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3 years ago

7

A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. what is the probability of reachi

ng into the bag and selecting a yellow marble?

2 answers:

Anastasy [175]3 years ago

8 0

Its probably 2 to 13

andre [41]3 years ago

7 0

Answer: $\frac{2}{13}$

Step-by-step explanation:

Given: The number of yellow marbles in the bag = 2

The total number of marbles in the bag = $6+2+4+1=13$

Now, the probability of reaching into the bag and selecting a yellow marble is given by:-

$P(\text{yellow})=\frac{\text{yellow marble}}{\text{total marbles}}\times100\\\\\Rightarrow\ P(\text{yellow})=\frac{2}{13}$

Hence, the probability of reaching into the bag and selecting a yellow marble= $\frac{2}{13}$

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Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

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Answer:

Step-by-step explanation:

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2 years ago

A half-filled cylindrical water tank has a water level of 20 feet high. The tank can hold 6000 cubic feet of water. Find the dia

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Answer:

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Step-by-step explanation:

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