All categories

2 years ago

If 8 widgets equal 4 curlicues and

1 answer:

6 0

So 8w=4c and 2c=3g. divide the first equation by 2 and you get 4w=2c. merge the two equation give you 4w=2c=3g, or 4w=3g. multiply 4 on both sides give you 16w=12g. So 16 widgets equal how 12 goof-ups?

You might be interested in

Evaluate the integral Integral ∫ from (1,2,3 ) to (5, 7,-2 ) y dx + x dy + 4 dz by finding parametric equations for the line seg

n200080 [17]

$\vec F(x,y,z)=y\,\vec\imath+x\,\vec\jmath+3\,\vec k$

is conservative if there is a scalar function $f(x,y,z)$ such that $\nabla f=\vec F$ . This would require

$\dfrac{\partial f}{\partial x}=y$

$\dfrac{\partial f}{\partial y}=x$

$\dfrac{\partial f}{\partial z}=3$

(or perhaps the last partial derivative should be 4 to match up with the integral?)

From these equations we find

$f(x,y,z)=xy+g(y,z)$

$\dfrac{\partial f}{\partial y}=x=x+\dfrac{\partial g}{\partial y}\implies\dfrac{\partial g}{\partial y}=0\implies g(y,z)=h(z)$

$f(x,y,z)=xy+h(z)$

$\dfrac{\partial f}{\partial z}=3=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=3z+C$

$f(x,y,z)=xy+3z+C$

so $\vec F$ is indeed conservative, and the gradient theorem (a.k.a. fundamental theorem of calculus for line integrals) applies. The value of the line integral depends only the endpoints:

$\displaystyle\int_{(1,2,3)}^{(5,7,-2)}y\,\mathrm dx+x\,\mathrm dy+3\,\mathrm dz=\int_{(1,2,3)}^{(5,7,-2)}\nabla f(x,y,z)\cdot\mathrm d\vec r$

$=f(5,7,-2)-f(1,2,3)=\boxed{18}$

8 0

3 years ago

Instructions: Find the missing length indicated.

nata0808 [166]

Answer:

x = 12

Step-by-step explanation:

By applying geometric root theorem in the given triangle,

$\frac{BD}{DC}= \frac{AD}{BD}$

$BD^2=AD\times DC$

$x^{2} =16\times 9$

$x=\sqrt{144}$

$x=12$

Therefore, x = 12 will be the answer.

8 0

3 years ago

Consider the sets A = fa; b; c; ; ; ; 1; 2; 3g, B = f ; ; ; ; ; g , C = f1; 2; 3; 4; 5; 6g and D = fa; b; cg. (a) List the eleme

Ilya [14]

Answer:

hsad

Step-by-step explanation:

4 0

3 years ago

A number is selected, at random, from the set {1,2,3,4,5,6,7,8}.

Olegator [25]

Applying the formula, you have:

A = the number is prime

B = the number is odd

I assume that with "random" you imply that all numbers can be chosen with the same probability. So, we have

$P(A) = \dfrac{4}{8} = \dfrac{1}{2}$

because 4 out of 8 numbers are prime: 2, 3, 5 and 7.

Similarly, we have

$P(B) = \dfrac{4}{8} = \dfrac{1}{2}$

because 4 out of 8 numbers are odd: 1, 3, 5 and 7.

Finally,

$P(A \land B) = \dfrac{3}{8}$

because 3 out of 8 numbers are prime and odd: 3, 5 and 7.

So, applying the formula, we have

$P(\text{prime } | \text{ odd}) = \dfrac{P(\text{prime and odd})}{P(\text{odd})} = \dfrac{\frac{3}{8}}{\frac{1}{2}} = \dfrac{3}{8}\cdot 2 = \dfrac{3}{4}$

Note:

I think that it is important to have a clear understanding of what's happening from a conceptual point of you: conditional probability simply changes the space you're working with: you are not asking "what is the probability that a random number, taken from 1 to 8, is prime?"

Rather, you are adding a bit of information, because you are asking "what is the probability that a random number, taken from 1 to 8, is prime, knowing that it's odd?"

So, we're not working anymore with the space {1,2,3,4,5,6,7,8}, but rather with {1,3,5,7} (we already know that our number is odd).

Out of these 4 odd numbers, 3 are primes. This is why the probability of picking a prime number among the odd numbers in {1,2,3,4,5,6,7,8} is 3/4: they are literally 3 out of 4.

5 0

3 years ago

Help!!!!!!!!!!!!

labwork [276]

Answer:

None of the Above

Step-by-step explanation:

As it is given that

cosФ= 3/2

and Ф lies in quadrant 4

Now in quadrant 4 we know that by the rules of trigonometry that

cos Ф is positive in 4th quadrant also in 4th quadrant