T/F : There are exactly three vectors in span {a1,a2, a3}
Answers
False.
The number of vectors in the span of a set of vectors depends on the linear independence of the vectors.
The number of vectors in the span of a set of vectors depends on the linear independence of the vectors. If a set of vectors is linearly independent, then only the zero vector is in the span of the set. If a set of vectors is linearly dependent, then the span of the set contains infinitely many vectors.
So, the number of vectors in span {a1, a2, a3} can be 1, 2, or 3, depending on whether the set {a1, a2, a3} is linearly dependent or independent.
For example, if a1 = (1,0,0), a2 = (0,1,0), and a3 = (0,0,1), then {a1, a2, a3} is a linearly independent set, and the span of {a1, a2, a3} is just the set of all linear combinations of these vectors, which is the entire space R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.
On the other hand, if a1 = (1,0,0), a2 = (2,0,0), and a3 = (0,1,0), then {a1, a2, a3} is a linearly dependent set, since a2 is a scalar multiple of a1. In this case, the span of {a1, a2, a3} is just the set of all linear combinations of a1 and a3, which is a plane in R3. So, there are infinitely many vectors in the span of {a1, a2, a3}.
Visit to know more about Vectors:-
brainly.com/question/25705666
#SPJ11
Related Questions
In a post office, the mailboxes are numbered from 1 to 4,500. These numbers represent a) qualitative data b) quantitative data c) either qualitative or quantitative data d) since the numbers are sequential, the data is quantitative
Answers
Answer:
A
Step-by-step explanation:
Because they will be assigned to a renter, represented by each of their unique identity. Each mail box will received different mails addressed to their owners.
if the mail boxes are all nameless and not for rent, and just sit there used as bins to collect mails, i.e., ALL identical, then they will be quantitative.
You have a $250 gift card to use from a sporting goods
catalogue. (See price list to the left.) You will order a
pair of running shoes and several pairs of socks.
Create and solve an inequality to show the possible
number of socks you could order by only using the gift
card.
Answers
Answer:
The answer cannot be given as exact prices are not listed. How to do it could be explained as below:
Step-by-step explanation:
The first thing you have to do is find the price of the shoes. Then you take $250 (the amount of money in the gift card) and subtract it from the price of the shoes.
Then, we take the number we got from above and divide it by how much 1 pair of socks costs. You could get a decimal, and if you do, pretend that the numbers after the decimal don't exist. This number is the number of possible socks you could order only using the gift card.
Message:
Hope this helped! <3
answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!answer, please!
Answers
Step-by-step explanation:
The total amount of seat in the train is the total number of carriages multiplied by the number on each carriages = 32 × 15 = 480seats
A. number of trains needed for 350,000 passengers = 350,000/ 480 = 729 trains approximately
Answer:
like he said up their.
Step-by-step explanation:
E(y∣x)=β 0 +β 1 x (a) Now apply the properties of expected value to write the unconditional expectation E(y) as a function of the unconditional expectation E(x). That is, simplify the following expression. [Hint: you should recognize the result as following from the Law of Iterated Expectations.] E(y)=E(β 0 +β 1 x+u)=
Answers
The unconditional expectation of y (E(y)) equals β0 + (β1 * E(x)), derived using the Law of Iterated Expectations.
To simplify the expression for the unconditional expectation E(y), we can apply the properties of expected value and the Law of Iterated Expectations. The Law of Iterated Expectations states that the unconditional expectation of a conditional expectation is equal to the unconditional expectation itself.
Starting with the expression for E(y):
E(y) = E(β0 + β1x + u)
We can break down this expression using the linearity of expectation:
E(y) = E(β0) + E(β1x) + E(u)
Since β0 and β1 are constants, their expected values are equal to themselves:
E(y) = β0 + β1E(x) + E(u)
Now, since u is the error term and it is assumed to have a mean of zero (E(u) = 0), the expression simplifies to:
E(y) = β0 + β1E(x)
Therefore, we can conclude that the unconditional expectation of y (E(y)) is equal to the constant term β0 plus the product of the slope coefficient β1 and the unconditional expectation of x (E(x)). This result follows from the Law of Iterated Expectations, which allows us to simplify the expression by considering the expected values of the individual terms separately.
