We apply the Gram-Schmidt process to these vectors to find an orthonormal basis:
v1 = x1 = [3, -4, 1
To find a basis of the null space N(A), we need to find all vectors x such that Ax = 0, where 0 is the zero vector.
To do this, we set up the augmented matrix [A | 0] and row reduce:
[ 1 2 1 3 2 | 0 ]
[ 4 1 0 6 1 | 0 ]
[ 1 1 2 4 5 | 0 ]
R2 - 4R1 -> R2:
[ 1 2 1 3 2 | 0 ]
[ 0 -7 -4 6 -7 | 0 ]
[ 1 1 2 4 5 | 0 ]
R3 - R1 -> R3:
[ 1 2 1 3 2 | 0 ]
[ 0 -7 -4 6 -7 | 0 ]
[ 0 -1 1 1 3 | 0 ]
R2 / -7 -> R2:
[ 1 2 1 3 2 | 0 ]
[ 0 1 4/7 -6/7 1 | 0 ]
[ 0 -1 1 1 3 | 0 ]
R1 - 2R2 - R3 -> R1:
[ 0 0 0 0 0 | 0 ]
[ 0 1 4/7 -6/7 1 | 0 ]
[ 0 0 11/7 -1/7 1 | 0 ]
We can write the system of equations corresponding to this row echelon form as:
x2 + (4/7)x3 - (6/7)x4 + x5 = 0
(11/7)x3 - (1/7)x4 + x5 = 0
Solving for the variables in terms of the free variables x3, x4, and x5, we get:
x1 = -[(4/7)x3 - (6/7)x4 - x5]/2
x2 = -(4/7)x3 + (6/7)x4 - x5
x3 = x3 (free variable)
x4 = x4 (free variable)
x5 = x5 (free variable)
So the null space N(A) is the set of all vectors of the form:
x = [ -[(4/7)x3 - (6/7)x4 - x5]/2, -(4/7)x3 + (6/7)x4 - x5, x3, x4, x5 ]
To find an orthogonal basis for N(A), we can use the Gram-Schmidt process. Let's call the columns of A a1, a2, a3, a4, and a5.
First, we need to find a basis for N(A) by setting the free variables to 1 and the others to 0:
x1 = [3, -4, 1, 0, 0]
x2 = [-2, 3, 0, 1, 0]
x3 = [-2, 1, 0, 0, 1]
Next, we apply the Gram-Schmidt process to these vectors to find an orthonormal basis:
v1 = x1 = [3, -4, 1
To learn more about orthonormal visit:
https://brainly.com/question/30218173
#SPJ11
(1 point) For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral. A. [(5x (5x² – 2)3/2 dx – X = b. X2 dx 4x2 + 6 X = C. | xV5x + 50x + 118dx X = d. El 19-50 х dx –119 – 5x2 + 50x X =
All Trigonometric Expressions:
a. ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx = ∫2sin³θ cos²θ dθ
b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]= ∫tan²θ sec²θ dθ
c. ∫x√(5x + 50)/(x + 118)dx = ∫(5tan²θ – 25)tanθ sec³θ dθ
d. ∫(19 – 50x)/(119 – 5x² + 50x)dx = -2∫dθ/(25tan²θ + 94)
a. The integral ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx, we can use the substitution x = (2/5)sinθ. This gives dx = (2/5)cosθ dθ and 5x² – 2 = 5(2/5 sinθ)² – 2 = 2cos²θ. Substituting these expressions into the integral, we get:
∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx
= ∫2sin³θ cos²θ dθ
b. For the integral ∫x²dx/(4x² + 6), we can use the substitution x = tanθ. This gives dx = sec²θ dθ and 4x² + 6 = 4tan²θ + 6 = 2sec²θ. Substituting these expressions into the integral, we get:
∫x²dx/(4x² + 6) = ∫tan²θ sec²θ dθ
c. For the integral ∫x√(5x + 50)/(x + 118)dx, we can use the substitution
x + 25 = 5tan²θ.
This gives x = 5tan²θ – 25 and dx = 10tanθ sec²θ dθ, and
5x + 50 = 25sec²θ. Substituting these expressions into the integral, we get:
∫x√(5x + 50)/(x + 118)dx
= ∫(5tan²θ – 25)tanθ sec³θ dθ
d. For the integral:
∫(19 – 50x)/(119 – 5x² + 50x)dx,
we can use the substitution
5x – 5 = √(50x – 5)tanθ.
This gives x = (1/10)[(tanθ)² + 1] and
dx = (1/5)(tanθ sec²θ) dθ, and 119 – 5x² + 50x
= (25tan²θ + 94)².
Substituting these expressions into the integral, we get:
∫(19 – 50x)/(119 – 5x² + 50x)dx
= -2∫dθ/(25tan²θ + 94)
Learn more about integrals visit: brainly.com/question/27419605
#SPJ4
Correct Question:
For each of the following integrals find an appropriate trigonometric substitution of the form x = f(t) to simplify the integral.
a. ∫5x * ∫5x * [tex](5x^{2} - 2)^{(3/2)[/tex]dx
b. ∫[tex]x^{2} dx/(4x^{2} + 6)[/tex]
c. ∫x√(5x + 50)/(x + 118)dx
d. ∫(19 – 50x)/(119 – 5x² + 50x)dx
An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with L = 16.9 and 3.3. What is the probability that in a given week the airline will lose less than 20 suitcases?
The probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.
We are given that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with a mean of [tex]$\mu = 16.9$[/tex] and standard deviation of [tex]$\sigma = 3.3$[/tex]. We need to find the probability that in a given week the airline will lose less than 20 suitcases.
Let X be the number of suitcases lost in a week. Then we need to find P(X < 20).
Using the Z-score formula, we can standardize the variable X as:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
Substituting the given values, we get:
[tex]Z=\frac{20-16.9}{3.3}=0.91[/tex]
Now, we need to find the probability that Z is less than 0.91. We can use a standard normal distribution table or calculator to find this probability, which is approximately 0.8186.
Therefore, the probability that in a given week the airline will lose less than 20 suitcases is approximately 0.8186 or 81.86%.
To learn more about airline visit:
https://brainly.com/question/12738360
#spj11
Find each of the following probabilities when n independent Bernoulli trials are carried out with probability of success p.(a) the probability of no successes(b) the probability of at least one success(c) the probability of at most one success(d) the probability of at least two successes(e) the probability of no failures(f) the probability of at least one failure(g) the probability of at most one failure(h) the probability of at least two failures
The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].
The probability of a success in one Bernoulli trial is given by p, and the probability of a failure is q = 1 - p.
(a) The probability of no successes is (1-p)^n.
(b) The probability of at least one success is 1 minus the probability of no successes, which is 1 - (1-p)^n.
(c) The probability of at most one success is the sum of the probabilities of 0 and 1 successes, which is (1-p)^n + np(1-p)^(n-1).
(d) The probability of at least two successes is 1 minus the probability of 0 or 1 success, which is 1 - [(1-p)^n + np(1-p)^(n-1)].
(e) The probability of no failures is the same as the probability of n successes, which is p^n.
(f) The probability of at least one failure is 1 minus the probability of no failures, which is 1 - p^n.
(g) The probability of at most one failure is the sum of the probabilities of 0 and 1 failures, which is p^n + nqp^(n-1).
(h) The probability of at least two failures is 1 minus the probability of 0 or 1 failure, which is 1 - [p^n + nqp^(n-1)].
To learn more about Bernoulli visit:
https://brainly.com/question/30509621
#SPJ11
a box has a volume of 140 cm Square if its breadth is 5 cm and it's length is 7 cm find it's height
Answer:
To find the height of the box, we need to use the formula for volume of a box: Volume = length x breadth x height
Given the values for length and breadth, we can substitute them into the formula and solve for height: 140 = 7 x 5 x height
Simplifying the equation, we get: 140 = 35 x height
Dividing both sides by 35, we get: height = 4
Therefore, the height of the box is 4 cm
Identify the true and false statements about 95% confidence intervals
The given statement, "You can infer statistical significance from a 95% CI. "A 95% CI gives you information about the precision of the association." and "A study with a small sample will have a wider 95% CI." are true and "A 95% CI gives you information about the precision of the association, but not the strength of the association." is false.
The statement You can infer statistical significance from a 95% CI is true, as it is a measure of the precision of the association between two variables.
