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3 years ago

Evalaute the following without using a calculator: cos(13pi/6)

Mathematics

2 answers:

strojnjashka [21]3 years ago

6 0

Answer is in the attachment below. Please open it up in a new window to see it in full.

Harman [31]3 years ago

5 0

$the\ cos\ function\ is\ periodic:\ \ \ the\ period=2 \pi\\\\cos(2 \pi + \alpha )=cos \alpha \\\\------------------------\\\\cos\bigg{(} \frac{\big{13 \pi }}{\big{6}}\bigg{)}=cos\bigg{(} 2 \pi +\frac{\big{ \pi }}{\big{6}}\bigg{)}=cos\bigg{(} \frac{\big{ \pi }}{\big{6}}\bigg{)}= \frac{\big{ \sqrt{3} }}{\big{2}}$

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PLEASE HELP AND ASAP!!!! look at screenshot (10 pts)

Ne4ueva [31]

Answer:

Step-by-step explanation:

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Pencils come in boxes of 10. How many boxes should Erika buy if she needs 127 pencils

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What is 150% as a fraction

Helen [10]

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Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below

mafiozo [28]

Answer:

a) $\bar X = 369.62$

b) $Median=175$

c) $Mode =450$

With a frequency of 4

d) $MidR= \frac{Max +Min}{2}= \frac{49+3000}{2}= 1524.5$

<u>e)</u> $s = 621.76$

And we can find the limits without any outliers using two deviations from the mean and we got:

$\bar X+2\sigma = 369.62 +2*621.76 = 1361$

And for this case we have two values above the upper limit so then we can conclude that 1500 and 3000 are potential outliers for this case

Step-by-step explanation:

We have the following data set given:

49 70 70 70 75 75 85 95 100 125 150 150 175 184 225 225 275 350 400 450 450 450 450 1500 3000

Part a

The mean can be calculated with this formula:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

Replacing we got:

$\bar X = 369.62$

Part b

Since the sample size is n =25 we can calculate the median from the dataset ordered on increasing way. And for this case the median would be the value in the 13th position and we got:

$Median=175$

Part c

The mode is the most repeated value in the sample and for this case is:

$Mode =450$

With a frequency of 4

Part d

The midrange for this case is defined as:

$MidR= \frac{Max +Min}{2}= \frac{49+3000}{2}= 1524.5$

Part e

For this case we can calculate the deviation given by:

$s =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

And replacing we got:

$s = 621.76$

And we can find the limits without any outliers using two deviations from the mean and we got:

$\bar X+2\sigma = 369.62 +2*621.76 = 1361$

And for this case we have two values above the upper limit so then we can conclude that 1500 and 3000 are potential outliers for this case

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3 years ago

20 POINTS PLEAE HELP!!!!!!!!!!!!!!!

Alina [70]

His first payment is $100, thus a₁ = 100.

the next "term", month will be 1.1 times more than the one before, namely r = 1.1, the common ratio.

$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
\\\\
S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
r=\textit{common ratio}\\
----------\\
a_1=100\\
r=1.1\\
n=20
\end{cases}$

$\bf \sum\limits_{i=1}^{20}~100(1.1)^{i-1}\qquad \qquad\qquad \qquad S_{20}=100\left( \cfrac{1-1.1^{20}}{1-1.1} \right)
\\\\\\
S_{20}=100\left( \cfrac{1-\stackrel{\approx}{6.727499949}}{-0.1} \right)\implies S_{20}\approx 100(57.27499949)
\\\\\\
S_{20}\approx 5727.4999493256$

is the serie divergent or convergent?

well, to make it short, when the common ratio is 0 < | r | < 1, namely a fraction between 0 and 1, only then the serie is convergent, namely it reaches a fixed value, now in this case, 1.1 is a value larger than anything between 0 and 1, so no dice.

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