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miskamm [114]
3 years ago
5

Give a correct interpretation of a 99% confidence level of 0.328 < μ < 0.486.

Mathematics
1 answer:
stepladder [879]3 years ago
5 0

Answer:

D

Step-by-step explanation:

Lower bound of the population mean is 0.328

Upper bound of the population mean is 0.486

Confidence level is 99%

Therefore, the correct interpolation of the confidence interval is that we are 99% confident that the true value of the population mean is between 0.328 and 0.486

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Answer:

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What is the greatest common factor of 14 and 22​
Alecsey [184]

Answer:

2

Step-by-step explanation:

greatest common factor means the greatest number we can divide by for each of the number and still get a whole number

14 and 22. they are both even so one factor is 2

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Solve the nonhomogeneous differential equation y′′+25y=cos(5x)+sin(5x). Find the most general solution to the associated homogen
Marrrta [24]

Answer:

y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)

Step-by-step explanation:

The general solution will be the sum of the complementary solution and the particular solution:

y(x)=y_c(x)+y_p(x)

In order to find the complementary solution you need to solve:

y''+25y=0

Using the characteristic equation, we may have three cases:

Real roots:

y(x)=c_1e^{r_1x} +c_2e^{r_2x}

Repeated roots:

y(x)=c_1e^{rx} +c_2xe^{rx}

Complex roots:

y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i

Hence:

r^{2} +25=0

Solving for r :

r=\pm5i

Since we got complex roots, the complementary solution will be given by:

y_c(x)=c_1cos(5x)+c_2sin(5x)

Now using undetermined coefficients, the particular solution is of the form:

y_p=x(a_1cos(5x)+a_2sin(5x) )

Note: y_p was multiplied by x to account for cos(5x) and sin(5x) in the complementary solution.

Find the second derivative of y_p in order to find the constants a_1 and a_2 :  

y_p''(x)=10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)

Substitute the particular solution into the differential equation:

10a_2cos(5x)-25a_1xcos(5x)-10a_1sin(5x)-25a_2xsin(5x)+25(a_1xcos(5x)+a_2xsin(5x))=cos(5x)+sin(5x)

Simplifying:

10a_2cos(5x)-10a_1sin(5x)=cos(5x)+sin(5x)

Equate the coefficients of cos(5x) and sin(5x) on both sides of the equation:

10a_2=1\\\\-10a_1=1

So:

a_2=\frac{1}{10} =0.1\\\\a_1=-\frac{1}{10} =-0.1

Substitute the value of the constants into the particular equation:

y_p(x)=-0.1xa_1cos(5x)+0.1xsin(5x)

Therefore, the general solution is:

y(x)=y_c(x)+y_p(x)

y(x)=c_1cos(5x)+c_2sin(5x)+0.1xsin(5x)-0.1xcos(5x)

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3 years ago
Twice a number m minus three equals the sum of m and five
Leya [2.2K]

2m - 3 = m + 5

m = 8

2(8) - 3 = 13

(8) + 5 = 13

m = 8

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3 years ago
What value of n makes the equation true? -2n + 1.8 =3.2
stich3 [128]

Answer:

-0.7

Step-by-step explanation:

-2n+1.8=3.2

-2n=3.2-1.8

-2n=1.4

n=1.4/-2

n=-0.7

4 0
3 years ago
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