To learn more about unconditional expectation from the given link
https://brainly.com/question/30653295
#SPJ4
2 questions please answer
Answers
Answer:
this equation has exactly 1 solution
Step-by-step explanation:
An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?
Answers
The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
To determine the upper and lower control limits for the sample means, we can use the formula:
Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))
Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))
In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.
For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.
Given:
Mean = 2.0 litres
Standard Deviation = 0.01 litres
Sample size (n) = 5
Using the formula, we can calculate the upper and lower control limits:
UCL = 2.0 + (1.96 * 0.01 / sqrt(5))
LCL = 2.0 - (1.96 * 0.01 / sqrt(5))
Calculating the values:
UCL ≈ 2.0018 litres
LCL ≈ 1.9982 litres
Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997
Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.
Learn more about means from
https://brainly.com/question/1136789
#SPJ11
Question
Graph x=−6.
Answers
A graph of the given mathematical expression (x = -6) is shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
In this scenario, a number line would be used to graph the given mathematical expression because it only contains one (1) variable.
Read more on number line here: brainly.com/question/17325155
#SPJ1
The circumference of a circle is 98.596 millimeters. What is the radius of the circle? Use 3.14 for π.
197.2 mm
49.3 mm
31.4 mm
15.7 mm
Answers
Answer: D) 15.7
Step-by-step explanation:
Start with the formula C=2 πr
Then solve for r r=C2π = 98.62·π = 15.69(7)204
The radius of the circle is 15.7 mm.
What is Circumference?The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.
The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.
We have,
The circumference of Circle = 2πr
Also, The circumference of a circle is 98.596 millimeters.
So, circumference of Circle = 2πr
98.596 = 2πr
98.596 = 6.28r
r= 98. 596 / 6.28
r = 15.7 mm
Thus, the radius is 15.7 mm.
Learn more about Circumference here:
https://brainly.com/question/28757341
#SPJ2
In the diagram, mAngleFLI is 106°, mAngleFLG = (2x – 1)°,
mAngleGLH = (x + 17)°, and mAngleHLI = (4x – 15)°.What is the measure of the smallest angle in the diagram?
15°
29°
32°
45°
Answers
Answer:
29o
Step-by-step explanation:
Answer:
29
Step-by-step explanation:
edge 2020
a cyclist bikes a certain distance in 45 minutes , write an equation that shows the relationship between speed,s, and time,t, whne the distance is 100 miles
Answers
Step-by-step explanation:
d = 100miles
t = 45 × 60 = 2700sec
dis = speed × time
relationship btw speed and time when d distance is 100miles is
100 = speed × 2700sec
speed = 100 = 0.037m/s
2700
What is the value of x if e squared 3x+6=8
Answers
Step-by-step explanation:
there is explanation in the answer
The given planes intersect in a line. Find parametric equations for the line of intersection. [Hint: The line of intersection consists of all points (x, y, z) that satisfy both equations. Solve the system and designate the unconstrained variable as t .]
x + 2y + z = 1, 2x+5y + 32 = 4
Answers
The parametric equations for the line of intersection are:
x = 61 - 5t
y = 2t - 30
z = t
To find the parametric equations for the line of intersection of the given planes, we first need to solve the system of equations:
1. x + 2y + z = 1
2. 2x + 5y + 32 = 4
Step 1: Solve for x from equation 1:
x = 1 - 2y - z
Step 2: Substitute x in equation 2 with the expression found in step 1:
2(1 - 2y - z) + 5y + 32 = 4
Now we can use elimination to solve for one variable. Let's eliminate y by multiplying the first equation by 5 and subtracting it from the second equation:
Step 3: Simplify and solve for y:
2 - 4y - 2z + 5y + 32 = 4
y - 2z = -30
Step 4: Designate z as the parameter t:
z = t
Step 5: Substitute z with t in the expression for y:
y = 2t - 30
Step 6: Substitute z with t in the expression for x:
x = 1 - 2(2t - 30) - t
x = 1 - 4t + 60 - t
x = 61 - 5t
Now we have the parametric equations for the line of intersection:
x = 61 - 5t
y = 2t - 30
z = t
Note that we can choose any value of z for the parameter t, since z is unconstrained.
