Answers
[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]
Answer:
[tex]\large \boxed{560x^3}[/tex]
Step-by-step explanation:
[tex](x+2)^7[/tex]
Expand brackets.
[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]
[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]
[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]
[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]
The fifth term is 560x³.
Related Questions
Will Give Brainliest Please Answer Quick
Answers
Answer:
Option (2)
Step-by-step explanation:
If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.
By using this property,
Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.
By applying Pythagoras theorem in right triangle KNJ,
(KJ)² = (KN)² + (NJ)²
(33)² = (6√10)² + (NJ)²
NJ = [tex]\sqrt{1089-360}[/tex]
NJ = [tex]\sqrt{729}[/tex]
= 27 units
Since, GJ = 2(NJ)
GJ = 2 × 27
GJ = 54 units
Option (2) will be the answer.
Need Help
Please Show Work
Answers
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is the x-value of point A?
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 5
▹ Step-by-Step Explanation
The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Answer:
The x value is 5
Step-by-step explanation:
The x value is the value going across
Starting where the two axis meet, we go 5 units to the right
That is the x value
WILLL GIVE ALL MY POINT PLUS MARK BRAILIEST PLS HELP ASAP TY <3
Answers
Answer:
The unknown integer that solves the equation is 6.
Step-by-step explanation:
In order to find the missing number, we can set up an equation as if we are solving for x.
x + (-8) = -2
Add 8 on both sides of the equation.
x = 6
So, the unknown integer is 6.
Answer:
6
Step-by-step explanation:
6 plus -8 is -2
Consider the distribution of exam scores graded 0 from 100, for 79 students. When 37 students got an A, 24 students got a B and 18 students got a C. How many peaks would you expect for distribution?
Answers
Answer:
Three
Step-by-step explanation:
Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores
PLEASE HELP!!! TIMED QUESTION!!! FIRST CORRECT ANSWER WILL BE BRAINLIEST!!!
The bar graph shows the number or each item sold at a bake sale. Which statement about the graph is true?
Answers
Let me know if you need the working out. Hope it helps :)
Find the equation of the circle in standard form for the given center (h, k) and radius R:(H,K)=(4/3,-8/8),R=1/3
Answers
Answer:
The answer is option BStep-by-step explanation:
Equation of a circle is given by
( x - h)² + ( y - k)² = r²
where r is the radius and
( h , k) is the center of the circle
From the question the radius R = 1/3
the center ( h ,k ) = (4/3 , -8/3)
Substituting the values into the above equation
We have
[tex](x - \frac{4}{3} )^{2} + {(y - - \frac{8}{3}) }^{2} = ({ \frac{1}{3} })^{2} [/tex]
We have the final answer as
[tex](x - \frac{4}{3} )^{2} + {(y + \frac{8}{3}) }^{2} = \frac{1}{9} [/tex]
Hope this helps you
What is the name of a geometric figure that looks an orange
A. Cube
B. Sphere
C. Cylinder
D. Cone
Answers
Answer:
b . sphere
Step-by-step explanation:
Solve for x. Question 12 options: A) 8 B) 5 C) 14 D) 10
Answers
Answer:
B) 5
Step-by-step explanation:
Proportions:
8 ⇒ 10
20 ⇒ 5x
5x = 20*10/8
5x = 25
x = 25/5
x = 5
Raul and his friends each way 1/20 of a ton are standing on a truck scale . The total weight shown by the scale is 3/4 of a ton . How can I find the total number of people on the scale when Raul and his friends are weighed?
Answers
Answer: There are 15 friends.
Step-by-step explanation:
We know that there is N friends (N is the number that we are looking for)
Each friend weights 1/20 ton.
Now, the weight of the N friends together is N times 1/20 ton.
Then we have:
N*(1/20) ton = 3/4 ton
We solve this for N.
First multiply both sides by 20.
20*N*(1/20) = N = 20*(3/4) = 60/4 = 15
Answer:
I can find the total number of people by dividing the total weight by the weight of one person.
Step-by-step explanation:
A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.
