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The expanded form of the function f(x) = \((3x - 4)^4 is 81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

To expand the function f(x) =\((3x - 4)^4\) we can apply the binomial theorem, which states that for any real number a and b, and a positive integer n, the expansion of (a + b)^n can be computed using the following formula:

\((a + b)^n = C(n, 0) * a^n * b^0 + C(n, 1) * a^(n-1) * b^1 + C(n, 2) * a^(n-2) * b^2 + ... + C(n, n-1) * a^1 * b^(n-1) + C(n, n) * a^0 * b^n\)

where C(n, k) represents the binomial coefficient, which can be computed as C(n, k) = n! / (k! * (n-k)!), where "!" denotes the factorial function.

Now, let's apply this formula to expand the function\((3x - 4)^4:\)

f(x) =\(C(4, 0) * (3x)^4 * (-4)^0 + C(4, 1) * (3x)^3 * (-4)^1 + C(4, 2) * (3x)^2 * (-4)^2 + C(4, 3) * (3x)^1 * (-4)^3 + C(4, 4) * (3x)^0 * (-4)^4\)

Simplifying this expression will give us the expanded form of f(x). Let's calculate each term step by step:

f(x) = \((1 * 1 * 81x^4 * 1) + (4 * 3 * 27x^3 * -4) + (6 * 9 * 9x^2 * 16) + (4 * 27 * 3x * -64) + (1 * 81 * 1 * 256)\)

Simplifying further:

f(x) = \(81x^4 - 432x^3 + 864x^2 - 768x + 256\)

Therefore, the expanded form of the function f(x) = \((3x - 4)^4 is 81x^4 - 432x^3 + 864x^2 - 768x + 256.\)

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Answer:

The Father's birthday is on April 11.

Step-by-step explanation:

Ben: After the 10th, but before 20th, so 11, 12, 13, 14, 15, 16, 17, 18, or 19

Bob: After 5th, but before 12th, so 6, 7, 8, 9, 10, 11

Only overlapping date is the 11th

Answer:

18 monthly payments are required to complete payment

Step-by-step explanation:

We start with our $1,424.

Then subtract $560 from the original number above.

Leaving us with $864.

We then divide the $864 by $48 and we end up with 18.

So our answer is 18 monthly payments are required to complete payment.

Answer:

B

Step-by-step explanation:

See how the lowest it goes is -6 at 0 and 1, but then the further you go from those points f(x) increases

The end behavior of the given function is x=> -∞ f(x) => ∞ and x=>∞, f(x)=>∞.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

From the graph attached below, we can say that the function f(x) is a quadratic function.

Since for quadratic function,

Thus, option B is correct. As x=> -∞ f(x) => ∞ and x=>∞, f(x)=>∞.

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Answer:

hope you can understand

Answer:

D

Step-by-step explanation:

From the graph, the y-intercept of f(x) is 2 and since the y-intercept is when x = 0, it would fall into the x ≤ 1 category so the y-intercept of g(x) is 0 - 4 = -4. Since 2 > -4, the answer is D.

Answer:

APT

Step-by-step explanation:

Make sure they are corresponding with each other so BRO in lefthand triangle corresponds with APT in the righthand one, therefore your answer is APT

Answer:

The answer is APT!

Step-by-step explanation:

The triangle is flipped, but is otherwise the same. So, wherever BRO is on the first triangle, APT will be on the second! I don't know if that explanation makes much sense, but I hope it helps haha.

When a circle is inscribed in a semicircle, the diameter of the circle is equal to the radius of the semicircle. So, the diameter of the circle in this case is equal to 4.

Let O be the center of the circle and A, B, C be three points of intersection between the circle and the semicircle.   Area of the shaded region = (Area of the semicircle) - (Area of the circle) - (Area of ΔABC)Area of the semicircle with radius 2 = (1/2)π(2)² = 2πArea of the circle with diameter 4 = π(2²) = 4π Side of triangle ΔABC = 2, Radius of the circle = 2. The height of the triangle is equal to the radius of the circle, i.e., 2. Therefore, ΔABC is an equilateral triangle with a side of length 2. Area of an equilateral triangle with side s = (s²√3)/4. Area of the equilateral triangle ΔABC = (2²√3)/4 = √3The area of the shaded region = 2π - 4π - √3 = 2π - 4π/3 = 2π/3. Fraction of the semicircle's area that is shaded = Shaded area / Total area of the semicircle= (2π/3)/ (2π)= 1/3Therefore, the fraction of the semicircle's area that is shaded is 1/3. Answer: (D) 2/3.

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Answer:

option A is the correct answer

Answer:

A, 62+x=90

Step-by-step explanation:

Complementary angles are two angles that add up to 90.