A 95% CI will be wider for a study with a smaller sample size, but this does not necessarily indicate a weaker association. In other words, the width of a 95% CI does not indicate the strength of the association, and so the statement that A 95% CI gives you information about the precision of the association, but not the strength of the association is false.
To know more about significance, click here.
brainly.com/question/30092425
#SPJ4
Full Question ;
Identify the true and false statements about 95% confidence intervals.
- You can infer statistical significance from a 95% CI.
- A 95% CI gives you information about the precision of the association.
- A study with a small sample will have a wider 95% CI.
-A 95% CI gives you information about the strength of the association.
you have determined that you need a showing rate of 79.62 kg/ha
for a wheat crop. if you have 12.560 kg of wheat seed,what
percentage of 250 ha paddock could you sow?
To calculate the percentage of the 250 ha paddock that can be sowed with 12.560 kg of wheat seed, we first need to determine how much seed is needed per hectare and this will give the answer 0.063%.
Given that the showing rate is 79.62 kg/ha, we can divide the total seed amount by the showing rate to get the number of hectares that can be sown with the given amount of seed:
12.560 kg / 79.62 kg/ha = 0.1576 ha
This means that 0.1576 hectares of land can be sown with 12.560 kg of wheat seed.
To calculate the percentage of the 250 ha paddock that can be sown, we can divide the sown land area by the total paddock area and then multiply by 100:
0.1576 ha / 250 ha x 100% = 0.063%
Therefore, you can sow approximately 0.063% of the 250 ha paddock with 12.560 kg of wheat seed, assuming a showing rate of 79.62 kg/ha.
Learn more about showing rate: https://brainly.com/question/19493296
#SPJ11
an extrinsic reward is enjoying what one does for its own sake and an intrinsic reward is an inducement such as money, grades, or recognition.True or False
False. An intrinsic reward is enjoying what one does for its own sake, while an extrinsic reward is an inducement such as money, grades, or recognition.
Intrinsic and extrinsic rewards are two different types of motivational factors that can influence behavior.
Intrinsic rewards are those that come from within oneself, such as the enjoyment of doing a task or the sense of accomplishment that comes from completing it. These rewards are inherently satisfying and enjoyable, and they motivate people to continue doing the task or activity because of the pleasure they derive from it. For example, a person may engage in a hobby like playing music, painting, or playing a sport simply because they find it enjoyable and rewarding in itself.
On the other hand, extrinsic rewards are external motivators that are used to induce or encourage behavior. These rewards are typically tangible, such as money, grades, or recognition, and are given as a result of completing a task or activity. They are designed to incentivize individuals to perform specific actions, often with the aim of achieving a specific goal or outcome. For example, a person may work hard at their job in order to earn a promotion or raise, or may study hard in school to earn good grades.
Intrinsic and extrinsic rewards can both be effective motivators, but they operate in different ways. Intrinsic rewards are powerful because they come from within the individual and are based on personal enjoyment and satisfaction. Extrinsic rewards, on the other hand, are often seen as less powerful and may only work in the short term, because they are not inherently satisfying and may not motivate people to continue performing the task or activity once the reward is removed. However, when used effectively, extrinsic rewards can be a useful tool for motivating people and achieving specific outcomes.
To learn more about motivational factors visit: https://brainly.com/question/25492018
#SPJ11
Write an explicit rule for each sequence
1. 3200, 1600, 800, 400, ...
2. 12, 84, 588, 4116, ...
3. 1395, 465, 155, 51.67, ...
i need this as soon as possible
posting more soon
The explicit rule for sequence 3200,1600,800, 400,... is aₙ = 3200(1/2)⁽ⁿ⁻¹⁾, the explicit rule for sequence 12, 84, 588, 4116, .. is aₙ = 12(7)⁽ⁿ⁻¹⁾, the explicit rule for sequence 1395, 465, 155, 51.67,... is aₙ = 1395(1/3)⁽ⁿ⁻¹⁾.
The common ratio in this geometric sequence is 1/2. Thus, the explicit rule for this sequence is given by
aₙ = 3200(1/2)⁽ⁿ⁻¹⁾
where aₙ represents the nth term of the sequence.