Answers
Answer:
109
Step-by-step explanation:
Use a chart or calculator to find the z-score corresponding to a probability of 1%.
P(Z > z) = 0.01
P(Z < z) = 0.99
z = 2.33
Now find the sample standard deviation.
z = (x − μ) / s
2.33 = (30.5 − 30) / s
s = 0.215
Now find the sample size.
s = σ / √n
s² = σ² / n
0.215² = 5 / n
n = 109
Suppose a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207]. The population standard deviation used for the analysis is known to be $14,900.
Required:
a. What is the point estimate of the mean salary for all college graduates in this town?
b. Determine the sample size used for the analysis.
Answers
Answer: a. $40,800 b. 36
Step-by-step explanation:
Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].
[tex]\sigma= \$14,900[/tex]
a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.
Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]
= 40,800
hence, the point estimate of the mean salary for all college graduates in this town = $40,800
b. Since lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.
Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]
Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.
z-value for 99% confidence level = 2.576
So,
[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]
The sample size used for the analysis =36
In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Use the P-value method of testing hypotheses.
H0:
H1:
Test Statistic:
Critical Value:
Do you reject H0?
Conclusion:
If you were told that the p-value for the test statistic for this hypothesis test is 0.014, would you reach the same decision that you made for the Rejection of H0 and the conclusion as above?
Answers
Answer:
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
Step-by-step explanation:
Mean x`= 518 +548 +561 +523 + 536 + 499+ 538 + 557+ 528 +563 /10
x`= 537.1
The Variance is = 20.70
H0 μ≤ 520
Ha μ > 520
Significance level is set at ∝= 0.05
The critical region is t ( with df=9) for a right tailed test is 1.8331
The test statistic under H0 is
t=x`- x/ s/ √n
Which has t distribution with n-1 degrees of freedom which is equal to 9
t=x`- x/ s/ √n
t = 537.1- 520 / 20.7 / √10
t= 17.1 / 20.7/ 3.16227
t= 17.1/ 6.5459
t= 2.6122
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
identify(describe) each part of the ellipse as labeled by a letter
Answers
Answer: see below
Step-by-step explanation:
A) y has the smaller radius so this is the Minor Axis
B) y has the smaller radius so these are the CoVertices
C) x has the bigger radius so these are the Vertices
D) This is the Center of the ellipse.
F & G) These are the Foci (plural for Focus)
H) x has the bigger radius so this is the Major Axis
A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.
Answers
Answer:
[tex]V(m) = (2 + 5m)^3[/tex]
Step-by-step explanation:
Given
Solid Shape = Cube
Edge = 2 feet
Increment = 5 feet per minute
Required
Determine volume as a function of minute
From the question, we have that the edge of the cube increases in a minute by 5 feet
This implies that,the edge will increase by 5m feet in m minutes;
Hence,
[tex]New\ Edge = 2 + 5m[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Edge^3[/tex]
Substitute 2 + 5m for Edge
[tex]Volume = (2 + 5m)^3[/tex]
Represent Volume as a function of m
[tex]V(m) = (2 + 5m)^3[/tex]
hich statement best describes the domain and range of p(x) = 6–x and q(x) = 6x? p(x) and q(x) have the same domain and the same range. p(x) and q(x) have the same domain but different ranges. p(x) and q(x) have different domains but the same range. p(x) and q(x) have different domains and different ranges.
Answers
Answer:
[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.
Step-by-step explanation:
[tex]p(x) = 6-x[/tex] and
[tex]q(x) = 6x[/tex]
First of all, let us have a look at the definition of domain and range.
Domain of a function [tex]y =f(x)[/tex] is the set of input value i.e. the value of [tex]x[/tex] for which the function [tex]f(x)[/tex] is defined.
Range of a function [tex]y =f(x)[/tex] is the set of output value i.e. the value of [tex]y[/tex] or [tex]f(x)[/tex] for the values of [tex]x[/tex] in the domain.
Now, let us consider the given functions one by one:
[tex]p(x) = 6-x[/tex]
Let us sketch the graph of given function.
