Answer:
30
Step-by-step explanation:
You’re correct
Answer:
Step-by-step explanation:
i think it is 7.5
Answer:
Q1: No solutions
Q2: x=2, y=-2
Q3: x=1, y=4
Step-by-step explanation:
Q1: Found out 0y = 18 which is impossible therefore no solution.
Q2:
In the first equation: ![2x - 4y = 12](https://tex.z-dn.net/?f=2x%20-%204y%20%3D%2012)
Let's express x in terms of y by changing the subject. Follow my steps.
![2x = 12+4y](https://tex.z-dn.net/?f=2x%20%3D%2012%2B4y)
![x = \frac{12+4y}{2}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B12%2B4y%7D%7B2%7D)
Now let's put the x above into the second equation: ![-14x-4y=-20](https://tex.z-dn.net/?f=-14x-4y%3D-20)
It becomes:
. Follow my steps.
![-7(12+4y)=-20+4y](https://tex.z-dn.net/?f=-7%2812%2B4y%29%3D-20%2B4y)
![-84-28y=-20+4y](https://tex.z-dn.net/?f=-84-28y%3D-20%2B4y)
![-32y=64](https://tex.z-dn.net/?f=-32y%3D64)
![y=-2](https://tex.z-dn.net/?f=y%3D-2)
Put y = -2 into the first equation:
![2x-4(-2)=12](https://tex.z-dn.net/?f=2x-4%28-2%29%3D12)
![2x+8=12](https://tex.z-dn.net/?f=2x%2B8%3D12)
![2x=12-8](https://tex.z-dn.net/?f=2x%3D12-8)
![2x=4](https://tex.z-dn.net/?f=2x%3D4)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Q3:
Multiply the first equation by 3 and the second equation by 7, so that both are 21x.
1st equation:
![3(7x-3y)=3(-5)](https://tex.z-dn.net/?f=3%287x-3y%29%3D3%28-5%29)
![21x-9y=-15](https://tex.z-dn.net/?f=21x-9y%3D-15)
2nd equation:
![7(3x+2y) = 7(11)](https://tex.z-dn.net/?f=7%283x%2B2y%29%20%3D%207%2811%29)
![21x+14y = 77](https://tex.z-dn.net/?f=21x%2B14y%20%3D%2077)
We can now substract the 2nd equation with the 1st equation so that both 21x cancels out and only the variable y remains.
![21x-9y-(21x+14y)=-15-77](https://tex.z-dn.net/?f=21x-9y-%2821x%2B14y%29%3D-15-77)
![21x-9y-21x-14y=-92](https://tex.z-dn.net/?f=21x-9y-21x-14y%3D-92)
![-23y=-92](https://tex.z-dn.net/?f=-23y%3D-92)
![y=4](https://tex.z-dn.net/?f=y%3D4)
Put y = 4 into the second equation to find x.
![3x+2(4)=11](https://tex.z-dn.net/?f=3x%2B2%284%29%3D11)
![3x+8=11](https://tex.z-dn.net/?f=3x%2B8%3D11)
![3x=11-8](https://tex.z-dn.net/?f=3x%3D11-8)
![3x = 3](https://tex.z-dn.net/?f=3x%20%3D%203)
![x=1](https://tex.z-dn.net/?f=x%3D1)
It depends on what ingredients you need , and omg i love bts too who’s your bio??
<h2><u>
Answer with explanation:</u></h2>
Let
be the population mean.
Null hypothesis : ![\mu=12](https://tex.z-dn.net/?f=%5Cmu%3D12)
Alternative hypothesis : ![\mu](https://tex.z-dn.net/?f=%5Cmu%3C12)
Since Alternative hypothesis is left tailed so , the test is a left tailed test.
Given : n=33 > 30 , so we use z-test.
Test statistic : ![z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B%5Coverline%7Bx%7D-%5Cmu%7D%7B%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
i.e. ![z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B11.2-12%7D%7B%5Cdfrac%7B1.6%7D%7B%5Csqrt%7B33%7D%7D%7D%5Capprox-2.87)
Using z-value table,
P-value for left tailed test =![P(z](https://tex.z-dn.net/?f=P%28z%3C-2.87%29%3D0.0020524)
Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.
Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.