This sequence appears to be a geometric sequence where the common ratio is 7. Thus, the explicit rule for this sequence is
aₙ = 12(7)⁽ⁿ⁻¹⁾
where aₙ represents the nth term of the sequence.
This sequence appears to be a geometric sequence where the common ratio is 1/3. Thus, the explicit rule for this sequence is
aₙ = 1395(1/3)⁽ⁿ⁻¹⁾.
where aₙ represents the nth term of the sequence.
To know more about sequence here
https://brainly.com/question/24432840
#SPJ1
Amani is saving for a scooter with a regular price of $70. The scooter is one sale for 10% off and there is a 5% sales tax. Amani wants to know the total price of the scooter
Amani would need to pay $66.15 for the scooter with the discount and sales tax included.
If the regular price of the scooter is $70, and it is on sale for 10% off, the sale price would be:
Sale price = Regular price - 10% of Regular price
Sale price = $70 - 0.1*$70
Sale price = $63
So the sale price of the scooter is $63.
Next, we need to add the 5% sales tax to the sale price to get the total price of the scooter. To do this, we can calculate the amount of sales tax as:
Sales tax = 5% of the Sale price
Sales tax = 0.05*$63
Sales tax = $3.15
Therefore, the total price of the scooter, including the 10% discount and 5% sales tax, would be:
Total price = Sale price + Sales tax
Total price = $63 + $3.15
Total price = $66.15
So Amani would need to pay $66.15 for the scooter with the discount and sales tax included.
Learn more about sales tax
https://brainly.com/question/29442509
#SPJ4
A boat is heading towards a lighthouse, where Tyee is watching from a vertical distance of 115 feet above the water. Tyee measures an angle of depression to the boat at point AA to be 15^{\circ}
∘
. At some later time, Tyee takes another measurement and finds the angle of depression to the boat (now at point BB) to be 50^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.
The distance form point A to point B is 333 feet.
What is an angle of depression?An angle of depression is the measure of an angle formed when an object is viewed below the horizontal plane by an observer.
In the given question, let the distance from point A to the base of the lighthouse be represented by x, and that of B to the base of the lighthouse as y.
So that to determine x, we have;
Tan θ = opposite/ adjacent
Tan 15 = 115/ x
x = 115/ 0.2680
= 429.1045
x = 429.1045 feet
To determine y, we have;
Tan θ = opposite/ adjacent
Tan 50 = 115/ y
y = 115/ 1.1918
= 96.492y
y = 96.4927 feet
The distance from point A to point B = x - y
= 429.1045 - 96.4927
= 332.6118
The distance from point A to point B is 333 feet.
Learn more about angle of depression at https://brainly.com/question/17193804
#SPJ1
the estimated resale value (in dollars) of a company car after years is given by 23,351 0.783 . what is the rate of depreciation (in dollars per year) after 2 years? round to the nearest cent. the car is depreciating at $ per year. note: the rate of depreciation is |r'(t)|. your answer should be positive.
To find the rate of depreciation after 2 years, we need to find the derivative of this function at t = 2.
V(t) = 23,351(0.783)^t
V'(t) = 23,351(0.783)^t * ln(0.783) [Using the chain rule]
V'(2) = 23,351(0.783)^2 * ln(0.783) ≈ -2,346.29
Since we are interested in the absolute value of the rate of depreciation, we can ignore the negative sign. Therefore, the car is depreciating at $2,346.29 per year (rounded to the nearest cent).
Note that this is the instantaneous rate of depreciation at t = 2. The average rate of depreciation over the first two years would be the difference in resale value divided by the number of years, which would be:
[(23,351(0.783)^2) - 23,351] / 2 ≈ $2,336.67 per year
Hi! To find the rate of depreciation after 2 years, we need to first determine the resale value of the car after 2 years and then find the difference in value per year. Here's a step-by-step explanation:
1. Plug in the given years (t=2) into the formula for the estimated resale value: V(t) = 23,351(0.783^t)
2. Calculate the resale value after 2 years: V(2) = 23,351(0.783^2) ≈ 14,342.76 (rounded to the nearest cent)
3. Find the depreciation value by subtracting the resale value from the initial value: Depreciation = Initial Value - Resale Value = 23,351 - 14,342.76 ≈ 9,008.24
4. Calculate the rate of depreciation per year: Rate of Depreciation = Depreciation / Years = 9,008.24 / 2 ≈ 4,504.12
The car is depreciating at approximately $4,504.12 per year after 2 years, rounded to the nearest cent.
