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Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the general equation of an ellipse
![\frac{\mleft(x-h\mright)^2}{a^2}+\frac{(y-h)^2}{b^2^{}}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmleft%28x-h%5Cmright%29%5E2%7D%7Ba%5E2%7D%2B%5Cfrac%7B%28y-h%29%5E2%7D%7Bb%5E2%5E%7B%7D%7D%3D1)
STEP 2: Identify the parameters
the length of the major axis is 2a
the length of the minor axis is 2b
![\begin{gathered} 2a=24,a=\frac{24}{2}=12 \\ 2b=20,b=\frac{20}{2}=10 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202a%3D24%2Ca%3D%5Cfrac%7B24%7D%7B2%7D%3D12%20%5C%5C%202b%3D20%2Cb%3D%5Cfrac%7B20%7D%7B2%7D%3D10%20%5Cend%7Bgathered%7D)
STEP 3: Get the equation of the ellipse
![\begin{gathered} By\text{ substitution,} \\ \frac{(x-h)^2}{a^2}+\frac{(y-h)^2}{b^2}=1 \\ \frac{(x-0)^2}{12^2}+\frac{(y-0)^2}{10^2}=1=\frac{x^2}{144}+\frac{y^2}{100}=1 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20By%5Ctext%7B%20substitution%2C%7D%20%5C%5C%20%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D%2B%5Cfrac%7B%28y-h%29%5E2%7D%7Bb%5E2%7D%3D1%20%5C%5C%20%5Cfrac%7B%28x-0%29%5E2%7D%7B12%5E2%7D%2B%5Cfrac%7B%28y-0%29%5E2%7D%7B10%5E2%7D%3D1%3D%5Cfrac%7Bx%5E2%7D%7B144%7D%2B%5Cfrac%7By%5E2%7D%7B100%7D%3D1%20%5Cend%7Bgathered%7D)
STEP 4: Pick the nearest equation from the options,
Hence, the equation of the ellipse in the image is given as:
![\frac{x^2}{144}+\frac{y^2}{95}=1](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%7D%7B144%7D%2B%5Cfrac%7By%5E2%7D%7B95%7D%3D1)
OPTION A
Answer:
A.
Step-by-step explanation:
A. City voters were asked about candidates. That seems to be random.
B. A survey about singers took place at a specific concert. Naturally, the people who are there like this singer. It is not random.
C. Customers were asked about food at a pizza shop. Naturally, they like pizza. This is not random.
D. An email survey was sent. Mostly people who own computers will respond. This is not random.
Answer: A.
Answer:
x = 26 , y = 33
Step-by-step explanation:
3x + 2y = 144 (1)
2x + 5y = 217 (2)
3x + 2y = 144
(divide the equation by 3)
x + (2/3)y = 48
x = 48 - (2/3)y
Plug into (2)
2[48 - (2/3)y] + 5y = 217
96 - (4/3)y + 5y = 217
11y/3 = 217 - 96
11y/3 = 121
y = 121×3/11
y = 33
x = 48 - (2/3)y
x = 48 - (2/3)(33)
x = 48 - 22
x = 26
48 books
1 yard = 36in
2 yard = 72in
72 / 1.5 = 48
4 can go into 72 18 times