This question is incomplete, the complete question is;
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
Answer:
the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
Step-by-step explanation:
Given the data in the question;
coefficient matrix
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]
Now, from linear system;
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]
So, with the matrix, the associated equation is;
x₁ + x₄ = 0, x₃ = 0
Number of variables is 4 and ranked of the matrix is 2,
Hence, there are infinite solutions,
There are also two free variables;
from the question,
Let x₄ = t and x₂ = s be the free variables
so
x₁ + x₄ = 0
x₁ + t = 0
x₁ = -t
Therefore, the solution for the given system is;
( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
A Driver’s Ed program is curious if the time of year has an impact on number of car accidents in the U.S. They assumethat weather may have a significant impact on the ability of drivers to control their vehicles. They take a randomsample of 150 car accidents and record the season each occurred in. They found that 27 occurred in the Spring, 39 inthe Summer, 31 in the Fall, and 53 in the Winter.
Required:
Can it be concluded at the 0.05 level of significance that caraccidents are not equally distributed throughout the year?
Answer:
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
Step-by-step explanation:
Given the data in the question;
Hypothesis;
Null hypothesis : H₀ : Car accidents are equally distributed throughout the year
Alternative hypothesis : Hₐ : Car accidents are NOT equally distributed throughout the year
significance level ∝ = 0.05
x ;
Spring = 27
Summer = 39
Fall = 31
Winter = 53
Test Statistics;
Chi Square = ∑[ (O – E)²/E ]
O E (O – E)²/E
Spring 27 37.4 2.94
Summer 39 37.4 0.06
Fall 31 37.4 1.1267
Winter 53 37.4 6.4067
Total 150 150 10.5334
so; z = ∑[ (O – E)²/E ] = 10.5334
{from table}
p-value = 0.0145
Hence, Since p-value ( 0.0145 ) is less than significance level ( 0.05 )
we reject null hypothesis.
Therefore, there is sufficient evidence to conclude that Car accidents are NOT equally distributed throughout the year
In this exercise we have to use probability knowledge to calculate the distribution during the year, so we find that:
There is sufficient evidence to conclude that car accidents are not equally distributed throughout the year.
Given the data in the question;
[tex]Null \ hypothesis: H_0[/tex][tex]Alternative \ hypothesis : H_a[/tex] [tex]Significance\ level = 0.05[/tex]Now the values given in the statement can be exemplified below as:
[tex]Spring = 27[/tex][tex]Summer = 39[/tex][tex]Fall = 31[/tex][tex]Winter = 53[/tex]In this way, we can assemble a table of values with the statistical data previously informed and using the formula given below:
[tex]Z=\sum[\frac{(O-E)^2}{E}][/tex]
[tex]Z = 10.5334[/tex]
So:
[tex]\ \ \ \ \ \ \ \ \ \ \ O \ \ \ \ \ E \ \ \ \ (O - E)^2/E\\Spring \ \ 27 \ \ 37.4 \ \ \ \ 2.94\\Summer \ 39 \ 37.4 \ \ \ \ 0.06\\Fall \ \ \ \ \ \ 31 \ 37.4 \ \ \ \ 1.1267\\Winter \ \ \ 53 \ 37.4 \ \ \ 6.4067\\Total \ 150 150 \ 10.5334[/tex]
Hence, Since pvalue ( 0.0145 ) is less than significance level ( 0.05 ), so we reject null hypothesis.
See more about probability at brainly.com/question/795909
Consider randomly selecting a single individual and having that person test drive different vehicles. Define events , , and by Suppose that , , , , , and . What is the probability that the individual likes both vehicle
Answer:
[tex]P(A_1\ n\ A_2) = 0.40[/tex]
Step-by-step explanation:
Let:
[tex]A_1 \to[/tex] An Individual likes vehicle 1
[tex]A_2 \to[/tex] An Individual like vehicle 2
[tex]P(A_1) = 0.55[/tex]
[tex]P(A_2) = 0.65[/tex]
[tex]P (A_1\ u\ A_2 ) = 0.80[/tex]
Required
[tex]P(A_1\ n\ A_2)[/tex] --- probability that both vehicles are liked by the individual.
This is calculated as:
[tex]P(A_1\ n\ A_2) = P(A_1) + P(A_2) - P(A_1\ u\ A_2)[/tex]
So, we have:
[tex]P(A_1\ n\ A_2) = 0.55 + 0.65 - 0.80[/tex]
[tex]P(A_1\ n\ A_2) = 0.40[/tex]
Find the value of x.
A.6 B.5 C. 50/3 D.7
The value of x is 7.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The two triangles PQR and P'Q'R' are similar triangles
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Firstly let us find the P'Q' by using pythagoras theorem
R'Q'²=PR'²+P'Q'²
12²=10²+P'Q'²
144-100=P'Q'²
44=P'Q'²
P'Q'=6.6
The value of PR is x
The value of x is 7. as R it is a midpoint of P'Q'R'
Hence the value of x is 7
To learn more on Triangles click:
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A (non-zero) number multiplied by zero equals zero, whereas a non-zero number divided by zero is undefined.
a. True
b. False
help please. I cant figure it out and it’s hard.
