Driving to your friend's house, you travel at an average rate of 35 miles per hour. On your

2 answers:

6 0

The distance from my residence to my friend's house is 14 miles Step-by-step explanation: Let's clarify the method we used to solve the question: - While driving to my friend's abode, my speed is 35 miles per hour. - On my return home, the speed is 40 miles per hour. - The complete round trip duration was 45 minutes. - Our task is to find out the distance from my house to theirs. - First, converting 45 minutes into hours is necessary since the speed is expressed as miles per hour. Since we know that 1 hour is 60 minutes, we conclude that 45 minutes corresponds to hours. - Assuming the distance to be d, the times for each segment of the trip are introduced, establishing: d = 35 × (time taken to get there) and d = 40 × (time taken to return). - Equating these two expressions enables us to assert: - When simplifying, we divide both sides by 35 to yield: - This results in the overall round trip duration as hours. - By plugging this back into the equation, we ascertain that the distance d equals 40(0.35), which confirms that the distance from my home to my friend's house is indeed 14 miles.

AnnZ [12.3K]2 months ago

4 0

The distance from my home to my friend's residence is 14 miles Step-by-step explanation: Let me clarify the solution process: - When heading to my friend's house, my driving speed is 35 miles per hour. - In returning home, the driving speed increases to 40 miles per hour. - The total duration of the trip was 45 minutes. - Our goal is to determine the distance separating my home from my friend's house. - First, we will convert 45 minutes into hours since the driving speed is expressed in miles per hour. Knowing that 1 hour equals 60 minutes, it follows that 45 minutes equates to hours. - Let’s assume that the distance between my home and my friend's place is d; thus, the time taken to reach my friend's house will be and the time for the ride back will be. Since the distance between the two is d, the corresponding equations will be: d = 35 ×, and d = 40 ×. - Setting both equations equal we derive:. - After dividing both sides by 35, it leads to. - This indicates that the total time of the round trip is hours. - Utilizing this information, we then substitute back into the equations to compute d, leading to the conclusion that the distance from my home to my friend's is indeed 14 miles.

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$\bf \qquad \qquad \textit{Annual Yield Formula}
\\\\
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~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
\\\\
\begin{cases}
r=rate\to 4.0784\%\to \frac{4.0784}{100}\to &0.040784\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
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\end{array}\to &12
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\\\\\\
\left(1+\frac{0.040784}{12}\right)^{12}-1\\\\
-------------------------------\\\\
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$\bf ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1
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\begin{cases}
r=rate\to 4.0798\%\to \frac{4.0798}{100}\to &0.040798\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2
\end{cases}
\\\\\\
\left(1+\frac{0.040798}{2}\right)^{2}-1\\\\
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$\bf ~~~~~~~~~~~~\textit{4.0730\% compounded daily}\\\\
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n=
\begin{array}{llll}
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Detailed explanation:

In Problem 8-4, the computer time-sharing system experiences teleport inquiries at an average rate of 0.1 per millisecond. We are tasked with determining the probabilities of the inquiries over a specific period of 50 milliseconds:

Given that

$\lambda=0.1\ per\ millisecond=5\ per\ 50\ millisecond=5$