Find the first four nonzero terms in a power series expansion about xequals0 for the solution to the given initial value problem. w prime prime plus 3 xw prime minus wequals0; w(0)equals4, w prime (0 )equals0
Answers
Answer:
The first four terms are;
w(x)= 4 + 2x² - ⁵/₆x⁴+ ¹¹/₃₆x⁶ +......
Step-by-step Explanation:
This is the interpretation of the question
w″ + 3xw′ -w=0
W(0)=4
W′(0)=0
CHECK THE ATTACHMENT FOR STEP BY STEP EXPLANATION
Related Questions
QUESTION 8
Find Future Value Using Compound Interest Formula:
You deposit $6,000 in an account earning 4% interest compounded monthly. How much will you have in the account in 5 years?
A $9,677.95
B. $6,100.67
C. $7,325.98
D. $7,200
QUESTION 9
Find Future Value Using Compound Interest Formula:
You deposit $5,000 in an account earning 5% interest compounded quarterly. How much will you have in the account in 10 years?
A $5,661.35
B. $7,500
C. $8,235.05
D. $8,218.10
Answers
Answer:
8.) $7325.98
9.) $8218.10
Step-by-step explanation:
Compounded Interest Rate Formula: A = P(1 + r/n)^nt
Simply plug in our known variables into the formula:
A = 6000(1 + 0.04/12)^60 = 7325.98
A = 5000(1 + 0.05/4)^40 = 8218.10
i need this fast plz
Answers
Answer:
180-130 = 50 degrees because its same side angle
m<2 = 50
Step-by-step explanation:
the second one m<1 is 105 for the same reason
Use the function below to find f(4).
f(x)=1/3x4^x
A. 8/3
B.256/3
C.64/3
D.16/3
Answers
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
Simply replace X with 4
Answer:
F(4)=1/3*4^4
F(4)=256/3
Step-by-step explanation:
4^4=256
(1/3)*(256)=
256/3
A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 7 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 7 workers has the same chance of being selected as does any other group (drawing 7 slips without replacement from among 45).
1. How many selections result in all 7 workers coming from the day shift?
2. What is the probability that all 7 selected workers will be from the day shift?
3. What is the probability that all 7 selected workers will be from the same shift?
4. What is the probability that at least two different shifts will be represented among the selected workers?
5. What is the probability that at least one of the shifts will be un-represented in that sample of workers?
Answers
Answer:
1. 77520
2. [tex]P_1[/tex] = 0.0017
3. [tex]P_2[/tex] = 0.0019
4. [tex]P_3[/tex] = 0.9981
5. [tex]P_4[/tex] = 0.2036
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n can be calculated as:
[tex]nCx = \frac{n!}{x!(n-x)!}[/tex]
So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:
[tex]20C7 = \frac{20!}{7!(20-7)!}=77520[/tex]
At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:
[tex]P_1=\frac{20C7}{45C7} =0.0017[/tex]
The probability that all 7 selected workers will be from the same shift is calculated as:
[tex]P_2=\frac{20C7+15C7+10C7}{45C7} =0.0019[/tex]
Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).
On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:
[tex]P_3 = 1- P_2=1 - 0.0019 = 0.9981[/tex]
Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:
[tex]P_4=\frac{25C7+30C7+35C7}{45C7} =0.2036[/tex]
Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.
Plz help me plzzzzzz!!!!
Answers
Answer: D, 6
Step-by-step explanation:
Match each side from XYZ to ABC (you are trying to find the scale factor of triangle 1 to triangle 2) into a fraction then simplify
Ex 30/5= 6 or 24/6= 6 or 18/3
In an aquarium, there are 7 large fish and 6 small fish. Half of the small fish are red.
One fish is selected at random. Find the probability that it is a small, red fish.
Write your answer as a fraction in simplest form.
Answers
Answer:
3/13
Step-by-step explanation:
There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.
Jacob and Dustin collected 245 cast for the school can job they give 55 cast to Dustin's little sister to take to her class how many cans does this leave for the boys class
Answers
Answer:
190 cans
Step-by-step explanation:
Total cans collected by Jacob and Dustin for the school can job = 245
Amount of cans they both gave to Dustin's little sister = 55
Now because they gave out cast out of the total they initially had, there would be a deduction in the amount both boys would now have.
To determine the amount the boys are left with, we would deduct 55 casts from the amount they had which 245.
Amount of cans left = 245-55 = 190
Amount of cans left for the boys class = 190 cans
Classify the following triangle. Check all that apply.
A. Isosceles
B. Right
C. Obtuse
D. Equilateral
E. Scalene
F. Acute
Answers
Answer:
Equilateral
Acute
Step-by-step explanation:
The sides are all equal as indicated by the lines on each side - Equilateral
The angles are all equal by the angle marks 180/3 = 60 which is less than 90 degrees. This makes the angles acute
What is the circumference of the circle below? (Round your answer to the nearest tenth.)
