The transformation matrix for the mapping T is the matrix T such that
[tex]\mathbf T(\vec x)=T\,\vec x[/tex]
where
[tex]T=\begin{bmatrix}1&4&0&0\\0&0&0&0\\0&3&0&1\\0&1&0&-1\end{bmatrix}[/tex]
The correct matrix A is
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
To find the matrix A that represents the linear transformation T, we need to determine the coefficients that map the input vector (X₁, X₂, X₃, X₄) to the output vector (x₁ +4x₂, 0, 3x₂ +x₄, x₂ -x₄)
By comparing the corresponding entries in the input and output vectors, we can determine the coefficients of the matrix A.
The first row of A will have the coefficients for X₁ and X₂, which are 1 and 4 respectively. The second row will have all zeros since the output vector has a zero in the second position. The third row will have the coefficient 3 for X₂ and 1 for X₄. Finally, the fourth row will have the coefficient 1 for X₂ and -1 for X₄.
Thus, the matrix A that implements the mapping T is:
[tex]A=\left[\begin{array}{cccc}1&4&0&0\\0&0&0&0\\0&3&0&1&0&1&0&-1\end{array}\right][/tex]
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Savings accounts are a reliable way to store money for the future
Answer:
true
Step-by-step explanation:
just took test
what variable will you use to represent the number of brochures
Answer: always “X”
Step-by-step explanation:
Answer:
i would use the variable b because b = brochures.
Step-by-step explanation:
i hope this helped heh
Which of the following is not approximately equivalent to one of the metric units: 1 meter, 1 kilogram, or 1 liter
Answer:
A meter is not part of the metric system. It's part of the U.S. customary system.
What is the size of angle YXZ?
We have a right triangle and we're given the leg lengths.
tan X = |YZ| / |XZ| = 20/8 = 5/2
X = arctan(5/2) = 68.2°
Answer: 68.2°
tan X = YZ / XZ = 20/8 = 5/2
X = arctan(5/2) = 68.2°
Answer: 68.2°
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.
a. Level of significance, null and alternative hypothesis
b. What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
c. Find or estimate the P-value
d. Based on your answers to part a and c will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha?
e. Interpret your conclusion in the context of the application
Answer:
a) Level of significance α=0.05
Two-tailed test, with null and alternative hypothesis:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.
Test statistic t=-2.4
c) P-value = 0.018
d) Rejection of the null hypothesis.
The data is statistically significant.
e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that there is a significant difference in average off-schedule times for this bus lines.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.
The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.
The difference between sample means is Md=-7.
[tex]M_d=M_1-M_2=53-60=-7[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=51+60-2=109[/tex]
This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]
As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.
A newspaper posted this question on its web "How often do you seek medical information online?" Of 1072 Internet users who chose to respond, 38% of them responded with "frequently." What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond? What is wrong with this type of sampling method? What term is used to describe this type of survey? Select all that apply.
What term is used to describe this type of survey in which the people surveyed consist of those who decided to respond?
a. The respondents are a census.
b. The respondents are a population.
c. The respondents are a voluntary response sample.
d. The respondents are a self-selected sample.
What is wrong with this type of sampling method?
a. The survey question is "loaded," or intentionally worded to elicit a desired response.
b. It is too expensive.
c. Many people may choose not to respond to the survey.
d. Responses may not reflect the opinions of the general population.
e. It is too time consuming
Answer:
1. Option c
2. Option d
Step-by-step explanation:
This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.
This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.
Part A: The respondents are a voluntary response sample (Option C)
Part B: Responses may not reflect the opinions of the general population (Option D)
The total number of internet users = 1072
Percentage of the total number of people that chose to respond = 38%
Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.
Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.
In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples
The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population
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Two positive, consecutive, odd integers have a product of 143.
Complete the equation to represent finding x, the greater integer.
x(x –
) = 143
What is the greater integer?
Step-by-step explanation:
x and x+2 are the numbers
x(x+2)=143
x²+2x-143=0
x²+13x-11x-143=0
x(x+13)- 11(x+13)=0
(x+13). (x-11)=0
x+13=0. x=-13
x-11=0. x=11
leave answer in simplest radical form
Answer:
[tex]\dfrac{5\pm\sqrt{47}}{6}[/tex]
Step-by-step explanation:
Let's start by setting y to 0 to find the roots of the quadratic.
