Answer:
k(x) + g(x) = x² - 3x + 4
General Formulas and Concepts:
<u>Alg I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = 3x - 7
g(x) = 2x² - 3x + 1
h(x) = 4x + 1
k(x) = -x² + 3
<u>Step 2: Find k(x) + g(x)</u>
- Substitute: k(x) + g(x) = -x² + 3 + 2x² - 3x + 1
- Combine like terms (x²): k(x) + g(x) = x² + 3 - 3x + 1
- Combine like terms (Z): k(x) + g(x) = x² - 3x + 4
A
Volume of the Cylinder
Givens
H = 60 yards.
Diameter = 20 yards
pi = 3.14
Formula
V = pi * r^2 * h
Calculations
r = d/2
r = 32/2
r = 16
V = 3.14 * 16^2 * 60
V = 48230 cubic yards [Cylinder's Volume]
Cone
<em>Formula</em>
V = 1/3 pi r^2 H
<em>Givens</em>
pi = 3.14
r = 16 yards
h = 20 yards
<em>Sub and solve</em>
V = 1/3 3.14 * 16^2 * 20
V = 5359 cubic yards.
<em>Total Volume of the structure</em>
48230 + 5359 = 53589 Cubic Yards
<em>Water Content</em>
The answer to this part requires a proportion.
1 Cubic yard will hold 201.97 gallons.
53589 yd^3 = x
1/201.97 = 53589 /x [ You should get a pretty big answer]
x = 201.87 * 53589
x = 10 819 092 gallons can be held by the tank.
10 819 092 gallons <<<< answer
B
If the height of both the cylinder and the cone remain the same. If the radius doubles in both the cylinder and the cone then the tank will hold 4 times as much.
Total volume before doubling the radius = pi * r^2 h + 1/3 pi r^2 h
New Total Volume = pi * (2*r)^2 h + 1/3 pi * (2r)^2 h
New Total volume = pi * 4r^2 h + 1/3 pi *4 r^2 h
New Total Volume = 4 [pi r^2 h + 1/3 pi r^2 h]
but pi r^2 h + 1/3 pi r^2 h is the total volume before doubling the radius
New volume = 4 original volume. <<<<< answer to part B
Based on the information represented by the boxplot ;
- Latasha's lowest sale amount = 50
- Kayla's median is between 200 and 300
- Latasha has a greater spread due to higher IQR value
1.) <em><u>The Lowest amount of sale made by Latasha in one month </u></em>
- The minimum value is denoted by the starting position of the lower whisker on a boxplot.
- Lowest amount of sale made by Latasha = 50
2.) <em><u>50</u></em><em><u>%</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>sales</u></em><em><u> </u></em><em><u>made</u></em><em><u> </u></em><em><u>by</u></em><em><u> </u></em><em><u>Kayla</u></em><em><u> </u></em><em><u>:</u></em>
- 50% of sales made marks the median value in a boxplot, it is denoted by the vertical line in between the box.
- 50% of sales made by Kayla is between 200 and 300
- With median sale value being 250
3.) <em><u>Spread</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>middle</u></em><em><u> </u></em><em><u>50</u></em><em><u>%</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>sales</u></em><em><u> </u></em><em><u>:</u></em>
- The measure of spread of the middle 50% of a distribution on a boxplot is the Interquartile range (IQR) of the distribution
- IQR = Upper Quartile (Q3) - Lower quartile(Q1)
<u>For Latasha</u> :
- Q3 = 450 (Endpoint of the box)
- Q1 = 150 (starting point of the box)
<u>For</u><u> </u><u>Kayla</u><u> </u><u>:</u><u> </u>
- Q3 = 375 (Endpoint of the box)
- Q1 = 100 (starting point of the box)
- IQR = 375 - 100 = 275
- Since, Latasha's IQR is greater than Kayla's, then Latasha has a greater mid 50% spread than Kayla.
Learn more :brainly.com/question/24582786
Answer:
His equation is correct but his calculations are incorrect.
Step-by-step explanation:
180-40=140 so y=140
Hope this helps!
