Solve the homogeneous linear system corresponding to the given coefficient matrix.
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
This question is incomplete, the complete question is;
Solve the homogeneous linear system corresponding to the given coefficient matrix. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, set x4 = t and x2 = s and solve for x1 and x3 in terms of t and s.)
[1 0 0 1]
[0 0 1 0]
[0 0 0 0]
(x1, x2, x3, x4) =________
Answer:
the solution for the given system is; ( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
Step-by-step explanation:
Given the data in the question;
coefficient matrix
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right][/tex]
Now, from linear system;
[tex]\left[\begin{array}{cccc} 1&0&0&1 \\ 0&0&1&0 \\ 0&0&0&0 \end{array}\right] \left[\begin{array}{ccc}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{ccc}0\\0\\0\\0\end{array}\right][/tex]
So, with the matrix, the associated equation is;
x₁ + x₄ = 0, x₃ = 0
Number of variables is 4 and ranked of the matrix is 2,
Hence, there are infinite solutions,
There are also two free variables;
from the question,
Let x₄ = t and x₂ = s be the free variables
so
x₁ + x₄ = 0
x₁ + t = 0
x₁ = -t
Therefore, the solution for the given system is;
( x₁, x₂, x₃, x₄ ) = ( -t, s, 0, t )
find the median of the data in the dot plot below. Mass of each rock in Nija's collection
Answer:
40
Step-by-step explanation:
The median is the middle number
There are 10 numbers
The middle is between 5th and 6th number
Take the 5th and 6th numbers and average them
(39+41)/2 = 80/2 = 40
The median is 40
Mass of each rock in Nija's collection is 40.
Answer:
The median is the middle number
n=10 numbers
The middle is between 5th and 6th number
Taking the 5th and 6th numbers:
average(39+41)/2 = 80/2 = 40
The probalityof raining today is 30% what is the probality tha it will nat rain?
A survey of 2392 adults ages 18 and over asked what type of food they would be most likely to choose at a restaurant. The results are shown in the figure.
A circle graph titled Survey Results is divided into 6 regions showing different types of restaurants. Starting from the top right, the regions are labeled, American 670, Italian 526, Mexican 407, Chinese 383, Japanese 167, Other 239.
What is the probability that an adult chosen at random prefers Italian food? Round your answer to the nearest whole percent.
Answer:
22%
Step-by-step explanation:
their is a total of 2392 adults, the number of people, who would be most likely to chose Italian food is 526.
p= 526/ 2392=22%
The probability of choosing Italian food is 21.9%.
What is probability?"Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one".
For the given situation,
Total number of adults = 2392
American food = 670
Italian food = 526
Mexican food = 407
Chinese food = 383
Japanese food = 167
Others = 239
The event is the probability of choosing Italian food.
[tex]P(e)=\frac{526}{2392}[/tex]
⇒[tex]P(e)=0.219[/tex]
Rounded to nearest whole percent = [tex]0.219[/tex] × [tex]100[/tex]
⇒[tex]21.9\%[/tex]
Hence we can conclude that the probability of choosing Italian food is 21.9%.
Learn more about probability here
brainly.com/question/13604758
#SPJ2
The managers of a fast food chain want their products to be as similar as possible across locations. They suspect that the burgers at their Albuquerque branch have bigger parties than the burgers at the Santa Fe branch, so they take a sample of 7 patties from each restaurant and measure their weights in gransk
Albuquerque 11011 110 110 111 112 106
Santa Fe 107 111 110 108 109 110 109
The managers want to test if the parties in the Albuquerque branch have a higher average weight than the patties in the Santa Fe branch. Assume that all conditions for inference have been met
Which of these is the most appropriate test and alternative hypothesis?
a. Pairedt test with H>0 3
b. Pairedt test with H > 0
c. Pairedt test with Ht0
d. Two-sample t test with H. > 0
Answer:
H0 : μd = 0
H1 : μd > 0
Step-by-step explanation:
The scenario described above can be compared statistically using a paired test mean as the mean if the two groups are dependent, the two restaurants, Albuquerque and Santa Fe are both restaurant locations of a single restaurant company. Hence, to test the mean difference, we use the paired test statistic. Defined thus `
Null hypothesis ; H0 : μd = 0 and the Alternative hypothesis ; H1 : μd > 0
Answer:
Two Sample T test with Ha = Albernuque>Santa Fe
Step-by-step explanation:
Khan
Which of the following is most likely the next step in the series?