[tex]x=\dfrac{5\pm \sqrt{25+12}}{6}=\\\\\dfrac{5\pm\sqrt{47}}{6}[/tex]
Hope this helps!
Based on the type of equations in the system, what is the greatest possible number of solutions? StartLayout Enlarged left-brace 1st Row x squared + y squared = 9 2nd row 9 x + 2 y = 16 EndLayout
Answer:
2
Step-by-step explanation:
Given the system of equations:
[Tex]x^2+y^2=9\\9x+2y=16[/tex]
Comparing [Tex]x^2+y^2=9[/tex] with the general standard equation of a circle [Tex](x-h)^2+(y-k)^2=r^2[/tex].
The first equation is an equation of a circle centred at (0,0) with a Radius of 3.
The second equation 9x+2y=16 is a straight line equation.
A straight line can only intersect a circle at a maximum of 2 points.
Therefore the greatest possible number of solutions to the equations in the system is 2.
Answer:
2
Step-by-step explanation:
and jj is gay of outer banks
ASAPPPP
I HAVE AND IMAGE BELOW
Answer:
#1
Step-by-step explanation:
The associative property of addition states that we can "flip" two expressions that are being added. Therefore, our answer is the first one because it can be rewritten as 3x + (-7y) which then is equivalent to -7y + 3x.
the graph of f (x) shown below has the same shape as the graph of G (x) equals x ^ 4 but it is shifted 4 units to the right what is the equation
Answer:
D
Step-by-step explanation:
shifting 4 units to the right means that the new root = old root + 4
what that means is that the equation must have a transformation such that it equates to 0 with the root being 4 larger.
the root/vertex for x^4 is at x=0
we want the root to be at x=4
so that means we can subtract 4 from x
and get (x-4)^4
-23d + 81 <-98d + 1
Solve for d
Step-by-step explanation:
-23d + 81 < - 98d + 1
81 - 1 < - 98d + 23d
80 < - 75d
80/ - 75 < d
10/ - 3 < d
1. In an arithmetic sequence, the first term is -2, the fourth term is 16, and the n-th term is 11,998
(a) Find the common difference d
(b) Find the value of n.
pls help...
Answer:
see explanation
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
(a)
Given a₁ = - 2 and a₄ = 16, then
a₁ + 3d = 16 , that is
- 2 + 3d = 16 ( add 2 to both sides )
3d = 18 ( divide both sides by 3 )
d = 6
--------------
(b)
Given
[tex]a_{n}[/tex] = 11998 , then
a₁ + (n - 1)d = 11998 , that is
- 2 + 6(n - 1) = 11998 ( add 2 to both sides )
6(n - 1) = 12000 ( divide both sides by 6 )
n - 1 = 2000 ( add 1 to both sides )
n = 2001
------------------
Please help. I’ll mark you as brainliest if correct!
Answer:
g(x)= 1/4 |x-2| + 1
Step-by-step explanation:
line:
g(x)points on same line:
(2, 1) and (6, 2)slope based on the points
m= (2-1)/(6-2)= 1/4And the line is moved to the right by 2 units:
So the function becomes:
g(x)= 1/4|x-2|Considering movement up by 1 unit as well:
g(x)= 1/4 |x-2| + 1This is the final of equation for the line.
Please answer this correctly
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
------------
total 5
DuraBurn claims that the mean lifetime of its SuperGlo light bulbs is 904 hours. A researcher wants to perform a hypothesis test to determine whether the mean lifetime is actually less than this. A random sample of 10 DuraBurn SuperGlo bulbs exhibited an average lifetime x-805 hours with a standard deviation s 158 hours. Using the hypotheses H0: μ = 904 vs Ha: μ < 904, find the P-value and state your conclusion. Use a significance level of 0.05.
1. P-value 0.039, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
3. P-value 0.079, there is not sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
4. P-value0.079, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: μ = 904
For the alternative hypothesis,
Ha: μ < 904
This is a left tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 10,
Degrees of freedom, df = n - 1 = 10 - 1 = 9
t = (x - µ)/(s/√n)
Where
x = sample mean = 805
µ = population mean = 904
s = samples standard deviation = 158
t = (805 - 904)/(158/√10) = - 1.98
We would determine the p value using the t test calculator. It becomes
p = 0.039
Since alpha, 0.05 > than the p value, 0.03953, then we would reject the null hypothesis. Therefore, the correct option is:
2. P-value 0.039, there is sufficient evidence to conclude the mean lifetime of its SuperGlo light bulbs is less than 904 hours.
