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2 years ago

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A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag. The probability of n

ot drawing a black marble is. The probabilty of drawing a red marble is?

1 answer:

solniwko [45]2 years ago

4 0

Answer:

1/10 or 3/10 i think if im wrong im sorry

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Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

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1 year ago

-4=x-15 show how you got the answer<br><br> A.) -4/15<br> B.) -19<br> C.) -60<br> D.) 11

8090 [49]

The answer is bee haha ha

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2 years ago

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Which shape must have opposite sides that are parallel and congruent, and diagonals that are perpendicular bisectors of each oth

n200080 [17]

Answer:

Rectangle or square

Step-by-step explanation:

The diagonals are perpendicular bisectors of each other. C) All four angles of the parallelogram are right angles. Congruent diagonals eliminates the rhombus. This leaves the rectangle or the square.

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3 years ago

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A house cost $120,000 when it was purchased. The value of the house increases by 10% each year. Find the rate of growth each mon

Svetllana [295]

1200,000(1+.1)=(the answer) sorry I don't have a calculator with me.

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2 years ago

Find the mean, meadian, mode and range for each set of data 6, 9, 2, 4, 3, 6, 5

Helga [31]

Mean: Add up the numbers and divide the sum by the number of values in the set.

6 + 9 + 2 + 4 + 3 + 6 + 5 = 35

35 / 7 = 5

Median: Sort the set from the smallest value to the largest value and select the number in the middle. If the count of the set if even, then select the two middle values and take their mean average.

2, 3, 4, 5, 6, 6, 9

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So, the median average is 5.

Mode: What number appears the most frequently?

The mode of the set is 6 because it appears twice.

Range: Sort the set by ascending order and take the smallest value and subtract that from the largest value in the set.

9 - 2 = 7

The range is 7.

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2 years ago

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