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DochEvi [55]
3 years ago
5

Caroline needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer f

or 2.75 hours and charged her $114 for parts. The total was $320.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.​
Mathematics
1 answer:
Elden [556K]3 years ago
3 0
2.75(x)+114=320.25
-114 -114
2.75(x)=206.25
/2.75. /2.75
X=75

It costs 75$ per hour


This is because we don’t know how much they charge per hour but we know the number of hours spend working on the computer, so you have to do 2.75(x) where x represents the cost per hour And we also know that the cost of the part is $114 so we have to add that to
(2.75(x)+114) the equation then finally you have to make the expression equal to 320.25 since we know the final cost so

2.75(x)+114=320.25
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Step-by-step explanation:


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Simplify using exponent rules.<br><br> (3x^4) (-6x)<br><br><br> (SHOW YOUR WORK)
ehidna [41]

Answer:

Step-by-step explanation:

3x^4(−6x)

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4 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.

__________________________________________________________

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.

__________________________________________________________

Topics

Sequence & Series — Geometric Series

__________________________________________________________

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
A tropical storm has been moving at 15 miles per hour for the past two days. Bess recorded that the storm moved 135 miles yester
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Answer:

Bess has been keeping track of the storm for 14 hours.

Step-by-step explanation:

The tropical storm has been moving at 15 miles per hour.

Bess recorded that the storm moved 135 miles yesterday and 75 miles today. Total distance covered by storm is

135+75=210

The relationship between distance speed and time is defined as

speed=\frac{distance}{time}

15=\frac{210}{time}

time=\frac{210}{15}

time=14

Therefore, Bess has been keeping track of the storm for 14 hours.

8 0
3 years ago
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