Answer:
0.73001
Step-by-step explanation:
1 month = 730.01 hours
730.01 * $0.001
= 0.73001
Approximately 0.73 or 0.7.
Is it possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space? Ex- plain.
Let a; be a nonzero column vector of an m x n matrix A. Is it possible for a j, to be in N(AT)? Explain.
It is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space. Let's explain why.
Let A be an m × n matrix, and let x be a nonzero vector in the null space of A, so Ax = 0. We can also say that x is in the null space of A transpose. So x is an element of N(AT).Let’s prove the contradiction that arises from the initial claim by assuming that 3,1,2 is a row vector in the row space of A and 2,1,1 is a column vector in N(AT).We have that A[3 1 2]T = 0 and 2,1,1 is in the null space of A transpose. We also know that if a vector v is in the row space of A, then there exists a vector y such that v = A*y, where y is a column vector. So in this case, we can say that 3,1,2 is in the row space of A if there is a column vector y such that A * y = [3 1 2]T. But if that's the case, then we have the following equation: A* y = [3 1 2]. This can be written as: TA* = [3 1 2]If we then take the transpose of both sides, we have: A* y = [3 1 2]T and TA = [3 1 2]. However, this implies that TA* = TA, which can only be true if A is a symmetric matrix. But A is an m × n matrix, where m and n are not equal, so A cannot be a symmetric matrix. Therefore, it is not possible for a matrix to have the vector (3, 1, 2) in its row space and (2, 1, 1)T in its null space.
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Evaluate the expression for the given value of x.
3/4 x − 12 for x = 16
Answer:
if x is 16 then 3/4(16) - 12
when you simplify 4 by 16
3(4)-12
12-12=0
The answer 3h - 5 < 13?
Answer: h < 6
Step-by-step explanation:
3h - 5 < 13
3h < 18
h < 6
Answer:
h<6
Step-by-step explanation:
What is the area of the polygon given below
What is the description of angle 4 as it relates to the situation below?
angle 4 is the angle of elevation from the person to the radar tower.
angle 4 is the angle of depression from the radar tower to the person.
angle 4 is the angle of depression from the person to the radar tower.
angle 4 is the angle of elevation from the radar tower to the person.
In the given situation, "angle 4 is the angle of elevation from the radar tower to the person" is the description of angle 4.In trigonometry, an angle of elevation or inclination is the angle between the horizontal and the line of sight of an observer looking upwards. An angle of depression is the angle between the horizontal and the line of sight of an observer looking downwards.
In the given situation, angle 4 refers to the angle formed between the horizontal and the line of sight from the radar tower to the person. As the angle is formed while looking upwards from the radar tower to the person, it is called the angle of elevation. Hence, the correct description of angle 4 in this situation is "angle 4 is the angle of elevation from the radar tower to the person."
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2.
It cost Enica $9 75 for the ingredients to make 30 cupcakes. She sold them for $1.00 each. What was
Erica's total profit?
Answer:
$8.75
Step-by-step explanation:
Cost price= $9.75
Selling price= $1.00
profit= C.P-.SP
= 9.75-1.00
= $8.75
Sophie has a box filled with trail mix the box has a length
Identify each scatterplot below with an appropriate value of r.
Answer:
A would be the answer
Step-by-step and
Hey guy pls help me with dis due today pls help no links pls
I did number one
pls explain answer
mode is 4 and the median is also 4
mode is the number that appears the most which is 4 and median is the number that is in the middle when you line up all the numbers in order (0,2,2,3,3,4,4,4,4,5,5,5,6,6,10)
Please help me with the question please ASAP
Answer:
The ratio of perimeter of ABCD to perimeter of WXYZ = [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
First, we have to determine the multiplicative factor of the dimensions for both figures.
Considering sides AB and WX,
multiplicative factor = [tex]\frac{12}{8}[/tex]
= 1.5
So that:
XY = 6 x 1.5 = 9
YZ = 7 x 1.5 = 10.5
ZW = 7 x 1.5 = 10.5
Perimeter of ABCD = 6 + 7 + 7 + 8
= 28
Perimeter of WXYZ = 9 + 10.5 + 10.5 + 12
= 42
The ratio of the perimeters of the two quadrilaterals can be determined as;
ratio = [tex]\frac{perimeter of ABCD}{Perirmeter of WXYZ}[/tex]
= [tex]\frac{28}{42}[/tex]
= [tex]\frac{2}{3}[/tex]
The ratio of the perimeter of ABCD to perimeter of WXYZ is [tex]\frac{2}{3}[/tex].
Thomas walks 10 miles in 120 minutes. Select all of the unit rates below that
describe Thomas' walk. Show your work.
a) He can walk 1 mile in 12 minutes
b) He can walk 12 miles in 1 minute
c) He can walk of a mile in 1 minute
1
d) it takes him of a minute to walk 1 mile
12
12
Answer:
Hi! The answer to your question is B) He can walk 12 miles in 1 minute.
To find Unit rate divide the biggest number by the smallest; Example: [tex]120/10[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka
Which function matches the table?
Answer:
The A matches the table x+3
a circle has an arc of length 48π that is intercepted by a central angle of 120°. what is the radius of the circle? enter your answer in the box. 72 units
The radius of the circle is 144 units.
To find the radius of the circle, we can use the formula that relates the circumference of a circle to its radius and the central angle intercepted by an arc.
The formula is:
Arc length = 2πr * (θ/360)
Where:
Arc length is the length of the intercepted arc
r is the radius of the circle
θ is the central angle in degrees
In this case, we are given that the arc length is 48π and the central angle is 120°. Let's substitute these values into the formula and solve for r:
48π = 2πr * (120/360)
Simplifying the equation:
48 = 2r * (120/360)
48 = r * (1/3)
r = 48 * 3
r = 144
Therefore, the radius of the circle is 144 units.
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Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The null and alternative hypothesis would be: 0.7 Hop 0.7 Hop - 0.7 H:P < 0.7 HP >0.7 HP 0.7 HOP The test is: right tailed left-tailed two-tailed Based on a sample of 500 people, 62% wned cats The p-value is:
Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.
The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:
H0: p = 0.7 (null hypothesis
)H1: p ≠ 0.7 (alternative hypothesis)
The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7
Based on a sample of 500 people, 62% owned cats.
This means that the sample proportion, p = 0.62.
To calculate the p-value, we will use the z-test statistic.
The formula for calculating the z-test statistic is given as:
z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.
Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52
The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.
The area in both tails beyond the z-score of 2.52 is 0.012.
Therefore, the p-value is:
p-value = 2 × 0.012 = 0.024
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What type of continuous distribution (normal, positively or negatively skewed, bimodal, exponential) would best represent the following situations? a) The age of people who have retired. b) The number of red Smarties in boxes of Smarties. c) The shoe sizes of Stouffvillians. d) The wait time between calls to Pizza Pizza.
If the continuous distribution is given then The age of people who have retired represents Normal distribution.
a) The age of people who have retired would likely follow a normal distribution, as it tends to have a symmetric bell-shaped curve.
b) The number of red Smarties in boxes of Smarties would have a discrete distribution, as it can only take on certain whole numbers and cannot be fractionally or continuously measured.
c) The shoe sizes of Stouffvillians may exhibit a bimodal distribution, as there might be two distinct peaks indicating two groups with different average shoe sizes.
d) The wait time between calls to Pizza Pizza could potentially follow an exponential distribution, as it is often used to model the time between events in a Poisson process, such as the arrival of phone calls. The distribution would have a long tail, representing longer wait times occurring less frequently.
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The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that 2 1 0 1 2 [AB] 0 -1 31 0 0 mln where m and n are real numbers. State all values of m and/or n such that the following statements are true. (a) Matrix A is invertible. (b) The system AX = B has no solutions. (c) The system AX = B has an infinite number of solutions. (d) Columns of the augmented matrix (AB) are linearly independent. (e) The system AX = 0 has a unique solution. (f) At least one eigenvalue of the matrix A is zero. (g) Columns of the matrix A form a basis in R3.
a. Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
Given that,
The augmented matrix of a system of linear equations AX = B was reduced to upper-triangular form so that
[A|B] = [tex]\left[\begin{array}{ccc}2&1&0 \ | \ 2\\0&-1&3 \ | \ 1 \\0&0&m \ | \ n\end{array}\right][/tex]
Where m and n are real numbers.
We know that,
a. We have to prove matrix A is invertible.
For A to be invertible.
|A| ≠ 0
|A| is the determinant of the matrix A.
|A| = 2(-m) -1(0) + 0(0) = -m
Here, m is the real number.
So, |A| = -m ≠ 0
Therefore, Matrix A is invertible when |A| = -m ≠ 0 then statement true.
b. We have to prove the system AX = B has no solution.
When Rank[A|B] > Rank[A]
m = 0 and n ≠ 0 has a real number
Therefore, The system AX = B has no solution when m = 0 and n ≠ 0 has a real number then statement true.
c. We have to prove the system AX = B has an infinite number of solutions.
When m = n = 0, and Rank[A] < 3
Therefore, The system AX = B has an infinite number of solutions when m = n = 0 then statement true.
d. We have to prove columns of the augmented matrix (AB) are linearly independent.
When m ≠ 0 and m∈R and n= 0
Therefore, Columns of the augmented matrix (AB) are linearly independent when m ≠ 0 and n= 0 then statement true.
e. We have to prove the system AX = 0 has a unique solution.
When [tex]\left[\begin{array}{ccc}2&1&0 \\0&-1&3 \\0&0&m \end{array}\right]\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}0\\0\\0\end{array}\right][/tex]
The equation are 2x + y = 0, -y + 3z = 0 and mz = 0
m ≠ 0 should be any real number except zero.
Therefore, The system AX = 0 has a unique solution when m ≠ 0 then statement true.
f. We have to prove at least one eigenvalue of the matrix A is zero.
When λ = 2, 1, m
m = 0 then eigen value is zero
Therefore, At least one eigenvalue of the matrix A is zero when m = 0 then statement true.
g. We have to prove columns of the matrix A form a basis in R³.
When m ≠ 0
Therefore, Columns of the matrix A form a basis in R³ when m ≠ 0 then statement true.
