Pls answer
woth 28 points!!

The function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.

Function is a set of instructions or statements that perform a specific task or calculation. It is a fundamental building block of a program, allowing the same code to be used multiple times. Functions help to organize code and make it easier to read and debug. They also allow for code reuse, meaning that the same code can be used in different parts of the program. Additionally, functions can be used to create libraries of code that can be shared and reused among different programs.

A function f(n) that represents the nth term of the sequence given above can be written as follows:
f(n) = 2n – 2

This function can be explained as follows:
The function f(n) represents the nth term of the given sequence. The first term of the sequence is 0, which is equal to f(1). The second term of the sequence is 2, which is equal to f(2). This pattern can be seen throughout the sequence, as each subsequent term is two more than the preceding one. Thus, the general form of the function can be written as f(n) = 2n – 2, where n represents the nth term of the sequence.

For example, when n = 5, the function f(n) = 2n – 2 = 10. This is equal to the fifth term of the sequence, 8.

Therefore, the function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.

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The standard form of the equation of f(x) is f(x) = -x² + 4x + 12

The standard form of the equation of a parabola is:

                           y = a(x - h)²+ k

Where (h, k) is the vertex of the parabola and a determines whether the parabola opens up or down.

If a is positive, the parabola opens up, and if a is negative, the parabola opens down. The value of 'a' also determines the "steepness" of the parabola.

Here we have the function f(x) shows a graph.

The graph shows a downward opening parabola with a vertex at (2, 16) a point at (-2, 0) a point at (6, 0) a point at (0, 12), and a point at (4, 12)

The vertex of the parabola is at (2, 16), which means that the axis of symmetry is x = 2. This also tells us that the equation is of the form:

f(x) = a(x - 2)² + 16

Where "a" is a constant that determines whether the parabola is upward or downward opening.

We can find the value of "a" by using one of the other points on the graph. Let's use the point (0, 12):

=> 12 = a(0 - 2)² + 16

=> -4 = 4a

=> a = -1

So the equation is:

f(x) = -(x - 2)² + 16

Expanding and simplifying this equation gives:

f(x) = -x²+ 4x + 12

Therefore,

The standard form of the equation of f(x) is f(x) = -x² + 4x + 12

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Answer:

  17.2 cubic miles

Step-by-step explanation:

You want the volume of Mt. St. Helens after an eruption removed 0.043 cubic miles of volume from its cone shape. Its radius is 3 miles, and its height was about 1.83 miles.

The formula for the volume of a cone is ...

  V = 1/3πr²h

The volume of the tip is removed from that to find the volume after the eruption.

  V = 1/3π(3 mi)²(1.83 mi) - 0.043 ≈ 17.2 mi³

After the eruption, the volume of Mount St. Helens is about 17.2 cubic miles.

__

Additional comment

The volume rounded to 1 decimal place is unaffected by the amount removed. That amount only changes the volume in the 2nd decimal place.

The simplified expression for given problem will be [tex]x^{-7}[/tex].

For the given problem,

[tex]x^2/x^9[/tex] = [tex]x^{(2-9)}[/tex] = [tex]x^{(-7)}[/tex]     (∵[tex]a^m / a^n = a^{(m-n)}[/tex])

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Answer: 170

Step-by-step explanation:

170/10=17

θ = - sin^-1(4/3)

θ = -1.18 radians

Therefore:

sin θ + cot θ = -0.8 + -0.9104 = -1.7104

So the final answer is:

-1.7104

Does this make sense? Let me know if you need more details!

Answer:

Option B

Step-by-step explanation:

sqrt(22x^6) / sqrt(11x^4) = sqrt(2x^2)
sqrt(2x^2) can be rewritten as x sqrt(2)

Answer:

The first step is to calculate the total number of months in the 8-year loan term:

8 years * 12 months/year = 96 months

Next, we can use the monthly payment amount to calculate the total payback amount:

Total payback amount = Monthly payment * Total number of months

Total payback amount = $264.64 * 96

Total payback amount = $25,455.04

So the total payback amount for the loan is $25,455.04.

To calculate the total interest paid over the life of the loan, we can use the formula:

Total interest = Total payback amount - Loan amount

The loan amount in this case is $18,000, so:

Total interest = $25,455.04 - $18,000

Total interest = $7,455.04

So the total interest paid over the life of the loan is $7,455.04.

