Complete Question
Let A be an n x n matrix, b be a nonzero vector, and x_0 be a solution vector of the system Ax = b. Show that x is a solution of the non-homogeneous system Ax = b if and only if y = x - x_0 is a solution of the homogeneous system Ay = 0.
Answer:
Step-by-step explanation:
From the question we are told that
A is an n × n matrix
b is a zero vector
[tex]x_o[/tex] us the solution vector of [tex]Ax = b[/tex]
Which implies that
[tex]Ax_o = b[/tex]
So first we show that
if [tex]x[/tex] is the solution matrix of [tex]Ax = b[/tex]
and [tex]y= x-x_o[/tex] is the solution of [tex]Ay = 0[/tex]
Then
[tex]A(x-x_o) = 0[/tex]
=> [tex]Ax -Ax_o = 0[/tex]
=> [tex]b-b = 0[/tex]
Secondly to show that
if [tex]y= x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
then x is the solution of the non-homogeneous system
[tex]Ax = b[/tex]
Now we know that [tex]y = x-x_o[/tex] is the solution of [tex]Ay =0[/tex]
So
[tex]Ay = 0[/tex]
=> [tex]A(x- x_o) = 0[/tex]
=> [tex]Ax - Ax_o = 0[/tex]
=> [tex]Ax - b = 0[/tex]
=> [tex]Ax = b[/tex]
Thus this has been proved
A sociologist recently conducted a survey of citizens over 60 years of age who have net worths too high to qualify for Medicaid but have no private health insurance. The ages of the 25 uninsured senior citizens were as follows:
68 73 66 76 86 74 61 89 65 90 69 92 76
62 81 63 68 81 70 73 60 87 75 64 82
Find the upper quartile of the data.
a) 65.5
b) 92
c) 81.5
d) 073
Answer:
c) 81.5
Step-by-step explanation:
Listing the 25 ages in crescent order:
60 61 62 63 64 65 66 68 68 69 70 73 73 74 75 76 76 81 81 82 86 87 89 90 92
The upper or third quartile's position is given by:
[tex]Q_3=N_{\frac{3}{4}(n+1)}\\Q_3}=N_{\frac{3}{4}(25+1)}=N_{19.5}[/tex]
This means that the third quartile is the average between the 19th and 20th numbers:
[tex]Q_3=\frac{81+82}{2} \\Q_3 = 81.5[/tex]
The upper quartile is 81.5.
you and a group of friends spent at least $73.00 at a local pizzeria. Drinks for the table totaled $13 and it was $15 per pizza. how many pizzas could they order
Answer:
4 pizza's
Step-by-step explanation:
hope this helps :)
— 3х + 7 < 19 ?
Help plz
Answer:
x > -4
Step-by-step explanation:
— 3х + 7 < 19
Subtract 7 from each side
— 3х + 7-7 < 19-7
-3x < 12
Divide each side by -3, remembering to flip the inequality
-3x/-3 > 12/-3
x > -4
Just like any of your two-step equations, in this inequality,
start by isolating the x term which in this case is -3x by
subtracting 7 from both sides.
This gives us -3x < 12.
Solving from here, we divide both sides by -3.
However, when solving inequalities, you need to watch out.
When you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
Please give this idea your full attention. Even the most advanced algebra students will sometimes forget to switch the direction of the inequality sign when dividing both sides of an inequality by a negative.
So we end up with x > -4.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
c
Step-by-step explanation:
when the absolute value of slope gets smaller, the graph of line gets less steeper.
Please answer this correctly
Answer:
3.14
Step-by-step explanation:
We find the total circumference of a circle with radius 2 to be
2 * pi * r
= 2 * 3.14 * 2
= 12.56
We divide by 4 to get the perimeter of the quarter circle
12.56/4 = 3.14
How do you find arc length???
Answer:
π
Step-by-step explanation:
For a circle, arc length is equal to the radius times the angle.
s = rθ
s = (1) (π − 0)
s = π
Felicia walks 3 blocks west, 4 blocks south, 3 more blocks west, then
2 blocks south again. How far is Felicia from her starting point?
Answer:
blocks
Answer: i did the question i told you the steps
Step-by-step explanation:
From the starting point move three to the left. Then move four down. Then move three times to the left. Lastly move two down.
