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3 years ago

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The inside diameter of a randomly selected piston ring is a normally distributed random variable with mean 12 cm and standard de

viation 0.04 cm. (a) What is the diameter that is exceeded by only 5% of the piston rings

1 answer:

victus00 [196]3 years ago

3 0

Answer:

$x=12.07$

Step-by-step explanation:

From the question we are told that:

Mean $\=x =12cm$

Standard deviation $\sigma=0.04$

Significance level $\alpha=5\%=0.05$

Therefore

Confidence level $95\%=0.95$

From table $P(z$

Generally the equation for Z-score is mathematically given by

$z=\frac{x-\mu}{\sigma}$

$x=z\sigma+\mu$

$x=1.645*0.04+12$

$x=12.07$

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(1st pic) What is the equation of the line shown in this graph?

vredina [299]

Answer:

For figure 1: The equation of a line is y=1

For figure 2: The equation of a line is y=(-4)x+1

For figure 3:The equation of a line is y= $\frac{-5}{2}x+5$

Step-by-step explanation:

The equation of line slope-intercept form is given by y=mx+c

Where m is the slope of the line and c is the y-intercept.

For figure 1:

Here, Line is parallel to x-axis

Hence, Slope m=0

Also, Line passing to y axis at (0,1)

Y-intercept is c=1

Therefore,

The equation of line is

y=0x+1

y=1

For figure 2:

Figure show a line passing through point (1,-3) and (-1,5)

The slope of the line is given by m= $\frac{Y2-Y1}{X2-X1}$

Using given points to find out the slope of a line

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{5-(-3)}{(-1)-1}$

m= $\frac{8}{-2}$

m=(-4)

Also, Line is intersecting y-axis at (0,1)

Hence, c=1

We can write the equation of line as

y=mx+c

y=(-4)x+1

Thus, The correct option is D). y=(-4)x+1

For figure 3:

From the figure, a line is passing through points (-2,0) and (0,5)

The slope of the line is given by m= $\frac{Y2-Y1}{X2-X1}$

Using given points to find out the slope of a line

m= $\frac{Y2-Y1}{X2-X1}$

m= $\frac{5-0}{0-(-2)}$

m= $\frac{-5}{2}$

Also, Line is intersecting y-axis at (0,5)

Hence, c=5

We can write the equation of line as

y=mx+c

y= $\frac{-5}{2}x+5$

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Solve r = 1/2m^2p for p

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You just have to arrange the equation such that the p is the only term at the left hand side of the equation. Express it in terms of r and m.

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4 years ago

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

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