Learn more about :
Depreciation : brainly.com/question/29748690
#SPJ11
PLEASE HELP ANSWER! ! : (
The dot plots show the distribution of heights, in inches, for third grade girls in two classrooms. Which statement is true?
A.
The center of the graph of class 1 is best measured by the median, and the center of the graph of class 2 is best measured by the mean.
B.
The center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.
C.
The centers of the graphs of class 1 and class 2 are best measured by the median.
D.
The centers of the graphs of class 1 and class 2 are best measured by the mean.
The correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.
Given is a dot plots show the distribution of heights, in inches, for third grade girls in two classrooms.
The dot plot of class 1 is uneven and that of class 2 is even.
So, the center of the graph will be calculated by mean and that of class 2 by median.
Hence. the correct statement is: the center of the graph of class 1 is best measured by the mean, and the center of the graph of class 2 is best measured by the median.
Learn more about mean and median, click;
https://brainly.com/question/30891252
#SPJ1
What is the difference in minutes between 55 minutes and 1 3/4 hours
The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.
We have,
To convert 1 3/4 hours to minutes, we can multiply it by 60 (since there are 60 minutes in an hour):
So,
1 3/4 hours
= (1 x 60) + (3/4 x 60)
= 60 + 45
= 105 minutes
Now we can find the difference between 105 minutes and 55 minutes:
= 105 minutes - 55 minutes
= 50 minutes
Therefore,
The difference in minutes between 55 minutes and 1 3/4 hours is 50 minutes.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ1
Please explain in detail how to use the formula for this
problem.
6.21. Telephone calls to a customer service center occur according to a Poisson process with the rate of 1 call every 3 minutes. Compute the probability of re- ceiving more than 5 calls during the nex
The probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.
To solve this problem, we will use the Poisson probability distribution formula, which is:
P(X = k) = (e^(-λ) * λ^k) / k!
where:
P(X = k) is the probability of getting k events in a specific time interval
e is Euler's number (approximately equal to 2.71828)
λ is the average rate of events per interval (also known as the Poisson parameter)
k is the number of events we want to calculate the probability for
k! is the factorial of k (i.e., k! = k x (k-1) x (k-2) x ... x 2 x 1)
In this problem, we are given that the rate of calls to a customer service center follows a Poisson process with a rate of 1 call every 3 minutes. Therefore, the average rate of calls per minute (i.e., λ) is:
λ = 1 call / 3 minutes = 1/3 calls per minute
Now, we want to find the probability of receiving more than 5 calls during the next 15 minutes. We can use the Poisson formula to calculate this probability as follows:
P(X > 5) = 1 - P(X ≤ 5)
= 1 - ∑(k=0 to 5) [e^(-λ) * λ^k / k!]
= 1 - [(e^(-λ) * λ^0 / 0!) + (e^(-λ) * λ^1 / 1!) + ... + (e^(-λ) * λ^5 / 5!)]
Substituting λ = 1/3 and simplifying the equation, we get:
P(X > 5) = 1 - [(e^(-1/3) * 1^0 / 0!) + (e^(-1/3) * 1^1 / 1!) + ... + (e^(-1/3) * 1^5 / 5!)]
≈ 0.0322
Therefore, the probability of receiving more than 5 calls during the next 15 minutes is approximately 0.0322.
To learn more about minutes visit:
https://brainly.com/question/15600126
#SPJ11
Q let u- look, for n-4 Express the codeword in polynomial form anduring: q(x) u (x) n X X) +1+ + x Solve for the third end around shift of the Codeword
We first need to clarify a few terms and the question itself. It seems like you are asking about a codeword in polynomial form and finding the third circular shift of the codeword. Let's express the codeword in polynomial form:
Let u(x) be the original polynomial codeword, and let n = 4. Based on the information provided, assuming that q(x) = u(x)n(x) = u(x)(1 + x^4).
To find the third circular shift of the codeword, follow these steps:
1. Express the original codeword u(x) in polynomial form, for example, u(x) = a_0 + a_1x + a_2x^2 + a_3x^3 (where a_i are coefficients).