[tex]x = \frac{b + - \sqrt{{b}^{2} - 4ac } }{2a} [/tex]
O True
O False
If it is asking if that equation is the quadratic formula, then the answer is false. The reason why is that the first 'b' should be negative
The quadratic formula is
[tex]x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]
The sales tax in Pennsylvania is 4%. If the tax on an item is $94, find the cost of the item
Answer:
$2350
Step-by-step explanation:
If 94 is 4%, multiply it by 25 to get $2350, or 100%
the cost of the item is $ 2350.
To find the cost of the item, we can set up an equation using the information given.
Let's denote the cost of the item as $ x.
According to the given information, the sales tax on the item is 4 % and is equal to $ 94. We can express this as:
0.04 x = 94
To solve for x, we divide both sides of the equation by 0.04:
x = tax on item / sales tax
x = 94 / 0.04
x = 2350
Therefore, the cost of the item is $ 2350.
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Find the values
Y = 3x - 7
Y = x - 1
X = Y =
Answer: Y=3x -7
Y=x-1
X=Y=
Step-by-step explanation:
Really easy math question!
the answer is A: 146 ≤ 9c + 10
Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards. A sample of 20 cards are selected from the lot without replacement for functional testing. (a) If 20 cards are defective, what is the probability that at least one defective card appears in the sample
Answer:
The probability that at least one defective card appears in the sample
P(D) = 0.9644 or 96.44%
Step-by-step explanation:
Given;
Total number of cards t = 140
Number of defective cards = 20
Number of non defective cards x = 140-20 = 120
The probability that at least one defective card = 1 - The probability that none none is defective
P(D) = 1 - P(N) ........1
For 20 selections; r = 20
-- 20 cards are selected from the lot without replacement for functional testing
The probability that none none is defective is;
P(N) = (xPr)/(tPr)
P(N) = (120P20)/(140P20)
P(N) = (120!/(120-20)!)/(140!/(140-20)!)
P(N) = (120!/100!)/(140!/120!) = 0.035618370821
P(N) = 0.0356
The probability that at least one defective card appears in the sample is;
P(D) = 1 - P(N) = 1 - 0.0356 = 0.9644
P(D) = 0.9644 or 96.44%
Note: xPr = x permutation r
What are the next two numbers in the pattern of numbers 45,15,44,17,40,20,31,25
Answer:
14, 32
Step-by-step explanation:
45,15,44,17,40,20,31,25
this is combination of 2 series:
45-44-40-31- ?15-17-20-25-?In the first series we can see the pattern as:
-1, -4, -9 = -1², -2², -3² so next difference must be -4², which is 31- 16= 14In the second series we can see the pattern as:
2, 3, 5 prime numbers, so next difference must be 7, which is 25+7=32The series will continue as:
45, 15, 44, 17, 40, 20, 31, 25, 14, 32Use the area to find the radius. If you could include steps that’ll be very helpful :)
Answer:
Area = PI * radius^2
radius^2 = Area / PI
radius^2 = 169*PI/PI
radius^2 = 169
radius = 13
Step-by-step explanation:
Ania kupiła w księgarni dwie książki i zapłaciła 37,20, a jurek za swoje zapłacił trzy razy więcej. Ile zapłacił jurek
Answer:
111.60
Question:
Ania bought two books in a bookstore and paid 37.20, and Jurek paid three times more for his. How much did Jurek pay?
Step-by-step explanation:
This is a question on multiplying decimals by natural numbers.
Number if books bought by Ania = 2
Cost for the two books = 37.20
Jurek paid = 3 times the amount Ania paid
Amount Jurek paid = 3×37.20
To multiply decimals with whole numbers, first multiply without the decimals
3×3720 = 11160
3 has no decimal place
37.20 has 2 decimal place
Therefore the answer would be in two decimal place = 111.60
So 3× 37.2= 111.60
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
D (4,11)
Step-by-step explanation:
Answer: it’s d
x is just going up by 1 and y is going up by 2
In △ ABC, ∠C = 57° and ∠A = 103°. Side CB= 6.5 cm. Draw △ A′B′C′ under the same condition as △ ABC. Leave all construction marks as evidence of your work, and label all side and angle measurements(use text box). What can you conclude about △ ABC and △ A′B′C′? Justify your response.