Step-by-step explanation:

To test the claim, we need to conduct a hypothesis test with the null hypothesis being that the proportion of drowning deaths of children attributable to beaches is 0.25 and the alternative hypothesis being that it is more than 0.25.

Using a one-sample z-test with a significance level of 0.05, we can calculate the test statistic as:

z = (0.3 - 0.25) / sqrt(0.25 * 0.75 / 681) = 3.01

Since the alternative hypothesis is that the proportion is greater than 0.25, we need to find the area to the right of the test statistic in the standard normal distribution.

Using a standard normal table or calculator, we can find the p-value to be approximately 0.0013.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the proportion of drowning deaths of children attributable to beaches is more than 0.25.

Therefore, the answer is 3.01.

The Newton-Raphson formula to compute the square root of a > 0  is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]

From the question, we have the following parameters that can be used in our computation:

The list of options

Generally, the Newton-Raphson formula for a > 0 is

[tex]x_{n+1} = \frac{1}{2}(x_n + \frac{a}{x_n})[/tex]

Substitute i for n

So, we have

[tex]x_{i+1} = \frac{1}{2}(x_i + \frac{a}{x_i})[/tex]

When expanded, we have

[tex]x_{i+1} = x_i - (\frac{x_i - a}{2x_i})[/tex]

Remove brackets

So, we have

[tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]

Hence, the solution is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]

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The value of x is,

⇒ x = 8

Given that;

In a triangle,

Perpendicular = 4 feet

Hypotenuse = x

Hence, We can formulate;

⇒ cos 60 = 4 / x

⇒ 1/2 = 4/x

⇒ x = 8

Thus, The value of x is,

⇒ x = 8

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The missing section according to the pattern given is the option B or 3, 2, 8, 8.

If observed carefully, it can be noted that:

This means that for the missing section to be completed we need to consider:

Based on this, the missing section would be section 2.

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actually is really "x", which oddly enough is the 100%, and we also know that 24.5% of that is 15, so

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} x & 100\\ 15& 24.5 \end{array} \implies \cfrac{x}{15}~~=~~\cfrac{100}{24.5} \implies 24.5x=1500\implies x=\cfrac{1500}{24.5} \\\\\\ x=\cfrac{1500}{~~ \frac{245 }{10 } ~~}\implies x=\cfrac{15000}{245}\implies x=\cfrac{3000}{49}\implies x\approx 61.22[/tex]

In hypothesis testing, null hypothesis (H0) is a claim that the person conducting the research wants to test while an alternative hypothesis (H1) is a contradiction of the null hypothesis.

There are two types of tests in hypothesis testing is known.

One tailed test: In first tailed test, a claim that a parameter is greater than/ less than a value is being tested.

mean > value or mean < value.

Second tailed test: In a two tailed test, a claim that a value is equal to a value is tested,

mean = value.

Since we can see that Colleen is testing the claim that the average score of her class is the same as others against that it is different from others.

Hence, the null hypothesis is H0: mean = 514

and the alternative hypothesis is H1: mean ≠ 514

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The value of the function h(x) at x = 33 will be 550.

Given that:

Table

 x            h(x)

 3             40

 5             74

 11            176

14            227

19            312

33              a

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The relation is a linear relation. Then the slope will remain constant. Then the value of a is calculated as,

(312 - 227) / (19 - 14) = (a - 312) / (33 - 19)

85 / 5 = (a - 312) / 14

a - 312 = 238

a = 550

h(33) = 550

The value of the function h(x) at x = 33 will be 550.

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The proportion of red drum fish are less than 23 inches in length is 0.2389. So, correct option is B.

To solve this problem, we need to standardize the value of 23 inches using the given mean and standard deviation of the red drum fish length distribution. This is done by calculating the z-score using the formula:

z = (x - μ) / σ

where x is the value we want to standardize (in this case, 23 inches), μ is the mean of the distribution (24 inches), and σ is the standard deviation of the distribution (1.4 inches).

Substituting these values, we get:

z = (23 - 24) / 1.4 = -0.71

Using the z-table, we can find the proportion of the distribution that is less than -0.71, which is the same as finding the proportion of the distribution that is less than 23 inches. From the z-table, we find that the proportion is 0.2389. Therefore, approximately 23.89% of red drum fish are less than 23 inches in length.

