Answer:
Step-by-step explanation:
In order to find the value of y, first we need to find the length of the perpendicular dropped from one of the vertices of the triangle to its opposite side.
By geometric mean theorem:
Length of the perpendicular
Next, by Pythagoras theorem:
![{y}^{2} = {9}^{2} + {( \sqrt{27} )}^{2} \\ \\ {y}^{2} = 81 + 27 \\ \\ {y}^{2} = 108 \\ \\ y = \sqrt{108} \\ \\ y = \sqrt{36 \times 3} \\ \\ y = \sqrt{ {6}^{2} \times 3} \\ \\ y = 6 \sqrt{3} \: units](https://tex.z-dn.net/?f=%20%7By%7D%5E%7B2%7D%20%20%3D%20%20%7B9%7D%5E%7B2%7D%20%20%2B%20%20%7B%28%20%5Csqrt%7B27%7D%20%29%7D%5E%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%20%7By%7D%5E%7B2%7D%20%20%3D%2081%20%2B%2027%20%5C%5C%20%20%5C%5C%20%20%7By%7D%5E%7B2%7D%20%20%3D%20108%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B108%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B36%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%20%20%5Csqrt%7B%20%7B6%7D%5E%7B2%7D%20%20%5Ctimes%203%7D%20%20%5C%5C%20%20%5C%5C%20y%20%3D%206%20%5Csqrt%7B3%7D%20%20%5C%3A%20units)
Answer:
6 square units
Step-by-step explanation:
Given shape is of a trapezoid:
![area \: of \: trapezoid \\ = \frac{1}{2} \times (4 + 2) \times 2 \\ \\ = 6 \: {units}^{2}](https://tex.z-dn.net/?f=area%20%5C%3A%20of%20%5C%3A%20trapezoid%20%20%5C%5C%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20%284%20%2B%202%29%20%5Ctimes%202%20%5C%5C%20%20%5C%5C%20%20%3D%206%20%5C%3A%20%20%7Bunits%7D%5E%7B2%7D%20)
Area of shape = area of square + area of triangle
![= 2^2 + \frac{1}{2} \times 2\times 2\\= 4 + 2\\= 6\: units^2 \\](https://tex.z-dn.net/?f=%20%3D%202%5E2%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%202%5Ctimes%202%5C%5C%3C%2Fp%3E%3Cp%3E%3D%204%20%2B%202%5C%5C%3C%2Fp%3E%3Cp%3E%3D%206%5C%3A%20units%5E2%20%5C%5C)
1 is not. 2 is. 3 is not. 4 is. 5 is. 6 is. 7 is not. 8 is.
Answer:
0
Step-by-step explanation:
The + on the zero means the limit as x approaches 0 from the right side
![\lim_{x \to 0^{+} } (\frac{1}{x} - \frac{1}{|x|})\\ \lim_{x \to 0^{+} } (\frac{1}{x} - \frac{1}{x})\\ \lim_{x \to 0^{+} } (0)\\0](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%20%7D%20%28%5Cfrac%7B1%7D%7Bx%7D%20-%20%5Cfrac%7B1%7D%7B%7Cx%7C%7D%29%5C%5C%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%20%7D%20%28%5Cfrac%7B1%7D%7Bx%7D%20-%20%5Cfrac%7B1%7D%7Bx%7D%29%5C%5C%20%5Clim_%7Bx%20%5Cto%200%5E%7B%2B%7D%20%7D%20%280%29%5C%5C0)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Population mean (μ) = 2.55
Population standard deviation (σ) = 0.5
Sample size (n) = 30
Sample mean (x) = 2.76
α = 0.05
STEP 1:
Stress score in general executive (s1)
Stress score in exercising executive (s2)
Null : s1 = s2
Alternative : s1 < s2
STEP 2:
Shape of distribution = normal
Population mean (μ) = 2.55
Population standard deviation (σ) = 0.5
Sample size (n) = 30
Sample mean (x) = 2.76
α = 0.05
Decision rule :
α = 0.05 which corresponds to a t score (t0) ;
df = n - 1 = 30 - 1= 30 at 0.05 = 1.699
If :
(Test statistic (t) > t0) ; reject the Null
(right tailed test)
Test statistic (t) :
(x - μ) / (σ/√n)
(2.76 - 2.55) / (0.5/√30)
0.21 / 0.0913
= 2.30
t > t0
2.30 > 1.699
t is more extreme than t0
Hence, reject the null at α = 0.05