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Victoria ate 4\16 of a small pizza for lunch. How is this fraction written as a decimal?
Answer:
0.25
Step-by-step explanation:
4/16 --> 1/4 and 1/4 = 0.25
How would I do this??
4 people can dig a trench in 3 hours.
How long would it take 9 people?
Give your answer in minutes.
Answer:
80 minutes.
Step-by-step explanation:
do I need to explain? I hate explaining :(
A system of equations consists of two lines. One line passes through (8,4) and (6.3) and the second line passes through (0, -2) and (4.0).
Answer:
system is:
y = 1/2x
y = 1/2x - 2
No Solution to this system
Step-by-step explanation:
Answer!!!!! Help!!!
Answer:
The answer is postulate
Determine a series of transformations that would map Figure C onto Figure D plz help asap
Answer:
Rotation about 180*
Translation about 7 units to the right and 8 down
Step-by-step explanation:
Find the GCF of the monomials: 18x² and 21x²y
A)3x
B)3x²
C)3xy
D)3x²y
PLEASE HELP MEEE
How much money would produce $70 as simple interest at 3.5% per
annum?
Answer:
$2000
Step-by-step explanation:
Simple Interest = $70
Rate = 3.5%
Time = 1
Principal = ?
Simple Interest = (Principal × Rate × Time)/100
Principal = (Simple Interest × 100)/(Rate × Time)
Principal = (70 × 100)/(3.5 × 1)
Principal = 7000/3.5
Principal = 14000/7
Principal = 2000
$12 with a 85% markup
12+85% is $22.20
80%x12=9.6
5%x12=0.6
9.6+0.6=10.2
12+10.2=22.20
Answer: $22.20
∑ = {C,A,G,T}, L = { w : w = CAjGnTmC, m = j + n }. For example, CAGTTC ∈ L; CTAGTC ∉ L because the symbols are not in the order specified by the characteristic function; CAGTT ∉ L because it does not end with C; and CAGGTTC ∉ L because the number of T's do not equal the number of A's plus the number of G's. Prove that L ∉ RLs using the RL pumping theorem.
If We consider the string w = [tex]CA^pG^pT^pC[/tex], then L ∉ RLs by pumping lemma.
To prove that L ∉ RLs using the RL pumping theorem, we assume L is a regular language and apply the pumping lemma for RLs. Let p be the pumping length of L.
We consider the string w = [tex]CA^pG^pT^pC[/tex], where |w| ≥ p. According to the pumping lemma, we can decompose w into uvxyz such that |vxy| ≤ p, |vy| > 0, and for all k ≥ 0, the string [tex]u(v^k)x(y^k)z[/tex] is also in L.
However, by examining the structure of L, we see that the number of A's and G's is dependent on each other and must match the number of T's.
Since pumping up or down would alter this balance, there is no way to satisfy the condition for all k, leading to a contradiction. Therefore, L cannot be a regular language, and we conclude that L ∉ RLs.
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someone please help!
Answer:
12 units
Step-by-step explanation:
1st, I found the distance for the two parallel sides on the hexagon. I counted the lines to be 2 units each, which makes 4 units. And since all sides of a hexagon are equal. All the sides make 12 units, or centimeters. Therefore, the perimeter is 12 units
You guy's will get 40 points if you help me!
Answer:
mean = 5+9+9+6+6+11+8+4/7 = 8.29
median = 6
mode = 6
range = 11 - 4 = 7
Answer:
Step-by-step explanation:
5 , 9 , 6 , 6 , 11 , 8 , 4
Mean = sum of all data ÷ number of data
[tex]= \frac{5+9+6+6+11+8+4}{7}\\\\= \frac{49}{7}\\\\= 7[/tex]
Median: To find median, arrange in ascending order and medianis the middle term
4 , 5 , 6 , 6 , 8 , 9 , 11
Middle term = 4th term
Median = 6
Mode: a number that appears most often is mode
6 appears 2 times
Mode = 6
Range:
Range = maximum value - minimum value
= 11 - 4
= 7
The roots of 3x2 + x = 14 are
1. imaginary
2. real,rational,equal
3.real,rational,unequal
4.real,irrational,unequal
Answer:
3
Step-by-step explanation:
3x2 +x −14 = 0 12 −4(3)(−14) = 1+168 =169 = 132
The roots of 3x² + x = 14 are real, irrational and unequal
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x, ax² + bx +c=0 with a ≠ 0 .
Given equation is :
3x² + x = 14
3x² + x - 14=0
we have, a=3, b=1 c=-14
D= b²-4ac
= 1²-4*3*(-14)
= 1+168
= 169
As, D>0
Hence, the roots are real.
Now,
x= -b±√b²-4ac/2a
= -1±√169/2*3
=-1±13/6
x= -1-13/6 and x= -1+13/6
x= -7/3 and x= 12/6=2
Hence, the roots are real, irrational and unequal.
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Does anyone know this
Answer:
I belive the answer is A
Step-by-step explanation:
So any answer with 22t would make sense, so you have A and C. In C though, it is subtracting 22, but since 6195 is the total it would have to include the 22 so it is A.