So, correct option is B.

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The simplified form of expression [tex]\frac{(5m^3n^3)^2}{n}[/tex] is [tex]25m^6n^5[/tex]

Consider the expression [tex]\frac{(5m^3n^3)^2}{n}[/tex]

We know that the exponent rule that [tex](a\times b)^m=a^m \times b^m[/tex]

and [tex](a^m)^n=a^{m\times n}[/tex]

where a, b, m and n real numbers.

Consider the numerator of above expression.

[tex](5m^3n^3)^2[/tex]

Using the rule  [tex](a\times b)^m=a^m \times b^m[/tex] ,

[tex](5\times m^3\times n^3)^2\\\\= 5^2\times (m^3)^2\times (n^3)^2\\[/tex]

We know that the square of 5 is 25

so, 5² = 25

Now we use the rule [tex](a^m)^n=a^{m\times n}[/tex]

so, above expression becomes,

[tex]5^2\times (m^3)^2\times (n^3)^2\\\\=25\times m^{3\times 2}\times n^{3\times 2}\\\\=25\times m^6 \times n^6[/tex]

Also, we know that inverse of any value can be written as [tex]\frac{1}{a} =a^{-1}[/tex]

So, using this rule of exponent the value of 1/n would be [tex]n^{-1}[/tex]

So, the expression [tex]\frac{(5m^3n^3)^2}{n}[/tex] becomes,

[tex]\frac{(5m^3n^3)^2}{n}\\\\=\frac{25\times m^6 \times n^6}{n}\\\\=(25\times m^6 \times n^6)\times n^{-1}\\\\=25\times m^6 \times n^6\times n^{-1}[/tex]

We know that if the base of exponents are same then we add the powers of exponents.

So, our expression becomes,

[tex]=25\times m^6\times n^{6-1}\\\\=25\times m^6\times n^5[/tex]

This is the required expression.

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If the radius increases, height decreases, Therefore option no 4 is correct

If the radius of a cylinder changes, however its volume remains the same, then the height of the cylinder have to change.

Mainly, if the radius increases, then the height must decrease & if the radius decreases then the height must to increase. this is because the volume of a cylinder is given by means of the formulation:

[tex]V = \pi r^2h[/tex]

In which V is the volume, r is the radius &h is the height. If we keep the volume constant, and increase the radius, then we ought to lower the height in order to make amends for the increased extent.

Similarly, if we decrease the radius, then we must increase the height to catch up on the reduced volume.

Therefore, the appropriate answer is:

If the radius increases, height decreases

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Answer:

x= -0.461

x= 1.086

Step-by-step explanation:

using the quadratic formula

A=8, B=-5, C=-4

The evaluate

[tex]x=\frac{-(-5) +\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8} and x=\frac{-(-5) -\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8}[/tex]

calculate

[tex]x=\frac{5+\sqrt{25+128} }{16} } and x=\frac{5-\sqrt{25+128} }{16} }[/tex]
Simplify

[tex]x=\frac{5+3\sqrt{17} }{16} and x=\frac{5-3\sqrt{17} }{16}[/tex]

simply  

x= -0.461 and x= 1.086

Answer:

£77

Step-by-step explanation:

If his nan gave him 30%, he would have to pay the remaining 70%.

70% of 110:

10%=£11

so, 11x7= 77

The area of the figure is determined as 126 in².

option D.

The area of a shape describes the measure of the amount of space enclosed by a two-dimensional shape or surface. It is typically expressed in square units.

The area of the figure is calculated as follows;

Total area = area of triangle + area of rectangle

Area of triangle = ¹/₂ x base x height

Area of triangle = ¹/₂ x 18 in x 6 in

Area of triangle = 54 in²

Area of rectangle = 18 in x 4 in

Area of rectangle = 72 in²

Total area of the figure = 54 in² + 72 in² = 126 in²

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The circumference of the given circle is 22.26 meters.

For a circle of diameter D, the circumference is defined by the following formula:

C = pi*D

Where pi = 3.14

Here we know taht the diameter is 7.09 meters, then we can input that in the formula above to get:

C = 3.14*7.09 m

C = 22.2626 m

Rounding to 2 decimals, we will get:

C = 22.26 meters.