Answer:

Step-by-step explanation:

Prime factorize 12 , 28 , 21  and 16

12 = 2 * 2 * 3 = 2² * 3

28 = 2 * 2 * 7 = 2² *7

21 = 3 * 7

16 = 2 * 2 * 2 * 2 = 2⁴

\(\dfrac{12^{7}*28^{6}}{21^{7}*16^{6}}=\dfrac{(2^{2}*3)^{7}*(2^{2}*7)^{6}}{(3*7)^{7}*(2^{4})^{6}}\\\\\\\\=\dfrac{2^{2*7}*3^{7}*2^{2*6}*7^{6}}{3^{7}*7^{7}*2^{4*6}}\\\\\\=\dfrac{2^{14}*3^{7}*2^{12}*7^{6}}{3^{7}*7^{7}*2^{24}}\\\\\\=\dfrac{2^{14+12-24}*3^{7-7}}{7^{7-6}}\\\\\\=\dfrac{2^{2}*3^{0}}{7^{1}}\\\\\\=\dfrac{2^{2}}{7}\)

Hint:

\(a^{m}*a^{n}=a^{m+n}\\\\\\(a^{m})^{n}=a^{m*n}\\\\\dfrac{a^{m}}{a^{n}}=a^{m-n} \ if \ m >n\\\\\\\dfrac{a^{m}}{a^{n}}=\dfrac{1}{a^{n-m}} \ if \ n>m\)

The given formula represents a binomial distribution, and the probability of success in this formula is 0.35.

In a binomial distribution, we are interested in the probability of achieving a specific number of successes in a fixed number of independent trials, where each trial has the same probability of success.

The formula P(x = 3) = 9C3 (0.35)³ (0.65)⁶ represents the probability of getting exactly 3 successes in 9 trials.

The term 9C3 represents the number of ways to choose 3 successes from 9 trials, and (0.35)³ (0.65)⁶ represents the probability of getting 3 successes and 6 failures.

The binomial distribution is commonly used in situations where there are only two possible outcomes, such as success or failure, and the trials are independent of each other.

The probability of success, denoted as p, is a key parameter in the binomial distribution.

In this formula, the probability of success is 0.35, indicating that each individual trial has a 35% chance of being successful.

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Answer:

ight, whats good.

To calculate the percentage of students who brought lunch from home, we can use the following formula:

Percentage = (Number of students who brought lunch from home / Total number of students) * 100

Given:

Number of students who ate school lunch = 114

Number of students who brought lunch from home = 266

Total number of students = Number of students who ate school lunch + Number of students who brought lunch from home = 114 + 266 = 380

Plugging in these values into the formula:

Percentage = (266 / 380) * 100 = 70%

So, 70% of the students brought lunch from home.

The correct answer is option  A: The random variable is discrete. A decibel is a unit of measure used to quantify the loudness or intensity of sound.

From 0 dB (the quietest level of sound) to 140 dB (the loudest level of sound), it is measured on a logarithmic scale (the highest level of sound).

The decibel level of a siren is normally between 110 and 120 dB, which is regarded to be within or close to the threshold of human hearing.

The decibel level of a siren is measured on a logarithmic scale, making it a discrete variable. This indicates that it is measured in whole numbers rather than fractions of a decibel.

For instance, a siren's decibel level can be 110 dB, 111 dB, 112 dB, etc., but it cannot be 110.5 dB or 111.5 dB. Therefore, the decibel level of a siren is a discrete variable.

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Answer:

12 sides

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

since the polygon is regular then the exterior angles are congruent

number of sides = 360° ÷ 30 = 12

Answer:

12.

Step-by-step explanation:

Answer:

The area of the base of the rectangular box is 2x² + 4x - 3 square units and the height is x units.

So the volume of the box can be found by multiplying the area of the base by the height:

V = (2x² + 4x - 3) x (x)

V = 2x³ + 4x² - 3x

Therefore, the polynomial expression for the volume of the box is 2x³ + 4x² - 3x.

Answer:

2x^3 + 4x^2 - 3x

Step-by-step explanation:

area of base = 2x^2 + 4x - 3 = Length x Breadth

Height of box = x

volume of box = Height x Length x Breadth

= (2x^2 +4x - 3) x

= 2x^3 + 4x^2 - 3x

Answer:

Step-by-step explanation:

42 because we do

4x19=76+8=84 which is the total for br and the total for x stays constant which. is 19 so we so

(2x19)+4 2x19=38+4=42

Using the combination formula, the probabilities are given as follows:

a) P(4 seniors) = 0.0008.

b) P(1 of each) = 0.0999.

c) P(2 sophomore, 2 freshmen) = 0.0225.

d) P (at least one senior) = 0.5866.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the formula presented below, involving factorials.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this problem, 4 captains are taken from a set of 13 + 13 + 10 + 16 = 52, hence the number of outcomes is:

\(C_{52,4} = \frac{52!}{4!48!} = 270725\)

The number of outcomes with four seniors is given as follows:

\(C_{10,4} = \frac{10!}{4!6!} = 210\)

Hence the probability is:

p = 210/270725 = 0.0008.

