The table shows different possibilities for the number of students to the number of fans present at a football game. Which ratio
of the number of students to the number of fans at a football game could also be included in this table?
Question 10 options:
2:32
7:49
16:110
63:9
Question 10 options:
2:32
7:49
16:110
63:9
1 answer:
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Answer:
a) 40 feet
b) 54 ft/min
c) 4 mins
Step-by-step explanation:
Solution:-
- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.
- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:
h ( t ) = −16t² + 54t + 40
Which gives the height of the baton from ground at time t mins.
- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.
- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:
h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40
h ( 0 ) = hi = 0 + 0 + 40 = 40 feet
Answer: The height of the platform hi is 40 feet.
- The speed ( v ) during the parabolic path of the baton also varies with time t.
- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.
v ( t ) = dh / dt
v ( t )= d ( −16t² + 54t + 40 ) / dt
v ( t )= -2*(16)*t + 54
v ( t )= -32t + 54
- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.
Hence,
v ( 0 ) = vi = -32*( 0 ) + 54
v ( 0 ) = vi = 54 ft / min
Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min
- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.
- The height of the ball at ground is zero. Hence,
h ( t ) = 0
0 = −16t² + 54t + 40
0 = -8t^2 + 27t + 20
- Use the quadratic formula to solve the quadratic equation:
Answer: The time taken for the baton to hit the ground is t = 4 mins
Answer:
Obese people
Lean People
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution, "almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ). Broken down, the empirical rule shows that 68% falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ)".
Solution to the problem
Obese people
Let X the random variable that represent the minutes of a population (obese people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
Lean People
Let X the random variable that represent the minutes of a population (lean people), and for this case we know the distribution for X is given by:
Where and
On this case we know that 95% of the data values are within two deviation from the mean using the 68-95-99.7 rule so then we can find the limits liek this:
The interval for the lean people is significantly higher than the interval for the obese people.
The easiest way to solve this is to divide the shape into 2 rectangles.
The first rectangle being the big one on the left with the 12 and 6
and the second one being the little one on the right, next to it with the 5
So 12 x 6 = 72 (dont pay attention to the 7, 5, or 10, because all we need is 1 length and 1 width)
And for the smaller one it is a little bit trickier.
So on the bottom we see that is says 10ft, but we cant use that because what we really need is the measurement between the 5 and 7 on the top of the little rectangle
At the top we see that it says 6ft
We can do 10-6 to find the missing measurement.
Because the length of the whole like is 10, and the length of one of the little lines is 6, so the length of 6 + some number =10
So 10-6 = 4
Which means the number we need is 4
So now we have 5 x 4 = 20
72 + 20 = 92
Answer: 92
I also attatched an image, I hope this helps! Ask me if you have any other questions about this problem!
The first rectangle being the big one on the left with the 12 and 6
and the second one being the little one on the right, next to it with the 5
So 12 x 6 = 72 (dont pay attention to the 7, 5, or 10, because all we need is 1 length and 1 width)
And for the smaller one it is a little bit trickier.
So on the bottom we see that is says 10ft, but we cant use that because what we really need is the measurement between the 5 and 7 on the top of the little rectangle
At the top we see that it says 6ft
We can do 10-6 to find the missing measurement.
Because the length of the whole like is 10, and the length of one of the little lines is 6, so the length of 6 + some number =10
So 10-6 = 4
Which means the number we need is 4
So now we have 5 x 4 = 20
72 + 20 = 92
Answer: 92
I also attatched an image, I hope this helps! Ask me if you have any other questions about this problem!