Answer: The weaknesses of content analysis include: if you make a coding error you must recode all of your data.
Explanation:
Content analysis is a method for analyse documents,communication artifacts, which might be of various formats such as pictures, audio or video. Content analysis can provide valuable or cultural insights over time through analysis .
But it is more time consuming and subject to increased error . There is no theoretical base in order to create relationship between text. So in case if we make coding error then we must recode all data .
Hence option (B) is correct
Content analysis weaknesses include potential influence on subject under study, the need to recode all data if a coding error occurs, limitation to studying social artifacts, requirement of special equipment, and misconception that it can't study change over time.
Explanation:The weaknesses of content analysis include:
Its use influences that which is being studied. This is a potential bias that can affect the reliability of results as the very act of studying a social artifact can change it.If you make a coding error, you must recode all of your data. This can be time-consuming and introduce additional errors.It's limited to examining social artifacts. This means it might not be a suitable method for all research questions.It requires special equipment. Although not a primary issue, but it may make the method inaccessible for some researchers.A researcher cannot use it to study change over time. This isn't entirely true, content analysis can be longitudinal, studying changes over designated periods.Learn more about Content Analysis here:https://brainly.com/question/32294663
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If f(x) = 3x^2 - 2 and g(x) = 4x + 2
what is the value of (f + g)(2) ?
please show work!!
The answer is:
[tex](f+g)(2)=20[/tex]
Why?To solve the problem, we need to add the given functions, and then, evaluate the resultant function with the given value of "x" which is equal to 2.
We need to remember that:
[tex](f+-g)(x)=f(x)+-g(x)[/tex]
So, we are given the functions:
[tex]f(x)=3x^2-2\\g(x)=4x+2\\[/tex]
Then, adding the functions , we have:
[tex](f+g)(x)=f(x)+g(x)=(3x^2-2)+(4x+2)[/tex]
[tex](f+g)(x)=3x^2-2+4x+2=3x^2+4x-2+2=3x^2+4x[/tex]
Therefore, we have that:
[tex](f+g)(x)=3x^2+4x[/tex]
Now, evaluating the function, we have:
[tex](f+g)(2)=3(2)^2+4(2)=3*4+4*2=12+8=20[/tex]
Hence, we have that the answer is:
[tex](f+g)(2)=20[/tex]
Have a nice day!
Times for a surgical procedure are normally distributed. There are two methods. Method A has a mean of 33 minutes and a standard deviation of 8 minutes, while method B has a mean of 37 minutes and a standard deviation of 4.0 minutes. (a) Which procedure is preferred if the procedure must be completed within 34 minutes?
Answer:
Method A.
Step-by-step explanation:
For solving this question we need to find out the z-scores for both methods,
Since, the z-score formula is,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where, [tex]\mu[/tex] is mean,
[tex]\sigma[/tex] is standard deviation,
Given,
For method A,
[tex]\mu = 33[/tex]
[tex]\sigma=8[/tex]
Thus, the z score for 34 is,
[tex]z_1=\frac{34-33}{8}=0.125[/tex]
While, for method B,
[tex]\mu = 37[/tex]
[tex]\sigma = 4[/tex]
Thus, the z score for 34 is,
[tex]z_2=\frac{34-37}{4}=-0.75[/tex],
Since, [tex]z_1 > z_2[/tex]
Hence, method A is preferred if the procedure must be completed within 34 minutes.
Comparison of two normal distribution can be done via intermediary standard normal distribution. The procedure to be preferred for getting the procedure completed within 34 minutes is: Method A
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
Firstly, we need to figure out what the problem is asking, and a method which we can apply. Two normal distributions have to be compared. We can convert them to standard normal distribution for comparison. Then, we will get the p-value for 34 minutes(converted to standard normal variate's value) which will tell about the probability of obtaining time as 34 minutes(or under it)(this can be obtained with p value) in method A or B. The more the probability is there, the more chances for that method would be for getting completed within 34 minutes (compared to other method).
For method A:Let X = time taken for completion of surgical procedure by method A,
Then, by given data, we have: [tex]X \sim N(\mu = 33, \sigma = 8)[/tex]
The probability that X will fall within value 34 is [tex]P(X \leq 34)[/tex]
Converting this whole thing to standard normal distribution, we get the needed probability as:
[tex]P(X \leq 34) = P(Z = \dfrac{X - \mu}{\sigma} \leq \dfrac{34 - 33}{8} ) = P(Z \leq 0.15)[/tex]
From the z-tables, the p value for Z = 0.15 is 0.5596
Thus, we get:
[tex]P(X \leq 34) = P(Z \leq 0.15 ) \approx 0.5596[/tex]
For method B:Let Y = time taken for completion of surgical procedure by method B,
Then, by given data, we have: [tex]Y \sim N(\mu = 37, \sigma = 4)[/tex]
The probability that X will fall within value 34 is [tex]P(Y \leq 34)[/tex]
Converting this whole thing to standard normal distribution, we get the needed probability as:
[tex]P(Y \leq 34) = P(Z = \dfrac{Y - \mu}{\sigma} \leq \dfrac{34 - 37}{4} ) = P(Z \leq -0.25)[/tex]
From the z-tables, the p value for Z = -0.25 is 0.4013
Thus, we get:
[tex]P(Y \leq 34) = P(Z \leq -0.25 ) \approx 0.4013[/tex]
Thus, we see that:
P(method A will make surgical procedure last within 34 minutes) = 0.5596 > P(method B will make surgical procedure last within 34 minutes) = 0.4013
Thus, method A should be preferred, as there is higher chances for method A to get the surgery completed within 34 minutes than method B.
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Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the line y=2, and y=e^x about the y-axis. Round your answer to three decimal places.
Answer:
0.592
Step-by-step explanation:
The volume of the solid, rounded to three decimal places is 18.257.