Learn more about Parametric:
brainly.com/question/15585522
#SPJ11
Why are the solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFraction x over 40 EndFraction = StartFraction 10 over 8 EndFraction the same? because both result in the equation 8 x = 400, which simplifies to x = 5 because both result in the equation 8 x = 400, which simplifies to x = 50 because both result in the equation 40 x = 80, which simplifies to x = 2 because both result in the equation 40 x = 80, which simplifies to x = 20
Answers
Answer:
The answer is a
Step-by-step explanation:
hope this helps :}
Answer:
A
Step-by-step explanation:
l
v
HELP ASAP pls help me i'll give brainliest.
answer both and give brainliest fosho ;,(
this is finals week ugh help pls
Answers
Answer:
wHaT?
Step-by-step explanation:
Which ratio is the odd one out?
6:24
4:16
1:4
3:12
8:31
Answers
Answer:
8:31
Step-by-step explanation:
all of them are equal with 1:4 except 8:31
6
Your sister works as a tutor in the evenings.
Last school year she charged $25 per hour
for her services. After taking some
certification classes over the summer, she
increased her hourly charge by 40%. How
much does your sister now charge per hour
for her tutoring services?
Answers
Answer:
$35
Step-by-step explanation:
rewrite 4 x 4 x 4 x 4 As a exponent
rewrite A x A x A as an exponent
Answers
Answer:
Step-by-step explanation:
\(4^4\\A^3\)
Answer:
\(4^{4}\) and \(A^{3}\)
Step-by-step explanation:
Please help!! Thank you :)
Answers
Answer:
(a). | b - a | = a - b
Step-by-step explanation:
If a > b, then
(a). b - a < 0 ⇒ - ( b - a ) = a - b (true)
(b). \(\frac{a}{b}\) > 0 for some "a" and "b" is true
(c). \(\frac{b}{a}\) > 0 is true for some "a" and "b"
(d). | \(\frac{b}{a}\) | < 0 (false)
(e). | \(\frac{a}{b}\) | > 1 (true if b ≠ 0)
What is the slope of the equation between the two points (9,8) and (-3,6)
Answers
Answer:
\(\bold{m=\dfrac16}\)
Step-by-step explanation:
\(\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}\)
(9, 8) ⇒ x₁ = 9, y₁ = 8
(-3, 6) ⇒ x₂ = -3, y₂ = 6
So the slope:
\(\bold{m=\dfrac{6-8}{-3-9}=\dfrac{-2}{-12}=\dfrac16}\)
How do the measures of the angles of polygon ABCD compare with those of the translated images? Based on your observation, what can you conclude about preservation of angle measurements during a translation?
Answers
Answer: the measures of the angles of polygon ABCD are equal to the measures of the corresponding angles of both translated images. this means that the angles of the polygon are preserved as the figure is translated in any direction
Answer:
The opposite sides of quadrilateral ABCD have equal slopes, which means the opposite sides are parallel. Therefore, by definition, quadrilateral ABCD is a parallelogram.
Plato
Brad, Stella, and Gilbert want to get a thank you gift for Maria. They will split the cost evenly. They buy 6 roses at $2.15 each and a box of chocolates for $7.90. The store has a "no sales tax" day.
Brad estimates the cost per person to be $8. Is this reasonable?
A yes or no
Stella estimates the cost per person to be $7. Is this reasonable?
B yes or no
Gilbert estimates the cost per person to be $6. Is this reasonable?