Answer:
ΔA'B'C' is congruent to ΔABC
Step-by-step explanation:
See attached for the construction of ΔA'B'C'. (The vertices are labeled ABC.)
We computed angle B to be ...
∠B = 180° -∠A -∠C
∠B = 180° -103° -57° = 20°
We constructed segment BC of length 6.5. Then we constructed angles of 20° and 57° from B and C, respectively. The location where the rays from those angles cross is point A', and the angle there is 103°, as required.
__
ΔA'B'C' is congruent to ΔABC by the ASA congruence postulate.
If the mean of 5 positive integers is 15, what is the maximum possible difference between the largest and the smallest of these 5 numbers?
Answer:
if the 5 numbers are different, the maximum difference is 64
Step-by-step explanation:
We have 5 positive (different) integers, a, b, c, d and e (suppose that are ordered from least to largest, so a is the smallest and b is the largest.
The mean will be:
M = (a + b + c + d + e)/5 = 15.
Now, if we want to find the largest difference between a and e, then we must first select the first 4 numbers as the smallest numbers possible, this is:
a = 1, b = 2, c = 3 and d = 4
M = (1 + 2 + 3 + 4 + d)/5 = 15
M = (10 + d)/5 = 15
10 + d = 15*5 = 75
d = 75 - 10 = 65
then the difference between a and d is = 65 - 1 = 64.
Now, if we take any of the first 4 numbers a little bit bigger, then we will see that the value of d must be smaller, and the difference between d and a will be smaller.
For the graph y = 4 find the slope of a line that is perpendicular to it.
Answer:
Slope is 4
slope of the line perpendicular to it: x=-1/4
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, and asymptotes. f(x)=-2cot x
Answer:
(See explanation below for further details)
Step-by-step explanation:
The domain of the function is:
[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]
The range of the function is:
[tex]f(x) \in \{-\infty, +\infty \}[/tex]
There are no absolute extrema and such function is not bounded.
Function is symmetric, whose period is π.
Lastly, the set of asymptotes is:
[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]
Answer:
Step-by-step explanation:
edge
b. Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.) c. Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.) d. Find the expected value of X. (Round your answer to one decimal place.) e. Find the standard deviation of X. (Round your answer to three decimal places.)
Answer:
(a) Probability distribution is prepared below.
(b) The probability that two or fewer heads are observed in three tosses is 0.875.
(c) The probability that at least one head is observed in three tosses is 0.875.
(d) The expected value of X is 1.5.
(e) The standard deviation of X is 2.121.
Step-by-step explanation:
The complete question is: A fair coin is tossed three times. Let X be the number of heads observed in three tosses of this fair coin.
(a) Find the probability distribution of X.
(b) Find the probability that two or fewer heads are observed in three tosses. (Round your answer to three decimal places.)
(c) Find the probability that at least one head is observed in three tosses. (Round your answer to three decimal places.)
(d) Find the expected value of X. (Round your answer to one decimal place.)
(e) Find the standard deviation of X. (Round your answer to three decimal places.)
Now, firstly the sample space obtained in three tosses of a fair coin is given as;
Sample Space (S) = {HHH, HHT, HTH, THH, HTT, TTH, THT, TTT}
(a) The Probability distribution of X is given below;
Number of Heads (X) P(X) [tex]X \times P(X)[/tex] [tex]X^{2} \times P(X)[/tex]
0 [tex]\frac{1}{8}[/tex] = 0.125 0 0
1 [tex]\frac{3}{8}[/tex] = 0.375 0.375 0.375
2 [tex]\frac{3}{8}[/tex] = 0.375 0.75 3
3 [tex]\frac{1}{8}[/tex] = 0.125 0.375 3.375
Total 1.5 6.75
(b) The probability that two or fewer heads are observed in three tosses is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= 0.125 + 0.375 + 0.375
= 0.875
(c) The probability that at least one head is observed in three tosses is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.125
= 0.875
(d) The expected value of X = E(X) = [tex]\sum (X \times P(X))[/tex]
= 1.5
(e) The Variance of X = V(X) = [tex]E(X^{2} ) - ( E(X))^{2}[/tex]
= [tex]\sum (X^{2} \times P(X))- (\sum (X \times P(X)))^{2}[/tex]
= [tex]6.75 - 1.5^{2}[/tex] = 4.5
Now, Standard deviation of X = [tex]\sqrt{V(X)}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.121.