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3 years ago

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Numbered disks are placed in a box and one disk is selected at random. If there are 6 red disks numbered 1 through 6, and 2 yell

ow disks numbered 7 through 8, find the probability of selecting a red disk, given that an odd-numbered disk is selected.

1 answer:

Tatiana [17]3 years ago

6 0

Answer:

$\frac{3}{4}$

Step-by-step explanation:

Total number of red disk=6

Total number of yellow disk=2

Total disk=6+2=8

Odd number=1,3,5,7=4

Odd number on red disk=1,3,5=3

Probability, $P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}$

Using the formula

The probability of getting odd number disk= $\frac{4}{8}=\frac{1}{2}$

The probability of getting odd numbered red disk= $\frac{3}{8}$

The probability of selecting a red disk,given that an odd numbered disk is selected= $\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}$

Using conditional probability

$P(A/B)=\frac{P(A\cap B)}{P(B)}$

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Given:

The leading coefficient of a polynomial is 8.

Polynomial roots are 1 and 2.

The graph passes through the point (4,5).

To find:

The 3rd root and the equation of the polynomial.

Solution:

The factor form of a polynomial is:

$y=a(x-c_1)(x-c_2)...(x-c_n)$

Where, a is a constant and $c_1,c_2,...,c_n$ are the roots of the polynomial.

Polynomial roots are 1 and 2. So, $(x-1)$ and $(x-2)$ are the factors of the polynomial.

Let the third root of the polynomial by c, then $(x-c)$ is a factor of the polynomial.

The leading coefficient of a polynomial is 8. So, a=8 and the equation of the polynomial is:

$y=8(x-1)(x-2)(x-c)$

The graph passes through the point (4,5). Putting $x=4,y=5$ , we get

$5=8(4-1)(4-2)(4-c)$

$5=8(3)(2)(4-c)$

$5=48(4-c)$

Divide both sides by 48.

$\dfrac{5}{48}=4-c$

$c=4-\dfrac{5}{48}$

$c=\dfrac{192-5}{48}$

$c=\dfrac{187}{48}$

Therefore, the 3rd root on the polynomial is $\dfrac{187}{48}$ .

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

The image of the point (2, 1) under a translation is (5, -3).

It means when we horizontally move 3 units to the RIGHT i.e. adding 3 units to the x-coordinate and vertically move 4 units DOWN i.e. subtracting 4 units from the y-coordinate of the original point (2, 1), we get the coordinates of the image (5, -3).

Thus,

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