Answer:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Step-by-step explanation:
In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.
For a second order differential equation of type:
[tex]ay''+by'+cy=0[/tex]
Has characteristic equation:
[tex]a r^{2} +br+c=0[/tex]
Whose solutions [tex]r_1 , r_2 ,.., r_n[/tex] are the roots from which the general solution can be formed. There are three cases:
Real roots:
[tex]y(x)=c_1e^{r_1 x} +c_2e^{r_2 x}[/tex]
Repeated roots:
[tex]y(x)=c_1e^{r x} +c_1 xe^{r x}[/tex]
Complex roots:
[tex]y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i[/tex]
Therefore:
The characteristic equation for:
[tex]y''+6y'+13y=0[/tex]
Is:
[tex]r^{2} +6r+13=0[/tex]
Solving for [tex]r[/tex] :
[tex]r_1_,_2= -3 \pm 2i[/tex]
So:
[tex]\mu = 2\\\\and\\\\\lambda=-3[/tex]
Hence, the general solution of the differential equation will be given by:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Really in need of help :( please !
Answer:
A
Step-by-step explanation:
(2,1) - only one in the table. Remember (x,y)
I NEED HELP PLEASE I have been on this question for a hour
Answer:
A-8
Step-by-step explanation:
Any other higher number plugged in makes the equation false
pls help it due tomorrow
Answer:
Finding 1/5 of something is the same as dividing that number by 5. Since 24 isn't divisible by 5, 24 / 5 is not an integer. Since you can't have 4.8 species of animals the answer to (a) is no.
For (b), 1/3 * 24 = 8 and 24 - 8 = 16.
Find the value of a. a) 15 b) 10 c) 25 d) 20
Answer:
answer d) 20
Step-by-step explanation:
Because the two lines are parallel two by two, the figure is a parallelogram.
In a parallelogram the opposite corners are identical.
Given:
opposite corner1 = 130°
opposite corner2= (6a + 10)°
Because corner1 = corner2 we now have:
(6a + 10) = 130
6a + 0 = 130 -10
6a = 120
a = 20
Which is answer d).
2. Students who wish to represent the school at a school board meeting are asked to stop
by the office after lunch. After lunch, 5 students wish to represent the school.
Answer: Biased sample
Step-by-step explanation:
This is a biased sample because only students with strong opinions are likely going to volunteer or show interest in representing the school at the board meeting. This sample is a voluntary type sample, and at such the conclusion is not valid. This sample is biased because a group or population of students have a higher or lower sampling probability.
find the area enclosed by the curve y^2=x^2-x^4
Answer: 4/3
Step-by-step explanation:
As you know this graph is a lemniscate
[tex]4\int\limits^1_0 {x\sqrt{1-x^{2} } \, dx =\frac{4}{3} =1.33$[/tex]
A bag contains 7 red and 10 white balls. In how many ways 4 balls are selected if there are more than 2 red balls? (Please solve it using counting rule; combination rule.)
Answer:
385 ways
Step-by-step explanation:
Given;
7 red balls
10 white balls
In how many ways can 4 balls be selected if there are more than 2 red balls.
Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.
= 3 red balls and 1 white ball OR 4 red balls
= 7C₃ x 10C₁ + 7C₄
[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]
Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.
A four-year study of various brands of bottled water found that 25% of bottled water is just tap water packaged in a bottle. Consider a sample of sevenseven bottled-water brands, and let x equal the number of these brands that use tap water. Complete parts a through d.
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Answer:
Answers below
Step-by-step explanation:
a. Is x (approximately) a binomial random variable?
b. Give the probability distribution for x as a formula.
c. Find p(x = 2).
d. Find P(x <= 1).
