Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x,y2=e−6x B. y1=e3x,y2=e1x C. y1=e2x,y2=e−2x D. y1=e−12x,y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x,y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.
What's 2|–9| – |–2|?
Answer:
Step-by-step explanation: AS YOU KHOW THW ABSOLUTE VALUE OF A QUESTION IS NUMBER ITSELF IF THERE IS MINUS SIGH THEN THE SIGH OF A NUMBER WILL BECOME PLUS OR IF THERE IS A PLUS SIGH THEN THERE IT WILL REMAIN AS IT IS. IF THERE IS NO NUMBER WITH THE MINUS SIGH THEN THE MINUS SIGH WILL REAMIN AS IT IS.
+2 +9 - +2
The answer has same sigh, then Plus answer will you get is
+11 - 2 then you will minus the answer will be
+9
HOPE IT HELP YOU
PLEASE HELP ME GUYS!!
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
csc(Ф) is equivalent to the inverse of sin(Ф)
[tex]csc = \frac{1}{sin}[/tex]Since sin(Ф) = 3/7, the inverse of this would be 7/3
So, [tex]csc = \frac{1}{\frac{3}{7} }=\frac{7}{3}[/tex]
Environmental Protection Agency standards require that the amount of lead in drinking water be less than 15 ppb. Twelve samples of water from a particular source have the following concentrations, in ppb. 11.4 13.9 11.2 14.5 15.2 8.1 12.4 8.6 10.5 17.1 9.8 15.9 A hypothesis test will be performed to determine whether the water from this source meets the EPA standard.
Required:
a. State the appropriate null and alternate hypotheses.
b. Compute the P-value.
c. Can you conclude that the water from this source meets the EPA standard? Explain.
Answer:
Step-by-step explanation:
Mean = (11.4 + 13.9 + 11.2 + 14.5 + 15.2 + 8.1 + 12.4 + 8.6 + 10.5 + 17.1 + 9.8 + 15.9)/12 = 12.4
Standard deviation = √(summation(x - mean)²/n
n = 12
Summation(x - mean)² = (11.4 - 12.4)^2 + (13.9 - 12.4)^2 + (11.2 - 12.4)^2+ (14.5 - 12.4)^2 + (15.2 - 12.4)^2 + (8.1 - 12.4)^2 + (12.4 - 12.4)^2 + (8.6 - 12.4)^2 + (10.5 - 12.4)^2 + (17.1 - 12.4)^2 + (9.8 - 12.4)^2 + (15.1 - 12.4)^2 = 89.62
Standard deviation = √(89.62/13) = 2.7
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
a) For the null hypothesis,
µ ≤ 15
For the alternative hypothesis,
µ > 15
This is a right tailed test
b) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 12,
Degrees of freedom, df = n - 1 = 12 - 1 = 11
t = (x - µ)/(s/√n)
Where
x = sample mean = 12.4
µ = population mean = 15
s = samples standard deviation = 2.7
t = (12.4 - 15)/(2.7/√12) = - 3.34
We would determine the p value using the t test calculator. It becomes
p = 0.0034
c) Assuming level of significance = 0.05.
Since alpha, 0.05 > than the p value, 0.0034, then we would reject the null hypothesis. Therefore, At a 5% level of significance, we can conclude that the water from this source does meets the EPA standard. They are higher than 15ppb
Using the t-distribution, we have that:
a)
The null hypothesis is: [tex]H_0: \mu \geq 15[/tex]
The alternative hypothesis is: [tex]H_1: \mu < 15[/tex]
b) The p-value is of 0.0051.
c) Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.
Item a:
At the null hypothesis, it is tested if the mean is of at least 15 ppb, that is:
[tex]H_0: \mu \geq 15[/tex]
At the alternative hypothesis, it is tested if the mean is of less than 15 ppb, that is:
[tex]H_1: \mu < 15[/tex]
Item b:
We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.In this problem, we have that [tex]\mu = 15, n = 12[/tex]. Additionally, using a calculator, the other parameters are: [tex]\overline{x} = 12.38, s = 2.93[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{12.38 - 15}{\frac{2.93}{\sqrt{12}}}[/tex]
[tex]t = -3.1[/tex]
The p-value is found using a left-tailed test, as we are testing if the mean is less than a value, with t = -3.1 and 12 - 1 = 11 df.
Using a calculator, this p-value is of 0.0051.Item c:
Since the p-value is of 0.0051, which is less than the standard significance level of 0.0051, it can be concluded that the mean is less than 15 ppb, and thus, this source meets the EPA standard.
