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3 years ago

How to find 0.36 repeating in a equivalent fraction form?

1 answer:

kondor19780726 [428]3 years ago

3 0

$x=0.\overline{36}\\
100x=36.\overline{36}\\
100x-x=36.\overline{36}-0.\overline{36}\\
99x=36\\
x=\dfrac{36}{99}=\dfrac{4}{11}

$

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Mixed numbers from 0-2 with intervals of 1/3

prisoha [69]

0, 1/3, 2/3, 1, 1 1/3, 1 2/3, 2

5 0

3 years ago

Johnnas reading rate is 150 words per minute she is reading a 364 page book that has about 275 words on each page at this rate w

ch4aika [34]

Answer:

11 hrs 1 min (i think so based on math)

Step-by-step explanation:

If Johnna's reading rate is 150 words per min and there are 364 pages with about 275 words, you need to multiply 364 and 275 to get 100100 and divide that by 150 to get 667.3333333 round to the nearest tenth which will give you 667.3 and divide that by 60 because there are 60 minutes in an hour to get 11.12222222 and round that to the nearest tenth to get 11.1 which means it will take Johnna 11 hours and 1 minute to read the book. I hope this is correct I'm really sorry if it isn't. :P

8 0

3 years ago

Find the measures of EAF DAE and CAD

sdas [7]

You have to build an equation to find the answer,

angles in a straight line add upto 180°
so your equation would be,

12x+30°=180°
-30 -30
=12x=150°
÷12 ÷12
=x=12.5°

now find the measures of the angles by using 12.5 as x.

angle EAF= 2x
=2×12.5
=25° degrees

angle DAE= 4x
=4×12.5
=50°degrees

angle CAD=6x
=6×12.5
=75°degrees

check,
30+25+50+75=180°degrees

hope this helps.......

7 0

3 years ago

A manufacturer produces piston rings for an automobile engine. It is known that ring diameter is normally distributed with σ=0.0

oksian1 [2.3K]

<h2>Answer with explanation:</h2>

The confidence interval for population mean is given by :-

$\overline{x}\pm z^* SE$ (1)

, where $\overline{x}$ = sample mean

z* = critical value.

SE = standard error

and $SE=\dfrac{\sigma}{\sqrt{n}}$ , $\sigma$ = population standard deviation.

n= sample size.

As per given , we have

$\overline{x}=74.021$

$\sigma=0.001$

n= 15

It is known that ring diameter is normally distributed.

$SE=\dfrac{0.001}{\sqrt{15}}=0.000258198889747\approx0.000258199$

By z-table ,

The critical value for 95% confidence = z*= 1.96

A 99% two-sided confidence interval on the true mean piston diameter :

$74.021\pm (2.576) (0.000258199)$ (using (1))

$74.021\pm 0.000665120624$

$74.021\pm 0.000665120624\\\\=(74.021- 0.000665120624,\ 74.021+ 0.000665120624)\\\\=(74.0203348794,\ 74.0216651206)\approx(74.020,\ 74.022)$ [Rounded to three decimal places]

∴ A 99% two-sided confidence interval on the true mean piston diameter = (74.020, 74.022)

By z-table ,

The critical value for 95% confidence = z*= 1.96

A 95% lower confidence bound on the true mean piston diameter:

$74.021- (1.96) (0.000258199)$ (using (1))

$74.021- 0.00050607004=74.02049393\approx74.020$ [Rounded to three decimal places]

∴ A 95% lower confidence bound on the true mean piston diameter= 74.020

7 0

3 years ago

General solutions of sin(x-90)+cos(x+270)=-1<br> {both 90 and 270 are in degrees}

mixer [17]

Answer:

$\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

Step-by-step explanation:

Given:

$\sin (x-90^{\circ})+\cos(x+270^{\circ})=-1$

First, note that

$\sin (x-90^{\circ})=-\cos x\\ \\\cos(x+270^{\circ})=\sin x$

So, the equation is

$-\cos x+\sin x= -1$

Multiply this equation by $\frac{\sqrt{2}}{2}:$

$-\dfrac{\sqrt{2}}{2}\cos x+\dfrac{\sqrt{2}}{2}\sin x= -\dfrac{\sqrt{2}}{2}\\ \\\dfrac{\sqrt{2}}{2}\cos x-\dfrac{\sqrt{2}}{2}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos 45^{\circ}\cos x-\sin 45^{\circ}\sin x=\dfrac{\sqrt{2}}{2}\\ \\\cos (x+45^{\circ})=\dfrac{\sqrt{2}}{2}$

The general solution is

$x+45^{\circ}=\pm \arccos \left(\dfrac{\sqrt{2}}{2}\right)+2\pi k,\ \ k\in Z\\ \\x+\dfrac{\pi }{4}=\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{4}\pm \dfrac{\pi }{4}+2\pi k,\ \ k\in Z\\ \\\left[\begin{array}{l}x=2\pi k,\ \ k\in Z\\ \\x=-\dfrac{\pi }{2}+2\pi k,\ k\in Z\end{array}\right.$

4 0

3 years ago