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3 years ago

7

Karen measures the width of a garden plot and records that it is 44.25 meters. Its actual width is 45.5 meters.

1 answer:

vazorg [7]3 years ago

3 0

Answer

Find out the what is the percent error in the measurement, to the nearest tenth of a percent .

To prove

Formula

$Percentage\ error = \frac{error\times 100}{exact}$

Where error = | Approx - Exact |

As given

Karen measures the width of a garden plot and records that it is 44.25 meters. Its actual width is 45.5 meters.

Approx value = 44.25 meters

Actual value = 45.5 meters

error = | 44.25 - 45.5 |

= |-1.25|

= 1.25

Put in the formula

$Percentage\ error = \frac{1.25\times 100}{45.5}$

$Percentage\ error = \frac{125}{45.5}$

Percentage error = 2.7%

Therefore the percentage error is 2.7% .

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a rectangular room is twice as long as its breadth and its peimeter is 540 m. find the number of bricks of size 20 cm ×12cm to p

balu736 [363]

Answer:

Step-by-step explanation:

breadth = x

length = 2x

Perimeter = 540m

2*( length + breadth ) = 540

2 *(2x + x) = 540

3x = 540/2

3x = 270

x = 270/3

x = 90 m

Breadth = 90m = 90 *100 = 9000 cm

Length = 2*90 = 180 m = 180 * 100 = 18000 cm

No.of bricks = Area of room/ area of one brick

= 9000 * 18000 / 20 * 12

= 675000 bricks

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3 years ago

The sum of 30 times (1/3)^(n-1) from 1 to infinity

sergeinik [125]

Let

$S_n=\displaystyle1+\frac13+\frac1{3^2}+\cdots+\frac1{3^n}$

Then

$\dfrac13S_n=\displaystyle\frac13+\frac1{3^2}+\frac1{3^3}+\cdots+\frac1{3^{n+1}}$

and

$S_n-\dfrac13S_n=\dfrac23S_n=1-\dfrac1{3^{n+1}}\implies S_n=\dfrac32-\dfrac1{2\cdot3^n}$

and as $n\to\infty$ , we end up with

$\displaystyle\lim_{n\to\infty}S_n=\lim_{n\to\infty}\sum_{i=1}^{n+1}\frac1{3^{i-1}}=\lim_{n\to\infty}\left(\frac32-\frac1{2\cdot3^n}\right)=\frac32$

So we have

$\displaystyle\sum_{n=1}^\infty30\left(\frac13\right)^{n-1}=30\cdot\frac32=45$

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3 years ago

An ice sculpture measures 52 inches and melts continuously by 3% per minute. Fine the height

neonofarm [45]

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Use inductive reasoning to determine the units digit of the number 3 to the 58 power

I am Lyosha [343]

We must find a pattern in the powers of 3:

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$3^2 = 9$

$3^3 = 27$

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$3^{4k+0} \text{ ends with } 1$

$3^{4k+1} \text{ ends with } 3$

$3^{4k+2} \text{ ends with } 9$

$3^{4k+3} \text{ ends with } 7$

Since $58 = 14\cdot 4 + 2$ , we can deduce that $3^{58}$ ends with 9.

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Graph a line that contains the point (-5,-3) and has a slope of -2

nikitadnepr [17]

Given:

The line contains the point (-5,-3) and has a slope of -2.

To find:

The graph of the line.

Solution:

The line contains the point (-5,-3) and has a slope of -2. So, the equation of line is

$y-y_1=m(x-x_1)$

where, m is slope.

$y-(-3)=-2(x-(-5))$

$y+3=-2(x+5)$

$y+3=-2x-10$

Subtracting 3 from both sides, we get

$y=-2x-10-3$

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So, the equation of line is $y=-2x-13$ .

Putting x=0, we get

$y=-2(0)-13$

$y=0-13$

$y=-13$

It means, the line also passes through (0,-13).

Plot the points (0,-13) and (-5,-3) on a coordinate plane and connect them by a straight line.

Therefore, the graph of given line is shown below.

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3 years ago