The volume of the solid obtained by rotating the region around the y-axis can be found using the method of discs or washers. Since the region is bounded by the x-axis, the y-axis, the line y=2, and the curve [tex]y=e^x[/tex], we will integrate with respect to y.
The volume V of the solid of revolution is given by the integral:
[tex]\[ V = \pi \int_{a}^{b} [R(y)]^2 dy - \pi \int_{a}^{b} [r(y)]^2 dy \][/tex]
where [tex]\( R(y) \)[/tex] is the outer radius and [tex]\( r(y) \)[/tex] is the inner radius of the discs or washers.
In this case, the outer radius [tex]\( R(y) \)[/tex] is given by the line y=2, which is a horizontal line, so the outer radius is constant and equal to 2. The inner radius [tex]\( r(y) \)[/tex] is given by the curve [tex]y=e^x[/tex]. To express x in terms of y, we take the natural logarithm of both sides to get [tex]\( x = \ln(y) \)[/tex].
Now we can set up our integrals:
[tex]\[ V = \pi \int_{0}^{2} [2]^2 dy - \pi \int_{0}^{2} [\ln(y)]^2 dy \][/tex]
[tex]\[ V = \pi \int_{0}^{2} 4 dy - \pi \int_{0}^{2} [\ln(y)]^2 dy \][/tex]
The first integral is straight forward:
[tex]\[ \pi \int_{0}^{2} 4 dy = \pi \left[ 4y \right]_{0}^{2} = \pi [4(2) - 4(0)] = 8\pi \][/tex]
The second integral requires integration by parts. Let [tex]\( u = [\ln(y)]^2 \)[/tex]and [tex]\( dv = dy \)[/tex], then [tex]\( du = \frac{2\ln(y)}{y} dy \)[/tex] and [tex]\( v = y \)[/tex]. Applying integration by parts gives:
[tex]\[ \pi \int_{0}^{2} [\ln(y)]^2 dy = \pi \left[ y[\ln(y)]^2 - \int_{0}^{2} 2\ln(y) dy \right] \][/tex]
Now, we need to integrate [tex]\( 2\ln(y) \)[/tex] by parts again, with [tex]\( u = \ln(y) \)[/tex] and [tex]\( dv = dy \)[/tex], then [tex]\( du = \frac{1}{y} dy \)[/tex] and [tex]\( v = y \)[/tex]. This gives:
[tex]\[ \int_{0}^{2} 2\ln(y) dy = \left[ 2y\ln(y) - \int_{0}^{2} 2 dy \right] \][/tex]
[tex]\[ \int_{0}^{2} 2\ln(y) dy = \left[ 2y\ln(y) - 2y \right]_{0}^{2} \][/tex]
[tex]\[ \int_{0}^{2} 2\ln(y) dy = 2(2)\ln(2) - 2(2) - (0) \][/tex]
[tex]\[ \int_{0}^{2} 2\ln(y) dy = 4\ln(2) - 4 \][/tex]
Putting it all together:
[tex]\[ \pi \int_{0}^{2} [\ln(y)]^2 dy = \pi \left[ y[\ln(y)]^2 - (4\ln(2) - 4) \right]_{0}^{2} \][/tex]
[tex]\[ \pi \int_{0}^{2} [\ln(y)]^2 dy = \pi \left[ 2[\ln(2)]^2 - (4\ln(2) - 4) \right] - \pi \left[ \lim_{y \to 0} y[\ln(y)]^2 - (4\ln(2) - 4) \right] \][/tex]
The limit as y approaches 0 of [tex]\( y[\ln(y)]^2 \)[/tex] is 0, so we have:
[tex]\[ \pi \int_{0}^{2} [\ln(y)]^2 dy = \pi \left[ 2[\ln(2)]^2 - 4\ln(2) + 4 \right] \][/tex]
[tex]\[ \pi \int_{0}^{2} [\ln(y)]^2 dy = 2\pi[\ln(2)]^2 - 4\pi\ln(2) + 4\pi \][/tex]
Now, subtract this from the first integral:
[tex]\[ V = 8\pi - (2\pi[\ln(2)]^2 - 4\pi\ln(2) + 4\pi) \][/tex]
[tex]\[ V = 8\pi - 2\pi[\ln(2)]^2 + 4\pi\ln(2) - 4\pi \][/tex]
[tex]\[ V = 4\pi + 4\pi\ln(2) - 2\pi[\ln(2)]^2 \][/tex]
[tex]\[ V = 4\pi(1 + \ln(2) - \frac{1}{2}[\ln(2)]^2) \][/tex]
Rounded to three decimal places, the volume is:
[tex]\[ V \approx 4\pi(1 + \ln(2) - \frac{1}{2}[\ln(2)]^2) \approx 4\pi(1 + 0.693 - \frac{1}{2}(0.693)^2) \][/tex]
[tex]\[ V \approx 4\pi(1 + 0.693 - 0.240) \][/tex]
[tex]\[ V \approx 4\pi(1.453) \][/tex]
[tex]\[ V \approx 5.812\pi \][/tex]
[tex]\[ V \approx 18.257 \][/tex]
Therefore, the volume of the solid, rounded to three decimal places, is:
[tex]\[ \boxed{18.257} \][/tex].
The complete question is:
Find the volume of the solid obtained by rotating the region bounded by the x-axis, the y-axis, the line y=2, and [tex]y=e^x[/tex] about the y-axis. Round your answer to three decimal places.
Continuing the previous problem, use the data points (1950, 0.75) and (1997, 5.15) to find the slope. Show all work necessary for your calculations. If necessary, round your answer to the hundredths place. What does the slope represent in the context of the problem?
Answer:
Slope is 0.094,
It represents the average rate of change.