Answer:
B
Step-by-step explanation:
Hi there!
TL;DR: Observe the vertices of the shapes inside the circles and their relationship with the circle.
For the first figure, the rectangle has 4 vertices and there are 4 dots on the perimeter of the circle.
For the second figure, the triangle has 3 vertices and there are 3 dots on the perimeter of the circle.
For the third figure, the line has 2 points and there are 2 dots on the perimeter of the circle.
For the fourth figure, there would most likely be only one dot on the perimeter of the circle (4, 3, 2, 1). The only option that shows this is B.
I hope this helps!
A video game that usually costs $30.65 is marked down 60%. Kelvin determined that the new price of the game would be $18.39. Look at Kelvin's work and find his error. ($30.65)(0.60) = $18.39
*Please give an explanation longer than 1 sentence :,)
Answer:
Kelvin’s error is that when he got the final result, that was the amount that was marked down. He still needed to find the price after the original price was marked down by that number wich in this case is $18.39. So using one of his steps, 30.65(0.6)=18.39. We can subtract 30.65 (original price) and 18.39 (mark down price). You’d get 11.26 dollars as the final price.
what is
3⋅f(−4)−3⋅g(−2)=
Answer:
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
Step-by-step explanation:
Given
This question has a missing graph (See online)
Required
[tex]3 * f(-8) - 3 * g(-2)[/tex]
From the graph:
[tex]f(-8) = -2[/tex]
and
[tex]g(-2) = -4[/tex]
So, we have:
[tex]3 * f(-8) - 3 * g(-2) = 3 * -2 -3 * -4[/tex]
[tex]3 * f(-8) - 3 * g(-2) = 6[/tex]
Find the final total value of a 5-year investment of $2600 at a simple annual rate of
3.53%
Answer:
A = $3,101.09
A = P + I where
P (principal) = $2,600.00
I (interest) = $501.09
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.53/100
r = 0.0353 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 2,600.00(1 + 0.0353/12)(12)(5)
A = 2,600.00(1 + 0.002941667)(60)
A = $3,101.09
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $2,600.00 at a rate of 3.53% per year compounded 12 times per year over 5 years is $3,101.09.
An ice cube is melting, and the lengths of its sides are decreasing at a rate of 0.8 millimeters per minute At what rate is the volume of the ice cube decreasing when the lengths of the sides of the cube are equal to 18 millimeters? Give your answer correct to the nearest cubic millimeter per minute. Rate of decrease: millimeters3 per minute.
Answer:
The rate of decrease is: [tex]43.2mm^3/min[/tex]
Step-by-step explanation:
Given
[tex]l = 18mm[/tex]
[tex]\frac{dl}{dt} = -0.8mm/min[/tex] ---- We used minus because the rate is decreasing
Required
Rate of decrease when: [tex]l = 18mm[/tex]
The volume of the cube is:
[tex]V = l^3[/tex]
Differentiate
[tex]\frac{dV}{dl} = 3l^2[/tex]
Make dV the subject
[tex]dV = 3l^2 \cdot dl[/tex]
Divide both sides by dt
[tex]\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}[/tex]
Given that: [tex]l = 18mm[/tex] and [tex]\frac{dl}{dt} = -0.8mm/min[/tex]
[tex]\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)[/tex]
[tex]\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min[/tex]
[tex]\frac{dV}{dt} = -43.2mm^3/min[/tex]
Hence, the rate of decrease is: 43.2mm^3/min
ASAP:
Consider the word pROPOSITION. How many five letter words can be formed if two letters are alike and three letters are different? Consider the cases.
Answer:
The letters M, N, A , E appear twice and G, T appear once.
So, the first case was where all the letters were different, thus, the number of words formed were:
6C5 . 5!(further permutation) = 720
the second case was where there were two groups of two alike letters and one different letter. Thus, the number of words formed were:
2C1 . 4C2 . 3! = 72
the third case was where there were one group of two alike letters and three different letters.
Thus, the number of words formed were:
4C1 . 5C3 . 4!= 960
thus, the total number of words were:
720 + 72 + 960 = 1752
but this answer is wrong as the Real answer is 1824.
