Part A:
Given a square with sides 6 and x + 4. Also, given a rectangle with sides 2 and 3x + 4
The perimeter of the square is given by 4(x + 4) = 4x + 16
The area of the rectangle is given by 2(2) + 2(3x + 4) = 4 + 6x + 8 = 6x + 12
For the perimeters to be the same
4x + 16 = 6x + 12
4x - 6x = 12 - 16
-2x = -4
x = -4 / -2 = 2
The value of x that makes the <span>perimeters of the quadrilaterals the same is 2.
Part B:
The area of the square is given by

The area of the rectangle is given by 2(3x + 4) = 6x + 8
For the areas to be the same

Thus, there is no real value of x for which the area of the quadrilaterals will be the same.
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Answer:

I hope this is good enough:
4)
4 is for the Library, 6 is for the park, Police is 5 north up...
Distance of Police from park is by using Pythagoras Theorem:
x^2 = 5^2 + 6^2
x^2 = 25 +36
x^2 = 61 Take the square root of both sides.
x = square root (61) = 7.81.
x = 7.8 miles to the nearest tenth.
5)
Since it is a square garden, let the side be = x.
The length of the fence = x + x +x +x = 4x.
Let length of diagonal = d =34.
By Pythagoras theorem.
x^2 + x^2 = d^2.
2x^2 = 34^2. Divide both sides by 2.
x^2 = (34 *34) / 2 = 17 * 34, Use your calculator.
x^2 = 578. Take square root of both sides.
x = square root (578)
x = 24.04
Total fence = 4x = 4*24.04 = 96.16.
Total fence = 96 feet to the nearest feet.
Answer:
The alternative hypothesis is:
<em>Hₐ</em>: The workers with automatic dispensers are more productive than restaurant with manual dispensers.
Step-by-step explanation:
In this case we need to determine whether the workers with automatic dispensers are significantly more productive than restaurant with manual dispensers.
To test this a random sample of 9 workers from a restaurant with automatic dispensers and 9 works from a restaurant with manual dispensers are selected.
The significance level of the test is, <em>α</em> = 0.01.
A Mann-Whitney U test is used to determine whether the randomly selected value from one population is either more than or less than the same value selected from another population.
The hypothesis can be defined as follows:
<em>H₀</em>: The workers with automatic dispensers are as productive as restaurant with manual dispensers.
<em>Hₐ</em>: The workers with automatic dispensers are more productive than restaurant with manual dispensers.