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3 years ago

What is the missing value of n that will make the equation true? 3^8 . 3^n= 3^14

Mathematics

1 answer:

marissa [1.9K]3 years ago

7 0

Answer:

n = 6

Step-by-step explanation:

${3}^{8} . {3}^{n} = {3}^{14} \\ {3}^{8 + n} = {3}^{14} \\ 8 + n = 14 \\ n = 14 - 8 \\ n = 6$

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You are driving to a different location and it takes you 90 minutes to get tere if you drive 70 miles per hour. How long will it

xxTIMURxx [149]

<h2>Answer:</h2><h2>The time taken to reach if we drive 50 miles per hour = 126 minutes = 2.1 hours</h2>

Step-by-step explanation:

The time taken to reach the location = 90 minutes = 1.5 hours

The speed driven = 70 miles per hour

By formula, speed = distance traveled / time taken

70 miles per hour = distance traveled / 1.5 hours

distance traveled in miles = 70 * 1.5 = 105 miles

Speed = 50 miles per hour

Distance = 105 miles

Time taken = ?

speed = distance traveled / time taken

50 = 105 / time taken

time taken in hours = 2.1 hours = 126 minutes

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3 years ago

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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3 years ago

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Sveta_85 [38]

Answer: 8 liters can.

Step-by-step explanation:

First we need to find the volume of the cart tank . Since it is in the shape of a rectangular prism we have to multiply the length by the width by the height to find the volume.

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3 years ago

According to industry sources, online banking is expected to take off in the near future. The projected number of households (in

Airida [17]

Answer:

(a) The least-square regression line is: $y=4.662+2.709x$ .

(b) The number of households using online banking at the beginning of 2007 is 31.8.

Step-by-step explanation:

The general form of a least square regression line is:

$y=\alpha +\beta x$

Here,

<em>y</em> = dependent variable

<em>x</em> = independent variable

<em>α</em> = intercept

<em>β</em> = slope

(a)

The formula to compute intercept and slope is:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \end{aligned}$

The values of ∑<em>X</em>, ∑<em>Y</em>, ∑<em>XY</em> and ∑<em>X</em>² are computed in the table below.

Compute the value of intercept and slope as follows:

$\begin{aligned} \alpha &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 68.6 \cdot 55 - 15 \cdot 218.9}{ 6 \cdot 55 - 15^2} \approx 4.662 \\ \\\beta &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 6 \cdot 218.9 - 15 \cdot 68.6 }{ 6 \cdot 55 - \left( 15 \right)^2} \approx 2.709\end{aligned}$

The least-square regression line is:

$y=4.662+2.709x$

(b)

For the year 2007 the value of <em>x</em> is 10.

Compute the value of <em>y</em> for <em>x</em> = 10 as follows:

$y=4.662+2.709x$

$=4.662+(2.709\times10)\\=4.662+27.09\\=31.752\\\approx 31.8$

Thus, the number of households using online banking at the beginning of 2007 is 31.8.

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3 years ago