That is the circumference of the circle.

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If ∆ABC and ∆DEF are similar and angle B is 62° then angle E is also 62°

Similar triangles are triangles that have the same shape, but their sizes may vary.

These are some of the rules that let us know if two triangles are similar.

1. The corresponding angles of similar triangles are congruent i.e they are equal

2. The ratio of the corresponding sides of similar triangles are equal.

With these rules, it shows that;

angle C = angle F

angle A = angle D

angle B = angle E

Therefore if angle B = 62°, then angle E is also 62°.

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The function rule is solved and the equation is g ( x ) = 3x + 5

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = 3x + 5

On simplifying , we get

when x = { -2 , 0 , 1 , 3 , 4 }

Now , the values of y are given by

g ( -2 ) = 3 ( -2 ) + 5

g ( -2 ) = -1

g ( 0 ) = 5

g ( 1 ) = 8

g ( 3 ) = 14

g ( 4 ) = 17

Hence , the function is solved

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The solution is, 4/27 is the probability of picking a red marble, replacing it, and then picking a blue marble.

We have,

6 red marbles, 8 blue marbles and 4 yellow marbles.= 18 total marbles

P(red marble) = number red marbles / total

                      =6/18 = 1/3

We put the marble back

6 red marbles, 8 blue marbles and 4 yellow marbles.= 18 total marbles

P(blue marble) = number blue marbles / total

                      =8/18 = 4/9

P(red, replace. blue) = P(red) * P (blue)

                                  = 1/3 * 4/9 = 4/27

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complete question:

A bag has 6 red marbles, 8 blue marbles and 4 yellow marbles. What is the probability of picking a red marble, replacing it, and then picking a blue marble?

Answer:

Answer: (C) $2,518.59.

Step-by-step explanation:

To find the amount of money you will have in the account after 2 years, we can use the formula for the future value of an annuity:

FV = P * (((1 + r/n)^(nt) - 1) / (r/n))

where:

FV = the future value of the annuity

P = the monthly payment, which is $100

r = the annual interest rate, which is 4% expressed as a decimal (0.04)

n = the number of times the interest is compounded in a year, which is 12 (monthly)

t = the time the money is invested for, which is 2 years

Substituting the given values into the formula, we get:

FV = 100 * (((1 + 0.04/12)^(12*2) - 1) / (0.04/12))

FV = 100 * (((1.00333333333)^24 - 1) / (0.00333333333))

FV = 2,518.59 (rounded to the nearest cent)

Therefore, you will have $2,518.59 in the account after 2 years. Answer: (C) $2,518.59.

Answer:

Step-by-step explanation:

The 90% confidence interval for the mean amount of time spent in stage IV sleep is (45.04, 50.96) minutes.

To compute the confidence interval, we can use the formula:

CI = x ± z*(σ/√n)

where:

x = sample mean = 48 mins

σ = sample standard deviation = 14 mins

n = sample size = 61

z = z-score corresponding to the confidence level of 90%, which can be found using a z-table or calculator. For a 90% confidence level, the z-score is 1.645.

Plugging in the values, we get:

CI = 48 ± 1.645*(14/√61)

CI = 48 ± 2.96

Therefore, the 90% confidence interval for the mean amount of time spent in stage IV sleep is (45.04, 50.96) minutes.

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The inequality that would represent the number line given is expressed as: D. x > -1.

The inequality of a number line tells the possible values of x. It shows where the values lies on a number line.

First, identify the inequality sign in question. In this number line given, there is an open or unshaded circle at -1, and an arrow that points to your right. This means the inequality sign would be >.

Thus, it implies that the values of x does not include -1, which means that possible values of x are greater than -1 but not equal to 1.

The inequality would be: x > -1.

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well, let's find out how much will it be in each state.

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 45}}{\left( \cfrac{6.5}{100} \right)45} ~~ \approx ~~ \stackrel{ \textit{tax in Florida} }{2.93} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{4.5\% of 45}}{\left( \cfrac{4.5}{100} \right)45}~~ \approx ~~ \stackrel{ \textit{tax in Alaska} }{2.03}\hspace{5em}2.93-2.03~~ \approx ~~ \text{\LARGE 0.90}[/tex]