Answers
Answer:
Its 69.1 cm
Step-by-step explanation:
To find circumstance of any circle main formula is 2*pie*r .
Here pie is equal to 3.14 approx and r =11 cm
so
2*3.14*11 = 69.08 cm
This little difference is just because of pie's approximately value used
4 years ago, the population of a city was of "x" inhabitant, 2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610. Using this data, find the population of four years ago.
Answers
Answer:
The population of four years ago was 100,783 inhabitants
Step-by-step explanation:
The population of the city after t years is given by the following equation:
[tex]P(t) = P(0)(1-r)^{t}[/tex]
In which P(0) is the initial population and r is the decrease rate, as a decimal.
2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610.
This means that:
[tex]P(2) = 81000, P(4) = 65610[/tex]
We are going to use this to build a system, and find P(0), which is the initial population(four years ago).
P(2) = 81000
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]81000 = P(0)(1-r)^{2}[/tex]
[tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]
P(4) = 65610
[tex]P(t) = P(0)(1-r)^{t}[/tex]
[tex]65100 = P(0)(1-r)^{4}[/tex]
[tex]65100 = P(0)((1-r)^{2})^{2}[/tex]
Since [tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]
[tex]65100 = P(0)(\frac{81000}{P(0)})^{2}[/tex]
Using P(0) = x
[tex]65100 = x(\frac{81000}{x})^{2}[/tex]
[tex]65100 = \frac{6561000000x}{x^{2}}[/tex]
[tex]65100x^{2} = 6561000000x[/tex]
[tex]65100x^{2} - 6561000000x[/tex]
[tex]x(65100x - 6561000000) = 0[/tex]
x = 0, which does not interest us, or:
[tex]65100x - 6561000000 = 0[/tex]
[tex]65100x = 6561000000[/tex]
[tex]x = \frac{6561000000}{65100}[/tex]
[tex]x = 100,783[/tex]
The population of four years ago was 100,783 inhabitants
which expression defies the arithmetic series 10 + 7 + 4 ... for six terms?
Answers
Answer:
[tex]a_n = 10-3(n - 1)[/tex]
10 + 7 + 4 + 1 + -2 + -5
Step-by-step explanation:
Explicit Arithmetic Formula: [tex]a_n = a_1 + d(n-1)[/tex]
To find d, take the common difference between 2 numbers.
To find the other terms of the sequence, plug them into the explicit formula or subtract 3 from the given numbers.
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.
a. Calculate a 95% two-sided confidence interval on the death rate from lung cancer.
b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03?
c. How large must the sample be if you wish to be at least 95% confident that the error in estimating p is less than 0.03, regardless of the true value of p?
Answers
Answer:
a) [tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
b) [tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
c) [tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
Step-by-step explanation:
Part a
[tex]\hat p=\frac{823}{1000}=0.823[/tex]
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values obtained we got:
[tex]0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799[/tex]
[tex]0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847[/tex]
The 95% confidence interval would be given by (0.799;0.847)
Part b
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.03[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79[/tex]
And rounded up we have that n=622
Part c
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11[/tex]
And rounded up we have that n=1068
PLZZZ I NEED HELP I’ll give 20 POINTS
What is the median of the following data set?
(6,3, 9, 1,7)
03
06
08
09
Answers
Answer:
6
Step-by-step explanation:
Arrange the data from smallest to largest
1,3,6,7,9
The median is the middle number
1,3 ,6, 7, 9
The middle number is 6
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
(a) Use a linear approximation to estimate g(2.95) and g(3.05).
g(2.95) =
g(3.05) =
(b) Are your estimates in part (a) too large or too small? Explain.
A) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small.
B) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small.
C) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large.
D) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Answers
Answer:
g(2.95) ≈ -1.8; g(3.05) ≈ -0.2A) tangents are increasing in slope, so the tangent is below the curve, and estimates are too small.Step-by-step explanation:
(a) The linear approximation of g(x) at x=b will be ...
g(x) ≈ g'(b)(x -b) +g(b)
Using the given relations, this is ...
g'(3) = 3² +7 = 16
g(x) ≈ 16(x -3) -1
Then the points of interest are ...
g(2.95) ≈ 16(2.95 -3) -1 = -1.8
g(3.05) ≈ 16(3.05 -3) -1 = -0.2
__
(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)
Simplify. Remove all perfect squares from inside the square root. \sqrt{30b^5}= 30b 5
Answers
Answer:
The answer is b=0 or b=9.085603
The equation is solved and the perfect squares are removed from the square root and A = b²√( 30b )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = √( 30b⁵ )
On simplifying the equation , we get
We can simplify the given expression by breaking down the number inside the square root into its prime factors:
30b⁵ = 2 x 3 x 5 x b⁵
Since we are looking to remove all perfect squares, we can remove the factors of 2 and 3, which are the only perfect squares present in the prime factorization of 30. This leaves us with:
30b⁵ = 2 x 3 x 5 x b⁵
= 2 x 3 x 5 x b⁴ x b
= 30b⁴ x b
Therefore, we can simplify the original expression as:
√(30b⁵) = √(30b⁴ x b) = √(30b⁴) x √b
A = b²√30 x √b
Hence , the expression √(30b⁵) simplifies to A = b²√30 x √b
To learn more about equations click :
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Question 3 of 10
2 Points
If h(x) =(fºg)(x) and h(x) = 3(x + 2), find one possibility for f (x) and g(x).
