One central triangle will have a central angle of α = 360°/n. For example, a hexagon has a central angle of α = 360°/6 = 60°. The area of that central triangle is given by the formula ...

A = (1/2)r²sin(α)

Since there are n such triangles, the area of the n-gon is ...

A = (n/2)r²sin(360°/n)

For a hexagon (n=6) with radius 10√3, the area is ...

A = (6/2)(10√3)²sin(360°/6) = 450√3 ≈ 779.4 . . . . square units

8 0

2 years ago

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Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,

REY [17]

Answer:

a) 217

b) 1351

c) 5403

Step-by-step explanation:

Given that:

confidence interval (c) = 0.95

$\alpha =1-0.95=0.05\\\frac{\alpha }{2} =\frac{0.05}{2}=0.025$

The Z score of $\frac{\alpha }{2}$ is from the z table is given as:

$Z_{\frac{\alpha }{2} }=Z_{0.025}=1.96$

Range = $45000 - $30000 = $15000

The standard deviation (σ) is given as:

$\sigma=\frac{Range}{4} =\frac{15000}{4}=3750$

Sample size (n) is given as:

$n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2$

a) E = $500

$n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{500} )^2$ ≈ 217

b) $n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{200} )^2$ ≈ 1351

c) $n=(\frac{Z_{\frac{\alpha}{2} }\sigma}{E} )^2= (\frac{1.96*3750}{100} )^2$ ≈ 5403

7 0

3 years ago

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A wall shaped like a trapezoid needs to be painted. the height of the wall is 16 feet and the bases are 20 feet and 24 feet. if

AURORKA [14]

Area of Trapezoid = h(b1+b2/2)
b1 and b2 are the lengths of each base and h is the height.

Area = 16(20+24/2)=352 Square Feet

352/20=17.6 Cans of paint.

Hope this helps and is correct, I haven't done this kind of math in a while.

4 0

3 years ago