Step-by-step explanation:
The following cylinder has a height of 7.2 in. and diameter of 6.8 in.
Cylinder with measures described in text.
What is the volume of the cylinder? Remember, the diameter of a circle is two times its radius.
Use 3.14 for π and round your answer to the nearest tenth.
Answer:
598.16
Step-by-step explanation:
Eh you should have the formula if not I can't really type it but ,trust, the answer is 598.16 in²
Answer:
261.3 in.
Step-by-step explanation:
which point lies on the line described by the equation below?
( I am pulling an all nighter for high school and this question is really important)
Answer:
F (5,-8)
Step-by-step explanation:
By rearranging,
y= 4x-28
Substitute each of the x values of the answers, eventually you will get to F and discover that when x = 5, y= -8
y= 4(5) - 28
y= -8
So, when x= 5, y= -8,
Point F is (5,-8)
help please quick please
Answer:
the answer is 3.5
Step-by-step explanation:
Four expressions are written in the table.
What value of n makes all of the expressions equivalent?
0
1
10
100
What is the value of x?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
x =___m
Answer:
<W=180 - (30+81)
<W=69°
Using Sine rule to evaluate x
x/sin30 = 19/sin69
x= 19sin30/sin69
x= 10.2m ( Nearest tenth)
you spend $40 on a meal for you and your friends. Sandwiches cost $5 and beverages cost $2 each. Write and equation in standard form where x is the number of sandwiches purchased and y is the number of beverages posted.
An auto repair shop charged a customer $496 to repair a car. The bill listed $96 for parts and the remainder for labor. If the cost of labor is $40 per hour, how many hours of labor did it take to repair the car?
1)Light travels at the speed of 3,00,000 km in one second ,if it has
already travelled 1,05,342 km, how much more distance is left for the
ray of light to travel?
Answer:
1,94,658km
Step-by-step explanation:
If you are talking about how much distance it has to travel in 1 second then you can simply subtract 1,05,342 from 3,00,000. This process gives total of 1,94,658km remaining for it to travel.
Goodluck
Find the amount of interest for a 18-year investment of $4300 at a simple annual rate
of 4.07%
PLEASE ANSWE QUICK
Will mark brainlest
find the domain and range of following
Answer:
Result:
{0, 3/7}
Decimal approximation:
{0, 0.428571}
Step-by-step explanation:
Find the norm...
and you know I wanna speedrun
Choose the solution set represented by the following graph.
{x | x R, x ≤ -2}
{x | x R, x > -2}
{x | x R, x < -2}
{x | x R, x ≥ -2}
Answer:
{x|x rx>-2}
Step-by-step explanation:
hope helpful answer
Suri and Carter want to start saving for the future. they each invest $4,000 into a certificate of deposit account. suri's investment earns 3% interest compounded annually. Carter's investment is 3% simple interest.
Two formulas:
Compound interest - A = P(1 + r/n)^nt
Simple interest = A = P(1 + rt)
A - final amount
P - initial principal balance
r - interest rate
n - number of times interest applied per time period
t - number of time periods elapsed
Suri --
A = 4,000(1+0.03/1)^5
A = $4,637.09
Carter --
A = 4,000(1+0.03*5)
A = $4,600
In 5 years, Suri makes $37.09 more than Carter
What is the slope of the line represented by the equation y =4/5x-3?
A. -3
B. - 4/5
C. 4/5
D. 3
Answer:
4/5
Step-by-step explanation:
y =4/5x-3
The equation is in slope intercept form
y = mx+b where m is the slope and b is the y intercept
The slope is 4/5
Answer:
4/5
Step-by-step explanation:
The slope will be in front of the x in slope intercept form.
Right answers only pls I am gonna fail rn pls help
Answer:
y = 5x – ¼
Step-by-step explanation:
The equation for the slope intercept form is given by:
y = mx + c
Where m and c are the slope and intercept on the y-axis respectively.
From the equation i.e y = mx + c, we can see that y is the subject of the equation.
Now, comparing the equation of the slope intercept form (i.e y = mx + c) with those given in the question above, we can see that only the equation:
y = 5x – ¼
has y as the subject of the equation.