Answers
Answer:
[tex]\boxed{\sf \ \ \ \text{one possibility is } f(x)=3x \ and \ g(x)=x+2 \ \ \ }[/tex]
Step-by-step explanation:
hello
h(x)=f(g(x))=3(x+2)
if we have f(x)=3x and g(x)=x+2 then
f(g(x))=f(x+2)=3(x+2)
hope this helps
Use a proportion to solve the problem. Round to the nearest tenth as needed.
Triangle in a triangle Find the height of the building. Assume that the height of the person is 5 ft.
104 ft
building
13 ft
5 ft
Answers
Answer:
Height of the building is 40 feet
Step-by-step explanation:
From the figure attached,
Height of the person DE = 5 feet
Let height of the building BC = h feet
Since, ΔABC ~ ΔADE,
Their corresponding sides will be proportional,
[tex]\frac{DE}{BC}=\frac{AD}{AB}[/tex]
[tex]\frac{5}{h}=\frac{13}{104}[/tex]
h = [tex]\frac{104\times 5}{13}[/tex]
h = 40 feet
Therefore, height of the building is 40 feet.
PLEASE HELP SOLVE THIS!!!!!
Answers
Answer:
20) -43
21) 25
22)-9
Step-by-step explanation:
20) -6 (-6 + 49)/6 = -43
21) 10 - (-10 - (-1 + 6)) = 25
22) 1 - 10/2 - 5 = -9
Step-by-step explanation:
22Let's calculate the expression khowing that m= 1 and n = 5
m-[tex]\frac{m+m}{2}[/tex] -nm- [tex]\frac{2m}{2}[/tex]-n m-m-n0-n0-5-520Let's calculate the expression khowing that n= -7 and p= - 6
[tex]\frac{p(p+n^{2}) }{6}[/tex] [tex]\frac{-6(-6+(-7)^{2}) }{6}[/tex][tex]\frac{-6(-6+49)}{2}[/tex] [tex]\frac{-6*43}{6}[/tex] -1*43-4321Let's calculate the expression khowing that n = -6 and m = -1 and p = -10
mp-(p-(m-n))mp-(p-m+n)mp-p+m-n(-1)*(-10)-(-10)+(-1)-(-6)10+10-1+620-1+619+625Given the figure below, find the values of x and Z.
Please explain step by step how to solve, this is a guide for a test.
Answers
Answer:
(x, z) = (7, 69)
Step-by-step explanation:
Easy first: 69° and z° are vertical angles, so congruent:
z = 69
__
The angle marked with an expression in x is supplementary to either of the other two:
(6x +69)° +69° = 180°
6x = 42 . . . . . . . . . . . . divide by °, subtract 138
x = 7 . . . . . . . . . . . . . . divide by 6
On average, a furniture store sells four card tables in a week. Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is most nearly Select one: a. 0.11 b. 0.075 c. 0.15 d. 0.060
Answers
Answer:
Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060
Step-by-step explanation:
In order to calculate the probability that the store will sell exactly seven card tables in a given week we would have to calculate the following formula:
probability that the store will sell exactly seven card tables in a given week= e∧-λ*λ∧x/x!
According to the given data furniture store sells four card tables in a week, hence λ=4
Therefore, probability that the store will sell exactly seven card tables in a given week=e∧-4*4∧7/7!
probability that the store will sell exactly seven card tables in a given week=0.060
Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060
The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.36, the analogous probability for the second signal is 0.51, and the probability that he must stop at least one of the two signals is 0.67.What is theprobability that he must stop.
a) At both signals?
b) At the first signal but not at the second one?
c) At exactly on signal?
Answers
Answer:
a) P(X∩Y) = 0.2
b) [tex]P_1[/tex] = 0.16
c) P = 0.47
Step-by-step explanation:
Let's call X the event that the motorist must stop at the first signal and Y the event that the motorist must stop at the second signal.