2. Perform the first circular shift by moving the last term to the front: a_3x^3 + a_0 + a_1x + a_2x^2.
3. Perform the second circular shift: a_2x^2 + a_3x^3 + a_0 + a_1x.
4. Perform the third circular shift: a_1x + a_2x^2 + a_3x^3 + a_0.
The third circular shift of the codeword u(x) is given by the polynomial a_1x + a_2x^2 + a_3x^3 + a_0.
polynomialhttps://brainly.com/question/15262220
#SPJ11
What is length of side a given the following coordinates?
A (0,0), B(3,0), and C(2, 10).
A. 10.2
B. 79
C. 10.0
D. 3
Answer: A. 10.2
Step-by-step explanation: For this problem we have to create a second right triangle to find the length. You can apply the pythagorean theorem which continues to 10^2+2^2=c^2 which would get us 104. Then find the root of 104 which is equal to 10.2
What is the slope of the line that passes through the points (3, –1) and (–2, –5)?
−5/4
−4/5
4/5
5/4
The slope of the line is 4/5.
Option C is the correct answer.
We have,
The slope of the line that passes through the points (3, -1) and (-2, -5) can be found using the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the coordinates, we get:
slope = (-5 - (-1)) / (-2 - 3) = -4 / (-5) = 4/5
Therefore,
The slope of the line is 4/5.
Learn more about slope here:
https://brainly.com/question/14511992
#SPJ1
Each month, Nadeem keeps track of the number of times he visits the library and the number of books he checks out Is there a correlation
you model his data with a linear equation? Is there a causal relationship?
We may draw a scatterplot of the data and compute the correlation coefficient to see whether there is a relationship between Nadeem's visits to the library and the number of books he checks out. Linear Equation = Y =mx+c. Option A is Correct.
The degree and direction of the linear link between two variables are measured by the correlation coefficient. If the correlation is positive, it suggests that if one variable rises, the other variable rises as well.
If there is a correlation, linear regression may be used to describe the data with a linear equation.
Y= mx+c
Based on how frequently Nadeem visits the library, we may use this equation to anticipate how many books he will borrow. Correlation does not always indicate cause, though. Option A is Correct.
Learn more about linear equation visit: brainly.com/question/28732353
#SPJ4
Correct Question:
Each month, Nadeem keeps track of the number of times he visits the library and the number of books he checks out Is there a correlation. you model his data with a linear equation? Is there a causal relationship?
A. There is a positive correlation and no causal relationship.
B. There is a negative correlation and no casual relationship.
C. There is a casual relationship but no positive correlation.
D. There is neither a correlation nor a casual relationship.
please please please i’m i’m so much trouble for not having this done
define a please w/ explanation
Answer:
do this solve in calc (a+1)^2+(a+3)^2=(a+5)^2
The graphs below have the same shape. What is the equation of the blue
graph?
g(x)=
f(x)=x²
g(x) = ?
Click here for long description
O A. gx)=(x+2)²-1
B. g(x)=(x-2)²+1
C. g(x) = (x + 2)² +1
D. g(x)=(x-2)²-1
The equation of the blue graph include the following: B. g(x) = (x - 2)² + 1.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right simply means adding a digit to the value on the x-coordinate of the pre-image.
In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (upward) is modeled by this mathematical equation g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent functions.In order to write an expression that models g(x), we would have to apply a vertical translation to f(x) by 1 units up and a horizontal translation by 2 units right;
f(x)=x²
g(x) = (x - 2)² + 1.
Read more on translation here: brainly.com/question/4521517
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
You have taken up being a barista and developed your own coffee that you call Simply Significant Coffee. You want to see how it fares against other coffee competitors and think people will prefer your coffee. You plan to perform a taste test between Simply Significant, Starbucks. Peets coffee and Caribou coffee with 15 participants to see if they prefer your coffee. How probable is it that your first 2 participants will prefer Simply Significant and then the rest will prefer the other coffee brands? Please report to 4 decimal places.
The probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.
Assuming that each participant has an equal chance of preferring any of the four coffee brands and that their preferences are independent of each other, we can model the preference of each participant as a Bernoulli random variable with probability p of preferring Simply Significant Coffee.
