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DENIUS [597]
3 years ago
5

07.03 LC)

Mathematics
2 answers:
SOVA2 [1]3 years ago
7 0
Question \ 1)  

Probability \ is \ simply \ how \ likely \ something \ is \ to \ happen.
We \ get \ the \ probabilities \ by \ dividing \ the \ frequencies \ by \ the \ total.
The \ probability \ of \ an \ event \ can \ only \ be \ between \ 0 \ and \ 1and \ can \ also \ be \ written \ as \ a \ percentage. 

The \ best \ example \ for \ understanding \ probability \ is \ flipping \ a \ coin:

There are two possible outcomes ------\ \ heads or tails.

Probability \ is \ always \ out \ of 100 \% 

\dfrac{P}{100\%} 

20\% =  \dfrac{20}{100} = 0.20 \ as \ a \ decimal 

0.2 * 500 = 100 

Question \ 2)   x+y+z=24 

7+8+9 = 24 =\ \textgreater \  Number \ of \ roses 

\dfrac{9}{24} *  \dfrac{8}{23} =  \dfrac{72}{552} 

Question \ 3) 

5 = Number \ of \ 2 

100 =  Total 

=\ \textgreater \   \dfrac{5}{100} 

Question \ 4)  x+y+z=16 

1 + 5 + 10 = 16, Total \ Number 

\dfrac{10}{16}* \dfrac{9}{15} = Solution 
Inga [223]3 years ago
4 0
Q1.\\p\%=\dfrac{p}{100};\ 20\%=\dfrac{20}{100}=0.20=0.2\\\\20\%-French\ of\ 500\ people\\\\0.2\cdot500=100\leftarrow Answer


Q2.\\\dfrac{white}{all}\cdot\dfrac{yellow}{all-1}\\\\7+8+9=24-number\ of\ all\ roses\\\\\dfrac{9}{24}\cdot\dfrac{8}{24-1}=\dfrac{9}{24}\cdot\dfrac{8}{23}=\dfrac{72}{552}\leftarrow Answer


Q3.\\5-number\ of\ 2\\100-number\ of\ all\\\\\dfrac{5}{100}\leftarrow Answer


Q4.\\1+5+10=16-number\ of\ all\ marbles\\\\\dfrac{10}{16}\cdot\dfrac{10-1}{16-1}=\dfrac{10}{16}\cdot\dfrac{9}{15}\leftarrow Answer
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For the following telescoping series, find a formula for the nth term of the sequence of partial sums {Sn}. Then evaluate limn→[
Ivenika [448]

Answer:

The following are the solution to the given points:

Step-by-step explanation:

Given value:

1) \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\2) \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}

Solve point 1 that is \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2}\\\\:

when,

k= 1 \to  s_1 = \frac{1}{1+1} - \frac{1}{1+2}\\\\

                  = \frac{1}{2} - \frac{1}{3}\\\\

k= 2 \to  s_2 = \frac{1}{2+1} - \frac{1}{2+2}\\\\

                  = \frac{1}{3} - \frac{1}{4}\\\\

k= 3 \to  s_3 = \frac{1}{3+1} - \frac{1}{3+2}\\\\

                  = \frac{1}{4} - \frac{1}{5}\\\\

k= n^  \to  s_n = \frac{1}{n+1} - \frac{1}{n+2}\\\\

Calculate the sum (S=s_1+s_2+s_3+......+s_n)

S=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....\frac{1}{n+1}-\frac{1}{n+2}\\\\

   =\frac{1}{2}-\frac{1}{5}+\frac{1}{n+1}-\frac{1}{n+2}\\\\

When s_n \ \ dt_{n \to 0}

=\frac{1}{2}-\frac{1}{5}+\frac{1}{0+1}-\frac{1}{0+2}\\\\=\frac{1}{2}-\frac{1}{5}+\frac{1}{1}-\frac{1}{2}\\\\= 1 -\frac{1}{5}\\\\= \frac{5-1}{5}\\\\= \frac{4}{5}\\\\

\boxed{\text{In point 1:} \sum ^{\infty}_{k = 1} \frac{1}{k+1} - \frac{1}{k+2} =\frac{4}{5}}

In point 2: \sum ^{\infty}_{k = 1} \frac{1}{(k+6)(k+7)}

when,

k= 1 \to  s_1 = \frac{1}{(1+6)(1+7)}\\\\

                  = \frac{1}{7 \times 8}\\\\= \frac{1}{56}

k= 2 \to  s_1 = \frac{1}{(2+6)(2+7)}\\\\

                  = \frac{1}{8 \times 9}\\\\= \frac{1}{72}

k= 3 \to  s_1 = \frac{1}{(3+6)(3+7)}\\\\

                  = \frac{1}{9 \times 10} \\\\ = \frac{1}{90}\\\\

k= n^  \to  s_n = \frac{1}{(n+6)(n+7)}\\\\

calculate the sum:S= s_1+s_2+s_3+s_n\\

S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(n+6)(n+7)}\\\\

when s_n \ \ dt_{n \to 0}

S= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{(0+6)(0+7)}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}....+\frac{1}{6 \times 7}\\\\= \frac{1}{56}+\frac{1}{72}+\frac{1}{90}+\frac{1}{42}\\\\=\frac{45+35+28+60}{2520}\\\\=\frac{168}{2520}\\\\=0.066

\boxed{\text{In point 2:} \sum ^{\infty}_{k = 1} \frac{1}{(n+6)(n+7)} = 0.066}

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do miles/hour =

10.6 miles/2.5 hours =

10.6/2.5 =

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Answer:

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