Classify the following triangle .check all that apply
Answer:
acute and scalene
Step-by-step explanation:
Answer:no entiendo esta en ingles
Step-by-step explanation:
to shift the graph of an equation some number of units to the_ you subtract that number from each X in the equation
Answer:
A. right
Step-by-step explanation:
Replacing x with (x-h) in a function shifts the graph to the right h units.
__
See the attachment for an example.
Find the area of a circle with radius, r = 19cm.
Give your answer rounded to 3 SF.
Answer:
1130
Step-by-step explanation:
since radius of the circle was given and the formula of the area is pie r square
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
The histogram to the right represents the weights (in pounds) of members of a certain high-school debate team. What is the class width? What are the approximate lower and upper class limits of the first class? The class width is_______.
Answer:
Class width = 20
Approximate lower class limit of the first class = 110
Approximate Upper class limit of the first class = 119
Step-by-step Explanation:
The class width of the histogram attached below can be gotten by finding the difference between successive lower class limits.
Thus, class width = 130 - 110 = 20
The approximate lower class limit of the first class is the lowest score we have in the first class = 110
The approximate upper class limit of the first class is the closest highest score that fall within the first class and is below the lower limit of the second class. Thus approximate upper class limit of the first class = 129
What’s the correct answer for this question?
Answer:
D
Step-by-step explanation:
It would be a cone with a radius of 4 units rotating around y-axis.
Use the following to answer questions
Employment statistics in the US are often based on two nationwide monthly surveys: the Current Population Survey (CPS) and the Current Employment Statistics (CES) survey. The CPS samples approximately 60,000 US households and collects the employment status, job type, and demographic information of each resident in the household. The CES survey samples 140,000 non-farm businesses and government agencies and collects the number of payrolls jobs, pay rates, and related information for each firm.
a. What is the population in the CPS survey?
b. What is the population in the CES survey?
Answer:
A. The population in the CPS survey are all US households.
B. The population in the CES survey are all the non-farm businesses and government agencies.
Step-by-step explanation:
A sample is the number of people from a whole population who actually participated in a survey. The population is the entire group of people whom the survey is meant to study. The sample is an off shoot of the population.
In the given question, the Current Population Survey is a study on the entire US households. Since every household cannot be interviewed because of the large population, a sample of 60,000 households is used. The whole households in the United States thus form the population under study.
For the Current Employment Statistics survey, the goal is to understand employment statistics in all the non-farm businesses and government agencies. This is the population. Since the entire population cannot be studied, a sample of 140,000 is used.
PLEASE HELP !!
Problem:
Find P(3).
Answers:
1/6
1/8
3/6
1
Answer:
The probability of spinning a 3 out of the 6 options is 1/6.
Answer: 1/6
Step-by-step explanation:
Im assuming the p stands for probability. There is a total of 6 slices, the 3rd slice takes up 1/6th of the circle
Which figure has two bases and one lateral face that is rectangular? cone cylinder rectangular prism rectangular pyramid
Answer: Cylinder
Step-by-step explanation:
Two bases first: that rules out cone and rectangular pyramid.
One lateral face: the only one with that is cylinder.
Hope that helped,
-sirswagger21
The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
What is mean by Triangle?Any triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
The shape have two bases and one lateral face that is rectangular.
We know that;
In a Cylinder,
It is a three-dimensional solid that contains two parallel bases connected by a curved surface.
And, The bases are usually circular in shape. The perpendicular distance between the bases is denoted as the height “h” of the cylinder and “r” is the radius of the cylinder.
Thus, The figure which has two bases and one lateral face that is rectangular is, ''Cylinder.''
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Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematical notation, and clearly identify the claim and type of testing.
Answer:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no
Step-by-step explanation:
For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:
Null hypothesis (H0): [tex]\mu \geq 2000[/tex]
Alternative hypothesis (H1): [tex]\mu <2000[/tex]
And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no
PLEASE HELP ME!!! (WILL MARK BRAINLIEST!
Answer:
A) 13/20
Step-by-step explanation:
65% in simplest form,
65/100
= 13/20 (Divided by five)
Answer:
[tex]\frac{13}{20}[/tex].
Step-by-step explanation:
We can begin by converting 65% to a fraction over 100. 65% converts to 0.65, or [tex]\frac{65}{100}[/tex].
We can simplify this down. Both 65 and 100 share a common factor of 5, which allows us to produce a new fraction:
[tex]\frac{65}{100} = \frac{13}{20}[/tex]
Therefore, the simplified version is [tex]\frac{13}{20}[/tex].
Solve the following system of equations using the elimination method. 5x – 5y = 10 6x – 4y = 4
Answer:
x=-2,y=-4
Step-by-step explanation:
By dividing to lowest terms
5x – 5y = 10= x-y=2.......(1)
6x – 4y = 4=3x-2y=2........(2)
By elimination method
Multiply equation (1) by 3 so as to correspond with equation (2)
3(x-y)=3(2)
3x-3y=6..........(3)
Multiply equation (2) by 1 so as to correspond with equation (1)
1(3x-2y)=1(2)
3x-2y=2..........(4)
Then equation (3)-equation (4)
(3x-3y=6)
-
(3x-2y=2)
__________
-y=4
y=-4
Substitute y=-4 into equation(1)
x-(-4)=2
x+4=2
x=-2
Therefore x=-2,y=-4
You are studying a population of squirrels on the south rim of the Grand Canyon and find that 9 squirrels out of 100 observed had a unique, solid black color variation. In other mammals, the solid black color variation is caused by a recessive allele, and you assume that to be the case with these squirrels. If the population is in Hardy-Weinberg equilibrium, which of the following would be true?
A. q2 = 0.09
B. .q2 = 0.9
C. The frequency of the black color allele is 0.3, the frequency of the dominant allele is 0.7
D. The frequency of the heterozygous genotype is 4.2%
E. A and C
Which of the following is/are possible applications for use of the CRISPR-Cas9 system?
A. Disable dominant deleterious genes
B. Turn on and off specific genes by disabling Cas9 nuclease activity and attaching it to a transcriptional activator or repressor protein
C. Study gene function
D. all of the above
Genome wide association studies are important for behavioral disorders because
A. Candidate genes can be identified for further study
B. They provide an association between genetic loci and phenotypes
C. They provide a tool to help understand how genetic and environmental factors interact to cause psychiatric disorders
D. all of the above
Answer:
Step-by-step explanation:
Ans-1.)
q 2 = 9 /100 (A) q = 0.3 (p + q) 2 = 1 p + q = 1 p = 1- q = 1 - 0.3 p = 0.7 * The frequency of black color allele is 0.3 and dominant allele is 0.7 (C)
* (A) and (C)Ans -2.) CRISPR -Cas 9 system has very wide application :
* can be used to disable the dominant deleterious genes .
* Turn on and off by disabling Cas9 nuclease activity and attaching to a transcriptional activator or repressor protein.
* widely used to study function
* All the above (answer)Ans-3.) Genome wide association studies are important to study behavioral disorders because
* candidate genes identified for further studies.
* Provide an association between genetic loci and phenotypes.
* Provide a tool to help understand how genetic and environmental factors interact to pyschiatric disorders
* All of the above (answer)There are two fields whose total area is 56 square yards. One field produces grain at the rateof34bushel per square yard; the other field produces grain at the rate of23bushel per squareyard. If the total yield is 40 bushels, what is the size of each field
Answer:
the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
Step-by-step explanation:
With the statement we can make a system of 2x2 equations, where:
"x" is the area of the first field
"y" is the area of the second field
However,
x + y = 56 => x = 56 - y
3/4 * x + 2/3 * y = 40
replacing we have:
3/4 * (56 - y) + 2/3 * y = 40
42 - 3/4 * y + 2/3 * y = 40
-0.0833 * y = 40 - 42
y = -2 / -0.0833
y = 24
now for x:
x = 56 - 24
x = 32
This means that the first field (rate 3/4) has 32 square yards and the second field (rate 2/3) has 24 square yards.
3. Bob the Builder wants to earn an annual rate of 10% on his investments,
how much (to the
nearest cent) should he pay for a note that will be worth $3,000 in 9 months?
Answer:
He should pay $2,790.7.
Step-by-step explanation:
This is a simple interest problem.