Please find attached graph.
There are no values of [tex]x[/tex] for which p(x) is not defined so domain is All real numbers.
So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Its range is also All Real Numbers
So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
[tex]q(x) = 6x[/tex]
Let us sketch the graph of given function.
Please find attached graph.
There are no values of [tex]x[/tex] for which [tex]q(x)[/tex] is not defined so domain is All real numbers.
So, domain is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Its range is also All Real Numbers
So, Range is [tex](-\infty, \infty)[/tex] or [tex]x\in R[/tex]
Hence, the correct answer is:
[tex]p(x)[/tex] and [tex]q(x)[/tex] have the same domain and the same range.
4 + (-13)
Yajmmsmssjsjsjjsnssnsnnsnsxxdddddddd
Answers
Answer:
-9
Step-by-step explanation:
4 + (-13)
=> 4 - 13
=> -9
-4-(-1) answer the question
Answers
Answer:
-3
Step-by-step explanation:
Since you are subtracting a negative, it turns positive so it will be.
-4+1
-3
Answer:
-3
Step-by-step explanation:
-4-(-1) = -4 + 1 = -3
Which equation will solve the following word problem? Jared has 13 cases of soda. He has 468 cans of soda. How many cans of soda are in each case? 13(468) = c 468c = 13 468/13 = c 13 = c/468
Answers
Answer:
c = 468 / 13
Step-by-step explanation:
If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.
Answer:
468/13 = c
Step-by-step explanation: Further explanation :
[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]
2/5 × 3/7? please help
Answers
Answer:
[tex]\frac{2}{5}[/tex] • [tex]\frac{3}{7}[/tex] = [tex]\frac{6}{35}[/tex]
Answer: 0.171
Step-by-step explanation:
First, do 2/5 which would equal 0.4
Second, so 3/7 which would equal 0.428571428571429
Lastly multiply the two answers together to get 0.171428571428571
Triangle ABC has vertices A(0, 6) , B(−8, −2) , and C(8, −2) . A dilation with a scale factor of 12 and center at the origin is applied to this triangle. What are the coordinates of B′ in the dilated image? Enter your answer by filling in the boxes. B′ has a coordinate pair of ( , )
Answers
Answer:
[tex]B' = (-96,-24)[/tex]
Step-by-step explanation:
Given
[tex]A(0,6)[/tex]
[tex]B(-8,-2)[/tex]
[tex]C(8,-2)[/tex]
Required
Determine the coordinates of B' if dilated by a scale factor of 12
The new coordinates of a dilated coordinates can be calculated using the following formula;
New Coordinates = Old Coordinates * Scale Factor
So;
[tex]B' = B * 12[/tex]
Substitute (-8,-2) for B
[tex]B' = (-8,-2) * 12[/tex]
Open Bracket
[tex]B' = (-8 * 12,-2 * 12)[/tex]
[tex]B' = (-96,-24)[/tex]
Hence the coordinates of B' is [tex]B' = (-96,-24)[/tex]
Answer:
Bit late but the answer is (-4,-1)
Step-by-step explanation:
Took the test in k12
[tex]4x - 2x = [/tex]
Answers
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.
0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8
Answers
Answer:
Thus percentile lies between 53.3% and 55.6 %
Step-by-step explanation:
First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N
where n is the ordinal rank of the given value
N is the number of values in ascending order.
The data in ascending order is
0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3
1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5
Number of observation = 45
4.9 lies between 3.3 and 5.5
x*n = 24 observation x*n = 25 observation
x*45= 24 x*45= 25
x= 0.533 x= 0.556
Thus percentile lies between 53.3% and 55.6 %
Which property of equality was used to solve this equation? x − 5 = -14 x − 5 + 5 = -14 + 5 x = -9 A. addition property of equality B. subtraction property of equality C. multiplication property of equality D. division property of equality
Answers
Answer:
A
Step-by-step explanation:
In the second step, they added 5 to both sides to get rid of the -5 on the left side. Since the same thing was done to both sides (addition), the answer is the addition property of equality.
