Answer:
B. Sometimes
Step-by-step explanation:
Opposite angles of a parallelogram are always congruent, and consecutive angles are always supplementary (first image).
However, consecutive angles can be congruent if they are each 90°. The parallelogram is then a rectangle or a square (second image).
Thus, pairs of consecutive angles of a parallelogram are <u>sometimes</u> congruent.
Answer:
A function can be any set of points where one input is equal to one output. You cannot have two X values with the same Y value, for example.
<u>I believe the answer is neither</u> because in both sets you can see they have different Y values for the X values 2 and 9.
Answer: (17.42, 20.78)
Step-by-step explanation:
As per given , we have
Sample size : n= 9
years
Population standard deviation is not given , so it follows t-distribution.
Sample standard deviation : s= 1.5 years
Confidence level : 99% or 0.99
Significance level : ![\alpha= 1-0.99=0.01](https://tex.z-dn.net/?f=%5Calpha%3D%201-0.99%3D0.01)
Degree of freedom : df= 8 (∵df =n-1)
Critical value : ![t_c=t_{(\alpha/2,\ df)}=t_{0.005,\ 8}= 3.355](https://tex.z-dn.net/?f=t_c%3Dt_%7B%28%5Calpha%2F2%2C%5C%20df%29%7D%3Dt_%7B0.005%2C%5C%208%7D%3D%203.355)
The 99% confidence interval for the population mean would be :-
![\overline{x}\pm t_c\dfrac{s}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Coverline%7Bx%7D%5Cpm%20t_c%5Cdfrac%7Bs%7D%7B%5Csqrt%7Bn%7D%7D)
![19.1\pm (3.355)\dfrac{1.5}{\sqrt{ 9}}\\\\=19.1\pm1.6775\\\\=(19.1-1.6775,\ 19.1+1.6775)\\\\=(17.4225,\ 20.7775)\approx(17.42,\ 20.78)](https://tex.z-dn.net/?f=19.1%5Cpm%20%283.355%29%5Cdfrac%7B1.5%7D%7B%5Csqrt%7B%209%7D%7D%5C%5C%5C%5C%3D19.1%5Cpm1.6775%5C%5C%5C%5C%3D%2819.1-1.6775%2C%5C%2019.1%2B1.6775%29%5C%5C%5C%5C%3D%2817.4225%2C%5C%2020.7775%29%5Capprox%2817.42%2C%5C%2020.78%29)
Hence, the 99% confidence interval for the population mean is (17.42, 20.78) .
<h2>Steps</h2>
So for this system, one equation will represent the number of fruit and the other equation will represent the combined total of the fruit. (Let x = apples and y = bananas):
![x+y=20\\0.5x+0.75y=11.50](https://tex.z-dn.net/?f=x%2By%3D20%5C%5C0.5x%2B0.75y%3D11.50)
Next, I will be using the substitution method to remove one of the variables. To do this, firstly subtract both sides by y in the first equation:
![x=20-y\\0.5x+0.75y=11.50](https://tex.z-dn.net/?f=x%3D20-y%5C%5C0.5x%2B0.75y%3D11.50)
Next, since we know that x is equal to 20 - y, substitute it into the second equation and solve for y:
![0.5(20-y)+0.75y=11.50\\10-0.5y+0.75y=11.50\\10+0.25y=11.50\\0.25y=1.50\\y=6](https://tex.z-dn.net/?f=0.5%2820-y%29%2B0.75y%3D11.50%5C%5C10-0.5y%2B0.75y%3D11.50%5C%5C10%2B0.25y%3D11.50%5C%5C0.25y%3D1.50%5C%5Cy%3D6)
Now that we have the value of y, substitute it into either equation to solve for x:
![x+6=20\\x=14\\\\0.5x+0.75(6)=11.50\\0.5x+4.5=11.50\\0.5x=7\\x=14](https://tex.z-dn.net/?f=x%2B6%3D20%5C%5Cx%3D14%5C%5C%5C%5C0.5x%2B0.75%286%29%3D11.50%5C%5C0.5x%2B4.5%3D11.50%5C%5C0.5x%3D7%5C%5Cx%3D14)
<h2>Answer</h2>
<u>In short, Angelo bough 14 apples and 6 bananas.</u>