With no seniors, the number of outcomes is:

\(C_{42,4} = \frac{42!}{4!38!} = 111930\)

Hence with at least one senior, the number of outcomes is:

270725 - 111930 = 158795.

Hence the probability is:

p = 158795/270725 = 0.5866.

With one of each, the number of outcomes is:

13 x 13 x 10 x 16 = 27040

Then the probability is:

27040/270725 = 0.0999.

With two sophomores and two freshmen, the number of outcomes is:

\(C_{13,2} \times C_{13,2} = \frac{13!}{2!11!} \times \frac{13!}{2!11!} = 6084\)

Then the probability is:

6084/270725 = 0.0225.

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There are several different sampling methods that could be employed for this study, including:

Simple random sampling: This method involves randomly selecting a certain number of students from each campus and measuring the distance between their hometowns and their campuses.

Stratified random sampling: This method involves dividing the student population at each campus into different strata (e.g. by major or year in school) and then randomly selecting a certain number of students from each stratum.

Cluster sampling: This method involves randomly selecting a certain number of campuses and then measuring the distance between the hometowns of all students at those campuses and their respective campuses.

Multi-stage sampling: This method involves using a combination of the above methods, such as first using cluster sampling to select a certain number of campuses and then using stratified random sampling to select a certain number of students from each campus.

This study would be an enumerative study because it seeks to measure the characteristics of a population, in this case, the average distance between the hometowns of students and their campuses, by counting and measuring them.

It is not an analytic study because it doesn't involve testing a hypothesis or making causal inferences.

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To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. This will shift the triangle in the desired direction.

To translate a triangle with coordinates, you need to add the same value to each of the x and y coordinates of each vertex of the triangle. For example, if you wanted to translate the triangle with coordinates (1,2), (3,4), and (5,6) by two units to the right and two units up, you would add two to each x-coordinate and two to each y-coordinate. The new triangle would have coordinates (3,4), (5,6), and (7, 8).

1. Identify the coordinates for the triangle: (1,2), (3,4), and (5,6).

2. Decide how much you want to translate the triangle: two units to the right and two units up.

3. Add two to each x-coordinate and two to each y-coordinate: (3,4), (5,6), and (7,8).

4. The triangle is now translated two units to the right and two units up.

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Answer:

Current insurance cost = \(685.43\) $

Step-by-step explanation:

Given

Reduced Amount = \(4.1\%\:\times\:714.73\)

                              \(=\left(\frac{4.1}{100}\right)\left(714.73\right)\)

                              \(=\frac{41\times \:714.73}{1000}\)

                               \(=29.30\) $

Current Insurance cost = \(714.73 - 29.30\)

                                       = \(685.43\) $

Thus,

Current insurance cost = \(685.43\) $

The ladder reaches a height of 5.6 feet on the house when the angle with the ground is 62 degrees

Given the following parameters

Angle with the ground = 62 degrees

Length of the ladder = 12 foot

The above parameters mean that the height of the ladder on the ladder can be calculated using the following trigonometry ratio from right triangles

cos(62) = h/12

Make h the subject of the formula

So, we have

h = 12 * cos(62)

Evaluate the equation

h = 5.6

Hence, the height is 5.6 feet

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Answer:

70%

Step-by-step explanation:

the camera is marked down 30 plus 40 which is 70%

Answer:no image

Step-by-step explanation:

Answer:

37 1/3

Step-by-step explanation:

10 2/3 * 3.5=37 1/3

Answer:

the answer is 16/7/76

Step-by-step explanation:

ucjss

Answer: 3 units up

Step-by-step explanation:

Answer:

The answer is C.

Step-by-step explanation:

This criterion can be defined based on the desired level of accuracy or when the change in the estimated parameters falls below a certain threshold.

When implementing a program for a nonlinear problem using the least square adjustment technique, it is essential to determine a termination condition. This condition dictates when the program should stop iterating and provide the final estimated parameters. A common approach is to set a convergence criterion, which measures the change in the estimated parameters between iterations.

One possible criterion is to check if the change in the estimated parameters falls below a predetermined threshold. This implies that the adjustment process has reached a point where further iterations yield minimal improvements. The threshold value can be defined based on the desired level of accuracy or the specific requirements of the problem at hand.

Alternatively, convergence can also be determined based on the objective function. If the objective function decreases below a certain tolerance or stabilizes within a defined range, it can indicate that the solution has converged.

Considering the chosen termination condition is crucial to ensure that the program terminates effectively and efficiently, providing reliable results for the nonlinear problem.

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Answer:

3,2

No explantation needed,