Answer: A. (636.9, 653.1)
Step-by-step explanation:
Given : Sample size : n=56
Significance level :![\alpha: 1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3A%201-0.95%3D0.05)
Critical value :![z_{0.05}=1.96](https://tex.z-dn.net/?f=z_%7B0.05%7D%3D1.96)
Sample mean : ![\overline{x}=645\text{ hours}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%3D645%5Ctext%7B%20hours%7D)
Standard deviation : ![\sigma= 31\text{ hours}](https://tex.z-dn.net/?f=%5Csigma%3D%2031%5Ctext%7B%20hours%7D)
The 95% confidence interval for population mean is given by :-
![\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=645\pm (1.96)\dfrac{31}{\sqrt{56}}\\\\=645\pm8.1\\\\=(636.9, 653.1)](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C%5C%5C%3D645%5Cpm%20%281.96%29%5Cdfrac%7B31%7D%7B%5Csqrt%7B56%7D%7D%5C%5C%5C%5C%3D645%5Cpm8.1%5C%5C%5C%5C%3D%28636.9%2C%20653.1%29%20)
Hence, 95% confidence interval for population mean is (636.9, 653.1).
Answer:
use the symmetric and transitive properties of congruence
Step-by-step explanation:
(1) ∠ABC ≅ ∠DEF and ∠GHI ≅ ∠DEF; given
(2) ∠DEF ≅ ∠GHI; symmetric property of congruence
(3) ∠ABC ≅ ∠GHI; transitive property of congruence (QED)
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<em>Additional comment</em>
The transitive property says if A≅B and B≅C, then A≅C. We used the symmetric property to swap sides of the congruence symbol with DEF and GHI to put the statement in the form to match the transitive property.
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You will note we used the form ...
(statement number) statement; reason
with statement and reason separated by a semicolon.
I believe the answer is 48.5 because 97 percent of 50 is 48.5
Hi there! :)
Answer:
![\huge\boxed{C}](https://tex.z-dn.net/?f=%5Chuge%5Cboxed%7BC%7D)
To simplify the process, convert each given weight into standard notation:
Lion:
![1 * 10^{5} = 1 * 100000 = 100,000 g](https://tex.z-dn.net/?f=1%20%2A%2010%5E%7B5%7D%20%3D%201%20%2A%20100000%20%3D%20100%2C000%20g)
Ant:
![2 * 10^{-3} = 2* 0.001 = 0.002](https://tex.z-dn.net/?f=2%20%2A%2010%5E%7B-3%7D%20%20%3D%20%202%2A%200.001%20%3D%200.002)
Divide the ant's weight from the lion's weight:
![100000 / 0.002 = 50,000,000](https://tex.z-dn.net/?f=100000%20%2F%200.002%20%3D%2050%2C000%2C000)
Convert to scientific notation: (use # of zeros to determine exponent)
Therefore, the correct answer is C.
Answer:
C, 8625
Step-by-step explanation:
The towns population was increased by 115%, so we have to get how much 15% of 7500 is.
15% x 7500 = 1125
We then add these two (1125, 7500) to get 8625.