For this case we define the following variables:
x: Number of party dresses
y: Number of suits
You have 30 hours per week to cut, that is, the first equation is given by:
![3x + 3y = 30\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C)
It is also known that 25 hours per week are available for sewing, that is:
![2x + 3y = 25\\](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%2025%5C%5C)
It has a system of two equations with two unknowns, solving we have:
![3x + 3y = 30\\\\2x + 3y = 25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C2x%20%2B%203y%20%3D%2025%5C%5C)
Multiplying the second equation by -1:
![3x + 3y = 30\\\\-2x-3y = -25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C-2x-3y%20%3D%20-25%5C%5C)
Adding up:
![x + 0 = 5\\\\x = 5\\](https://tex.z-dn.net/?f=x%20%2B%200%20%3D%205%5C%5C%5C%5Cx%20%3D%205%5C%5C)
Substituting x in the first equation:
![3 * 5 + 3y = 30\\\\15 + 3y = 30\\](https://tex.z-dn.net/?f=3%20%2A%205%20%2B%203y%20%3D%2030%5C%5C%5C%5C15%20%2B%203y%20%3D%2030%5C%5C)
Clearing and:
![3y = 30-15\\\\3y = 15\\](https://tex.z-dn.net/?f=3y%20%3D%2030-15%5C%5C%5C%5C3y%20%3D%2015%5C%5C)
![y = \frac{15}{3}\\\\y = 5\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B15%7D%7B3%7D%5C%5C%5C%5Cy%20%3D%205%5C%5C)
Thus, per week, the designer can produce 5 party dresses and 5 suits working at her maximum capacity.
Answer:
5 Party dresses
5 Suits
Assuming it's a linear equation, y= -1/2x
students that own a cell phone but don't own an MP3: 78 - 57 = 21
total number of student with no cell phone: 13 + 9 = 22
total number of student with a MP3 player: 57 + 13 = 70
total number of student without a MP3 player: 21 + 9 = 30
total number of students: 70 + 30 = 78 + 22 = 100
MP3 player no MP3 player Total
cell phone 57 21 78
no cell phone 13 9 22
Total 70 30 100
Answer:
Option D is right
Step-by-step explanation:
Given are two graphs. The first one is given as
![f(x) = log_{2} x\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%20log_%7B2%7D%20x%5C%5C)
The second one equation we have to find out.
Option A given as
is having x intercept as
(0,1/2). But our g(x) has x intercept as 1. Hence not correct.
Option B: ![g(x) = log_{2} \frac{1}{2} x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20log_%7B2%7D%20%5Cfrac%7B1%7D%7B2%7D%20x)
This has x intercept as (0,2). Since does not match with g(x) not correct
OPtion C:
![g(x) = log_{2} 2x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20log_%7B2%7D%202x)
Here x intercept = 1 matches with ours.
Also g(2) = 2, twice as that of original f(x)
Hence option C is not right
Option D is only right because x intercept should be 1 and also when x=4 y=2(log 4 to base 2)
Answer: 10/24
Hope that help :)