A similar problem is given at https://brainly.com/question/16194574
3. (05.01)
A pair of linear equations is shown below:
y = -x + 1
y = 2x + 4
Which of the following statements best explains the steps to solve the pair of equations graphically? (4 points)
On a graph, plot the line y = -x + 1, which has y-intercept = -1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of
Intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept - 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of
intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = -2 and slope = 2, and write the coordinates of the point
of intersection of the two lines as the solution.
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of
intersection of the two lines as the solution.
Answer:
On a graph, plot the line y = -x + 1, which has y-intercept = 1 and slope = -1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Step-by-step explanation:
Each equation is in slope-intercept form:
y = mx + b . . . . . where m is the slope, and b is the y-intercept
The first equation is ...
y = -x +1
so the slope is -1, and the y-intercept is +1.
__
The second equation is ...
y = 2x +4
so the slope is 2, and the y-intercept is 4.
__
The slopes and intercepts are properly described in the last selection.
Which expressions are equivalent to 64^1Check all that apply
The right answers are:
4^38^22^6Hope it helps.
please see the attached picture for full solution
Good luck on your assignment
Point R has coordinates (-5, -7) and point T has coordinates (3,-3).
Which point is located 1/4 of the distance from point R to point T?
Enter x-coordinate of the point here .......
and the y-
coordinate of the point here....
Answer:
(x, y) = (-3, -6)
Step-by-step explanation:
The (x, y) distance from R to T is ...
(Δx, Δy) = T - R = (3, -3) -(-5, -7) = (3 -(-5), -3 -(-7)) = (8, 4)
Then 1/4 of the distance is ...
(Δx, Δy)/4 = (8, 4)/4 = (2, 1)
This is added to the R coordinates to find the desired point:
point = R +(2, 1) = (-5, -7) +(2, 1) = (-5+2, -7+1) = (-3, -6)
The coordinates are ...
x-coordinate: -3
y-coordinate: -6
I would like to purchase 20 products at a cost of $65 per product. What would be my total with 3.5 sales tax
Answer:
Answer:
The total is: $ 1345.5
Step-by-step explanation:
It is given that:
I would like to purchase 20 products at a cost 65.00 per product.
This means that the cost of 20 products will be:
Also, there is a sales tax of 3.5%
This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.
i.e. he need to pay 3/5% on $ 1300
This means that the amount of tax he need to pay is: 3.5% of 1300
= 3.5%×1300
= 0.035×1300
= $ 45.5.
Hence, the total cost is: $ 1300+$ 45.5
This means that the total cost is: $ 134.5
11 — 9y = — 6у +8
solve for y
pleaseee
Answer:
-The value of [tex]y[/tex]:
[tex]y = 1[/tex]
Step-by-step explanation:
-Find the value of [tex]y[/tex]:
[tex]11- 9y = -6y + 8[/tex]
-Add both sides by [tex]6y[/tex] and combine [tex]9y[/tex] and [tex]6y[/tex] together:
[tex]11- 9y + 6y = -6y + 6y+ 8[/tex]
[tex]11 - 3y = 8[/tex]
-Subtract both sides by [tex]11[/tex]:
[tex]11 - 11 - 3y = 8 -11[/tex]
[tex]-3y = -3[/tex]
-Divide both sides by [tex]-3[/tex]:
[tex]\frac{-3y}{-3} = \frac{-3}{-3}[/tex]
[tex]y = 1[/tex]
So the final answer is [tex]y = 1[/tex] .
The Gleason family has a monthly budget of $4,500. Mr. Gleason has a full-time job and takes home $900 each week. Mrs. Gleason works part time and brings home $9 each week. For every hour she works. How many hours per month must Mrs. Gleason work to make sure that she and Mr. Gleason have met their monthly budget?
Answer:
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
Step-by-step explanation:
To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,
4,500 = 900(4) + 9x
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
I am sorry if you get this wrong.
A payday loan store charges $40 for a one month loan of $600. What’s the annual interest rate equivalent to?
Answer:
80%
Step-by-step explanation:
rate=100×Interest/ principal × time
Interest= 40
principal= 600
time= 1 month=1/12
100%×$40×12/$600×1=80%
Car engine needs ______________ to avoid friction.
a) water
b) smooth surface
c) oil
d) air
Answer:
Oil
Step-by-step explanation:
Car engine needs oil to avoid friction.
Answer:
[tex]oil \\ [/tex]
Answer C is correct
Step-by-step explanation:
car engine needs oil to avoid the friction .
hope this helps
brainliest appreciated
good luck! have a nice day!
