Inside a square with side length 10, two congruent equilateral triangles are drawn such that they share one side and each has on
e vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?
1 answer:
Answer:
5 length
Step-by-step explanation:
The diagram attached shows two equilateral triangles ABC & CDE. Since both squares share one side of the square BDFH of length 10, then their lengths will be 5 each. To obtain the largest square inscribed inside the original square BDFH, it makes sense to draw two other equilateral triangles AGH & EFG at the upper part of BDFH with length equal to 5.
So, the largest square that can be inscribe in the space outside the two equilateral triangles ABC & CDE and within BDFH is the square ACEG.
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Answer:
The weight of an adult male who is 158 cm tall is 59.32 kg.
Step-by-step explanation:
The regression equation representing the relationship between height and weight of a person is:
Here,
<em>y</em> = weight of a person (in kg)
<em>x</em> = height of a person (in cm)
The information provided is:
The significance level of the test is, <em>α</em> = 0.01.
The hypothesis to test the significance of the correlation between height and weight is:
<em>H₀</em>: There is no relationship between the height and weight, i.e. <em>ρ</em> = 0.
<em>Hₐ</em>: There is a relationship between the height and weight, i.e. <em>ρ</em> ≠ 0.
Decision rule:
If the <em>p</em>-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.
According to information provided:
<em>p</em>-value = 0.045 > 0.01
The null hypothesis will not be rejected at 1% level of significance.
Thus, concluding that there is no relationship between the height and weight.
Compute the weight of an adult male with height, <em>x</em> = 158 cm as follows:
Thus, the weight of an adult male who is 158 cm tall is 59.32 kg.
Answer:
Step-by-step explanation:
1. You must apply the formula for calculate the area of a triangle, which is shown below:
2. You know the height and the base, which are given in the problem. Then, you only need to substitute them into the equation shown above and simplify it, as following: