m₁ = mass hanged initially = 0.2 kg
x₁ = initial stretch in the spring = 8 cm = 0.08 m
k = spring constant of the spring
the weight of the mass hanged is balanced by the spring force by the spring hence
Spring force = weight of mass hanged
k x₁ = m₁ g
k (0.08) = (0.2) (9.8)
k = 24.5 N/m
m₂ = mass hanged later = 0.5 kg
x₂ = final stretch in the spring = ?
k = spring constant of the spring = 24.5 N/m
the weight of the mass hanged is balanced by the spring force by the spring hence
Spring force = weight of mass hanged
k x₂ = m₂ g
(24.5) x₂ = (0.5) (9.8)
x₂ = 0.2 m = 20 cm
Answer:
Step-by-step explanation:
Location Reflect over x Reflect over y
B -0.75 ,1 -0.75 ,-1 +0.75 ,1
C 1.75 ,-1 1.75,1 -1.75,+1
D -2,-2 -2,+2 +2 ,-2
Answer:
Then the minimum sample size in order to satisfy the condition of 0.1 for the margin of error is 97 and since the sample used is n =100 we can conclude that is sufficient and the best answer would be:
D. Yes.
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. We know that we require a 95% of confidence, our significance level would be given by 
and 
. And the critical value would be given by:
The margin of error for the proportion interval is given by this:
(a)
We want a margin of error of 
and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
Since we don't have prior info for the population proportion we can use as estimator the value of 0.5. And replacing into equation (b) the values from part a we got:
Then the minimum sample size in order to satisfy the condition of 0.1 for the margin of error is 97 and since the sample used is n =100 we can conclude that is sufficient and the best answer would be:
D. Yes.
Answer:
The answer is 60in^2
Step-by-step explanation:
Answer:
The rate of change was 3.5 degrees / h.
Step-by-step explanation:
In order to calculate the rate of change we need to divide the variation of temperature by the variation of time. Since the time is given to us in a 12 h format (am/pm), we first need to convert it to 24 h. To do that we sum the time that is "pm" by 12, we have:
time2 = 3 + 12 = 15
Therefore the rate of change in temperature is:
rate = variation of temp / variation of time
rate = (temp final - temp init) / (time final - time init)
rate = (82 - 54) / (15 - 7) = 28 / 8 = 3.5 degrees / h
The rate of change was 3.5 degrees / h.
