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poizon [28]
3 years ago
12

Find the area and the perimeter of a rectangle with a length of 5 feet and a width of 4 5/9 feet. Write each answer as a fractio

n and as a decimal. Use bar notation if necessary. Please help me out!!
Mathematics
1 answer:
Over [174]3 years ago
6 0

\bf \textit{area of a rectangle}\\\\ A=Lw~~ \begin{cases} L=5\\ w=4\frac{5}{9}\\[0.8em] \qquad \frac{4\cdot 9+5}{9}\\[0.8em] \qquad \frac{41}{5} \end{cases}\implies A=5\cdot \cfrac{41}{5}\implies \stackrel{fraction}{A=\cfrac{41}{1}}\implies \stackrel{decimal}{A=41} \\\\[-0.35em] \rule{34em}{0.25pt}


\bf \textit{perimeter of a rectangle}\\\\ A=2(L+w)\qquad \implies A=2\left(5+\cfrac{41}{5} \right) \implies A=2\left( \cfrac{25+41}{5} \right) \\\\\\ A=2\left( \cfrac{66}{5} \right)\implies A=\cfrac{132}{5}\implies \stackrel{fraction}{A=26\frac{2}{5}}\implies \stackrel{decimal}{A=26.4}

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Alona [7]

The business owner should be told to angle a spotlight mounted on the roof at the angle of =39°

<h3>Calculation of angle</h3>

The distance of the flagpole from the building = 55ft

The building has the height of = 45ft

The flagpole has the height of = 25ft

The angle can be calculated using the formula;

Tan θ = opposite/adjacent

Where opposite= 45ft

adjacent = 55ft

Tan θ = 45/55 = 0.82

θ = Tan–¹0.82

θ = 39°

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5 0
2 years ago
Suppose that the store manager of a small rural pharmacy is doing a linear regression of daily sales of over-the-counter (OTC) d
Doss [256]

Answer:

3.83

Step-by-step explanation:

Mean of x = Σx / n

Mean of x = (14 + 19 + 13 + 6 + 9) / 5 = 12.2

Sum of square (SS) :

(14-12.2)^2 + (19-12.2)^2 + (13-12.2)^2 + (6-12.2)^2 + (9-12.2)^2 = 98.8

Mean of y = Σy / n

Mean of y = (101 + 89 + 48 + 21 + 47) / 5 = 61.2

Σ(y - ybar)² = (101-61.2)^2 + (89-61.2)^2 + (48-61.2)^2 + (21-61.2)^2 + (47-61.2)^2 = 4348.8

df = n - 2 = 5 - 2 = 3

Σ(y - ybar)² / df = 4348.8 / 3 = 1449.6

√(Σ(y - ybar)² / df) = √1449.6 = 38.074

Standard Error = √(Σ(y - ybar)² / df) / √SS

Standard Error = 38.074 / √98.8

Standard Error = 3.83

4 0
2 years ago
AB = 5x -9; BC= -2x + 12
BaLLatris [955]

Answer:

X=-3

Step-by-step explanation:

5x - 9

-2x + 12

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7x = -21

X= -3

plz mark ice bear as Brainliest

3 0
3 years ago
Integrate the following
enot [183]

I suppose you mean to have the entire numerator under the square root?

\displaystyle\int_2^4\frac{\sqrt{x^2-4}}{x^2}\,\mathrm dx

We can use a trigonometric substitution to start:

x=2\sec t\implies\mathrm dx=2\sec t\tan t\,\mathrm dt

Then for x=2, t=\sec^{-1}1=0; for x=4, t=\sec^{-1}2=\frac\pi3. So the integral is equivalent to

\displaystyle\int_0^{\pi/3}\frac{\sqrt{(2\sec t)^2-4}}{(2\sec t)^2}(2\sec t\tan t)\,\mathrm dt=\int_0^{\pi/3}\frac{\tan^2t}{\sec t}\,\mathrm dt

We can write

\dfrac{\tan^2t}{\sec t}=\dfrac{\frac{\sin^2t}{\cos^2t}}{\frac1{\cos t}}=\dfrac{\sin^2t}{\cos t}=\dfrac{1-\cos^2t}{\cos t}=\sec t-\cos t

so the integral becomes

\displaystyle\int_0^{\pi/3}(\sec t-\cos t)\,\mathrm dt=\boxed{\ln(2+\sqrt3)-\frac{\sqrt3}2}

7 0
3 years ago
What is the main piece of computer software on which every other piece of software relies?
andrew-mc [135]
The main piece of computer software on which every other piece of software relies is referred to as the "operating system". It is responsible for all the major channels of communication between the software and the hardware. 
6 0
3 years ago
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