Using Gaussian elimination:
x + y + z = 9 / * ( - 2 ) / ( - 1 ) ( we will multiply by - 2 and add to the 2nd 2 x - 3 y + 4 z = 7 equation and multiply by - 1 and add to the 3rd equation )
x - 4 y + 3 z = - 2
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x + y + z = 9
- 5 y + 2 z = - 11 / * ( - 1 )
- 5 y + 2 z = - 11
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x + y + z = 9
- 5 y + 2 z = - 11
0 z = 0
There are infinitely many solutions to the system of equations.
z = t,
- 5 y + 2 t = - 11
5 y = 11 + 2 t
y = ( 11 + 2 t ) / 2
x + ( 11 + 2 t ) / 2 + t = 9 / * 2
2 x + 11 + 2 t + 2 t = 18
2 x = 18 - 11 - 4 t
x = ( 7 - 4 t ) / 2
( x, y , z ) = ( (7 - 4 t ) / 2, ( 11 + 2 t ) / 2, t )
Answer:
The probability of selecting a sample which doesn't capture the true value of μ would be 10% rather than 5% if they decide to calculate a 90% confidence interval rather than a 95% confidence interval from the sample they will select.
Step-by-step explanation:
The correct answer is the last statement, but first, let's look at the other statements:
<em>Their confidence interval would be less likely to capture the </em><em>sample </em><em>mean.</em>
This statement is not correct because the <em>confidence </em>of a confidence interval gives us the probability of capturing the true value of the population mean.
<em>They would </em><em>decrease </em><em>the margin of error of their confidence interval if they calculated a 90% rather than a 95% confidence interval.</em>
If we want more confidence we must establish more precision, which means more error. In other words if the confidence increases so does the error for a fixed sample size. The second statement is false.
<em>The probability of selecting a sample which doesn't capture the true value of μ would be 10% rather than 5% if they decide to calculate a 90% confidence interval rather than a 95% confidence interval from the sample they will select.</em>
As stated before the <em>confidence </em>of a confidence interval is the probability that the interval contains the true value of μ. Therefore, if we increase the confidence from 95% to 90% then this probability also increases. A 90% confidence means that there's a 10% probability of not containing the true mean. Likely, a 95% confidence means that there's a 5% probability of not containig the true mean. The third statement is true.
√ (( x - 1) / x^5) = 1/√x^4 · √(1 - 1/x )= 1/x² · √( 1 - 1/x )
Substitution:
u = 1 - 1/x
d u = 1/x² dx
You were right, A is 7/8.
So each bar contains 6 and she has 20 so 6 times 20=120
pyramid volume=legnth times width times height times 1/3
v=base times height times 1/2
v=1 times 2 times 1/3
v=2/3
volume of 1 pyramid is 2/3 cubic inches
divide 120 by 2/3 to find out how many pyrimds will fit into amount given
120/1 divide by 2/3=120/1 times 3/2=360/2=180
she can make 180 pyramids