The simple interest formula is given by:
[tex]E = P*I*t[/tex]
In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time, in years.
After t years, the total amount of money is:
[tex]T = E + P[/tex]
In this question:
Rate of 10%, so I = 0.1.
9 months, so [tex]t = \frac{9}{12} = 0.75[/tex]
How much should he pay for a note that will be worth $3,000 in 9 months?
We have to find P for which T = 3000. So
[tex]T = E + P[/tex]
[tex]3000 = E + P[/tex]
[tex]E = 3000 - P[/tex]
Then
[tex]E = P*I*t[/tex]
[tex]3000 - P = P*0.1*0.75[/tex]
[tex]1.075P = 3000[/tex]
[tex]P = \frac{3000}{1.075}[/tex]
[tex]P = 2790.7[/tex]
He should pay $2,790.7.
sarah can complete a project in 90 minutes and her sister betty can complete it in 120 minutes if they both work on the project at the same time how long will it take them to complete the project
Answer:
It will take them approximately 51.43 minutes to complete the project together
Step-by-step explanation:
This is what is called a "shared job" problem.
The best way to work on them is to start by finding the "portion" of the job done by each of the people in the unit of time.
So, for example, Sarah completes the project in 90 minutes, so in the unit of time (that is 1 minute) she completed 1/90 of the total project
Betty completes the project in 120 minutes, so in the unit of time (1 minute) she completes 1/120 of the total project.
We don't know how long it would take for them to complete the project when working together, so we call that time "x" (our unknown).
Now, when they work together completing the entire job in x minutes, in the unit of time they would have done 1/x of the total project.
In the unite of time, the fraction of the job done together (1/x) should equal the fraction of the job done by Sarah (1/90) plus the fraction of the job done by Betty. This in mathematical form becomes:
[tex]\frac{1}{x} =\frac{1}{90} +\frac{1}{120}\\\frac{1}{x} =\frac{4}{360} +\frac{3}{360}\\\frac{1}{x} =\frac{7}{360} \\x=\frac{360}{7} \\x=51.43\,\,min[/tex]
So it will take them approximately 51.43 minutes to complete the project together.
which is the domain of f(x) = 4^x
will give brainlist!
Answer:
all real numbers
Step-by-step explanation:
The domain is the input values
All values for x are valid as inputs to the function
9.2 An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780 hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm.
Answer:
765,795 = 96%
Step-by-step explanation:
confidence interval = 0.04
The Za/2 theorem = 1/2 = 0.04/2 = 0.02= /x = 720z
If ; 0.02 = 2.05 then the interval is 780-2.05 x 40/√30 x 780+2.05 x 30/√30 = 765,795 = 96%
We see 40/ √30 which is found in equation of finding the sample mean at point /x = 720z
σ 40/ n√30 = 7.3029674334 and is simply a fraction of /x 720z
By normal distribution we find
The 96% confidence interval for the population mean of all bulbs = 765,795
As 765, x 1.04 = 795 = 765, 795
To find Sampling mean.
The Sampling Distribution of the Sample Mean. If repeated random samples of a given size n are taken from a population of values for a quantitative variable, where the population mean is μ (mu) and the population standard deviation is σ (sigma) then the mean of all sample means (x-bars) is population mean μ (mu).
Confidence Level z*-value
80% 1.28
90% 1.645 (by convention)
95% 1.96
96% 2.05
98% 2.33
99% 2.58
An intravenous fluid is infused at the rate shown in the table. What is the missing value?
Minutes
Milliliters
3
ܢܚܪ
2.
?
3
9
4
12
3
6
9
24
Answer:
the answer is 6!!!!!!
Step-by-step explanation:
The missing value in the table is 5
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
An intravenous fluid is infused at the rate shown in the table
Minutes Milliliters
3 4
? 12
2. 3
? 6
3 9
9 24
Slope=24-9/9-3
=15/3
=5
Now 5=12-4/x-3
5=8/x-3
5x-15=8
5x=23
x=23/5
x=4.6
x=5
The missing number is 5.