So, P(X) = 0.36, P(Y) = 0.51 and P(X∪Y) = 0.67
Then, the probability P(X∩Y) that the motorist must stop at both signal can be calculated as:
P(X∩Y) = P(X) + P(Y) - P(X∪Y)
P(X∩Y) = 0.36 + 0.51 - 0.67
P(X∩Y) = 0.2
On the other hand, the probability [tex]P_1[/tex] that he must stop at the first signal but not at the second one can be calculated as:
[tex]P_1[/tex] = P(X) - P(X∩Y)
[tex]P_1[/tex] = 0.36 - 0.2 = 0.16
At the same way, the probability [tex]P_2[/tex] that he must stop at the second signal but not at the first one can be calculated as:
[tex]P_2[/tex] = P(Y) - P(X∩Y)
[tex]P_2[/tex] = 0.51 - 0.2 = 0.31
So, the probability that he must stop at exactly one signal is:
[tex]P = P_1+P_2\\P=0.16+0.31\\P=0.47[/tex]
Identify the correct HYPOTHESIS used in a hypothesis test of the following claim and sample data: Claim: "The average annual household income in Warren County is $47,500." A random sample of 86 households from this county is obtained, and they have an average annual income of $48,061 with a standard deviation of $2,351. Test the claim at the 0.02 significance level.
Answers
Answer:
We accept H₀
Step-by-step explanation:
Population mean μ₀ = 47500
Population standard deviation unknown
Sample size n = 86 degree of freedom df = 86 - 1 df = 85
Sample mean μ = 48061
Sample standard deviation 2,351
The claim implies a two tail test with t-studend distributon
Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ ≠ μ₀
Confidence Interval mean α = 0,02 and α/2 = 0,01
With α/2 and df = 85, from t-table we find t(c) critical value
t(c) = 2,3710
We compute t(s) as
t(s) = ( μ - μ₀ ) / s /√n
t(s) = ( 48061 - 47500 )/ 2351/√86
t(s) = 561 * 9,273 / 2351
t(s) = 2,212
Now we compare t(s) and t(c)
t(s) < t(c) 2,212 < 2,371
Then we are in the acceptance region. We accept H₀
Hurry!! Determine the intervals for which the function shown below is decreasing.
Answers
Answer:
everywhere except between 2 and 5
(between -inf and 2 and between 5 and inf)
Step-by-step explanation:
How many meters are in 18,200 milliliter
Answers
Answer:
18.2 :)
Have a great day!!!
11- In
how many ways 3 mathematics books, 4 history books ,3
chemisidy books and a biology books can be arranged
on an Shelf so thet all books of the same subjects are
together!
Answers
Answer: 20,736
Step-by-step explanation:
Math and History and Chemistry and Biology and Subjects
3! x 4! x 3! x 1! x 4! = 20,736
Simplfy the following expressions:
Answers
Answer:
1st one = d y^27
2nd one = b 2x^9
Step-by-step explanation:
1st one: since the power is being raised to the power of 3 you multiply the numbers
2nd one: the powers aren't being raised so you add the powers together.
12x^13y^10/6X^4y^10
then dividing for exponents is subtracting them so
2x^9 since y gets canceled out
Brainliest to whoever gets this correct This word problem has too much information. Which fact is not needed to solve the problem? Tanisha tried to sell all her old CDs at a garage sale. She priced them at $2 each. She put 80 CDs in the garage sale, but she sold only 35 of them. How many did she have left? A. All of the information is needed. B. Tanisha sold the CDs for $2 each. C. Tanisha put 80 CDs in the sale. D. Tanisha sold 35 of the CDs.
Answers
Answer:
B. Tanisha sold the CDs for $2 each.
Step-by-step explanation:
Pls help see the picture posted
Answers
Which of the following points is NOT a solution of the inequality y ≥ Ixl + 3?
A. (-3, 0)
B. (-3, 6)
C. (0, 4)
Answers
Hey there!
To solve this, we need to plug each of our answer options into the inequality and see if it is true. Which ever one doesn't make the inequality true when plugged in is the answer.
OPTION A
(x,y)=(-3,0)
We plug our values into the inequality.
0≥ I-3I+3
You may have noticed the bars surrounding the negative three.. If you didn't know, this is called absolute value. Absolute value is how far the number is from 0 on the number line. -7 is 7 away from 0 on a number line, so the absolute value of -7 is 7. The absolute value of 7 is 7. The absolute value of 0 is 0. Absolute value is signified by these bars. Le'ts finish evaluating.
0≥6
As you can see, zero is not greater than or equal to six. So, option A is false.
Since A is not a solution, we already know that that is the answer, so we don't even need to check B and C. But, we can still evaluate them if you want.
OPTION B
6≥I-3I+3
6≥6
This is true.
OPTION C
4≥I0I+3
4≥3
This is also true.
Therefore, the answer is A. (-3,0)
Have a wonderful day!
Use the standard normal table to find P(z ≥ 1.06). Round to the nearest percent.
Answers
Answer:
14%
Step-by-step explanation:
On edge 2020