Step-by-step explanation:
Since, the slope is the ratio of difference in y-coordinates and the difference in x-coordinates,
Also, in a order pair, first element shows the x-coordinate and second element shows the y-coordinate.
Here, the data points are (1950, 0.75) and (1997, 5.15),
Thus, the slope is,
[tex]m=\frac{5.15-0.75}{1997-1950}[/tex]
[tex]=\frac{4.4}{47}[/tex]
[tex]=0.0936170212766[/tex]
[tex]\approx 0.094[/tex]
Also, Slope represents the average rate of change.
The reading speed of second grade students in a large city is approximately normal, with a mean of 9090 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). (a) What is the probability a randomly selected student in the city will read more than 9494 words per minute? The probability is nothing.
Answer: 0.3446
Step-by-step explanation:
Given : Mean : [tex]\mu = 90[/tex]
Standard deviation : [tex]\sigma = 10[/tex]
Also, the reading speed of second grade students in a large city is approximately normal.
Then , the formula to calculate the z-score is given by :_
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 94
[tex]z=\dfrac{94-90}{10}=0.4[/tex]
The p-value = [tex]P(z>0.4)=1-P(z<0.4)=1-0.6554217[/tex]
[tex]\\\\=0.3445783\approx0.3446[/tex]
Hence, the probability a randomly selected student in the city will read more than 94 words per minute =0.3446
Find a second independent solution y1=x xy"-xy'+y=0
We can use reduction of order. Given that [tex]y_1(x)=x[/tex] is a known solution, we look for a solution of the form [tex]y_2(x)=v(x)y_1(x)[/tex]. It has derivatives [tex]{y_2}'=v'y_1+v{y_1}'[/tex] and [tex]{y_2}''=v''y_1+2v'{y_1}'+v{y_1}''[/tex]. Substituting these into the ODE gives
[tex]x(xv''+2v')-x(xv'+v)+xv=0[/tex]
[tex]x^2v''+(2x-x^2)v'=0[/tex]
Let [tex]w(x)=v'(x)[/tex] so that [tex]w'(x)=v''(x)[/tex] and we get an ODE linear in [tex]w[/tex]:
[tex]x^2w'+(2x-x^2)w=0[/tex]
Divide both sides by [tex]e^x[/tex]:
[tex]x^2e^{-x}w'+(2x-x^2)e^{-x}w=0/tex]
Since [tex](x^2e^{-x})=(2x-x^2)e^{-x}[/tex], we can condense the left side as the derivative of a product:
[tex](x^2e^{-x}w)'=0[/tex]
Integrate both sides and solve for [tex]w(x)[/tex]:
[tex]x^2e^{-x}w=C\implies w=\dfrac{Ce^x}{x^2}[/tex]
Integrate both sides again to solve for [tex]v(x)[/tex]. Unfortunately, there is no closed form for the integral of the right side, but we can leave the result in the form of a definite integral:
[tex]v=\displaystyle C_2+C_1\int_{x_0}^x\frac{e^t}{t^2}\,\mathrm dt[/tex]
where [tex]x_0[/tex] is any point on an interval over which a solution to the ODE exists.
Finally, multiply by [tex]y_1(x)[/tex] to solve for [tex]y_2(x)[/tex]:
[tex]y_2=\displaystyle C_2x+C_1x\int_{x_0}^x\frac{e^t}{t^2}\,\mathrm dt[/tex]
[tex]y_1(x)[/tex] already accounts for the [tex]C_2x[/tex] term above, so the second independent solution is
[tex]y_2=x\displaystyle\int_{x_0}^x\frac{e^t}{t^2}\,\mathrm dt[/tex]
A company builds a new wing for its east branch and knows that each additional room will gain $1200 of profit. The construction company will cost $44,000 to construct the wing.
How many rooms are need to break even? (Hint: You must PAY the fee to the construction company.)
If you wanted to make twice as much profit as you spent, how many rooms would need to be built?
Answer:
a. 37 rooms are need to break even.
b. 73 rooms are required to make twice as much profit as you spent.
Step-by-step explanation:
Revenue of the company from each additional room is $1200.
Total construction cost = $44,000.
At break even condition, total revenue is equal to total cost. In other words, the profit of the firm is zero at break even.
Let x be the number of rooms that are need to break even.
Total revenue of x room is
[tex]TR=1200x[/tex]
At break even,
Total revenue = Total cost
[tex]1200x=44000[/tex]
Divide both sides by 1200.
[tex]x=\frac{44000}{1200}=36.6667\approx 37[/tex]
Therefore, 37 rooms are need to break even.
Let y be the number of rooms to make twice as much profit as you spent.
Total revenue of y room is
[tex]TR=1200y[/tex]
Total revenue = 2 × Total cost
[tex]1200x=2\times 44000[/tex]
[tex]1200x=88000[/tex]
Divide both sides by 1200.
[tex]y=\frac{88000}{1200}=73.33\approx 73[/tex]
Therefore 73 rooms are required to make twice as much profit as you spent.
