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3 years ago

Write 2 In 6 + 3 In 4 - 5 In (1/3) as a single logarithm

Mathematics

1 answer:

liberstina [14]3 years ago

3 0

Answer:

ln 559872

Step-by-step explanation:

2 In 6 + 3 In 4 - 5 In (1/3) = ln 6² + ln 4³ - ln (⅓)⁵

= ln 36 + ln 64 - ln 1/243

= ln [(36×64)/(1/243)]

= ln 559872

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2root3 sin^<a href="/cdn-cgi/l/email-protection" class="__cf_email__" data-cfemail="ac9eec">[email protected]</a> - <a href

Phantasy [73]

Answer:

Step-by-step explanation:

$2\sqrt{3} sin^{2} \alpha -cos\alpha =0\\2\sqrt{3} (1-cos ^2 \alpha )-cos \alpha =0\\2\sqrt{3} -2\sqrt{3} cos^2 \alpha -cos \alpha =0\\2\sqrt{3} cos^2 \alpha +cos \alpha -2\sqrt{3} =0\\cos \alpha =\frac{-1 \pm\sqrt{1^2-4*2\sqrt{3}*(-2\sqrt{3}) } }{2*2\sqrt{3} } \\=\frac{-1 \pm\sqrt{1+48} }{4\sqrt{3} } \\=\frac{-1\pm7}{4\sqrt{3} } \\either~cos \alpha =\frac{6}{4\sqrt{3} }=\frac{\sqrt{3} }{2} \\=cos \frac{\pi }{6} ,cos(2\pi -\frac{\pi }{6} )\\=cos \frac{\pi}{6} ,cos \frac{11\pi }{6}$

$\alpha =2 n\pi+ \frac{\pi }{6} ,2n\pi +\frac{11\pi }{6} (general~solution)$

$or~cos\alpha =-\frac{7}{4\sqrt{3} } \\ \alpha =cos^{-1}( \frac{-7}{4\sqrt{3} } )$

5 0

4 years ago

Researchers measured the data speeds for a particular smartphone carrier at 50 airports. The highest speed measured was 76.676.6

faltersainse [42]

Answer:

Step-by-step explanation:

Researchers measured the data speeds for a particular smartphone carrier at 50 airports.

The highest speed measured was 76.6 Mbps.

n= 50

X[bar]= 17.95

S= 23.39

a. What is the difference between the carrier's highest data speed and the mean of all 50 data speeds?

If the highest speed is 76.6 and the sample mean is 17.95, the difference is 76.6-17.95= 58.65 Mbps

b. How many standard deviations is that [the difference found in part (a)]?

To know how many standard deviations is the max value apart from the sample mean, you have to divide the difference between those two values by the standard deviation

Dif/S= 58.65/23.39= 2.507 ≅ 2.51 Standard deviations

c. Convert the carrier's highest data speed to a z score.

The value is X= 76.6

Using the formula Z= (X - μ)/ δ= (76.6 - 17.95)/ 23.39= 2.51

d. If we consider data speeds that convert to z scores between minus−2 and 2 to be neither significantly low nor significantly high, is the carrier's highest data speed significant?

The Z value corresponding to the highest data speed is 2.51, considerin that is greater than 2 you can assume that it is significant.

I hope it helps!

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4 years ago

1. Evaluate<br>3 × (-2) × (-8)

zysi [14]

Answer:

Step-by-step explanation:

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4 years ago

Expression 1 6 x 7 – 3^2 x 9 + 4^3 =

matrenka [14]

16x7-3^2x9+4^3

2x5+4x2+6-2x2-1

i hope that helps

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3 years ago

Determine whether each number is rational or irrational

user100 [1]

Answer:

B C E G J

Step-by-step explanation:

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3 years ago