A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of
the sidewalk is 155 ft2, what is its width?
2 answers:
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Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
. That is, 
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
and replace 
and 
using expressions that contain an expression in terms of x from the first two equations we came up with.
That gives us:
which we solve for x as follows:
Now that we know x we can substitute 36 for x into the equation
and solve for z as follows:
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.
Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
There are three right triangles we can work with.
Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation
Triangle with sides 27, x and y. Here y is the hypotenuse so we get
Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get
We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation:
That gives us:
Now that we know x we can substitute 36 for x into the equation
This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.
<h2>Answer with explanation:</h2>
As per given , we have
Since , alternative hypothesis is right tailed, so the test is a right tailed test.
n= 1987
Proportion of adults believe that rudeness is a worsening problem :
Test statistic :
(since , the normal curve takes values of z from -7 to 7, so we use critical value to draw conclusion.)
The critical value for a significance level of 0.005= 1.645
Since , absolute test statistic value (12.09) is greater than the critical value (1.645), it means there is statistical significance and so we reject the null hypothesis.