Use the transforms in section 4.1 to find the Laplace transform of the function. t^3/2 - e^-10t
Answer:
Laplace transformation of [tex]L(t^\frac{3}{2}-e^{-10t})[/tex]=[tex]\frac{3\sqrt{\pi} }{4 s^\frac{5}{2} }\ -\frac{1}{s+10}[/tex]
Step-by-step explanation:
Laplace transformation of [tex]L(t^\frac{3}{2}-e^{-10t} )[/tex]
[tex]L(t^\frac{3}{2})=\int_{0 }^{\infty}t^\frac{3}{2}e^{-st}dt\\substitute \ u =st\\L(t^\frac{3}{2})=\int_{0 }^{\infty}\frac{u}{s} ^\frac{3}{2}e^{-u}\frac{du}{s}=\frac{1}{s^{\frac{5}{2}}}\int_{0 }^{\infty}{u} ^\frac{3}{2}e^{-u}{du}[/tex]
the integral is now in gamma function form
[tex]\frac{1}{s^{\frac{5}{2}}}\int_{0 }^{\infty}{u} ^\frac{3}{2}e^{-u}{du}=\frac{1}{s^{\frac{5}{2}}}\Gamma(\frac{5}{2})=\frac{1}{s^{\frac{5}{2}}}\times\frac{3}{2}\times\frac{1}{2} }\Gamma (\frac{1}{2} )=\frac{3\sqrt{\pi} }{4 s^\frac{5}{2} }[/tex]
now laplace of [tex]L(e^{-10t})[/tex]
[tex]L(e^{-10t})=\frac{1}{s+10}[/tex]
hence
Laplace transformation of [tex]L(t^\frac{3}{2}-e^{-10t})[/tex]=[tex]\frac{3\sqrt{\pi} }{4 s^\frac{5}{2} }\ -\frac{1}{s+10}[/tex]
The Laplace transform of the function [tex]t^3/2 - e^-10t[/tex] is (3/2√π)/[tex]s^5/2 - 1/(s + 10)[/tex].
To find the Laplace transform of the function[tex]t^3/2 - e-10t[/tex], we use the Laplace transform properties and tables.
Refer to the Laplace transform table: Apply to each term: Combine the results: The Laplace transform of the function is L{[tex]t^3/2 - e-10t[/tex]} = (3/2√π)/[tex]s^5/2 - 1/(s + 10)[/tex].Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x-y=5 and 4x+ky=2
Answer:
The system of linear equations has infinitely many solutions
Step-by-step explanation:
Let's modified the equations and find the answer.
Using the first equation:
[tex]2x-y=5[/tex] we can multiply by 2 in both sides, obtaining:
[tex]2*(2x-y)=2*5[/tex] which can by simplified as:
[tex]4x-2y=10[/tex] which is equal to:
[tex]4x=2y+10[/tex]
Considering the second equation:
[tex]=4x+ky=2[/tex]
Taking into account that from the first equation we know that: [tex]4x=2y+10[/tex], we can express the second equation as:
[tex]2y+10+ky=2[/tex], which can be simplified as:
[tex](2+k)y=2-10[/tex]
[tex](2+k)y=-8[/tex]
[tex]y=-8/(2+k)[/tex]
Because (-8) is being divided by (2+k), then (2+k) can't be equal to 0, so:
[tex]2+k=0[/tex] if [tex]k=-2[/tex]
This means that k can be any number different than -2, and for each of these solutions, there is a different solution for y, allowing also, different solutions for x.
For example, if k=0 then
[tex]y=-8/(2+0)[/tex] which give us y=-4, and, because:
[tex]4x=2y+10[/tex] if y=-4 then [tex]x=(-8+10)/4=0.5[/tex]
Now let's try with k=-1, then:
[tex]y=-8/(2-1)[/tex] which give us y=-8, and, because:
[tex]4x=2y+10[/tex] if y=-8 then [tex]x=(-16+10)/4=-1.5[/tex].
Then, the system of linear equations has infinitely many solutions
At Southern States University (SSU) there are 399 students taking Finite Mathematics or Statistics. 238 are taking Finite Mathematics, 184 are taking Statistics, and 23 are taking both Finite Mathematics and Statistics. How many are taking Finite Mathematics but not Statistics?
Answer:
215
Step-by-step explanation:
The 238 taking Finite Math includes those taking Finite Math and Statistics. Subtracting out the 23 who are taking both leaves 215 taking Finite Math only.
215 students are taking Finite Mathematics but not Statistics.
To find out how many students are taking Finite Mathematics but not Statistics at Southern States University (SSU), let's break down the information given and use set theory concepts.
Total number of students taking either Finite Mathematics or Statistics: 399
Number of students taking Finite Mathematics: 238
Number of students taking Statistics: 184
Number of students taking both Finite Mathematics and Statistics: 23
First, we need to figure out how many students are taking only Finite Mathematics. We can do this by subtracting the number of students taking both Finite Mathematics and Statistics from the total number of students taking Finite Mathematics.
Number of students taking only Finite Mathematics = Total taking Finite Mathematics - Total taking both Finite Mathematics and Statistics
So,
Number of students taking only Finite Mathematics = 238 - 23
Number of students taking only Finite Mathematics = 215
John has won the mega-bucks lottery, which pays $1, 000, 000. Suppose he deposits the money in a savings account that pays an annual interest of 8% compounded continuously. How long will this money last if he makes annual withdrawals of $100, 000?
Answer:20.91
Step-by-step explanation:
Given
Principal amount invested=[tex]\$ 1,000,000[/tex]
Rate of interest=8%
Annual Withdrawl=[tex]\$ 100,000[/tex]
compound interest is given by
A=[tex]\left (1+ \frac{r}{100}\right )^t[/tex]
Therefore reamining Amount after certain years
Net money will become zero after t year
[tex]1,000,000\left (1+ \frac{8}{100} \right )^t - 100,000\left ( \frac{\left ( 1.08\right )^{t}-1}{0.08}\right )[/tex]=0
[tex]0.8\left ( 1.08\right )^t=\left ( 1.08\right )^{t}-1[/tex]
t=20.91 years
Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
x + 2y + z = −4
−2x − 3y − z = 2
2x + 4y + 2z = −8
(x, y, z) =
Answer:
The system of linear equations has infinitely many solutions. x=t, y=2-t and z=t-8.
