A giant fish tank at the zoo contains z Halibut. The tank contains 4times as many Bluefin Tuna as Halibut. Write an equation that
represents the total number of Bluefin Tuna, y in the tank.

Answer:

(a) P(X = 18) = 0.25

(b) P(X > 18) = 0.53

(c) P(X ≤ 18) = 0.47

(d) Mean = 19.76

(e) Variance = 22.2824

(f) Standard deviation = 4.7204

Step-by-step explanation:

We are given that discrete random variable X has the following probability distribution:

            X                    P (x)             X * P(x)                         * P(x)

           13                    0.22              2.86              169              37.18

           18                    0.25              4.5                324               81

           20                   0.20               4                  400               80

           24                    0.17              4.08              576              97.92

           27                    0.16              4.32              729             116.64

(a) P ( X = 18) = P(x) corresponding to X = 18 i.e. 0.25

     Therefore, P(X = 18) = 0.25

(b) P(X > 18) = 1 - P(X = 18) - P(X = 13) = 1 - 0.25 - 0.22 = 0.53

(c) P(X <= 18) = P(X = 13) + P(X = 18) = 0.22 + 0.25 = 0.47

(d) Mean of X, = ∑X * P(x) ÷ ∑P(x) = (2.86 + 4.5 + 4 + 4.08 + 4.32) ÷ 1

                                                         = 19.76

(e) Variance of X, = ∑ * P(x) -

                                 = 412.74 - = 22.2824

(f) Standard deviation of X, = = = 4.7204 .

Final answer:

The probabilities for the given X values are calculated by summing the relevant given probabilities. The mean of X is computed as a weighted average, and the variance and standard deviation are calculated using formula involving the mean and the individual probabilities.

Explanation:

The probability P(18) is given as 0.25 according to the distribution. The probability P(X > 18) is the sum of the probabilities for all x > 18, so we add the probabilities for x=20, x=24, and x=27, giving us 0.20 + 0.17 + 0.16 = 0.53. The probability P(X ≤ 18) includes x=18 and any values less than 18. As 18 is the lowest value given, P(X ≤ 18) is just P(18), or 0.25.

The mean μ of X is the expected value of X, computed as Σ(xP(x)). That gives us (13*0.22) + (18*0.25) + (20*0.20) + (24*0.17) + (27*0.16) = 2.86 + 4.5 + 4 + 4.08 + 4.32 = 19.76.

The variance σ 2 of X is computed as Σ [ (x - μ)^2 * P(x) ]. That gives us [(13-19.76)^2 * 0.22] + [(18-19.76)^2 * 0.25] + [(20-19.76)^2 * 0.20] + [(24-19.76)^2 * 0.17] + [(27-19.76)^2 * 0.16] = 21.61. The standard deviation σ of X is the sqrt(σ^2) = sqrt(21.61) = 4.65.

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Answer: B

Step-by-step explanation:

To find the inverse function, you switch x with y and y with x. Then, you solve for y.

                                 [switch x with y, and y with x]                        

                                 [add both sides by 4]

                                 [square root both sides]

                                   [add both sides by 1]

Now that we know the inverse function, we can actually tell that the answer is B. We know this because of the restriction that f(x) is x≤1. This makes it positive, and B the answer.

Answer:

B. -2t^2+3t+4

Step-by-step explanation:

The standard form as

ax^2 + bx + c

Option B meets that requirement, even though it has a '-' in front

Final answer:

All the given polynomials, A. t^4-1, B. -2t^2+3t+4 and C. 4t-7 are in standard form since their terms are written in descending order of their degrees.

Explanation:

In mathematical terms, a polynomial is in standard form if its terms are written in descending order of their degree, i.e. the power of the variable. This means the term with the highest power should be listed first, followed by the term with the next highest power, and so on. Let's look at the options:

• Option A: t^4-1 is in standard form because t^4 is the highest degree term and it is listed first.
• Option B: -2t^2+3t+4 is also in standard form as the terms are arranged in descending order of degree: 2 (in t^2), 1 (in t) and then 0 (in 4).
• Option C: 4t-7 is in standard form as well, with the degree of the term 4t being 1 and the degree of -7 being 0.

So, in conclusion, the polynomials in standard form from the provided options are A. t^4-1,  B. -2t^2+3t+4 and C. 4t-7.

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Answer:

Choice B: Only (-2, 9)

Step-by-step explanation:

Of the two choices, only the point (-2, 9) satisfies the equation:

... y = -2x +5

... 9 = -2(-2) +5 = 4 +5 = 9

Answer:

The correct answer is B. Only (-2,9) is a solution of the equation.

Step-by-step explanation:

To figure out if an ordered pair is a solution to an equation, you could perform a test.

Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

We have the equation

and two different ordered pairs (2, -9) and (-2, 9).

We use the x-value in the first ordered pair, x = 2, and we plug it into the equation.

If we compare with the ordered pair (2, -9), y must be equal to -9, but when we plugged x = 2 into the equation, we obtained that y = 1, so this is not a solution.

Using the x-value of the second ordered pair, x = -2, we get

Because we obtained y = 9, when we plugged x = -2, the ordered pair (-2, 9) is a solution of the equation.

The correct answer is B. Only (-2,9) is a solution of the equation.