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barxatty [35]
4 years ago
7

427+364 find the sum

Mathematics
2 answers:
prisoha [69]4 years ago
8 0
The answer is 791......
WINSTONCH [101]4 years ago
5 0

Answer by JKismyhusbandbae:

Line\:up\:the\:numbers\\\begin{matrix}\space\space&4&2&7\\ +&3&6&4\end{matrix}\\Add\:each\:column\:of\:digits,\:starting\:on\:the\:right\:and\:working\:left.\\\mathrm{If\:the\:sum\:of\:a\:column\:is\:more\:than\:ten,\:'carry'\:digits\:to\:the\:next\:column\:on\:the\:left.}\\\mathrm{Add\:the\:digits\:of\:the\:bolded\:column}:\quad \:7+4=11\\\begin{matrix}\space\space&4&2&\textbf{7}\\ +&3&6&\textbf{4}\end{matrix}\\

\mathrm{Carry\:}1\mathrm{\:to\:the\:column\:on\:the\:left\:and\:write\:}1\mathrm{\:in\:the\:bolded\:column}\\\frac{\begin{matrix}\space\space&\space\space&1&\textbf{\space\space}\\ \space\space&4&2&\textbf{7}\\ +&3&6&\textbf{4}\end{matrix}}{\begin{matrix}\space\space&\space\space&\space\space&\textbf{1}\end{matrix}}\\\mathrm{Add\:the\:digits\:of\:the\:bolded\:column}:\quad \:1+2+6=9\\

\frac{\begin{matrix}\space\space&\space\space&\textbf{1}&\space\space\\ \space\space&4&\textbf{2}&7\\ +&3&\textbf{6}&4\end{matrix}}{\begin{matrix}\space\space&\space\space&\textbf{9}&1\end{matrix}}\\\mathrm{Add\:the\:digits\:of\:the\:bolded\:column}:\quad \:4+3=7\\\frac{\begin{matrix}\space\space&\textbf{\space\space}&1&\space\space\\ \space\space&\textbf{4}&2&7\\ +&\textbf{3}&6&4\end{matrix}}{\begin{matrix}\space\space&\textbf{7}&9&1\end{matrix}}\\=791

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For what values of x is the in equality 2/3+x/3>1 true
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Answer:

b. x>1

Step-by-step explanation:

2/3+x/3>1

Multiply the inequality by 3 to get rid of the fractions

3(2/3+x/3)>1*3

2 +x >3

Subtract 2 from each side

2+x-2 >3-2

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A machine can wrap 110 candies per minute. At this production rate, how many candies can the machine wrap in 15 minutes
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4 years ago
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First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

a_{n}=a_{1}r^{n-1}

a_{1} = the first term of the series

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a_{1} would represent the height at which the ball is first dropped. Therefore:

a_{1} = k

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

r=\frac{3}{4}

Our general term would be:

a_{n}=a_{1}r^{n-1}

a_{n}=k(\frac{3}{4}) ^{n-1}

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

k represents the initial height:

k = 235\ ft

n represents the number of times the ball bounces:

n = 6

Plugging this back into our general term of the geometric series:

a_{n}=k(\frac{3}{4}) ^{n-1}

a_{n}=235(\frac{3}{4}) ^{6-1}

a_{n}=235(\frac{3}{4}) ^{5}

a_{n}=55.8\ ft

a_{n} represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. ​

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

S_{n}=\frac{a_{1}(1-r^{n})}{1-r}

We already know these variables:

a_{1}= k = 235\ ft

r=\frac{3}{4}

n = 12

Therefore:

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }

S_{n}=(4)(235)(1-\frac{3}{4} ^{12})

S_{n}=910.22\ ft

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