Step-by-step explanation:
The given educations are
[tex]x+2y+z=-4[/tex]
[tex]-2x-3y-z=2[/tex]
[tex]2x+4y+2z=-8[/tex]
Using the Gauss-Jordan elimination method, we get
[tex]\begin{bmatrix}1 & 2 & 1\\ -2 & -3 & -1\\ 2 & 4 & 2\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}-4\\ 2\\ -8\end{bmatrix}[/tex]
[tex]R_3\rightarrow R_3-2R_1[/tex]
[tex]\begin{bmatrix}1 & 2 &1\\ -2 & -3 & -1\\ 0 & 0 & 0\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}-4\\ 2\\ 0\end{bmatrix}[/tex]
Since elements of bottom row are 0, therefore the system of equations have infinitely many solutions.
[tex]0x+0y+0z=0\Rightarrow 0=0[/tex]
[tex]R_2\rightarrow R_2+2R_1[/tex]
[tex]\begin{bmatrix}1 & 2 &1\\ 0 & 1 & 1\\ 0 & 0 & 0\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}-4\\ -6\\ 0\end{bmatrix}[/tex]
[tex]R_1\rightarrow R_1-R_2[/tex]
[tex]\begin{bmatrix}1 & 1 &0\\ 0 & 1 & 1\\ 0 & 0 & 0\end{bmatrix}\begin{bmatrix}x\\ y\\ z\end{bmatrix}=\begin{bmatrix}2\\ -6\\ 0\end{bmatrix}[/tex]
[tex]x+y=2[/tex]
[tex]y+z=-6[/tex]
Let x=t
[tex]t+y=2\rightarrow y=2-t[/tex]
The value of y is 2-t.
[tex](2-t)+z=-6[/tex]
[tex]z=-6-2+t[/tex]
[tex]z=t-8[/tex]
The value of z is t-8.
Therefore the he system of linear equations has infinitely many solutions. x=t, y=2-t and z=t-8.
To solve the system of linear equations using the Gauss-Jordan elimination method, perform row operations on the augmented matrix to obtain the reduced row-echelon form. The solution is x = -2, y = 1, and z = 0.
Explanation:To solve the system of linear equations using the Gauss-Jordan elimination method, we need to perform row operations to transform the augmented matrix into row-echelon form and then into reduced row-echelon form. Let's start by representing the system of equations as an augmented matrix:
[1 2 1 -4; -2 -3 -1 2; 2 4 2 -8]
Performing row operations, you can transform the augmented matrix into reduced row-echelon form, obtaining:
[1 0 0 -2; 0 1 0 1; 0 0 1 0]
The solution to the system is x = -2, y = 1, and z = 0. Therefore, (x, y, z) = (-2, 1, 0).
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How many solutions does the system have? y=3x+2 y=3x-6
Answer:
None
Step-by-step explanation:
The slopes are the same. The y intercepts are 2 and - 6. These lines are parallel which means they never intersect. No intersection means no solution. Just to show you what this means, I graphed this on Desmos for you.
Red: y = 3x - 6
Blue: y = 3x + 2
These two never meet.
Answer:
Step-by-step explanation:
Explanation:
Graph both the equations and read the coordinates of the point of intersection as shown in the graph below:
Suppose 56% of the registered voters in a country are Republican. If a sample of 447 voters is selected, what is the probability that the sample proportion of Republicans will be less than 60%? Round your answer to four decimal places.
Answer: 0.9554
Step-by-step explanation:
Given : The proportion of the registered voters in a country are Republican = P=0.56
The number of voters = 447
The test statistic for proportion :-
[tex]z=\dfrac{p-P}{\sqrt{\dfrac{P(1-P)}{n}}}[/tex]
For p= 0.60
[tex]z=\dfrac{0.60-0.56}{\sqrt{\dfrac{0.56(1-0.56)}{447}}}\approx1.70[/tex]
Now, the probability that the sample proportion of Republicans will be less than 60% (by using the standard normal distribution table):-
[tex]P(x<0.60)=P(z<1.70)=0.9554345\approx0.9554[/tex]
Hence, the probability that the sample proportion of Republicans will be less than 60% = 0.9554
The process by which the bureaucracy produces what is effectively legislation is called
A.
rule-making.
B.
administrative discretion.
C.
activism.
D.
selective implementation.
E.
the formal hearing procedure.
Answer:
Step-by-step explanation:
Great question, it is always good to ask away and get rid of any doubts that you may be having.
This process is called Rule-Making. It is basically when the Federal Government makes regulations on certain topics. These Regulations help advance and set strict boundaries on projects so that people know what they can and cannot do, as well as protect others from being scammed or robbed by these projects. This is all done by the administrative process known as Rule Making.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
4, Find a number x such that x = 1 mod 4, x 2 mod 7, and x 5 mod 9.
4, 7 and 9 are mutually coprime, so you can use the Chinese remainder theorem.
Start with
[tex]x=7\cdot9+4\cdot2\cdot9+4\cdot7\cdot5[/tex]
Taken mod 4, the last two terms vanish and we're left with
[tex]x\equiv63\equiv64-1\equiv-1\equiv3\pmod4[/tex]
We have [tex]3^2\equiv9\equiv1\pmod4[/tex], so we can multiply the first term by 3 to guarantee that we end up with 1 mod 4.
[tex]x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5[/tex]
Taken mod 7, the first and last terms vanish and we're left with
[tex]x\equiv72\equiv2\pmod7[/tex]
which is what we want, so no adjustments needed here.
[tex]x=7\cdot9\cdot3+4\cdot2\cdot9+4\cdot7\cdot5[/tex]
Taken mod 9, the first two terms vanish and we're left with
[tex]x\equiv140\equiv5\pmod9[/tex]
so we don't need to make any adjustments here, and we end up with [tex]x=401[/tex].
By the Chinese remainder theorem, we find that any [tex]x[/tex] such that
[tex]x\equiv401\pmod{4\cdot7\cdot9}\implies x\equiv149\pmod{252}[/tex]
is a solution to this system, i.e. [tex]x=149+252n[/tex] for any integer [tex]n[/tex], the smallest and positive of which is 149.
The problem is about finding a number x that satisfies a system of modular arithmetic equations. It can be solved using the Chinese Remainder Theorem which is part of number theory in mathematics. More information is needed to solve this specific system.
Explanation:The problem at hand is to find a number x which satisfies the conditions x ≡ 1 (mod 4), x ≡ 2 (mod 7), and x ≡ 5 (mod 9). This falls under the mathematical concept of modular arithmetic.
Modular arithmetic is a system of arithmetic for integers, where numbers wrap around once reaching a certain value—the modulus.
The expressions x ≡ 1 (mod 4), x ≡ 2 (mod 7), and x ≡ 5 (mod 9) mean that when x is divided by 4, the remainder is 1; when x is divided by 7, the remainder is 2; and when x is divided by 9, the remainder is 5 respectively.
This is a type of problem known as a system of linear congruences, which can be solved by applying the Chinese Remainder Theorem. However, the information provided is insufficient to provide a specific numerical solution to the system of congruences. It is recommended that the student consults the section of their classroom material that discusses the Chinese Remainder Theorem and its applications.
Learn more about Modular Arithmetic here:https://brainly.com/question/13089800
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y"+4y = 8 sin 2x. Trial Solution using annihilator technique
Linear Algebra and Differential equations
I am so confused why would you multiple by X up(x)
A second order linear, non - homogeneous ODE has a form of [tex]ay''+by'+cy=g(x)[/tex]
The general solution to, [tex]a(x)y''+b(x)y'+c(x)y=0[/tex]
Can be written as,
[tex]y=y_h+y_p[/tex]
Where [tex]y_h[/tex] is a solution to the homogeneous ODE and [tex]y_p[/tex] the particular solution, function that satisfies the non - homogeneous equation.
We can solve [tex]y_h[/tex] by rewriting the equation,
[tex]ay''+by'+cy=0\Longrightarrow(e^{xy})''+4e^{xy}=0[/tex]
Which simplifies to,
[tex]e^{xy}(y^2+4)=0[/tex]
From here we get two solutions,
[tex]y_{h1}=2i, y_{h2}=-2i[/tex]
So the form here refines,
[tex]y_h=c_1\cos(2x)+c_2\sin(2x)[/tex]
The same thing we do with [tex]y_p[/tex] to get form of,
[tex]y_p=-2x\cos(2x)[/tex]
From here the final form emerges,
[tex]y=\boxed{c_1\cos(2x)+c_2\sin(2x)-2x\cos(2x)}[/tex]
Hope this helps.
r3t40
Translate the following ordinary-language sentences into logical symbolic form using capital letters for simple phrases and the standard symbols – “·,” “˅,” “¬,” “≡,” “⊃” – for the logical operators. 1. Either existing home sales will decrease or new housing starts will increase and unemployment will decrease only if the Federal Reserve decreases long-term interest rates and foreign trade deficits decrease or foreign trade deficits increase and manufacturing rates increase. 2. Germany will vote to limit the number of immigrants it admits and so will reject Angela Merkel’s international policies unless neighboring EU countries agree to a multi-national work visa program and either the World Bank revalues the Euro relative to the US dollar or the US-Russia brokered peace treaty is signed by Syria.
P - existing home sales will decrease
Q - new housing starts will increase
R - unemployment will decrease
S - the Federal Reserve decreases long-term interest rates
T - foreign trade deficits decrease
U - foreign trade deficits increase
V - manufacturing rates increase
[tex][(P \vee Q) \wedge R] \iff (S \wedge T) \vee (U \wedge V)[/tex]
P - Germany will vote to limit the number of immigrants it admits
Q - will reject Angela Merkel’s international policies
R - neighboring EU countries agree to a multi-national work visa program
S - the World Bank revalues the Euro relative to the US dollar
T - the US-Russia brokered peace treaty is signed by Syria.
[tex]\neg (R \wedge (S \vee T))\implies (P \implies R)\\[/tex]
Which of the following is true for the number of trials for a binomial experiment. Explain your answer. The number of trials in binomial experiment a) can be infinite, b) is unlimited, c) must be fixed.
Answer:
The correct option is C.
Step-by-step explanation:
Consider the provided information.
Four conditions of a binomial experiment:
There should be fixed number of trials
Each trial is independent with respect to the others
The maximum possible outcomes are two
The probability of each outcome remains constant.
Now, observe the provided options:
Option A and B are not possible as they doesn't satisfy the conditions of binomial experiment which is there must be fixed number of trials.
Now observe the option C which state that there must be fixed number of trials, it satisfy the condition of a binomial experiment.
Therefore, the correct option is C.
The number of trials in a binomial experiment must be fixed, with two possible outcomes and independent and identical trial conditions.
The number of trials in a binomial experiment must be fixed as one of the key characteristics of a binomial experiment is that there is a fixed number of trials (n). This characteristic distinguishes it from other types of experiments.
In a binomial experiment, there are only two possible outcomes (success and failure) for each trial, and these probabilities do not change from trial to trial. The trials are independent and identical in conditions.
For example, tossing a fair coin multiple times or conducting a series of independent Bernoulli trials involve a fixed number of trials, making them fit the criteria for a binomial experiment.
The distance between my house and Memphis is 150 km. If I drive in my car, it takes me 72 min to make the first 100 km of the drive. If I keep traveling at the same rate, how many more minutes will it take to drive the remaining distance? Round your answer to the nearest tenth.
Set up a ratio:
You drove 72 minutes and 100 km = 72/100
You want the number of minutes (x) to drive 150 km = x/150
Set the ratios to equal each other and solve for x:
72/100 = x/150
Cross multiply:
(72 * 150) = 100 * x)
Simplify:
10,800/100x
Divide both sides by 100:
x = 10800/100 = 108
This means it would take 108 minutes to drive 150 km.
Now subtract the time you have already driven to fin how much more you need:
180 - 72 = 36 more minutes.
Answer:
36 min
Step-by-step explanation:
It takes 72 min to drive 100 km. 50 km are left to drive.
Half of the driving above is: It takes 36 min to drive 50 km.
Ryan has deposited $100 into a retirement account at the end of every month for 50 years. The interest rate on the account is 1.5% compounded monthly. a) How much is in the account after 45 years? b) How much inte rest was earned over the 45 years?
Answer:
future payment is $77056.92
total interest is paid after 45 year is $23056.42
Step-by-step explanation:
Given data
payment (P) = $100
No of installment (n) = 12
rate of interest ( r ) = 1.5 % i.e. = 0.015
time period (t) = 45 years
to find out
future payment and interest after 45 year
solution
we know future payment formula i.e. given below
future payment = payment × [tex](1+\frac{r}{n})^{nt} - 1) / (r/n)[/tex]
now put all these value in equation
future payment = $ 100 × [tex](1+\frac{0.015}{12})^{12*45} - 1) / (0.015/12)[/tex]
future payment = $ 77056.92
payment paid in 45 year @ $100 total money is paid is 45 × 12 × $100 i.e. = $54000
total interest = future payment - money paid
total interest = $77056.42 - $54000
total interest = $23056.42
A recipe that makes 3 dozen peanut butter cookies calls for 1 and 1/4 cups of flour. How much flour would you need to make 7 dozen cookies?
Answer:
[tex]2\frac{11}{12}[/tex] cups of flour are nedeed
Step-by-step explanation:
we know that
3 dozen peanut butter cookies calls for 1 and 1/4 cups of flour
Convert mixed number to an improper fraction
[tex]1\frac{1}{4}\ cups=\frac{1*4+1}{4}=\frac{5}{4}\ cups[/tex]
using proportion
Find out how much flour would you need to make 7 dozen cookies
Let
x ----> the number of cups of flour
[tex]\frac{3}{(5/4)}\frac{dozen}{cups}=\frac{7}{x}\frac{dozen}{cups} \\ \\x=7*(5/4)/3\\ \\x=\frac{35}{12}\ cups[/tex]
Convert to mixed number
[tex]\frac{35}{12}\ cups=\frac{24}{12}+\frac{11}{12}=2\frac{11}{12}\ cups[/tex]
Answer:
2.92 or 2 and 23/25 cups are required for 7 dozen cookies
Step-by-step explanation:
Determine the required number of flour for 3 dozen cookies. Use it to find flour required for 7 dozen cookies.
Dozen cookies Flour
3 1 + 1/4
7 x
Cross multiply to find the value of x
3x = 7(1+1/4)
3x = 7(5/4)
12x = 35
x = 2.92 cups or 2 and 23/25 cups
Therefore, 2.92 cups or 2 and 23/25 cups of flour are required for 7 dozen peanut butter cookies.
!!
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the instructor indicated he would randomly select two grades and compute the final percent correct based on the two percents. How many different samples, without replacement, of two test grades are possible
Answer:
15 samples
Step-by-step explanation:
The total sample space consists of 6 items
{79,64,84,82,92,77}
So,
n=6
The instructor has to randomly select 2 test scores out of 6.
So, r=6
The arrangement of scores selection doesn't matter so combinations will be used.
[tex]C(n,r)=\frac{n!}{r!(n-r)!} \\C(6,2)=\frac{6!}{2!(6-2)!}\\=\frac{6!}{2!*4!}\\=\frac{6*5*4!}{2!*4!} \\=\frac{30}{2}\\=15\ ways[/tex]
Therefore, there are 15 different samples are possible without replacement ..
Let S={1,2,3,4,5,6}.
How many subsets of cardinality 4 contain at least one odd number?
Answer:
15 subsets of cardinality 4 contain at least one odd number.
Step-by-step explanation:
Here the given set,
S={1,2,3,4,5,6},
Since, a set having cardinality 4 having 4 elements,
The number of odd digits = 3 ( 1, 3, 5 )
And, the number of even digits = 3 ( 2, 4, 6 )
Thus, the total possible arrangement of a set having 4 elements out of which atleast one odd number = [tex]^3C_1\times ^3C_3+^3C_2\times ^3C_2+^3C_3\times ^3C_1[/tex]
By using [tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex],
[tex]=3\times 1+3\times 3+1\times 3[/tex]
[tex]=3+9+3[/tex]
[tex]=15[/tex]
Hence, 15 subsets of cardinality 4 contain at least one odd number.
What is the product of -3/1 3 and -8/ 7 8
Answer:
(2/13)²
Step-by-step explanation:
-3/13 x -8/78 ( - x - is + )
+ 3 x 8 / 13 x 78 = 24/1014 = 4/169 =(2/13)²
(show the supposition, proof and conclusion)
Use proof by contradiction to show that If a and b are rational numbers with b ≠ 0 and x is an irrational number, then a + bx is irrational.
Answer:
Step-by-step explanation:
We are given that a and b are rational numbers where [tex]b\neq0[/tex] and x is irrational number .
We have to prove a+bx is irrational number by contradiction.
Supposition:let a+bx is a rational number then it can be written in [tex]\frac{p}{q}[/tex] form
[tex]a+bx=\frac{p}{q}[/tex] where [tex]q\neq0[/tex] where p and q are integers.
Proof:[tex]a+bx=\frac{p}{q}[/tex]
After dividing p and q by common factor except 1 then we get
[tex]a+bx=\frac{r}{s}[/tex]
r and s are coprime therefore, there is no common factor of r and s except 1.
