Answer:
Step-by-step explanation:
![2x - 4y = - 20 \\ \\ - 4y = - 2x - 20 \\ \\ y = \frac{ - 2}{ - 4}x - \frac{20}{ - 4} \\ \\ y = \frac{1}{2} x + 5](https://tex.z-dn.net/?f=2x%20-%204y%20%3D%20%20-%2020%20%5C%5C%20%20%5C%5C%20%20-%204y%20%3D%20%20-%202x%20-%2020%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B%20-%202%7D%7B%20-%204%7Dx%20%20-%20%20%5Cfrac%7B20%7D%7B%20-%204%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20x%20%2B%205)
Answer:
When f or g are equivalent to a number you are solving for x. For example b, d, e, f. In the equation g(x) =2x2-5 I assumed 2 was a typo. So, if it's incorrect, please use same steps and just adjust the solution.
Step-by-step explanation:
![f(x)=-\frac{2}{3x}+3](https://tex.z-dn.net/?f=f%28x%29%3D-%5Cfrac%7B2%7D%7B3x%7D%2B3)
a)
![=\frac{5}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B5%7D%7B3%7D)
b) ![f(x)=-5](https://tex.z-dn.net/?f=f%28x%29%3D-5)
![-8=-\frac{2}{3x}](https://tex.z-dn.net/?f=-8%3D-%5Cfrac%7B2%7D%7B3x%7D)
![-24x=-2](https://tex.z-dn.net/?f=-24x%3D-2)
![x=\frac{1}{12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B12%7D)
![g(x)=2x-5](https://tex.z-dn.net/?f=g%28x%29%3D2x-5)
c) ![g(-3)=2(-3)-5](https://tex.z-dn.net/?f=g%28-3%29%3D2%28-3%29-5)
![=-6-5](https://tex.z-dn.net/?f=%3D-6-5)
![=-11](https://tex.z-dn.net/?f=%3D-11)
d) ![g(x)=-7](https://tex.z-dn.net/?f=g%28x%29%3D-7)
![-7=2x-5](https://tex.z-dn.net/?f=-7%3D2x-5)
![-2=2x](https://tex.z-dn.net/?f=-2%3D2x)
![x=-1](https://tex.z-dn.net/?f=x%3D-1)
e) ![g(x)=8](https://tex.z-dn.net/?f=g%28x%29%3D8)
![8=2x-5](https://tex.z-dn.net/?f=8%3D2x-5)
![12=2x](https://tex.z-dn.net/?f=12%3D2x)
![x=6](https://tex.z-dn.net/?f=x%3D6)
f) ![g(x)=9](https://tex.z-dn.net/?f=g%28x%29%3D9)
![9=2x-5](https://tex.z-dn.net/?f=9%3D2x-5)
![11=2x](https://tex.z-dn.net/?f=11%3D2x)
![x=\frac{11}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B11%7D%7B2%7D)
The answer is 24. To get from one term to the next, you have to find the difference. To get from 52 to 45, you minus 7. It is the same with the other terms. So 31 - 7 = 24
Answer:
Test:
< 20 with normal distⁿ
Hypothesis test:
H0:
20 (Null Hypothesis, H₀ :
= 20 is also correct)
H1:
< 20 (Alternative Hypothesis, also called H₁)
This is lower tailed test.
Since sample is large, sample standard deviation can be taken as an approximation of population standard deviation.
x = 19.3
= 11.1
n = 444
significance level,
= 0.05 (If no value is given, we take level of 0.05)
Test statistic ![z* = \frac{x-\mu}{\sigma/\sqrt{n}}](https://tex.z-dn.net/?f=z%2A%20%3D%20%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%2F%5Csqrt%7Bn%7D%7D)
![= \frac{19.3-20}{11.1/\sqrt{444}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B19.3-20%7D%7B11.1%2F%5Csqrt%7B444%7D%7D)
= - 1.33
The attached files contains additional information
The Brady family received 1 letter on July 28.
Step-by-step explanation:
Step 1:
Assume a = the number of letters, b = the number of bills, c = the number of ads, and d = the number of magazines.
From the question, they got 15 pieces of mail that day so ![a+b+c+d=15.](https://tex.z-dn.net/?f=a%2Bb%2Bc%2Bd%3D15.)
They got 5 more magazines than bills so ![d = b + 5.](https://tex.z-dn.net/?f=d%20%3D%20b%20%2B%205.)
The got the same number of letters as ads so ![a=c.](https://tex.z-dn.net/?f=a%3Dc.)
They got 3 more bills than ads so ![b= c + 3.](https://tex.z-dn.net/?f=b%3D%20c%20%2B%203.)
Step 2:
As we have only one equation to solve the values, we need to make every term in terms of a single term.
We make everything in terms of c.
So ![a=c, b = c+3, c=c, d = b+5 = (c+3)+5=c+8.](https://tex.z-dn.net/?f=a%3Dc%2C%20b%20%3D%20c%2B3%2C%20c%3Dc%2C%20d%20%3D%20b%2B5%20%3D%20%28c%2B3%29%2B5%3Dc%2B8.)
Substituting all this in the equation, we get
![a + b+c+d =(c)+(c+3)+(c)+(c+8) = 15, 4c+11=15.](https://tex.z-dn.net/?f=a%20%2B%20b%2Bc%2Bd%20%3D%28c%29%2B%28c%2B3%29%2B%28c%29%2B%28c%2B8%29%20%3D%2015%2C%204c%2B11%3D15.)
![4c=4, c = 1.](https://tex.z-dn.net/?f=4c%3D4%2C%20c%20%3D%201.)
Step 3:
Substituting c = 1 in other terms, we get
![a=c=1,](https://tex.z-dn.net/?f=a%3Dc%3D1%2C)
![b=c+3=1+3=4,](https://tex.z-dn.net/?f=b%3Dc%2B3%3D1%2B3%3D4%2C)
and
![d = c+8 = 1+8=9.](https://tex.z-dn.net/?f=d%20%3D%20c%2B8%20%3D%201%2B8%3D9.)
As a = 1, they received 1 letter that day.