What is the missing number for n 31.53=62.4?

Using the numbers 1, 2, 3, and 4 (ONLY ONCE), and the operations of adding, subtracting, multiplying, dividing, and the use of p

vazorg [7]

Step-by-step explanation:

=(4+3)×(2+1)

=7×3

=21

3 0

3 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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7 0

3 years ago

Marcos reads 3, books in 1 3/4 weeks.

Fofino [41]

Answer:

$x = \frac{12}{7}\ books$

Step-by-step explanation:

Given

$3\ books = 1\frac{3}{4}\ weeks$

Required

Number of books in 1 week

Represent the number of books in 1 week with x.

So, we have:

$3\ books = 1\frac{3}{4}\ weeks$

$x = 1\ week$

Cross Multiply

$x * 1\frac{3}{4} = 3 * 1$

$x * 1\frac{3}{4} = 3$

Convert fraction to improper fraction

$x * \frac{7}{4} = 3$

Multiply through by $\frac{4}{7}$

$x * \frac{7}{4}*\frac{4}{7} = 3 * \frac{4}{7}$

$x = 3 * \frac{4}{7}$

$x = \frac{12}{7}\ books$

<em>Hence: 12/7 books were read in a week</em>

7 0

3 years ago

A notebook costs $4.50 plus sales tax . After sales tax , the notebook is $4.86. What is the sales tax rate?

UkoKoshka [18]

Answer:

8%

Step-by-step explanation:

0.36/4.50=0.08=8%

6 0

3 years ago

Read 2 more answers

Henry worked for 8 days, Jack worked for 9.5 days while Steffi worked for 6.5 days to complete a project. If the amount earned f

trasher [3.6K]

Answer:

The ratio in which the amount is shared is 16:19:13

Step-by-step explanation:

The given parameters are;

The number of days Henry worked = 8 days

The number of days Jack worked = 9.5 days

The number of days Steffi worked = 6.5 days

The sharing formula for the amount earned for the project = The ratio of the number of days worked by each one

The total number of days worked by all three = 8 days + 9.5 days + 6.5 days = 24 days

The fraction of the total number of days Henry worked = (8 days)/(24 days) = 1/3 = 16/48

The fraction of the total number of days Jack worked = (9.5 days)/(24 days) = 19/48

The fraction of the total number of days Steffi worked = (6.5 days)/(24 days) = 13/48

Therefore. the ratio in which the amount is shared = 16:19:13 (which is the same as the ratio of the number of days worked)

5 0

3 years ago