Then, the probability of the first 2 participants preferring Simply Significant Coffee and the remaining 13 participants preferring one of the other coffee brands can be calculated as follows:
P(2 participants prefer Simply Significant and 13 prefer other brands) = P(Simply Significant)^2 * P(other brands)^13
where P(Simply Significant) is the probability of a participant preferring Simply Significant Coffee and P(other brands) is the probability of a participant preferring one of the other brands, which is 1/3 since there are three other brands besides Simply Significant.
Using the binomial probability formula, we can calculate P(Simply Significant) as follows:
P(Simply Significant) = C(15,2) * (1/4)^2 * (3/4)^13
where C(15,2) is the number of ways to choose 2 participants out of 15.
Plugging in the values, we get:
P(Simply Significant) = 105 * (1/16) * (0.3164) ≈ 0.0392
Therefore, the probability of the first 2 participants preferring Simply Significant and the remaining 13 participants preferring one of the other coffee brands is approximately 0.0392.
Note that this assumes that participants are choosing at random and are not influenced by factors such as the order in which the coffees are presented or any other external factors that could affect their preferences.
To learn more about Significant visit:
https://brainly.com/question/31037173
#SPJ11
Construct a matrix with the required property or explain why such construction is impossible. (a) The column space has basis {(1,0,2), (0,1,3)} and the mullspace has basis {(-1,0,1)). (b) The column space has basis {(2, 1, -1)} and the mullspace has basis {(1,3,2)). (c) The column space has basis {(1, 2, -3)} and the left nullspace has basis {(1, 0, -1)}. (d) The row space has basis {(1, -1,0,5), (1, 2, 3,0)} and mullspace has basis {(1,0,3, 2)}. (e) The row space has basis {(1,0, 2, 3,5)} and the left nullspace has basis {(-3,1)}
To construct a matrix with the required property (a), (d) & (e) are possible to construct the matrix. (b), (c) are not possible to construct the matrix.
(a) It is possible to construct a matrix with the given properties as follows:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The columns of this matrix span the column space, and the vector (-1,0,1) spans the nullspace.
(b) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the nullspace are different. The column space is a subspace of [tex]R^3[/tex], whereas the nullspace is a subspace of[tex]R^1[/tex].
(c) It is not possible to construct a matrix with the given properties because the dimensions of the column space and the left nullspace are different. The column space is a subspace of[tex]R^3[/tex], whereas the left nullspace is a subspace of [tex]R^2[/tex].
(d) It is possible to construct a matrix with the given properties as follows:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The rows of this matrix span the row space, and the vector (1,0,3,2) spans the nullspace.
(e) It is possible to construct a matrix with the given properties as follows:
[tex]\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right][/tex]. The rows of this matrix span the row space, and the vector (-3,1) spans the left nullspace.
Learn more about vector here:
https://brainly.com/question/31551501
#SPJ4
what are the answers to this
The effects of the interest rate in each situation are given as follows:
Theo: lower interest.Sarah: lower interest.Jacob: higher interest.Management: higher interest.Joey: higher interest.What is interest rate?The interest rate is the percentage by which an amount of money increases over a period of time.
For lower interest rate, loans or purchases are desired, as the person can pay back the loan after some time without a high additional tax.
For higher interest rates, investments are desired, as the balance of the investment should increase fast. Purchases, on the other hand, should be avoided with higher interest, as there will be a high tax for paying the purchase in installments.
More can be learned about interest rates at https://brainly.com/question/25793394
#SPJ1
!!will give brainliest!!!
Find WZ to the nearest tenth.
Assume that segments that appear
to be tangent are tangent.
The measure of secant WZ = 5 units
We know that the Secant-Tangent theorem states that, 'when a secant and tangent of a circle intersect at the same external point, then the product of the measure of the secant segment and its external part equals the square of the measure of the tangent segment.'
Here, VW is a tanget to a circle at point V and ZW is a secant of a circle.
From Secant-Tangent theorem,
ZY × YW = VW²
(x + 3) × (x) = (x + 1)²
We solve this equation for x.
x² + 3x = x² + 2x + 1
3x - 2x = 1
x = 1
So, the length of WY = 1 unit
So, the length of ZY would be,
x + 3
= 1 + 3
= 4
and the length of WZ = WY + YZ
= 1 + 4
= 5 units
This is the required length of WZ
Learn more about the secant here:
https://brainly.com/question/23026602
#SPJ1
If the probability is 0.05 that a certain column will fail under a given load, what are the probabilities that among 16 such columns given that the failure of columns are independents a) At most two will fail.