Therefore, y = 5x – ¼ gives the correct answer to the question.
uppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.5 and a standard deviation of 0.37. Using the empirical rule, what percentage of the students have grade point averages that are no more than 3.24
Answer:
[tex]P(x \le 3.24) = 0.97725[/tex]
Step-by-step explanation:
Given
[tex]\bar x = 2.5[/tex]
[tex]\sigma = 0.37[/tex]
Required
Percentage that is not more than 3.24
The above implies that:
[tex]x = 3.24[/tex]
Calculate z score
[tex]z = \frac{x - \bar x}{\sigma}[/tex]
[tex]z = \frac{3.24 - 2.5}{0.37}[/tex]
[tex]z = \frac{0.74}{0.37}[/tex]
[tex]z = 2[/tex]
So, the probability is represented s:
[tex]P(x \le 3.24) = P(z \le 2)[/tex]
From z probability
[tex]P(z \le 2) = 0.97725[/tex]
Hence:
[tex]P(x \le 3.24) = 0.97725[/tex]
Consider the function f(x) = 2^x
and function g
g(x) = f(x) + 6
How will the graph of function g differ from the graph of function ?
Answer:
The graph of function g is the graph of function f shifted 6 units up
Step-by-step explanation:
If you plug in the values, [tex]g(x) = 2^{x} + 6[/tex]. If the 6 was added or subtracted from the x in the exponent, it would shift horizontally (left and right), but adding 6 to f(x) separately moves the graph vertically (up and down). Hope this helps.
Which statement correctly identifies the line of reflection?
The triangles are reflected across the x-axis.
The triangles are reflected across the y-axis.
The triangles are reflected across the line y = x.
The triangles are reflected across the line y = –x.
A ball thrown in the air has a height of y = - 16x² + 50x + 3 feet after x seconds. a) What are the units of measurement for the rate of change of y? b) Find the rate of change of y between x = 0 and x = 2?
(a) ft/s
(b) 1ft/s
Step-by-step explanation:Given equation;
y = (- 16x² + 50x + 3)ft -------------(i)
Where;
y is measured in feet(ft)
x is measured in seconds(s).
(a) The rate of change of y with respect to x is found by dividing the total change in y by the total change in x. i.e
Δy / Δx
Where;
Δy = y₂ - y₁
Δx = x₂ - x₁
∴ Δy / Δx = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] --------------(ii)
Since y is measured in feet, Δy will also be measured in feet.
Also, since x is measured in seconds, Δx will also be measured in seconds.
Therefore, the rate of change of y with respect to x (Δy / Δx) will be measured in feet per second (ft/s)
(b) The rate of change of y between x = 0 and x = 2 can be found by using equation (ii)
Where;
y₂ is the value of y at x = 2 found by substituting x = 2 into equation (i)
y₁ is the value of y at x = 0 found by substituting x = 0 into equation (i)
=> y₂ = - 16(2)² + 50(2) + 3 = 39
=> y₁ = - 16(1)² + 50(1) + 3 = 37
Now, substitute the values of y₂, y₁, x₂ and x₁ into equation (ii)
Δy / Δx = [tex]\frac{39 - 37}{2 - 0}[/tex]
Δy / Δx = [tex]\frac{2}{2}[/tex]
Δy / Δx = 1
Therefore, the rate of change of y is 1 ft/s
Suppose annual salaries for sales associates from Geoff's Computer Shack have a mean of $32,500 and a standard deviation of $2,500.
a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
c. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
d. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.
Answer:
The answer is below
Step-by-step explanation:
Given that mean (μ) = $32500, standard deviation (σ) = $2500.
a) The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
For x < 36000:
[tex]z=\frac{36000-32500}{2500}=1.4[/tex]
From the normal distribution table, P(x < 36000) = P(z < 1.4) = 0.9192 = 91.92%
b) One standard deviation of mean = μ ± σ = (32500 ± 2500) = (30000, 35000)
Two standard deviation of mean = μ ± 2σ = (32500 ± 2*2500) = (27500, 37500)
Empirical rule states that 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviation from the mean and 99.7% falls within one standard deviation from the mean.
Hence 95% of salaries is between $27,500 and $37,500.
c) 95% of salaries is between $27,500 and $37,500.
P(x < 27500) = (100% - 95%) / 2 = 2.5%
d) If the z score is less than -3 or greater than 3, it is considered an outlier.
For x < 42000:
[tex]z=\frac{42000-32500}{2500}=3.8[/tex]
Hence $42000 is an outlier