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AfilCa [17]
3 years ago
14

Suppose that an urn contains 3 black marbles, 7 yellow marbles, and 10 green marbles. If one marble is selected, determine the p

robability that it is green. The answer should be an integer or a simplified fraction.
Mathematics
1 answer:
Yuliya22 [10]3 years ago
3 0

Answer:

1/2

Step-by-step explanation:

Simple probability is a ratio of the number of ways the thing we want to happen can to the total possible outcomes.

(For example, we flip a coin and want heads, but it can land on heads or tails. Our probability of getting heads is 1/2, one way to get heads over the 2 possible outcomes)

So for this problem, there's  20 possible things that CAN happen (3 + 7 + 10) and 10 ways we get what we want (a green marble).

Our probability of getting a green marble is \frac{10}{20\\}, which simplifies to \frac{1}{2}

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The number of salmon swimming upstream to spawn is approximated by the following function:
umka2103 [35]

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

S'(x) = -3\cdot x^{2}+4\cdot x +405 (Eq. 1)

S''(x) = -6\cdot x +4 (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for x:

-3\cdot x^{2}+4\cdot x +405 = 0

And all roots are found by Quadratic Formula:

x_{1} \approx 12.305\,^{\circ}C, x_{2}\approx -10.971\,^{\circ}C

Only the first root is inside the given interval of the function. Hence, the correct answer is:

x \approx 12.305\,^{\circ}C

Now we evaluate the second derivative at given result. That is:

S''(12.305) = -6\cdot (12.305)+4

S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

5 0
3 years ago
Which of the following statements best describes the graph of x + y = 4?
joja [24]

Answer: The correct option is, It is a line joining the points whose x and y coordinates add up to 4.

Step-by-step explanation:

The given equation is, x+y=4

when we take x = 1 then

1+y=4

y=3

when we take x = 2 then

2+y=4

y=2

From this we conclude that the sum of 'x' and 'y' coordinates is always equal to 4.

Hence, the correct answer is, It is a line joining the points whose x and y coordinates add up to 4.

5 0
3 years ago
The price of Veronica’s meal before tax and tip was $11.92. Veronica paid 8% tax, then added a 15% tip to the total. To the near
Alecsey [184]

Answer:

$14.80

Step-by-step explanation:

The price of Veronica's meal before tax and tip was $11.92. Veronica paid 8% tax, then added a 15% tip to the total

8 0
3 years ago
Saul earned $25 for painting his neighbor's fence. He spent $11 at the store and put the rest into his bank account.
PtichkaEL [24]
The answer is $14 Saul put into his bank accout
3 0
3 years ago
Which of these is a geometric sequence?
11Alexandr11 [23.1K]

Answer:

The correct answer is D

Step-by-step explanation:

7 0
3 years ago
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