Answer: Supply is the total amount of goods available; quantity supplied is how much is made available at each price level.
1. quantity supplied increases
2. Supply is the total amount of goods available; quantity supplied is how much is made available at each price level.
3. perfectly inelastic
4. an artist
5. Price and quantity supplied move in the same direction; as price decreases, quantity supplied decreases and as price increases, quantity supplied increases.
Answer:
![2x+3y\geq 60\\x>10](https://tex.z-dn.net/?f=2x%2B3y%5Cgeq%2060%5C%5Cx%3E10)
Step-by-step explanation:
We know that she will be selling bracelets for $2 each and earrings for $3 each. That means we will have 2x+3y, where x is the number of bracelets she sells and y is the number of earrings she sells. Then we will have
because she wants to sell <u>at least $60</u> worth of earrings and bracelets. That means the amount she makes from bracelets and earrings combined has to equal 60 or more, thus we use the greater than or equal to sign.
Now we have
, where x is still the number of bracelets sold. She said she will sell <u>more than 10</u>, which means we will just have
. If she said she wanted to sell <u>at least 10</u>, then it would be
.
Therefore the system of inequalities is:
![2x+3y\geq60\\x>10](https://tex.z-dn.net/?f=2x%2B3y%5Cgeq60%5C%5Cx%3E10)
Hope this helps!
Answer:
![x=-18](https://tex.z-dn.net/?f=x%3D-18)
Step-by-step explanation:
<u>Given</u>
<u />![-x-x+11-2x=83](https://tex.z-dn.net/?f=-x-x%2B11-2x%3D83)
<u>Step 1: Combine Like Terms on LHS</u>
<u />![-x-x+11-2x=83\\-2x+11-2x=83\\-4x+11=83](https://tex.z-dn.net/?f=-x-x%2B11-2x%3D83%5C%5C-2x%2B11-2x%3D83%5C%5C-4x%2B11%3D83)
<u>Step 2: Subtract 11 on both sides</u>
<u />![-4x+11=83\\-4x+11-11=83-11\\-4x=72](https://tex.z-dn.net/?f=-4x%2B11%3D83%5C%5C-4x%2B11-11%3D83-11%5C%5C-4x%3D72)
<u>Step 3: Divide both sides by -4 to isolate the x-variable</u>
<u />![-4x=72\\\\\frac{-4x}{-4}=\frac{72}{-4}\\ \\ x=-18](https://tex.z-dn.net/?f=-4x%3D72%5C%5C%5C%5C%5Cfrac%7B-4x%7D%7B-4%7D%3D%5Cfrac%7B72%7D%7B-4%7D%5C%5C%20%5C%5C%20x%3D-18)
<u>Final Answer</u>
<u />![x=-18](https://tex.z-dn.net/?f=x%3D-18)
Answer:
<em>The equation which has no solution is 5 + 2(3 + 2x) = x + 3(x + 1) . </em>(see below for work)
Step-by-step explanation:
4(x + 3) + 2x = 6(x + 2)
4x + 12 + 2x = 6(x + 12)
4x + 2x = 6x
6x = 6x
x ∈ ℝ
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3(x + 3)
11 + 4x = x + 3x + 3
11 + 4x = 4x + 3
11 = 3
x ∈ ∅ (CORRECT ANSWER)
5(x + 3) + x = 4(x + 3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 12 + 3
6x + 15 = 4x + 15
6x = 4x
6x - 4x = 0
2x = 0
x = 0
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
4 ÷ 12 = 16
16 = 16
x ∈ ℝ
Hope this helps! :)
Answer: a) 83, b) 28, c) 14, d) 28.
Step-by-step explanation:
Since we have given that
n(B) = 69
n(Br)=90
n(C)=59
n(B∩Br)=28
n(B∩C)=20
n(Br∩C)=24
n(B∩Br∩C)=10
a) How many of the 269 college students do not like any of these three vegetables?
n(B∪Br∪C)=n(B)+n(Br)+n(C)-n(B∩Br)-n(B∩C)-n(Br∩C)+n(B∩Br∩C)
n(B∪Br∪C)=![69+90+59-28-20-24+10=156](https://tex.z-dn.net/?f=69%2B90%2B59-28-20-24%2B10%3D156)
So, n(B∪Br∪C)'=269-n(B∪Br∪C)=269-156=83
b) How many like broccoli only?
n(only Br)=n(Br) -(n(B∩Br)+n(Br∩C)+n(B∩Br∩C))
n(only Br)=![90-(28+24+10)=28](https://tex.z-dn.net/?f=90-%2828%2B24%2B10%29%3D28)
c) How many like broccoli AND cauliflower but not Brussels sprouts?
n(Br∩C-B)=n(Br∩C)-n(B∩Br∩C)
n(Br∩C-B)=![24-10=14](https://tex.z-dn.net/?f=24-10%3D14)
d) How many like neither Brussels sprouts nor cauliflower?
n(B'∪C')=n(only Br)= 28
Hence, a) 83, b) 28, c) 14, d) 28.