If a 24-kg mass stretches a spring 15 cm, what mass will stretch the spring 10 cm
1 answer:
Answer:
<h2>16kg</h2>Step-by-step explanation:
This problem is borers on elasticity of materials.
according to Hooke's law,<em> "provided the elastic limit of an elastic material is not exceeded the the extension e is directly proportional to the applied force."</em>
where F is the applied force in N
k is the spring constant N/m
e is the extension in meters
Given data
mass m= 24kg
extensnion=15cm in meters= =
we can solve for the spring constant k
we also know that the force F = mg
assuming
therefore
We can use this value of k to solve for the mass that will cause an extension of
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<h2>Hello!</h2>
The answer is:
Center: (1,-2)
Radius: 4 units.
<h2>Why?</h2>To solve the problem, using the given formula of a circle, we need to find its standard equation form which is equal to:
Where,
"h" and "k"are the coordinates of the center of the circle and "r" is its radius.
So, we need to complete the square for both variable "x" and "y".
The given equation is:
So, solving we have:
Now, we have that:
So,
Center: (1,-2)
Radius: 4 units.
Have a nice day!
Note: I have attached a picture for better understanding.
Answer:
The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.
Step-by-step explanation:
In this case we need to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Assume that the significance level of the test is, <em>α</em> = 0.05.
The hypothesis can be defined as follows:
<em>H</em>₀: The proportion of the population believes that passwords should be replaced with biometric security is 50%, i.e. <em>p</em> = 0.50.
<em>Hₐ</em>: The proportion of the population believes that passwords should be replaced with biometric security is more than 50%, i.e. <em>p</em> > 0.50.
The information provided is:
Compute the test statistic value as follows:
The test statistic value is 1.35.
The decision rule is:
The null hypothesis will be rejected if the p-value of the test is less than the significance level.
Compute the p-value as follows:
<em>p</em>-value = 0.088 > <em>α</em> = 0.05.
The null hypothesis will not be rejected at 5% significance level.
Thus, there is not enough evidence to support the claim.
Conclusion:
The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.