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3 years ago

What is the area of an equilateral triangle with apothem 3

Mathematics

1 answer:

Orlov [11]3 years ago

6 0

Answer:

use formula of equilateral triangle = roots 3/4 a square.

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For a 95% confidence interval what would the sample size need to be as it's most conservative to have a 2% margin of error

aleksley [76]

Answer:

The size of the sample 'n' = 2401

Step-by-step explanation:

Step:1

Given that the margin of error = 2 % = 0.02

The margin of error is determined by

$M.E = \frac{Z_{0.05} \sqrt{p(1-p)} }{\sqrt{n} }$

we know that the proportion

$\sqrt{p(1-p)} < \frac{1}{2}$

Step:2

The margin of error is determined by

$0.02 = \frac{1.96( \frac{1}{2} ) }{\sqrt{n} }$

$\sqrt{n} = \frac{1.96}{2 X 0.02}$

√n = 49

Squaring on both sides, we get

n = 49 × 49

n = 2401

Final answer:-

The size of the sample 'n' = 2401

8 0

3 years ago

A parent died and left an estate to four children. One inherited

svetoff [14.1K]

1-0.5-0.125-0.25= 1-0.875=0.125

3 0

2 years ago

Best estimate of -15/16+-1/2

Paraphin [41]

Answer:-23/16

Step-by-step explanation:

-15/16+-1/2

-15/16-1/2 Lcm of 16 and 2=16

(-15-8)/16

-23/16

3 0

3 years ago

The curves r1(t) = 4t, t2, t3 and r2(t) = sin(t), sin(5t), 2t intersect at the origin. find their angle of intersection, θ, corr

san4es73 [151]

First get the tangent vectors by differentiating r1 and r2
$r_1 '(t) = (4,2t,3t^2) \\ \\ r_2'(t) = (cos (t), 5 cos(5t), 2)$
Evaluate at t=0
$r_1' = (4,0,0) \\ \\ r_2' = (1,5,2)$

Use identity for angle between 2 vectors:
$u*v = |u| |v| cos \theta$

Evaluate dot product and unit vectors:
$u*v = (4,0,0)*(1,5,2) = 4 \\ \\ |u| = \sqrt{4^2 +0^2+0^2} = 4 \\ \\ |v| = \sqrt{1^2 + 5^2+2^2} = \sqrt{30}$

Sub into identity and solve for theta:
$4 = 4 \sqrt{30} cos \theta \\ \\ cos\theta = \frac{1}{\sqrt{30}} \\ \\ \theta = 79.48$

Answer:
Angle of intersection is about 79 degrees.

5 0

3 years ago

Which equation is the inverse of y = x2 + 16? 0 y=x²-16 y=i -16 y=+-16 y = x2 - 4

denpristay [2]

Answer:

y = ±√(x-16)

Step-by-step explanation:

To find the inverse of an equation, swap the x- and y-variables:

y = x² + 16

x = y² + 16

Then, solve for the y-variable:

x = y² + 16

y² = x - 16

y = ±√(x-16)

8 0

3 years ago