Please answer this correctly
Answer:
Car: 60%
Motorcycle: 30%
Truck: 10%
Step-by-step explanation:
Car: [tex]\frac{12}{12+6+2} =\frac{12}{20} =\frac{60}{100}[/tex] or 60%
Motorcycle: [tex]\frac{6}{12+6+2} =\frac{6}{20} =\frac{30}{100}[/tex] or 30%
Truck: [tex]\frac{2}{12+6+2} =\frac{2}{20} =\frac{10}{100}[/tex] or 10%
A bank wants to attract new customers for its credit card. The bank tries two different approaches in the marketing campaign. The first promises a cash back reward; the second promises low interest rates. A sample of 500 people is called the first brochure; of these, 100 get the credit card. A separate sample of 500 people is called the second brochure; 125 get the credit card. The bank wants to know if the two campaigns are equally attractive to customers. What is a 95% confidence interval for the difference in the two proportions
Answer:
Step-by-step explanation:
Confidence interval for the difference in the two proportions is written as
Difference in sample proportions ± margin of error
Sample proportion, p= x/n
Where x = number of success
n = number of samples
For the first brochure,
x = 100
n1 = 500
p1 = 100/500 = 0.2
For the second brochure
x = 125
n2 = 500
p2 = 125/500 = 0.25
Margin of error = z√[p1(1 - p1)/n1 + p2(1 - p2)/n2]
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.025 = 0.975
The z score corresponding to the area on the z table is 1.96. Thus, the z score for confidence level of 95% is 1.96
Margin of error = 1.96 × √[0.2(1 - 0.2)/500 + 0.25(1 - 0.25)/500]
= 1.96 × √0.000695
= 0.052
Confidence interval = (0.2 - 0.25) ± 0.052
= - 0.05 ± 0.052
Do not answer or report What is -6 plus -6
Answer:
-12Step-by-step explanation:
it is -12 because -6 plus -6 is also like 6 plus 6
and then you have to add the negative Sign.
pls brainliest me
-6 - 6 = - 12
Happy to help! Please mark as the brainliest!
If 25% of a number is 100, what is the number?
OA.
50
B.
100
O C.
150
D.
200
o E.
400
Answer:
E. 400
Step-by-step explanation:
So this is how we set this up, and how we solve
[tex]0.25x=100\\x=100/0.25\\x=400[/tex]
Hope this helps!
So you are solving for circumference of a quarter circle: [tex]\frac{1}{4}2 \pi r[/tex]
r= 28
[tex]\pi=3.14[/tex]
[tex]\frac{1}{4}2(87.92)=\\43.96[/tex]
The table shows the daily sales (in $1000) of shopping mall for some randomly selected days Sales 1.1-1.5 1.6-2.0 2.1-2.5 2.6-3.0 3.1-3.5 3.6-4.0 4.1-4.5 Days 18 27 31 40 56 55 23 Use it to answer questions 13 and 14. 13. What is the approximate value for the modal daily sales? A. $3,129.41 B. $2,629.41 C. $3,079.41 14. The approximate median daily sales is ... A. $3,130.36 B. $2,680.36 C. $3,180.36 D. $3,123.53 D. $2,664.29
Answer:
Step-by-step explanation:
From the question; we are given the following inclusive frequency distribution information
Class Frequency f
1.1-1.5 18
1.6-2.0 27
2.1-2.5 31
2.6-3.0 40
3.1-3.5 56
3.6-4.0 55
4.1-4.5 23
Convert the above inclusive frequency distribution to exclusive frequency distribution with respect of the upper and lower class limit ; we have:
Class Frequency f
1.05 - 1.55 18
1.55 - 2.05 27
2.05 - 2.55 31
2.55 - 3.05 40
3.05 - 3.55 56
3.55 - 4.05 55
4.05 - 4.55 23
Class Frequency f cf
1.05 - 1.55 18 18
1.55 - 2.05 27 45
2.05 - 2.55 31 76
2.55 - 3.05 40 116
3.05 - 3.55 56 172
3.55 - 4.05 55 227
4.05 - 4.55 23 250
n = 250
To determine the daily sales; we can derive that from estimated Mode by using the relation :
Estimated Mode = L + fm − fm-1(fm − fm-1) + (fm − fm+1) × w
here:
L = the lower class boundary of the modal group
fm-1 = the frequency of the group before the modal group
fm = the frequency of the modal group
fm+1 = the frequency of the group after the modal group
w = the group width
However;
It is easier now to determine the modal group (i.e the group with the highest frequency), which is 3.05 -3.55
L = 3.05
fm-1 =40
fm =56
fm+1 = 55
w = 0.5
∴[tex]mode = 3.05 + \dfrac{56 - 40 }{(56 - 40) + (56 -55)} * 0.5 \\ \\ mode = 3.05 + 0.4705 \\ \\ mode = 3.5205[/tex]
To find Median Class ; we use the formula;
Median Class = value of (n / 2)th observation
Median Class = value of (250 / 2)th observation
Median Class = value of 125th observation
From the column of cumulative frequency cf,
we will see that the 125th observation lies in the class 3.05-3.55.
