<h3>Answer:</h3>
Equation of the ellipse = 3x² + 5y² = 32
<h3>Step-by-step explanation:</h3>
<h2>Given:</h2>
- The centre of the ellipse is at the origin and the X axis is the major axis
- It passes through the points (-3, 1) and (2, -2)
<h2>To Find:</h2>
- The equation of the ellipse
<h2>Solution:</h2>
The equation of an ellipse is given by,
Given that the ellipse passes through the point (-3, 1)
Hence,
Cross multiplying we get,
- 9b² + a² = 1 ²× a²b²
- a²b² = 9b² + a²
Multiply by 4 on both sides,
- 4a²b² = 36b² + 4a²------(1)
Also by given the ellipse passes through the point (2, -2)
Substituting this,
Cross multiply,
- 4b² + 4a² = 1 × a²b²
- a²b² = 4b² + 4a²-------(2)
Subtracting equations 2 and 1,
- 3a²b² = 32b²
- 3a² = 32
- a² = 32/3----(3)
Substituting in 2,
- 32/3 × b² = 4b² + 4 × 32/3
- 32/3 b² = 4b² + 128/3
- 32/3 b² = (12b² + 128)/3
- 32b² = 12b² + 128
- 20b² = 128
- b² = 128/20 = 32/5
Substituting the values in the equation for ellipse,
Multiplying whole equation by 32 we get,
3x² + 5y² = 32
<h3>Hence equation of the ellipse is 3x² + 5y² = 32</h3>
Answer:
There can be at most 
attendees in a corporate team-building event.
Step-by-step explanation:
Let 
denotes number of attendees in a corporate team-building event.
Fixed cost = $19
Cost charged per attendee = $1
Budget for the corporate team-building event = $31
Therefore,
So, there can be at most attendees in a corporate team-building event.
Answer:
A. simpson's paradox
Step-by-step explanation:
The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.
Answer:
$2.83
Step-by-step explanation:
Diameter of the pool = 24ft
Cost of 1 ft² = $0.15
Area of the pool=?
But the pool is a circular pool,
Area of a circle = Πr² or πd²/4
π = 3.142
Area of the pool = (π * 24) / 4
Area = (3.142 * 24) / 4
Area = 18.85ft²
If 1ft² = $0.15
18.85 = $x
x = (18.85 * 0.15) / 1
x = $2.8275 = $2.83
The cost of the pool is $2.83
The perimeter is 35. If we were to change the width, which is one of the dimensions of the flower bed, The perimeter will change. This means that perimeter will no longer be 35. So in order to keep the perimeter as it is, if we change one dimension, we must also change the other. Let's solve for the length, using the formula to see how much the length changes from. p = 2l + 2w 35 = 2l + 2(15) 35 = 2l + 30 5 = 2l 2.5 = l We must increase the length from 2.5 feet. This is because decreasing one dimension will decrease the perimeter. But if we increase the other dimension as well, it will restore the perimeter to where is was initially.
