Factor of 3x^2 - 6x 3

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Answer:

5

Step-by-step explanation:

Using the exponential decay function for Pacific halibut, it is calculated that approximately 24.7% of the original cohort is still alive after 7 years.

To approximate the percentage of the original number of Pacific halibut still alive after 7 years, we use the exponential decay model provided, N(t) = N0e^-0.2t. Plugging in t = 7 years into the equation gives us:

N(7) = N0e^-0.2(7) = N0e^-1.4.

To find this percentage, we can multiply the value of e^-1.4 by 100%. First, we calculate e^-1.4 approximately using a calculator:

e^-1.4 ≈ 0.24660

Multiplying by 100 to get the percentage: 0.24660 × 100% ≈ 24.7%.

Therefore, approximately 24.7% of the original Pacific halibut cohort is still alive after 7 years.

Answer:

C- x=y^2-7

Step-by-step explanation:

To find the inverse of the function you can just exchange the name of the variables, change x for y and y for x..

original (direct) function: y = x^2 - 7

inverse function x = y^2 - 7

Then, the answer is the option c.

To calculate the value of f(-2), a function definition f(x) is required. The information provided does not include this, making it impossible to determine the value of f(-2) without further details.

In the context given, it appears that the question f(-2) refers to finding the value of a function f when the variable is -2. However, the provided information does not include a function or formula for f(x) that can be evaluated at x = -2. The details given seem to be related to various mathematical and scientific principles such as lens formula, chemical reactions, and quadratic equations, but none of these can be directly linked to a function f(x) to evaluate f(-2). To answer the question about the value of f(-2), the explicit function definition f(x) is necessary. Without this definition, it is impossible to determine the value of f(-2).

The value of f(2) for the function f(x) = 2x^2+1 is 9. This is calculated by substituting '2' into the function, squaring it, multiplying by 2, and then adding 1.

To find the value of f(2) for the function f(x) = 2x^2+1, you simply substitute '2' for every instance of 'x' in the function's formula. Here's the step-by-step calculation:
Replace 'x' with '2': 2(2)^2 + 1

Multiply '2' by '4': 8 + 1
Add '1' to '8': 9
Therefore, the value of f(2) is 9.
The probable question maybe:
What is the value of f(2) if f(x) = 2x^2+1?

The number 112,300 written in word form is 'one hundred twelve thousand three hundred'.

To write the number 112,300 in word form, you would write it as one hundred twelve thousand three hundred.

When writing numbers in word form, it's important to break them down into their place values and then use conjunctions such as 'and' where appropriate, typically between the hundreds and smaller units. In this case, there are no smaller units, so 'and' isn't used. Instead, we clearly express each place value starting from the highest, which is the hundred thousands, followed by the thousands, then hundreds, tens, and ones, though here the tens and ones places are zero and do not need to be included in the word form.

we have

[tex] y=\frac{2}{3} x+1 [/tex] ----------> equation [tex] 1 [/tex]

[tex] y=-\frac{2}{3} x-1 [/tex] ----------> equation [tex] 2 [/tex]

using a graph tool

we know that

the intersection point of both lines is the solution of the system

so

the solution is the point [tex] (-1.5,0) [/tex]

see the attached figure

therefore

the answer is

The solution of the system is the point [tex] (-1.5,0) [/tex]

The graph in the attached figure

Answer:

[tex]3(k+d)[/tex]

Step-by-step explanation:

We have been given a sentence. We are supposed to represent our given statement as an expression.

Sentence:

3 times the sum of k and d.

We know that we can find sum of k and d by adding them as shown:

[tex]k+d[/tex]

Since 3 is multiplied to sum of k and d, so sum of k and d will be inside parenthesis.

[tex]3(k+d)[/tex]

Therefore, our required algebraic expression would be [tex]3(k+d)[/tex].

Final answer:

The sequence ln(2n² +1) - ln(n² +1) simplifies to ln[(2n² + 1)/(n² + 1)]. As n approaches infinity, the sequence converges and the limit is ln(2).

Explanation:

To determine whether the sequence ln(2n² +1) - ln(n² +1) converges or diverges, we can use the properties of logarithms and limits.

First, we rewrite the expression using the property of logarithms that ln(a) - ln(b) = ln(a/b).

Our sequence then becomes ln[(2n² + 1)/(n² + 1)]

As n approaches infinity, the terms 2n² and n² dominate the behavior of the sequence.

