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3 years ago

Find the mean of the data in the dot plot below vitamins

Mathematics

2 answers:

olchik [2.2K]3 years ago

8 0

Answer:

3.8

Step-by-step explanation:

Y_Kistochka [10]3 years ago

3 0

Answer:

there is no dot plot shown

Step-by-step explanation:

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-2.01 is the smaller number

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3 years ago

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Leokris [45]

I count n=12 observations, sorted they're

0 0 0 1 1 2 2 3 3 4 5 10

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3 years ago

A cable company charges $70 per month for cable service to existing customers

Pachacha [2.7K]

Answer:

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70 per month=y, the cost

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3 years ago

Trigonometric Identities and Applications?

alex41 [277]

21)

$\bf 8cos^2(\theta )-3cos(\theta )=0\implies \stackrel{common~factor}{cos(\theta )}[8cos(\theta )-3]=0\\\\
-------------------------------\\\\
cos(\theta )=0\implies \measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =90^o\\\\
-------------------------------\\\\
8cos(\theta )-3=0\implies 8cos(\theta )=3\implies cos(\theta )=\cfrac{3}{8}
\\\\\\
\measuredangle \theta =cos^{-1}\left( \cfrac{3}{8}\right)$

22)

$\bf \begin{cases}
y=cos(2x)\\
y=cos^2(x)-1
\end{cases}\implies \stackrel{intersection~at}{cos(2x)=cos^2(x)-1}
\\\\\\
2cos^2(x)-1=cos^2(x)-1\implies 2cos^2(x)-1-cos^2(x)+1=0
\\\\\\
2cos^2(x)-cos^2(x)=0\implies cos^2(x)=0\implies cos(x)=0
\\\\\\
\measuredangle \theta =cos^{-1}(0)\implies \measuredangle \theta =180^o~~,~~270^o$

4 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

4 years ago