5 gummy worms. 4 are red, 1 is blue. Two gummy worms are chosen at random and not replaced. What is probability of two red gummy worms.
Answer:
3/5
Step-by-step explanation:
because there are more red than blue and the fraction is 3/5 and the probability to pick a red worm is a lot higher than the blue. well there are 4 red worms and 1 blue so it would be 3 red worms out of 5 in total. this is more than 1 blue over 5. 3/5 is more than 1/5
hope this helped
Answer: 3/5
Step-by-step explanation:
Since 4 red gummies you have four out of 5 chance of getting red gummies. Without replacement there are now 4 gummies left and 3 red gummies. There for 3 out of 4 chance of getting another red gummy. Since at same time multiply. 4/5*3/4 = 12/20
Which can be simplified to 3/5
Please answer this correctly
Answer:
1.5 meters
Step-by-step explanation:
The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:
3.75=h*(1.7+3.3)/2
3.75=h*2.5
h=3.75/2.5=1.5
Hope this helps!
Answer:
Step-by-step explanation:
use the formula and rearrange for h.
1/2 x h x (a + b) = A
1/2 x (1.7 + 3.3) x h = 3.75
2.5 x h = 3.75
h = 1.5
hope this helps! :)
(5m+100) (2m+10) what’s the value of m
Answer:
m=-30
Step-by-step explanation:
5m+100=2m+10
We want to get the variable on one side of the equation. First we subtract 100 from both sides.
5m=2m-90
Subtract 2m from both sides.
3m=-90
Divide both sides by 3.
m=-30
I need help again♀️,
Answer:
The second choice.
Step-by-step explanation:
Answer:
2nd graph down
Step-by-step explanation:
3a+11 > 5
Subtract 11 from each side
3a+11-11 > 5-11
3a > -6
Divide each side by 3
3a/3 > -6/3
a >-2
Open circle at 02
line going to the right
Determine whether the underlined number is a statistic or a parameter. In a study of all 1963 employees at a college, it is found that "40%" own a computer. Choose the correct statement below.
1. Parameter because the value is a numerical measurement describing a characteristic of a population
2. Statistic because the value is a numerical measurement describing a characteristic of a population
3. Statistic because the value is a numerical measurement describing a characteristic of a sample.
4. Parameter because the value is a numerical measurement describing a characteristic of a sample.
Answer:
1. Parameter because the value is a numerical measurement describing a characteristic of a population
Step-by-step explanation:
A parameter is a fixed measure which describes the whole population while a statistic is a characteristic of a sample (which is a portion of the target population).
In a study of all 1963 employees at a college, it is found that "40%" own a computer.
The study involved the entire population of employees in the college, therefore the result describes the computer owning characteristics of the whole population under study. It is therefore a parameter.
The correct option is 1.
g Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. The 88% confidence interval for the population mean of waiting times is __________.
Answer:
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 64 - 1 = 63
88% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 63 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.88}{2} = 0.94[/tex]. So we have T = 1.9153
The margin of error is:
M = T*s = 1.9153*4 = 7.66.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 7.66 = 7.34 minutes
The upper end of the interval is the sample mean added to M. So it is 15 + 7.66 = 22.66 minutes.
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
Please answer this correctly
Answer:
1
Step-by-step explanation:
Set the height of the bar to 1 because there is only 1 number between 40-49 i.e. 49
Algebraically calculate the following limit exactly: lim ℎ→0
[tex]answer \\ \\ \frac{ \sqrt{5} }{2 \sqrt{a} } \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]
divide the following polynomials ( 9 x 4 + 3 x 3 y − 5 x 2 y 2 + x y 3 ) ÷ ( 3 x 2 + 2 x 2 y − x y 2 )
Answer:
2(-2y+9)/3+y
Step-by-step explanation:
got another math problem.. please help
the correct answer is 59.