C yes or no
Answers
Answer: Stella has a reasonable Answer
Step-by-step explanation:
When you add up all of the Costs, you get an answer of $20.80
You Divide $20.80 by 3
And you get your answer of 6.93333
Which estimates around 7 dollars making Stella Right!
Hope this helps :)
2. A function y = 6sin (x-π / 3) cos (x −π / 3) - 1, where 0 ≤ x ≤3π / 2
a. Find all stationary points
b. Find all the extreme values.
c. Find the increasing function interval and the decreasing function interval
d. Check interval of concave (concave up and concave downward)
Answers
Answer:
if your solving for y the answer would be y= - 3sin(2x)+3cos(2x)X√3 -1,x∈R /2
Step-by-step explanation:
If you also want extra help with these math problems you can also download Photomath
Write the slope-intercept form of the equation
(no spaces)
through: (3,-1)
perpendicular to y=3/5x+3
Answers
Answer:
y = -5/3x + 4
Step-by-step explanation:
slope = -5/3
-1 = -5/3(3) + b
-1 = -5 + b
4 = b
y = -5/3x + 4
Answer:
\(y=-\frac{5}{3}x+4\)
Step-by-step explanation:
To write down a line that is perpendicular to one line, make sure that their slopes give a product of -1:
\(\frac{3}{5}*m_2 =-1\\m_2=-\frac{5}{3}\)
Write down an equation in the point-slope form and replace everything in and simplify:
\(y_2-y_1=m(x_2-x_1)\\y-(-1)=-\frac{5}{3} (x-3)\\y+1=-\frac{5}{3}x+5\\y=-\frac{5}{3}x+4\\\)
Juliana wrote -16+x=8 on the board
Answers
Answer: x = 24
Step-by-step explanation:
-16 + 24 = 8
Simplify each expression completely.
7[3+2(x-4)-6(x-4)]
Answers
Answer:
21 + 14x - 56 - 42x + 168
= 133 - 28x
Step-by-step explanation:
Answer:
19 - 4x
Step-by-step explanation:
\(3 + 2(x - 4) - 6(x - 4)\)
\(3 + 2x - 8 - 6(x - 4)\)
\(3 + 2x - 8 - 6x + 24\)
\(19 + 2x - 6x\)
\(19 - 4x\)
A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?
Answers
Answer:
A. The equation of the line is y=−2.5x+10.
C. The y-intercept is k.
F. The value of k is 10.
Step-by-step explanation:
A line passes through points (0, k) and (4,0) and has a slope of –2.5. Which statements are true regarding the graph of the line?
A. The equation of the line is y=−2.5x+10.
B. The equation of the line is y=−2.5x.
C. The y-intercept is k.
D. The y-intercept is 4.
E. The value of k is 4.
F. The value of k is 10.
Solution:
The slope of a line is the ratio of the vertical change to the horizontal change. The slope (m) of a line passing through \((x_1,y_1)\ and\ (x_2,y_2)\) is:
\(m=\frac{y_2-y_1}{x_2-x_1}\)
Given that the line passes through (0, k) and (4,0)
\(m=\frac{y_2-y_1}{x_2-x_1}\)
\(-2.5=\frac{0-k}{4-0}\\\\-2.5=\frac{-k}{4}\\\\k=10\)
The equation of the line is given as:
\(y-y_1=m(x-x_1)\\\\y-10=-2.5(x-0)\\\\y = -2.5x+10\)
The y intercept is the value of y when x = 0, hence intercept = k
Given the line that passes through points (0, k) and (4,0) and has a slope of –2.5, we need to get the value of "k
The formula for calculating the slope of a line is expressed as:
\(m=\frac{y_2-y_1}{x_2-x_1}\\-2.5 = \frac{0-k}{4-0}\\-2.5=\frac{-k}{4} \\Cross \ multiply\\-2.5 \times 4 = -k\\-10 = -k\\k = 10\)
Hence the value of k is 10.