Answer:
The student is comparing the different heart rates due to the temperature. The independent variable is the Temperature and the dependent variable is the beats of the heart from the larva.
What is the range of the given function?
Answer:
-2
Step-by-step explanation:
range is y values
Answer:
-2
Step-by-step explanation:
That's the minimum range, which is basically the lowest point on the y-axis that the line touches
For each sequence, find the first 4 terms and the 10th term.
a) 12-n
B 5 - 2n
Answer:
Solution given:
a.
tn=12-n
1 st term =12-1=11
2nd term =12-2=10
3rd term=12-3=9
4th term=12-4=8
10th term=12-10=2
b.
tn=5-2n
1st term=5-2*1=3
2nd term=5-2*2=1
3rd term=5-2*3=-1
4th term=5-2*4=-3
10th term=5-2*10=-15
(a) Solution
T(n) = 12 - n
T(1) = 12 - 1 = 11
T(2) = 12 - 2 = 10
T(3) = 12 - 3 = 9
T(4) = 12 - 4 = 8
T(10) = 12 - 10 = 2
(b) Solution
T(n) = 5 - 2n
T(1) = 5 - 2 = 3
T(2) = 5 - 4 = 1
T(3) = 5 - 6 = -1
T(4) = 5 - 8 = -3
T(10) = 5 - 20 = -15
1.7p²q-1.5pq³+3.1p²q+7.1pq³
Answer:
see Image below:)
Step-by-step explanation:
Go here for steps
A student solves for v
Which statement explains how to correct the error that was made?
The subtraction property of equality should have been applied to move m to the other side of the equation.
O The multiplication property of equality should have been applied before the division property of equality.
The division property of equality should have been applied to move the fraction to the other side of the equation.
The square root property should have been applied to both complete sides of the equation instead of to select variables.
Answer:
D (The square root property should have been applied to both complete sides of the equation instead of to select variables)
Step-by-step explanation:
On edge 2021
what is the system of equations shown in the graph?
Answer:
bugo.ka pag answer bobo ka bah ha wag kanang umasa dito piste ka
3/7-2/14+1/21
What is the answer to this
Answer:
1/3
Step-by-step explanation:
Hope this is useful even though there isn't any working
PLEASE HELPPP !!!!! WILL MARK BRAINLIEST TO WHOEVER GETS IT RIGHT
Answer:
128° because it is corresponding with <4
[tex] < 5 = \: < 3 \\ = \: < 4 \\ < 5 = 128 \degree[/tex]
No links please :) Love you guys stay safe 3
Answer:
C
Step-by-step explanation:
I've completed the test before. :)
Two numbers are 10 units away in different directions from their midpoint, m, on a number line. The product of the numbers is –99.
Which equation can be used to find m, the midpoint of the two numbers?
(m – 5)(m + 5) = 99
(m – 10)(m + 10) = 99
m2 – 25 = –99
m2 – 100 = –99
Answer:
[tex]m {}^{2} - 100 = - 99[/tex]
Step-by-step explanation:
Set up the binomial.
[tex](m - 10)[/tex]
[tex](m + 10)[/tex]
Multiply the binomial.
[tex](m - 10)(m + 10) = - 99[/tex]
Apply difference of squares rule
[tex](p + q)(p - q) = p {}^{2} - q {}^{2} [/tex]
[tex]m {}^{2} - 100 = - 99[/tex]
Answer: m^2-100=-99
Step-by-step explanation:
Set up the binomial.
(m-10)
(m+10)
Multiply the binomial.
(m-10)(m+10)=-99
Apply difference of squares rule
(p+q)(p-q) = p2-q2
Answer: m^2-100=-99
PLSSSSSSS HELP ASAP !!! PLSSS
Answer:wpeleoe
Step-by-step explanation:
help me please thanks
Answer:
option 3
Step-by-step explanation:
ORIGINAL REFLECTED
A = ( 2, 0) A' = (-2, 0)
B = (5 , 0) B' = (-5, 0)
C = (5, -2) C' = (-5, -2)
D = (2, -2) D' = (-2, -2)
Find the radius of the circle,
Answer:
the correct answer is option D. 7
What is the volume, in cubic centimeters, of a rectangular prism with a height of 17 centimeters, a width of 17 centimeters, and a length of 11 centimeters?
Answer:
3179cm^3
Step-by-step explanation:
[tex]volum = height × width × length \\ = 17cm \times 17cm \times 11cm \\ = {3179cm}^{3} [/tex]
The average marks for 25 students in a mathematics was was 48.
what was the total marks scored by the students?
Answer:
total of the data points = 1200
Step-by-step explanation:
The 'average' of a data set is the total of the data points divided by the number of data points.
Here:
total of the data points
---------------------------------- = 48
25
Multiplying both sides of this equation by 25 yields:
total of the data points = 1200
1. tu no eres linda eres.
2. tu no eres buena tu eres.
3. tu no te metas en la cama tú te.