Hence, the missing value in the table is 5
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A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 5-year period from 2008 to 2012. The following is the resulting regression equation: log10 = 6.102 + 0.012 X - 0.129 Q1 - 0.054 Q2 + 0.098 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2008 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise To obtain a fitted value for the fourth quarter of 2009 using the model, which of the following sets of values should be used in the regression equation?1. In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02. Which of the following is the best interpretation of this result? a. The quarterly growth rate in revenues is significantly different from 0%. b. The quarterly growth rate in revenues is not significantly different from 0%. c. The quarterly growth rate in revenues is significantly different from 1.2%. d. The quarterly growth rate in revenues is not significantly different from 1.2%. e. The quarterly growth rate in revenues is significantly different from 1.2% 2. using the regression equation, the forecast for the revenues in the fourth quarter of 2004 is:______ a. 6,426 b. 2,666,858 c. 6,638 d. 2,741,574 e. 6,414
Answer:
The quarterly growth rate in revenues is significantly different from 1.2%.
b. 2,666,858
Step-by-step explanation:
Given that:
The regression equation can be represented as :
[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]
In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02.
The null and alternative hypothesis can be stated as;
[tex]H_0:[/tex] The quarterly growth rate in revenues is not significantly different from 1.2%.
[tex]H_a:[/tex] The quarterly growth rate in revenues is significantly different from 1.2%.
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From above ; the p-value = 0.02 which is less than 0.05.
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in revenues is significantly different from 1.2%.
b.
Since [tex]Q_1=Q_2=Q_3 = 0[/tex] ; X = 27
Thus ;
[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]
[tex]log_{10} \hat Y= 6.102+0.012 (27)[/tex]
[tex]\hat Y=10^{ 6.102+0.012 (27) }[/tex]
[tex]\hat Y =[/tex] 2666858.665
[tex]\hat Y =[/tex] 2,666,858
2x+3=-7 twenty Chanda long-standing look
Answer:
x =-5
Step-by-step explanation:
Answer:
x=-5
Step-by-step explanation:
Barbara can pay either $80 per month or one lump sum of $800 per year for car insurance. How much does she save yearly if she chooses the lump sum payment option?
Answer:
$160
Step-by-step explanation:
In the monthly payment option she would pay $80 per month, therefore in a year (12 months) she would pay:
$80*12 = $960
We can see that this amount is greater than the $800 she would pay in the lump sum payment option.
The money she would save is:
$960 - $800 = $160
She would save $160 yearly with the lump sum payment option.
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= -7x+3
y = -x-3
Answer: The answer has one solution:
_______________________________
→ x = 1 ; y = -4 ; or, write as: [1, -4].
_______________________________
Step-by-step explanation:
_______________________________
Given:
y = - 1x – 3
y = -7x + 3 ;
_______________________________
-1x – 3 = -7x + 3 ; Solve for "x" ;
Add: " +1x" ; and add " +3 " ; to Each Side of the equation:
Subtract " 1x " ; and Subtract " 1 " ; from Each Side of the equation:
-1x + 1x – 3 + 3 = -7x + 1x + 3 + 3 ;
to get:
0 = -6x + 6
↔ -6x + 6 = 0 ;
Now, subtract " 6 " from Each Side of the equation:
-6x + 6 – 6 = 0 – 6 ;
to get:
-6x = -6 ;
Now, divide Each Side of the equation by " -6 ";
to isolate "x" on one side of the equation;
& to solve for "x" ;
-6x /-6 = -6/-6 ;
to get:
x = 1 .
_______________________________
Now, let us solve for "y" ;
We are given:
y = -x – 3 ;
Substitute our solved value for "x" ; which is: " 1 " ; for " x " ; into this given equation; to obtain the value for " y " :
y = -x – 3 ;
= -1 – 3
y = - 4 .
_______________________________
Let us check our answers by plugging the values for "x" and "y" ;
" 1 " ; and " -4 "; respectively); into the second given equation; to see if these values for " x " and " y" ; hold true:
Given: y = - 7x + 3 ;
→ -4 =? -7(1) + 3 ?? ;
→ -4 =? -7 + 3 ?? ;
→ - 4 =? -4 ?? ;
→ Yes!
_______________________________
The answer has one solution:
→ x = 1 ; y = - 4 ; or, write as: [1, -4 ].
_______________________________
Hope this is helpful! Best wishes!
_______________________________