Thus, the sequence can be approximated by ln(2n²/n²), which simplifies to ln(2).

Since ln(2) is a constant, we can conclude that the sequence converges and the limit is ln(2).

To find the z-score that satisfies the condition of 20% of the total area being to the left of z, use the z-table to locate the closest area to 0.20 and its corresponding z-score.

To find the z-score that satisfies the condition of 20% of the total area being to the left of z, you can use the z-table. First, locate the area in the table that is closest to 0.20, which is 0.1995.

The corresponding z-score is approximately -0.85.

Therefore, the z-score that best satisfies the condition is -0.85.

Answer:

743.41 feet.

Step-by-step explanation:

In this question it is given that height of the tower OS is 175 feet and angle of depression ∠ASB = 13°15'

angle of depression to the boat B will be equal to the angle of elevation "∠B"

Now  ∠ASB = 13°15' ≈ 13° + [tex](\frac{15}{60})[/tex]°

= 13° + (0.25)°

= 13.25°

Now tan ∠B = [tex]\frac{SO}{OB}[/tex]

 tan (13.25) =  [tex]\frac{175}{x}[/tex]

            x     =  [tex]\frac{175}{0.2354}[/tex]

                   = 743.41 feet.

Motorboat is 743.41 feet far from the shore.

Given that tan(x) is -12/5 in Quadrant II where sin is positive and cos is negative, we can use the Pythagorean theorem to find sin(x) and cos(x), which are then used to calculate sin(2x), cos(2x), and tan(2x).

Given tan(x) = -12/5, x is in Quadrant II. Since tangent is negative in Quadrant II, we know that sin(x) is positive and cos(x) is negative. Using Pythagorean theorem, we can find sin(x) and cos(x). sin(x) = sqrt(1 - cos²(x)) and cos(x) = -sqrt(1-sin²(x)).

The values for sin(x) and cos(x) can then be plugged into the formulas sin2x = 2sin(x) cos(x), cos2x = cos²(x)-sin²(x) and tan2x = sin2x / cos2x to find sin(2x), cos(2x), and tan(2x).

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To calculate the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean, one must find the corresponding z-scores and use a standard normal distribution table. The probability is approximately 39.58%.

To find the probability that a windscreen wiper lasts for a time that is not within 1.7 years of the mean lifetime of three years, we can use the properties of the normal distribution. We are given a mean (μ) of 3 years and a standard deviation (σ) of 2 years. We are interested in the probability that a wiper lasts less than 1.3 years (3 - 1.7) or more than 4.7 years (3 + 1.7).

First, we need to calculate the z-scores for 1.3 and 4.7 years:

Z1 = (1.3 - 3) / 2 = -0.85

Z2 = (4.7 - 3) / 2 = 0.85

Using a standard normal distribution table or a calculator, we find the probabilities corresponding to these z-scores. The probability of a wiper lasting less than 1.3 years is P(Z < -0.85), and the probability of lasting more than 4.7 years is P(Z > 0.85).

Since the normal distribution is symmetric, P(Z < -0.85) is equal to P(Z > 0.85). Thus, we only need to calculate one of these probabilities and double it to find the total probability. Let's say P(Z > 0.85) = p, then the total probability is 2p.

Assuming P(Z > 0.85) = 0.1979 (from standard normal distribution tables), the total probability is:

Probability = 2 * 0.1979 = 0.3958

Therefore, the probability that a windscreen wiper lasts for a time not within 1.7 years of the mean lifetime is approximately 0.3958 or 39.58%.

Final answer:

By standardizing the values and using a standard normal distribution table, we can find the probability to be approximately 0.7422 or 74.22%.

Explanation:

To solve this problem, we can use the normal distribution. Given that the mean lifetime of the windscreen wipers is 3 years with a standard deviation of 2 years, we want to find the probability that the wiper lasts for a time that is not within 1.7 years of the mean lifetime.

First, we need to standardize the values by calculating the z-scores.

The z-score formula is (x - mean) / standard deviation. In this case, we have x = 1.7, mean = 3, and standard deviation = 2.

Plugging in these values, we get a z-score of -0.65.

Using a standard normal distribution table or calculator, we can find the probability corresponding to a z-score of -0.65.

The area under the curve to the left of -0.65 is approximately 0.2578. Since we want the probability that the wiper lasts for a time that is not within 1.7 years of the mean, we subtract this probability from 1.

Therefore, the probability is approximately 1 - 0.2578 = 0.7422, or 74.22%.