Answer:
59
Step-by-step explanation:
[2+ (4-2)+8²]-[2-(-1)][2+2+64]-[2-(-1)]²68-3²68-959The probability that a randomly chosen sales prospect will make a purchase is 20%. What is the probability (to three decimal places) that the salesperson will make four or more sales if six sales calls are made on a given day
Answer:
1.7%
Step-by-step explanation:
We have to calculate the probability that the salesperson will make four or more sales if six sales calls are made on a given day, that is:
P (x => 4)
Therefore, we must calculate when x = 4, when x = 5, and when x = 6 and add. p = 0.2, n = 6
P (x = r) = nCr * p ^ r * (1 - p) ^ (n-r)
Also, nCr = n! / (r! * (n-r) !, now replacing:
P (x = 4) = 6! / (4! * (6-4)! * 0.20 ^ 4 * 0.80 ^ (6-4)
P (x = 4) = 15 * 0.001024 = 0.01536
P (x = 5) = 6! / (5! * (6-5)! * 0.20 ^ 5 * 0.80 ^ (6-5)
P (x = 5) = 6 * 0.000256 = 0.001536
P (x = 6) = 6! / (6! * (6-6)! * 0.20 ^ 6 * 0.80 ^ (6-6)
P (x = 6) = 1 * 0.000064 = 0.000064
now,
P (x => 4) = P (x = 4) + P (x = 5) + P (x = 6)
P (x => 4) = 0.01536) + 0.001536 + 0.000064
P (x => 4) = 0.01696 = 0.017
It means that the probability is 1.7%
Here is a solid square-based pyramid.
The base of the pyramid is a square of side 12cm.
The height of the pyramid is 8cm.
X is the midpoint of QR and XT = 10cm.
A) Draw the front elevation of the pyramid from the direction of the arrow. Use a scale of 1 square to 1cm.
B) Work out the total surface area of the pyramid.
Answer:
Step-by-step explanation:
A. The front elevation of the pyramid in the direction of the arrow is herewith attached to this answer.
B. Base of the pyramid is a square of side 12 cm.
The height of the pyramid is 8 cm.
Slant height, XT, is 10 cm.
The total surface area of the pyramid can be determined by adding the surface areas that make up the shape.
Area of the triangular face = [tex]\frac{1}{2}[/tex] × base × slant height
= [tex]\frac{1}{2}[/tex] × 12 × 10
= 60 [tex]cm^{2}[/tex]
Area of the square base = length × length
= 12 × 12
= 144 [tex]cm^{2}[/tex]
Total surface area of the pyramid = area of the base + 4 (area of the triangular face)
= 144 + 4(60)
= 144 + 240
= 384 [tex]cm^{2}[/tex]
Therefore, total surface area of the pyramid is 384 [tex]cm^{2}[/tex].
Solve for n:
6 - 24n = 3n + 6
Answer:
0
Step-by-step explanation:
6-24n=3n+6
Add 24n to both sides of the equation:
6=27n+6
Subtract 6 from both sides:
27n=0
Therefore, n=0.
Hope this helps!
A spinner with 6 colors is spun and a number cube is tossed determine the number of outcomes
Answer:
36
Step-by-step explanation:
since there are six outcomes for the spinner and six outcomes for the cube,
6 x 6 = 36
What expression is equivalent to 6•6•6•6•6
Answer:
6^5
Step-by-step explanation:
6 multiplied with itself 5 times is equal to 6^5
The intensity of cosmic ray radiation decreases rapidly with increasing energy, but there are occasionally extremely energetic cosmic rays that create a shower of radiation from all the particles they create by striking a nucleus in the atmosphere as seen in the figure given below. Suppose a cosmic ray particle having an energy of converts its energy into particles with masses averaging .
(a) How many particles are created?
(b) If the particles rain down on a area, how many particles are there per square meter?
Answer:
(a) 5* 10¹⁰ (b) 5* 10⁴ particles / m²
Step-by-step explanation:
Solution
(a) We find the number of particles that is created
Now,
The energy will change into particles of masses that is averaging 200 MeV/c²
The number of particles that were created is stated as follows:
n = Ec/Er
Ec =This is the cosmic energy
Er =The rest mass energy
Thus, we replace 10¹⁰ with Ec and (0.200 GeV/c²)c² for Er
This gives us the following:
n = 10¹⁰ GeV/ (0.200 GeV/c²)c²
= 5* 10¹⁰
Hence the number of particle created is 5* 10¹⁰
(b) We now find how many particles are there per square meter
Thus,
n/m² = 5* 10¹⁰ particles/(1000 m)²
= 5* 10⁴ particles / m²
Hence, the particles that are there per square meter is 5* 10⁴ particles / m²
Note: Kindly find an attached copy of the complete question to this solution below.
Graph the image of the figure given the translation. 1. (x, y) → (x +4, y - 1)
Answer:
Y=(-1,0)
G=(0,1)
F=(-1,3)
Step-by-step explanation:
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, said that they some what agree, said they some what disagree, and said they strongly disagree with this statement.
Required:
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
Step-by-step explanation:
a. It would provide a quantitative data
b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.
c. 44% of the respondents strongly agree
d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.
