Which number sentences show how to solve the problem?

Mathematics

2 answers:

exis [7]3 years ago

8 0

72 ÷ 6 = 12 and 12 × 36 = 432 and 72 × 36 = 2,592 and 2,592 ÷ 6 = 432

kondaur [170]3 years ago

6 0

All of them are correct

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Josh exercises at the gym 3 3/4 hours a week. He spends 2/5 of his time at the gym lifting weights. How many hours a week does J

Natali5045456 [20]

Answer:

1.5hours

Step-by-step explanation:

Firstly in this question, we convert the time given to minutes.

Using the conversion of 60 seconds make a minute, we have 3/4 hours as 3/4 * 60 = 45 minutes. Let’s add this to a total of 3 hours which is 180 minutes. This gives a total of 225 minutes.

Now, we are told that he spends 2/5 of his time lifting weight. This is equivalent to 2/5 * 225 = 90 minutes

We convert this to hour = 90/60 = 1.5 hours

3 0

3 years ago

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

zaharov [31]

Answer:

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: