lizzy is tiling the kitchen floor for the first time. she had a tough time at first and placed only 5 tiles the first day. she started to go faster, and by the end of day 4 she had places 35 tiles. she worked at a steady rate after the first day. use an equation in point slope form to determine how many days lizzy took place all of 100 tiles needed to finish the floor

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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).

Answer:

5

Step-by-step explanation:

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.

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 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?

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.

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.

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].

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.

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.