[tex]a+bx=\frac{r}{s}[/tex] where r and s are integers.
[tex]bx=\frac{r}{s}-a[/tex]
[tex]x=\frac{\frac{r}{s}-a}{b}[/tex]
When we subtract one rational from other rational number then we get again a rational number and we divide one rational by other rational number then we get quotient number which is also rational.
Therefore, the number on the right hand of equal to is rational number but x is a irrational number .A rational number is not equal to an irrational number .Therefore, it is contradict by taking a+bx is a rational number .Hence, a+bx is an irrational number.
Conclusion: a+bx is an irrational number.
Consider the function V=g(x), where g(x) =x(6-2x)(8-2x), with x being the length of a cutout in cm and V being the volume of an open box in cm³, where x must between 0 and 3 cm. Determine the maximum volume of the open box in cm³. Round your answer to two decimal places. Also, indicate or show what process you used to obtain this answer. (Hint: graphing)
Answer:
The maximum volume of the open box is 24.26 cm³
Step-by-step explanation:
The volume of the box is given as [tex]V=g(x)[/tex], where [tex]g(x)=x(6-2x)(8-2x)[/tex] and [tex]0\le x\le3[/tex].
Expand the function to obtain:
[tex]g(x)=4x^3-28x^2+48x[/tex]
Differentiate wrt x to obtain:
[tex]g'(x)=12x^2-56x+48[/tex]
To find the point where the maximum value occurs, we solve
[tex]g'(x)=0[/tex]
[tex]\implies 12x^2-56x+48=0[/tex]
[tex]\implies x=1.13,x=3.54[/tex]
Discard x=3.54 because it is not within the given domain.
Apply the second derivative test to confirm the maximum critical point.
[tex]g''(x)=24x-56[/tex], [tex]g''(1.13)=24(1.13)-56=-28.88\:<\:0[/tex]
This means the maximum volume occurs at [tex]x=1.13[/tex].
Substitute [tex]x=1.13[/tex] into [tex]g(x)=x(6-2x)(8-2x)[/tex] to get the maximum volume.
[tex]g(1.13)=1.13(6-2\times1.13)(8-2\times1.13)=24.26[/tex]
The maximum volume of the open box is 24.26 cm³
See attachment for graph.
Please help me with this
Answer:
Right angles are congruent
Step-by-step explanation:
One right angle can be transformed to another using rigid transformations such as translation ,rotation and reflection.This is basically the definition of congruence because the idea is to transform one object to another.
A poll showed that 50.3% of Americans say they believe that some people see the future in their dreams. What is the probability of randomly selecting someone who does not believe that some people see the future in their dreams.
Answer:
The probability of randomly selecting someone who does not believe that some people see the future in their dreams =0.497.
Step-by-step explanation:
Given
Percent of Americans who Say they believe that some people see the future in their dreams=50.3%
Total percentages=100%
Therefore, Number of americans who say they believe that some people see the future in their dreams=50.3
The probability of randomly selecting someone who say they believe that some people see the future in their dreams =[tex]\frac{50.3}{100}[/tex]
Hence, the probability of randomly selecting someone who believe that some people see the future in their dreams, P(E)=0.503
Now, the probability of randomly selecting someone who does not believe that some people see the future in their dreams ,P(E')= 1-P(E)
The probability of randomly selecting someone who does not believe that some people see the future in their dreams =1-0.503
Hence,the probability of randomly selecting someone who does not believe that some people see the future in their dreams=0.497.
Answer: 0.497
Step-by-step explanation:
Let A be the event that Americans believe that some people see the future in their dreams.
Then , the probability that Americans believe that some people see the future in their dreams is given by :-
[tex]P(A)=50.3\%=0.503[/tex]
We know that the complement of a event X is given by :-
[tex]P(X')=1-P(X)[/tex]
Hence, the probability of randomly selecting someone who does not believe that some people see the future in their dreams is
[tex]P(A')=1-P(A)\\\\=1-0.503=0.497[/tex]
find a general solution of
t *(dy/dt)-(y^2)*lnt+y=0
[tex]t\dfrac{\mathrm dy}{\mathrm dt}-y^2\ln t+y=0[/tex]
Divide both sides by [tex]y(t)^2[/tex]:
[tex]ty^{-2}\dfrac{\mathrm dy}{\mathrm dt}-\ln t+y^{-1}=0[/tex]
Substitute [tex]v(t)=y(t)^{-1}[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dt}=-y(t)^{-2}\dfrac{\mathrm dy}{\mathrm dt}[/tex].
[tex]-t\dfrac{\mathrm dv}{\mathrm dt}-\ln t+v=0[/tex]
[tex]t\dfrac{\mathrm dv}{\mathrm dt}-v=\ln t[/tex]
Divide both sides by [tex]t^2[/tex]:
[tex]\dfrac1t\dfrac{\mathrm dv}{\mathrm dt}-\dfrac1{t^2}v=\dfrac{\ln t}{t^2}[/tex]
The left side can be condensed as the derivative of a product:
[tex]\dfrac{\mathrm d}{\mathrm dt}\left[\dfrac1tv\right]=\dfrac{\ln t}{t^2}[/tex]
Integrate both sides. The integral on the right side can be done by parts.
[tex]\displaystyle\int\frac{\ln t}{t^2}\,\mathrm dt=-\frac{\ln t}t+\int\frac{\mathrm dt}{t^2}=-\frac{\ln t}t-\frac1t+C[/tex]
[tex]\dfrac1tv=-\dfrac{\ln t}t-\dfrac1t+C[/tex]
[tex]v=-\ln t-1+Ct[/tex]
Now solve for [tex]y(t)[/tex].
[tex]y^{-1}=-\ln t-1+Ct[/tex]
[tex]\boxed{y(t)=\dfrac1{Ct-\ln t-1}}[/tex]