We are going to make simultaneous equations.
x will be our $3 ice cream and y will be our $5 ice cream
Equation1 ---- x + y = 50 (the sum of all the ice creams they sell)
Equation 2 ---- 3x + 5y = 180 Sum of all the $3 and $5 ice creams is $180
Since we can't solve for both variables we will put one of the variables in terms of the other.
Take x+y=50 and subtract y from both sides. (I could have done subtracted x - it did not matter). Now we have x= ₋ y +50 (negative y +50)
Now I am going to take equation 2 and replace the x with -y +50
3 (-y +50) + 5y = 180
Now I will use the distributive law on the 3 and what's in the parentheses:
-3y + 150 + 5y = 180
Now I will combine like terms (the -3y and the 5y)
2y + 150 = 180
Now subtract 150 from both sides of the equation
2y = 30
Divide both sides by 2
and get y= 15 They sold 15 ice creams that cost $5 each
Since equation 1 is x+y=50 we can replace y with 15
x + 15 = 50 Now subtract 15 from both sides x = 35
Since x represents the $3 ice creams, they sold 35 of those.
Check:
35 X 3 = $105
15 x 5 = + <u>75
</u> $180
Answer:
As per the given statement:
The region bounded by the given curves about the y-axis, 
, y=0, x = 0 and x = 1
Using cylindrical shell method:
The volume of solid(V) is obtained by rotating about y-axis and the region under the curve y = f(x) from a to b is;
where 
where x is the radius of the cylinder
f(x) is the height of the cylinder.
From the given figure:
radius = x
height(h) =f(x) =y=
a = 0 and b = 1
So, the volume V generated by rotating the given region:
![V =2 \pi \int_{0}^{1} x ( 13e^{-x^2}) dx\\\\V=2\pi\left [ -\frac{13}{2}e^{-x^2} \right ]_{0}^{1}\\\\V=2\pi\left (-\frac{13}{2e}-\left(-\frac{13}{2}\right) \right )\\\\V=-\frac{13\pi }{e}+13\pi](https://tex.z-dn.net/?f=V%20%3D2%20%5Cpi%20%5Cint_%7B0%7D%5E%7B1%7D%20x%20%28%2013e%5E%7B-x%5E2%7D%29%20dx%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%5B%20-%5Cfrac%7B13%7D%7B2%7De%5E%7B-x%5E2%7D%20%5Cright%20%5D_%7B0%7D%5E%7B1%7D%5C%5C%5C%5CV%3D2%5Cpi%5Cleft%20%28-%5Cfrac%7B13%7D%7B2e%7D-%5Cleft%28-%5Cfrac%7B13%7D%7B2%7D%5Cright%29%20%5Cright%20%29%5C%5C%5C%5CV%3D-%5Cfrac%7B13%5Cpi%20%7D%7Be%7D%2B13%5Cpi%20)
therefore, the volume of V generated by rotating the given region is 
Answer:
The revenue for Granton location is 175 thousand dollars
Step-by-step explanation:
Given
Cedarton 121
Rimber 189
Linton 147
Mean = 158
Required
Revenue for Granton location.
To calculate the revenue for Granton location, we make use of mean formula.
Mean is calculated by Summation of Observation divided by number of observations.
Since Granton location is unknown; Let it be represented by letter G.
So, the summation of observation becomes 121 + 189 + 147 + G
Summation = 457 + G
The number of observations = 4
Recall that Mean = Summation ÷ Number
By substituting 158 for mean, 457 + G for summation and 4 for number, we have
158 = (457 + G) ÷ 4
158 = ¼(457 + G)
Multiply both sides by 4
4 * 158 = = 4 * ¼(457 + G)
632 = 457 + G
Make G the subject of formula
G = 632 - 457
G = 175
Hence, the revenue for Granton location is 175 thousand dollars
Answer: the coomon factor that is missing from both sets of parentheses is 2x + 7.
Explanation:
These are the steps to factor the polynomial with the reasons that justify them:
Step Reason
1. 10x³ + 35x² - 4x - 14 Given
2. (10x³ + 35x²) - (4x + 14) Group the terms
3. 5x² (2x + 7) - 2 (2x + 7) Common factor 5x² and 2
After this, you extract common factor 2x + 7 and have the complete factored polynomial: (2x + 7) (5x² - 2).
Step-by-step explanation:
2y+3=5x-18
swap both sides
5x-18=2y+3
add 18 to both sides
5x-18+18=2y+3+18
5x=2y+21
divide both sides by
5x/5=2y+21/5
X=2y+21/5