Learn more here: https://brainly.com/question/12922257
From the coordinate given (0, 10) and (4, 0), we can see that the y intercept and x intercept of the graph is 10 and 4 respectively
Discuss the existence and uniqueness of a solution to the differential equations.
a) t(t−3)y′′+ 2ty′−y=t2
y(1) = y∘, y'(1) = y1, where y∘ and y1 are real constants.
b) t(t−3)y′′+ 2ty′−y=t2
y(4) = y∘, y'(4) = y1.
Answers
Both differential equations satisfy the conditions for the existence and uniqueness of a solution.
What is the existence and uniqueness of a solution for the given differential equations?a) To determine the existence and uniqueness of a solution to the given differential equation, we need to analyze the coefficients and boundary conditions. The equation is a second-order linear homogeneous ordinary differential equation with variable coefficients.
For the equation to have a unique solution, the coefficients must be continuous and well-behaved in the given interval. In this case, the coefficients t(t-3), 2t, and -1 are continuous and well-behaved for t ≥ 1. Therefore, the equation satisfies the conditions for existence and uniqueness of a solution.
The boundary conditions y(1) = y∘ and y'(1) = y1 provide specific initial conditions. These conditions help determine the particular solution that satisfies both the equation and the given boundary conditions. With the given constants y∘ and y1, a unique solution can be obtained.
b) Similar to part (a), the differential equation in part (b) is a second-order linear homogeneous ordinary differential equation with variable coefficients. The coefficients t(t-3), 2t, and -1 are continuous and well-behaved for t ≥ 4, satisfying the conditions for existence and uniqueness of a solution.
The boundary conditions y(4) = y∘ and y'(4) = y1 also provide specific initial conditions. These conditions help determine the particular solution that satisfies the equation and the given boundary conditions. With the given constants y∘ and y1, a unique solution can be obtained.
In summary, both parts (a) and (b) satisfy the conditions for the existence and uniqueness of a solution to the given differential equations.
learn more about solution
brainly.com/question/1616939
#SPJ11
For what value of x is the figure a rectangle? Please help
Answers
Answer:
x = 8
Hope this helps!
Step-by-step explanation:
( 2x + 42 )° + ( 4x )° = 90° ( right angle )
6x + 42 = 90
6x = 90 - 42
6x = 48
x = 8
(2x + 42) + 4x = 90 degrees
Add 4x + 2x to get 6x + 42 = 90
Then, subtract 42 from both sides to get, 6x = 48
Lastly, divide both sides by 6 to get your final answer of X = 8.
is 0. overline 19 rational or irrational? Explain.
Answers
Answer:
19/99
Step-by-step explanation:
the tennessean, an online newspaper located in nashville, tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. in a recent poll, 762 readers responded to the following question:
Answers
The Tennesseean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on current issues. In a recent poll, 762 readers responded to a question. To answer this question, we need more information about the question itself. However, I can provide a general format for an answer that includes the terms you mentioned.
The Tennesseean, an online newspaper, uses daily polls to gather opinions from readers. These polls allow the newspaper to gauge public sentiment on a variety of current issues. The recent poll in question received 762 responses, indicating a level of engagement from the readership.
The Tennesseean, an online newspaper located in Nashville, Tennessee, values reader input and conducts daily polls to gather opinions on a wide range of current issues. In a recent poll, a total of 762 readers responded to the question at hand. This high number of responses indicates that the readership is actively participating in the poll and shows a strong interest in expressing their opinions.
The Tennesseean's decision to conduct daily polls is a strategic approach to engage its audience and involve them in the newspaper's content creation process. By seeking reader opinions, the newspaper ensures that its reporting and coverage align with the interests and preferences of its audience. The high response rate of 762 readers suggests that the poll question was relevant and engaging to the readership.
The Tennesseean's use of daily polls to obtain reader opinions is a commendable effort to involve its audience in the news-making process. The substantial number of responses received in a recent poll, with 762 readers participating, demonstrates a strong level of engagement from the newspaper's readership. This feedback helps the newspaper to better understand the interests and perspectives of its audience, allowing it to deliver more relevant and informative content.
To know more about online visit
https://brainly.com/question/12972525
#SPJ11