The probability that at most 2 columns will fail is 0.98.
This is a binomial distribution problem, where the number of trials n = 16, the probability of success (a column failing) p = 0.05, and we want to find the probability of at most 2 columns failing.
To solve this, we need to calculate the probability of 0, 1, or 2 columns failing and add them up.
P(at most 2 columns failing) = P(0 columns failing) + P(1 column failing) + P(2 columns failing)
P(0 columns failing) = (n choose 0) * p^0 * (1-p)^(n-0) = (16 choose 0) * 0.05^0 * 0.95^16 = 0.45
P(1 column failing) = (n choose 1) * p^1 * (1-p)^(n-1) = (16 choose 1) * 0.05^1 * 0.95^15 = 0.38
P(2 columns failing) = (n choose 2) * p^2 * (1-p)^(n-2) = (16 choose 2) * 0.05^2 * 0.95^14 = 0.15
P(at most 2 columns failing) = 0.45 + 0.38 + 0.15 = 0.98
Therefore, the probability that at most 2 columns will fail is 0.98.
To learn more about failing visit:
https://brainly.com/question/17043986
#SPJ11
The graph of a quadratic function with vertex (1,-1) is shown in the figure below. Find the domain and the range. Write your answers as inequalities, using or as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer.
The domain of the function is all real numbers and range is y ≥ -1.
Since the vertex is at (1,-1), the axis of symmetry is x = 1.
This means that the domain of the function is all real numbers.
To find the range, we need to consider the y-values of the graph. Since the vertex is the lowest point of the graph, the range must be all y-values greater than or equal to -1.
However, since the parabola opens upwards, there is no upper bound on the y-values.
Therefore, the range is given by y ≥ -1.
Hence, the domain of the function is all real numbers and range is y ≥ -1.
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ1
Help need answers!!! 100 POINTS!!! what does x equal, and what does angle m
Answer:
x = 10.1, AXY = 71.7 degrees
Step-by-step explanation:
There are two ways to solve this problem. You could either do 7x+1+108.3=180 or 180-108.3, then take that number and set it equal to 7x+1.
I will be using the latter. (You can do this because angle YXB is a linear pair with angle AXY. This means they add up to 180. So to find angle AXY, you subtract 180 from 108.3)
[tex]180-108.3=71.7\\\\7x+1=71.7\\\\[/tex]
Subtract one from each side to move variables to the left and constants to the right.
[tex]7x+1-1=71.7-1\\\\7x=70.7[/tex]
Divide seven by both sides to isolate the variable.
[tex]\frac{7x}{7}=\frac{70.7}{7} \\\\x=10.1[/tex]
So now we know what x is. So to find AXY, you substitute it back into the equation.
[tex]7(10.1)+1=71.7\\\\70.1+1=71.7?\\\\71.1=71.7?[/tex]
need help ASAP, find the vertices of:
(x-2)^2/16-(y-1)^2/4=1
show work pls!!
Answer:
Step-by-step explanation:
(x - 2)²/16 - (y - 1)²/4 = 1
(x - 2)² - 4(y - 1)² = 16
x² + 4 - 4x - 4(y² + 1 - 2y) = 16
x² + 4 - 4x - 4y² - 4 + 8y = 16
x² - 4x + 8y - 4y² = 16
x² - 4x = 16 , -4y² + 8y = 16
x(x - 4) = 16 , 4y(-y + 2) = 16
x = 16, x = 20, y = 4, y = -14
Please help with my Aleks.
Answer:
64
Step-by-step explanation:
the total must be 60×4 =240
subtract the miles already given and that us your answer. You could also make an equation. (64+53+59+x)/4=
I need help with this problem.
Answer:
1414 tickets, in explanation
Hope this helps!
Step-by-step explanation:
1 ticket = $9.50
? tickets = $13,433
13,433 ÷ 9.50 = 1414
9.50 × 1414 = 13,433
1 ticket × 1414 = ? tickets
? tickets = 1414 tickets
