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snow_tiger [21]

4 years ago

10

A manufacturing machine has a 7% defect rate. if 5 items are chosen at random, what is the probability that at least one will ha

ve a defect? mhf

1 answer:

tekilochka [14]4 years ago

8 0

Answer:

30.4%

Step-by-step explanation:

Probability that the 5 chosen are not defective = (1 - 0.07)^5

= 0.93^5

= 0.696

So the probability that there is at least one defective = 1 - 0.696

= 0.304

= 30.4 %

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A business named Beyond Boxes is considering adding a box in the shape of a triangular prism as shown.

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3 years ago

Can you help me on this.

jeka57 [31]

Answer:

x=3

Step-by-step explanation:

6 10

---------- = ------------

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3 years ago

Use Stokes' Theorem to evaluate C F · dr where C is oriented counterclockwise as viewed from above. F(x, y, z) = yzi + 4xzj + ex

natima [27]

Answer:

The result of the integral is 81π

Step-by-step explanation:

We can use Stoke's Theorem to evaluate the given integral, thus we can write first the theorem:

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

Finding the curl of F.

Given $F(x,y,z) = < yz, 4xz, e^{xy} >$ we have:

$curl \vec F =\left|\begin{array}{ccc} \hat i &\hat j&\hat k\\ \cfrac{\partial}{\partial x}& \cfrac{\partial}{\partial y}&\cfrac{\partial}{\partial z}\\yz&4xz&e^{xy}\end{array}\right|$

Working with the determinant we get

$curl \vec F = \left( \cfrac{\partial}{\partial y}e^{xy}-\cfrac{\partial}{\partial z}4xz\right) \hat i -\left(\cfrac{\partial}{\partial x}e^{xy}-\cfrac{\partial}{\partial z}yz \right) \hat j + \left(\cfrac{\partial}{\partial x} 4xz-\cfrac{\partial}{\partial y}yz \right) \hat k$

Working with the partial derivatives

$curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(4z-z\right) \hat k\\curl \vec F = \left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k$

Integrating using Stokes' Theorem

Now that we have the curl we can proceed integrating

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot d\vec S$

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S curl \vec F \cdot \hat n dS$

where the normal to the circle is just $\hat n= \hat k$ since the normal is perpendicular to it, so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S \left(\left(xe^{xy}-4x\right) \hat i -\left(ye^{xy}-y\right) \hat j + \left(3z\right) \hat k\right) \cdot \hat k dS$

Only the z-component will not be 0 after that dot product we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3z dS$

Since the circle is at z = 3 we can just write

$\displaystyle \int\limits_C \vec F \cdot d\vec r = \int \int_S 3(3) dS\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 9\int \int_S dS$

Thus the integral represents the area of a circle, the given circle $x^2+y^2 = 9$ has a radius r = 3, so its area is $A = \pi r^2 = 9\pi$ , so we get

$\displaystyle \int\limits_C \vec F \cdot d\vec r = 9(9\pi)\\\displaystyle \int\limits_C \vec F \cdot d\vec r = 81 \pi$

Thus the result of the integral is 81π

5 0

4 years ago