∴ The median class is 3.05-3.55.
Thus;,
L=lower boundary point of median class =3.05
n=Total frequency =250
cf=Cumulative frequency of the class preceding the median class =116
f=Frequency of the median class =56
c=class length of median class =0.5
[tex]Median M=L+n2-cff- c \\ \\ =3.05+125-11656⋅0.5 \\ \\=3.05+0.08036 \\ \\ =3.13036[/tex]
hence median sales = $3130.36
................
...
...
Answer:
C............PAC-MAN
Step-by-step explanation:
The weekly salaries of sociologists in the United States are normally distributed and have a known population standard deviation of 425 dollars and an unknown population mean. A random sample of 22 sociologists is taken and gives a sample mean of 1520 dollars.
Find the margin of error for the confidence interval for the population mean with a 98% confidence level.
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
You may use a calculator or the common z values above. Round the final answer to two decimal places.
Answer:
[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:
[tex]z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]\sigma = 425[/tex] represent the population deviation
[tex] n =22[/tex] the sample size
[tex]\bar X =1520[/tex] represent the sample mean
We want to find the margin of error for the confidence interval for the population mean and we know that is given by:
[tex] ME =z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is 0.98 and the significance is [tex]\alpha=1-0.98 =0.02[/tex] and [tex]\alpha/2 =0.01[/tex] and the critical value using the table is:
[tex]z_{\alpha/2}= 2.326[/tex]
And replacing we got:
[tex] ME=2.326 \frac{425}{\sqrt{22}}= 210.760\ approx 210.76[/tex]
PLEASE HELP the inverse of the function graphed below is a function
True or false
Functions
Function NotationVertical Line Test
ApplicationStep 1: DefineLet's see what we are given.
We are given a graph of an inverse of a function.
Step 2: IdentifyWe need to figure out whether the graphed inverse function is a function or not.
By the definition of a function, we know that every x input must correlate with one y output. In layman's terms, each respective x input has its own specific y output.
This definition builds the foundation of the Vertical Line Test. We can use this simple "tool" to verify whether or not a given graph is a function or not.
By placing a vertical line "on" the graph, we can move it to determine whether an x input has only one y output.If a graph passes the Vertical Line Test, it is said to be a function.If a graph fails the Vertical Line Test, it is said to not be a function, but rather a relation, etc.Step 3: TestWhen we apply the Vertical Line Test to the graphed inverse function, we can see that every x input has only one specific y output.
∴ we can conclude that the graphed inverse function is indeed a function.
AnswerThe answer to the question would be A. True.
___
Learn more about functions: https://brainly.com/question/30017262
Learn more about Algebra I: https://brainly.com/question/17011730
___
Topic: Algebra I
Unit: Functions
Wisconsin Public Radio wants to duplicate a survey conducted in 2011 that found that 68% of adults living in Wisconsin felt that the country was going in the wrong direction. How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%? Be sure to show all your work and round appropriately
Answer:
655 people would need to be surveyed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
In this question, we have that:
[tex]\pi = 0.68[/tex]
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 3%?
We need to survey n adults.
n is found when M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.68*0.32}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.68*0.32}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.68*0.32}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645\sqrt{0.68*0.32}}{0.03})^{2}[/tex]
[tex]n = 654.3[/tex]
Rounding up
655 people would need to be surveyed.
A cereal box has a volume of 225 cubic inches. The length of the base is 9 inches and the width of the base is
2.5 inches. What is the height of the box?
Answer:
10
Step-by-step explanation:
First multiply 9 by 2.5
Then divide 225 by 22.5
7+2x/3=5 im stuck on this question pls hhelp my homework is due soon pls help
The value of X is 4
please see the attached picture for full solution
Hope it helps
Good luck on your assignment..
What is the domain of the function on the graph?
all real numbers
all real numbers greater than or equal to 0
O all real numbers greater than or equal to -2
all real numbers greater than or equal to -3
HELP PLEASE
Answer:
All real numbers greater than or equal to -3
Step-by-step explanation:
First look at graph where the line points to which direction of the graph
And look for any closed or open circles in the graph
Since in the graph has a close circle at (-3,-2) meaning it includes that x-value for its domain.
With the graph going to positive infinity it states that the domain is all real numbers.
So in conclusion it has a domain of all real numbers greater than or equal to -3
Consider the polynomial 9x2 – 16.
Answer: 2
Step-by-step explanation:
9 × 2 - 16
18 - 16
2
What is the greatest number of right angles a triangle can contain?
A. 0
B. 1
C. 3
D. 2
The answer is B..........
Answer:
B. 1
Step-by-step explanation:
If it was more than one it wouldn't be a triangle.
Classify the triangle by its sides, and then by its angles.
60 degrees
60 degrees
60 degrees
4 ft
4 ft
4 ft
Classified by its sides, the triangle is a(n)
▼
equilateral
scalene
isosceles
triangle.
Classified by its angles, the triangle is a(n)
▼
obtuse
acute
right
triangle.
Answer:
Equilateral, acute
Step-by-step explanation:
Equilateral triangles have all sides the same length (all sides are 4 ft in this triangle, so it is equilateral).
Acute triangles have no angles that are greater than or equal to 90 degrees (all angles are 60, which is less than 90, so it is acute).
ASAPPPPP
PICTURE BELOW
WILL HAVE MORE OF THESE
Answer: -6m-n+3
Step-by-step explanation:
The answer is -6m-n+3 because -3
times 2m is -6m and -n stays the same its outside of the parenthesis
and lastly -3 times -1 is positive 3
so answer maches up with the last one
the answer is -6m-n+3
Hope this helps :)
Answer:
-6m-n+3
Step-by-step explanation:
-3 x 2 is -6m (n stays same)
-3 x -1 is whole or positive 3
put it together and u get -6m-n+3
hope this helps
Solve for x.
6(x - 2) = 4
Answer:
8/3
Step-by-step explanation:
6(x-2)=4
x-2=4/6
x= 8/3
Answer:
x = 8/3
Step-by-step explanation:
Use Distributive Property
6(x-2) = 4
6x -12 = 4
add 12 on both sides
6x = 16
Divide by 6
x = 8/3
In decimal form: 2.667
Write down the definition of a random sample.
Answer:
Step-by-step explanation:
Random sampling is a procedure for sampling from a population in which (a) the selection of a sample unit is based on chance and (b) every element of the population has a known, non-zero probability of being selected.
Answer:
A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
I hope this helped...
What is the equation of the line perpendicular to y = 2/3x+1that passes through the point (12, -6)?
Answer:[tex]y=-\frac{3}{2} x+12[/tex]
Step-by-step explanation:
Perpendicular lines have inversely proportional slopes. So make the slope negative and switch it to its reciprocal.
2/3x would change into -3/2x
Lets write that down for a starting point for our perpendicular line.
y = -3/2x + b
We were given the x and y value via the coords. x = 12 and y = -6
Now we have -6 = -3/2(12) + b. Multiply -3 and 12 to get -36, then divide by 2 to get -18. Now it's -6 = -18 + b. Solve for b by adding 18 to both sides to get b = 12
3) Washing your hands kills germs. If there are 275 germs chilling on your hands and
you kill 4.75% per second of washing, how many germs left on your hands after 10
seconds. Round your answer to the nearest whole germ. (Remember, keep washing
those hands)
Answer:
So we can use geometric progression each time multiplying by 0.0475
so thats (275*0.0475)*10
So that means that we would get
130.625 so we subtract that from 275
275-130.625=144.375
That would be
Step-by-step explanation:
Isabella averages 152 points per bowling game with a standard deviation of 14.5 points. Suppose Isabella's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X∼N(152,14.5)______.
If necessary, round to three decimal places.
Suppose Isabella scores 187 points in the game on Sunday. The z-score when x=187 is ___ The mean is _________
This z-score tells you that x = 187 is _________ standard deviations.
Answer:
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 152, \sigma = 14.5[/tex]
The z-score when x=187 is ...
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{187 - 152}{14.5}[/tex]
[tex]Z = 2.41[/tex]
The z-score when x=187 is 2.41. The mean is 187. This z-score tells you that x = 187 is 2.41 standard deviations above the mean.
Help me which answer is it
Answer:
C.
Step-by-step explanation:
[tex]\frac{1}{5} +\frac{5}{6}[/tex] ≈ 1
5 + 8 + 1 = 14