Suppose that $2000 is invested at a rate of 4%, compounded semiannually. Assuming that no withdrawals are made, find the total amount after 5 years. Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
Step-by-step explanation:
A = P(1+r/n)^ nt
A = 2000(1+.04/2)^(5*2)
A = [tex]2000(1.02)^{10}[/tex] = $2437.99
Study the adjoining figure and then explain why x = y
Answer:
Step-by-step explanation:
y is the remote exterior angle. The remote exterior angle has the strange property that it is equal to the two remote interior angle. The two remote interior angles are the two, neither of which is the supplement of the exterior angle
So y = x/2 + x/2 which are marked as being opposite equal angles.
1/2 x + 1/2 x = x
y by substitution is = x /2 + x/2
y = x
Volume of square based pyramid is 1568 cm3 and half of the length of the
side of the base is 7cm. Calculate the area of triangular faces of pyramid.
answer:
1393.84
Step-by-step explanation:
since the formula for a square base pyramid is a^2×h/3
we can find out the height for the pyramid by dividing the a^2×h/3 by a^2 =h/3
1568/7^2=32 since 32 = h/3 we multiply by 3 to find the height which = 96
now that we have the height we usee the pathagorean Therom to find the height of one of the face triangles
so 96^2+3.5^2=L^2 so L =96.06
so now that we have all we need
the surface area of the square at the bottom of the pyramid is 7×7
the surface area of the triangles are 96.06 ×7/2 since the area of a triangle is h×b/2
since there are 4 triangles and on square 49+4(96.06×7/2)= 1393.84
36 apples cost $6. How many apples can you buy for $1?
Answer: you can buy 6apples for$1
Step-by-step explanation: you divide 36 by 6 and get 6 so it’s 6apples.
Find the measure of theta to the nearest tenth helpppp pleaseeee
Answer:
54.3°
Step-by-step explanation:
sinθ=opposite/hypotenuse
sinθ=26/32
sinθ=0.8125
θ=54.3°
What is the equation, written in vertex form, of a parabola with a vertex of (–2, 6) that passes through (1, –3)?
Answer:
Step-by-step explanation:
( x - 1 )2 + ( y + 3 )2 = 90
Look at the angle shown below.
Estimate the measure of the angle.
Answer:
A
Step-by-step explanation:
It's only slightly bigger than 90 degrees, so 110 is the only plausible conclusion
Answer:
110
Step-by-step explanation:
please help with the steps
Answer:
2821.51
73425.64
28124.24
4124.24
Step-by-step explanation:
Effective rate: .058/2 = .029
This question is kind of ambigous and I'll make the assumption that there is no payment at time 0
[tex]175000=x\frac{(1+.029)^{2*18}-1}{.029}\\x=2821.511[/tex]
interested earned:
175000-2821.51*36= 73425.64
2.)
Same assumption as question 1 (there is no payment at time 0)
effective rate: .063/12= .00525
[tex]400(\frac{(1+.00525)^{60}-1}{.00525})=28124.24[/tex]
Interest earned: 28124-400*60=4124.24
Answer:
First problem: monthly payment $2741.99; interest earned $76,288.36
Second problem: amount in account $28,271.90; interest earned $4271.90
Step-by-step explanation:
First problem:
You open an account with a deposit. The deposit is the first monthly payment. This means that this is an annuity in which you pay at the beginning of the pay period. That makes it into an "annuity due."
[tex] A = \dfrac{F}{\frac{(1 + i)^n - 1}{i} \times (1 + i)} [/tex]
where A = periodic payment,
F = future value
i = interest rate per compounding period, n = number of compounding periods
[tex]A = \dfrac{175000}{\frac{(1 + \frac{0.058}{2})^{2 \times 18} - 1}{\frac{0.058}{2}} \times (1 + \frac{0.058}{2})}[/tex]
[tex] A = 2741.99 [/tex]
Interest earned:
[tex] 2 \times 18 \times 2741.99 - 175000 = 76288.36 [/tex]
Second problem:
Once again, the account starts with a deposit of the monthly payment, so this is also an annuity due, meaning the payments occur at the beginning of each compounding period. Here, we are given the monthly payment, an d we need to find the future value.
[tex] F = A \times \dfrac{(1 + i)^n - 1}{i} \times (1 + i)} [/tex]
[tex] F = 400 \times \dfrac{(1 + \frac{0.063}{12})^{5 \times 12} - 1}{\frac{0.063}{12}} \times (1 + \frac{0.063}{12})} [/tex]
[tex] F = 28271.90 [/tex]
The interest earned is:
[tex] 28271.90 - 12 \times 5 \times 400 = 4271.90 [/tex]
PLEASE HELPPPPPPPP MEEE PLEASE!
Answer:
Root Multiplicity
-4 2
-1 2
2 1
5 3
---------------------------
y = a(x + 4)²(x + 1)²(x - 2)(x - 5)³
find "a" using point (0, 20000)
20000 = a(0 + 4)²(0 + 1)² (0 - 2)(0 - 5)³
20000 = a(16)(1)(-2)(-125)
20000 = a (4000)
a = 20000/4000
a = 5
y = 5(x + 4)²(x + 1)²(x - 2)(x - 5)³
the angle in a semi circle is?