#10 -1/3m - 7 = 5 Solve the equation
1 answer:
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Answer:
The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 27 - 1 = 26
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0518
The margin of error is:
In which s is the standard deviation of the sample and n is the size of the sample.
In this question:
. So
The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.
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:
(a)2(89x+84)
(b)
Step-by-step explanation:
The dimensions of the larger rectangular field are:
- Length=5x + 12; Width = 9x + 14.
The dimensions of the smaller rectangular soccer field are:
- Length=5x; Width = 9x.
(a)Area of the part of the field that is outside the soccer field
=Area of the larger rectangular field - Area of the Soccer Field
=(5x+12)(9x+14)-5x(9x)
=(5x)(9x)+70x+108x+168-5x(9x)
=178x+168
=2(89x+84)
(b)Radius of the Semicircular Fountain =2x
From Part (a),
Area of the larger rectangular field - Area of the Soccer Field=178x+168
Area of the Semicircular Fountain =
Area of the Field that does not include the soccer field or the fountain.
=Area of the larger rectangular field - Area of the Soccer Field-Area of the Semicircular Fountain