You entered a contest through your local television station. There is one first prize of a new car! There are 5 second place pri
2 answers:
Answer:
or 0.0025 0r 0.25%
Step-by-step explanation:
There are three categories that will get a prize
1) First place = 1 person
2) Second place = 5 persons
3) Third place = 20 persons
A total of 26 people will get prizes.
However, we want to determine your chance to win one of the second place prizes
There are 5 prizes in second place
This means out of a total of 2000 people, you could be among the 5
i.e 5 out of 2000
This is
This means you have a chance of 1 out of 400
= 0.25%
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1. The distance between the perihelion and the aphelion is 116 million miles
2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles
3. The equation of the elliptical orbit of Mercury is
4. The eccentricity of the ellipse is 0.207 to the nearest thousandth
5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle
Step-by-step explanation:
Let us revise the equation of the ellipse is
, where the major axis is parallel to the x-axis
- The length of the major axis is 2a
- The coordinates of the vertices are (± a , 0)
- The coordinates of the foci are (± c , 0) , where c² = a² - b²
∵ The Sun is located at a focus of the ellipse
∴ The sun located ate c
∵ The perihelion is the point in a planet’s orbit that is closest to the
Sun ( it is the endpoint of the major axis that is closest to the Sun )
∴ The perihelion is located at the vertex (a , 0)
∵ The closest Mercury comes to the Sun is about 46 million miles
∴ The distance between a and c is 46 million miles
∵ The aphelion is the point in the planet’s orbit that is furthest from
the Sun ( it is the endpoint of the major axis that is furthest from
the Sun )
∴ The aphelion is located at the vertex (-a , 0)
∵ The farthest Mercury travels from the Sun is about 70 million miles
∴ The distance from -a to c is 70 million miles
∴ The distance between the perihelion and the aphelion =
70 + 46 = 116 million miles
1. The distance between the perihelion and the aphelion is 116 million miles
∵ The distance between the perihelion and the aphelion is the
length of the major axis of the ellipse
∵ The length of the major axis is 2 a
∴ 2 a = 116
- Divide both sides by 2
∴ a = 58
∴ The distance from the center of Mercury’s elliptical orbit to the
closest end point to the sun is 58 million miles
∵ The distance between the sun and the closest endpoint is
46 million miles
∴ The distance from the center of Mercury’s elliptical orbit and
the Sun = 58 - 46 = 12 million miles
2. The distance from the center of Mercury’s elliptical orbit and the Sun is 12 million miles
∵ The major axis runs horizontally
∴ The equation is
∵ a = 58
∵ c is the distance from the center to the focus of the ellipse
∴ c = 12
∵ c² = a² - b²
∴ (12)² = (58)² - b²
- Add b² to both sides
∴ (12)² + b² = (58)²
- Subtract (12)² from both sides
∴ b² = (58)² - (12)² = 3220
- Substitute these values in the equation
∴
3. The equation of the elliptical orbit of Mercury is
The eccentricity (e) of an ellipse is the ratio of the distance from the
center to the foci (c) and the distance from the center to the
vertices (a) ⇒
∵ c = 12
∵ a = 58
∴ = 0.207
4. The eccentricity of the ellipse is 0.207 to the nearest thousandth
If the eccentricity is zero, it is not squashed at all and so remains a circle.
If it is 1, it is completely squashed and looks like a line
∵ The eccentricity of the ellipse is 0.207
∵ This number is closed to zero than 1
∴ The shape of the ellipse is near to the shape of the circle
5. The value of the eccentricity tell you that the shape of the ellipse is near to the shape of the circle
Learn more:
You can learn more about conics section in brainly.com/question/4054269
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Answer:
$16.
Step-by-step explanation:
Let t represent the cost of each tree.
We have been given that Yuri purchased 8 trees to have planted at his house. So the cost of 8 trees will be 8t.
We are also told that the store charged a delivery fee of $5 per tree. So the delivery charges of 8 trees will be
The total cost of purchasing 8 trees will be .
Since the total cost of the trees including the delivery was $168, so we can get an equation as:
Upon dividing both sides of our given equation by 8, we will get:
Therefore, the cost of each tree is $16.
Answer:
No, the bid is not correct.
Step-by-step explanation:
One of your employees is bidding on a carpet installation job.
They estimate that it will take 3 hours to install 12 square yards of carpeting.
we know that 1 square yard= 9 square foot.
12 square yard= 12×9 square foot=108 square foot
i.e. it takes 3 hours to carpet 108 square foot.
Hence time taken to carpet 1 square foot= hour
Now the dimension of room is:
11' 6"× 12' 9" i.e. we convert both the units to foot as:
1 foot= 12 inch
11'6"=11+(6/12)=11.5 foot.
and 12'9"=12+(9/12)=12.75 foot.
Hence, dimension of room=11.5 foot×12.75 foot
Hence area of room=11.5×12.75=146.625 square foot.
Time to carpet 146.625 square foot=
hour
=4.0729 hour
But it is given that it takes 12.3 hours to install the carpet.
Hence, the calculations were wrong.