An overhead garage door has two springs, one on each side of the door. A force of 15 pounds is required to stretch each spring 1
1 answer:
Answer:
120 pounds
Step-by-step explanation:
Data provided in the question:
Force applied, F₁ = 15 pounds
Displacement by Force F₁, x₁ = 1 foot
At natural length of the spring total movement of the door = 8 feet
Now,
we know,
Force in spring, F = kx
where, k is the spring constant
Thus,
15 = k(1) ............(1)
now when the door travels half the distance x₂ = = 4 feet
Therefore,
F₂ = k(4) ..........(2)
Dividing 2 by 1
we get
or
or
F = 15 × 4 = 60 pounds
Thus,
for 2 springs combined force applied = 2 × 60 pounds = 120 pounds
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9514 1404 393
Answer:
see the attachment
Step-by-step explanation:
The x- and y-intercepts are easily found:
<u><em>X-intercept</em></u>
Set y = 0 and divide by the coefficient of x.
-x +0 = 8
x = -8
__
<u><em>Y-intercept</em></u>
Set x = 0 and divide by the coefficient of y.
0 -2y = 8
y = -4
__
Now, we have two points on the graph: (-8, 0) and (0, -4). A third point can be one that is halfway between these: (-4, -2). The graph is attached.
Answer:
a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.
b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.
c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.
Step-by-step explanation:
For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?
The foreclosure rate is 1.31% for the Washington, DC area, which means that
We wanto to find, with :
In which
0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.
b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?
Foreclosure rate of 0.87% for the nation, which means that . So
0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.
c. Comment on the above findings.
The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.