dimensional vector
where x = 0, (λ^k) = 0
λ = 0
therefore, Nx = λx
Nx = 0, with x≠0
note: if N is nilpotent matrix, then the system Nx = 0 has non-trivial solution