QUIZ:

Brainliest to the first one that is correct

Natali5045456 [20]

Answer:

7 Units down

and

5 Units to the right

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

There are 9 people taking part in a raffle.

Marianna [84]

Answer:

Probability of event A: 1/504

Probablity of event B: 1/84

Explanation:

1. Event A: Bob is the first prize winner, Lena is second, and Ann is third,

The probability that Bob is the first prize winner is one outcome out of 9 possible outcomes, so it is 1/9

The probability that Lena is second, after Bob is the first prize winner is one outocome out of 8 possible outocmes, so it is 1/8

The probability Ann is third, after Bob y first and Lena is second is 1/7.

Thus, the joint probability that Bob is the first prize winner, Lena is second, and Ann is third is the product of the three calculated probabilities:

1/9 × 1/8 × 1/7 = 1 / (9×8×7) = 1/504 ← answer

2. Event B: The first three prize winners are Soo, Omar, and Kira, regardless of order

When the order does not matter, the number of combinations for three different persons win the 3 prizes is C(3,3), which is computed with the corresponding formula:

$C(m,n)=\dfrac{m!}{n!(m-n)!}$

Thus:

$C(3,3)=\dfrac{3!}{(3!(3-3)!}=1$

And the number of possible combinations of winners is C(9,3):

$C(9,3)=\dfrac{9!}{3!(9-3)!}=84$

Then, the probability is the number of favorable combinations, C(3,3) = 1, divided by the number of possible combinations, C(9,3) = 84:

1/84 ← answer

8 0

4 years ago

Find the general solution of the equation: (y^2-2xy)dx + (2xy-x^2)dy = 0

lys-0071 [83]

The ODE is exact, since

$\dfrac{\partial(y^2-2xy)}{\partial y}=2y-2x$

$\dfrac{\partial(2xy-x^2)}{\partial x}=2y-2x$

so there is solution $f(x,y)=C$ such that

$\dfrac{\partial f}{\partial x}=y^2-2xy$

$\dfrac{\partial f}{\partial y}=2xy-x^2$

Integrating both sides of the first PDE wrt $x$ gives

$f(x,y)=xy^2-x^2y+g(y)$

Differentiating both sides wrt $y$ gives

$\dfrac{\partial f}{\partial y}=2xy-x^2+\dfrac{\mathrm dg}{\mathrm dy}=2xy-x^2$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C$

Then the solution to the ODE is

$f(x,y)=\boxed{xy^2-x^2y=C}$

# # #

Alternatively, we can see that the ODE is homogeneous, since replacing $x\to tx$ and $y\to ty$ reduces to the same ODE:

$((ty)^2-2(tx)(ty))\,\mathrm d(tx)+(2(tx)(ty)-(tx)^2)\,\mathrm d(ty)=0$

$t^3(y^2-2xy)\,\mathrm dx+t^3(2xy-x^2)\,\mathrm dy=0$

$(y^2-2xy)\,\mathrm dx+(2xy-x^2)\,\mathrm dy=0$

This tells us we can solve by substituting $y(x)=xv(x)$ , so that $\mathrm dy(x)=x\,\mathrm dv(x)+v(x)\,\mathrm dx$ , and the ODE becomes

$(x^2v^2-2x^2v)\,\mathrm dx+(2x^2v-x^2)(x\,\mathrm dv+v\,\mathrm dx)=0$

$v(v-2)\,\mathrm dx+(2v-1)(x\,\mathrm dv+v\,\mathrm dx)=0$

$3v(v-1)\,\mathrm dx+x(2v-1)\,\mathrm dv=0$

which is separable as

$\dfrac{1-2v}{3v(v-1)}\,\mathrm dv=\dfrac{\mathrm dx}x$

Integrating both sides gives

$-\dfrac13\ln|v(1-v)|=\ln|x|+C$

$v(1-v)=\dfrac C{x^3}$

and solving in terms of $y(x)$ ,

$\dfrac yx\left(1-\dfrac yx\right)=\dfrac C{x^3}$

$xy(x-y)=C$

$\boxed{x^2y-xy^2=C}$

6 0

3 years ago

Erm I don't understand-

Lana71 [14]

Answer:

1. (7+3)/2

2. 6, 3

3. 5/6

4. 500, 4000

Step-by-step explanation:

1. We are adding 7 and 3 so use the plus sign, THEN we divide by 2

Because we are adding first, put parentheses

(7+3)/2

2. Nearest whole means whole number (so basically no decimal)

5.823 --> 6 (because 8 is closer to 10 than 0)

3.147 --> 3 (because 1 is closer to 0)

3. 1/3+1/2

Find a common difference, which is 6

Multiply to get 6

1/3*2= 2/6

1/2*3=3/6

3+2=5/6 (when adding keep denominator the same)

4. There are 100 centimeters in a meter

5*100= 500 centimeters

There are 1000 grams in a kilogram

4*1000= 4000 grams

Hope this helps, lemme know if somethings still unclear!!

6 0

3 years ago

Which of the following correctly combines these terms? 3a + 6b - 7a + (-3b) + 9c

ElenaW [278]

Answer:

I

Step-by-step explanation:

We have to added up the like therms

like therms are therms with the same literal parts

3a - 7a = -4a

6b-3b= 3b

-4a + 3b+ 9c

8 0

3 years ago