Answer:
Addition property of equality
Step-by-step explanation:
The equation is like:
=> x - 5 = -14
=> x - 5 + 5 = -14 + 5
=> x = -9
Since, we add 5 to both sides to solve for "x", the answer is "Addition Property of Equality".
Hope this helps.
A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 5000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1006 units of the product are demanded by consumers when the price is $5 per unit.
Answers
Answer:
q = 5000/x + 6
Step-by-step explanation:
D´= dq/dx = - 5000/x²
dq = -( 5000/x²)*dx
Integrating on both sides of the equation we get:
q = -5000*∫ 1/x²) *dx
q = 5000/x + K in this equation x is the price per unit and q demanded quantity and K integration constant
If when 1006 units are demanded when the rice is 5 then
x = 5 and q = 1006
1006 = 5000/5 +K
1006 - 1000 = K
K = 6
Then the demand function is:
q = 5000/x + 6
Let A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%. Lauren says that both events are independent because P(A) + P(B) = P(A and B) Shawn says that both events are not independent because P(A)P(B) ≠ P(A and B) Which statement is an accurate statement? Lauren is incorrect because the sum of the two events is not equal to the probability of both events occurring. Shawn is incorrect because the product of the two events is equal to the probability of both events occurring. Lauren is correct because two events are independent if the probability of both occurring is equal to the sum of the probabilities of the two events. Shawn is correct because two events are independent if the probability of both occurring is not equal to the product of the probabilities of the two events.
Answers
Answer:
Shawn is correct because two events are independent if the probability of both occurring is equal to the product of the probabilities of the two events.
Step-by-step explanation:
We are given that A represent going to the movies on Friday and let B represent going bowling on Friday night. The P(A) = 0.58 and the P(B) = 0.36. The P(A and B) = 94%.
Now, it is stated that the two events are independent only if the product of the probability of the happening of each event is equal to the probability of occurring of both events.
This means that the two events A and B are independent if;
P(A) [tex]\times[/tex] P(B) = P(A and B)
Here, P(A) = 0.58, P(B) = 0.36, and P(A and B) = 0.94
So, P(A) [tex]\times[/tex] P(B) [tex]\neq[/tex] P(A and B)
0.58 [tex]\times[/tex] 0.36 [tex]\neq[/tex] 0.94
This shows that event a and event B are not independent.
So, the Shawn statement that both events are not independent because P(A)P(B) ≠ P(A and B) is correct.
Answer:
Shawn is correct
Step-by-step explanation:
Find the sum. 31.25 + 9.38
Answers
Answer:
40.63
Step-by-step explanation:
31.25+9.38= 40.63
Hope this helps
Answer: 40.63
Look at the image for shown work.
A ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots. After 1 hour, the ship turns 90° toward the south. After 2 hours, maintain the same speed. What is the bearing to the ship from port?
Answers
Answer:
The bearing is N 55.62° W
Step-by-step explanation:
ship leaves the port of Miami with a bearing of S80°E and a speed of 15 knots.
It then turns 90° towards the south after one hour.
Still maintain the same speed and direction for two hours.
The bearing is just the angle difference from the ship current location to where it started.
Let the speed be km/h
Distance covered in the first round
= 15*1
= 15km
Distance covered in the second round
=15*2
= 30 km
Angle at C = (90-80)+90
Angle at C = 10+90= 100
Let the distance between the port and the ship be c
C²= a² + b² -2abcos
C²= 15²+30²-2(15)(30)cos 100
C²= 225+900+156.28
C²= 1281.28
C= 35.8 km
Using sine formula
30/sin x= 35.8/sin 100
30/35.8 * sin 100 = sinx
0.838*0.9848= sin x
0.8253= sin x
Sin ^-1 0.8253 = x
55.62° = x
The bearing is N 55.62° W
(x−1)(x−7)=0 PLEASE HELP
Answers
Answer:
1, 7
Step-by-step explanation:
Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Answers
Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
