The function f(x)=3(2.5)x is shown on the coordinate plane.

Select from the drop-down menus to correctly describe the end behavior of f(x) .
As x decreases without bound, the graph of f(x) .

As x increases without bound, the graph of f(x) .

An exponential curve on a coordinate plane with horizontal x axis ranging from negative 4 to 4 in increments of 1. The vertical y-axis ranges from negative 1 to 7 in increments of 1. The curve begins infinitely close to the x axis in the second quadrant. The curve increases through begin ordered pair 0 comma 3 end ordered pair. DO NOT DELETE THIS PLZ HOEFULLY SOMEONE CAN TRY TO ANSWER IT

The expression that represents the speed will be 35 m/s. Then the correct option is C.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

The velocity is the rate of change of the displacement. And it is a vector quantity.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

In options A, B, and D, then speed depend on the direction which means they are velocity.

The expression that represents the speed will be 35 m/s. Then the correct option is C.

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Answer:

Step-by-step explanation: vertical angel

The value of implicit differentiation of y"  of the 4x³ + 5y³ = 2 is [tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex].

To find y'', or the second derivative of y, by implicit differentiation, we'll differentiate both sides of the equation with respect to x, treating y as a function of x.

Step - 1:

Start by differentiating each term with respect to x using the chain rule:

Since we're differentiating with respect to x, we need to multiply dy/dx by y' to indicate the derivative of y with respect to x.

Step - 2:

The right-hand side of the equation, 2, has a derivative of 0 since it is a constant.

Putting it all together, we have the equation:

[tex]12x^2 + 15y^2 \times \frac{dy}{dx} = 0.[/tex]

Now, to find y'', we differentiate this equation with respect to x, treating dy/dx as a function of x.

Step - 3:

The right-hand side of the equation, 0, has a derivative of 0 since it is a constant.

Putting it all together, we have the equation:

[tex]30y \times \frac{dy}{dx} + 15y^2 \times \frac{d^2y}{dx^2} = 0\\[/tex]

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To find y'' by implicit differentiation from the equation 4x^3 + 5y^3 = 2, differentiate both sides with respect to x, apply the chain and product rules appropriately and then solve for y''.

To find the second derivative y'' by implicit differentiation for the equation 4x^3 + 5y^3 = 2, you follow these steps:

This process will provide you with the value of y''.

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Answer:  The required number of cups of frozen mango is 1.125.

Step-by-step explanation:  Given that a smoothie recipe calls for [tex]2\dfrac{1}{4}[/tex] cups of frozen mango and the recipe serves two.

We are to find the number of cups of frozen mango that is needed to serve one.

We will be using the UNITARY method to solve the problem.

We have

The number of cups of frozen mango that needs to serve two is

[tex]2\dfrac{1}{4}=\dfrac{9}{4}=2.25.[/tex]

Therefore, the number of frozen mango that needs to serve one is given by

[tex]\dfrac{2.25}{2}=1.125.[/tex]

Thus, the required number of cups of frozen mango is 1.125.

The standard deviation of the original comparison population is 45.

The standard deviation of the original comparison population can be calculated using the formula:

Standard deviation of the sampling distribution = standard error * sqrt(sample size)

Given that the standard error of the sampling distribution is 15 and the sample size is 9, we can substitute these values into the formula:

The standard deviation of the original comparison population can be determined by using the relationship between the standard deviation, standard error, and sample size in a sampling distribution. The formula is:

[tex]\[ \text{Standard deviation of the original comparison population} = \text{Standard error} \times \sqrt{\text{Sample size}} \][/tex]

Given a standard error of 15 and a sample size of 9, substitute these values into the formula:

\[ \text{Standard deviation of the original comparison population} =[tex]15 \times \sqrt{9} = 15 \times 3 = 45 \][/tex]

Therefore, the standard deviation of the original comparison population is 45.

Standard deviation of the original comparison population = 15 * sqrt(9) = 15 * 3 = 45

Therefore, the standard deviation of the original comparison population is 45.

Greatest perfect square that is a factor of 244 is 4 which is the perfect square of 2 .

Given, number 244 .

Firstly the factors of 244 :

244 = 2 × 2 × 61

244 = 4 × 61

Therefore the greatest perfect square that is the factor of 244 will be 4 .

4 is the perfect square of 2.

2² = 4.

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Final answer:

Sturges' rule suggests using 9 classes or bins for 256 data points.

Explanation:

Sturges' rule is a method for determining the number of classes or bins required for a histogram. According to Sturges' rule, the formula to calculate the number of classes is:

K = 1 + log2(n)

Where K is the number of classes and n is the number of data points. In this case, since you have 256 data points, the number of classes suggested by Sturges' rule would be:

K = 1 + log2(256)

K = 1 + log2(28)

K = 1 + 8

K = 9

Therefore, Sturges' rule would suggest using 9 classes or bins for the histogram.

Answer:

If a figure has four sides, then it is a kites.

Step-by-step explanation:

In 2156 ways the selection be made so that at least one of each color is drawn?

The question is asking for the number of ways to select balls from a bowl containing 8 red balls and 9 blue balls if 4 balls are drawn and at least one of each color is drawn.

To solve this, we must consider the different combinations of red and blue balls that meet the requirement.

Calculate the total possible outcomes: 17C4 = 2380

Calculate the outcomes where all balls of one color are drawn: 9C4 + 8C4 = 224

Subtract the outcomes where only one color is drawn from the total: 2380 - 224 = 2156 ways

To calculate mean and standard deviation for a binomial distribution, use the formulas μ = np and σ = √npq. Ensure both np and nq are greater than five to use the normal approximation.

To find the mean (μ) and standard deviation (σ) for a binomial distribution, you use the formulas μ = np and σ = √npq respectively. Here, 'n' represents the number of trials, 'p' is the probability of success on a single trial, and 'q' is the probability of failure on a single trial, which is calculated as q=1-p.

If you want to determine whether you can use the normal approximation to the binomial, it is essential to ensure that both np and nq are greater than five. This is because the normal approximation is most accurate when the binomial distribution is symmetrical, which typically occurs when both np and nq exceed five.

 1.1      Factoring:  x3-81 

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into
              (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =
            a3+a2b+ab2-ba2-b2a-b3 =
            a3+(a2b-ba2)+(ab2-b2a)-b3 =
            a3+0+0+b3 =
            a3+b3

Check :  81  is not a cube !! 
Ruling : Binomial can not be factored as the difference of two perfect cubes

 1.2    Find roots (zeroes) of :       F(x) = x3-81
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q  then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -81. 

 The factor(s) are: 

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,3 ,9 ,27 ,81 

 Let us test ....

Polynomial Roots Calculator found no rational roots

 2.1      Solve  :    x3-81 = 0 

 Add  81  to both sides of the equation : 
                      x3 = 81 
When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:  
                      x  =  ∛ 81  

 Can  ∛ 81 be simplified ?

Yes!   The prime factorization of  81   is
   3•3•3•3  
To be able to remove something from under the radical, there have to be  3  instances of it (because we are taking a cube i.e. cube root).

∛ 81   =  ∛ 3•3•3•3   =
                3 • ∛ 3 

The equation has one real solution
This solution is  x = 3 • ∛3 = 4.3267 

Answer:

The initial value is  

✔ 1/3

The simplified base is  

✔ 27

The domain is  

✔ all real numbers

The range is  

✔ y > 0

Step-by-step explanation:

The expression that represents the situation is:

                    $ 600+12x

cost of lot is: $ x

This means that 12 times the lot on which it was built is: $ 12x

Also, it is given that:

A house costs $600 more than 12 times the lot on which it was built.

This means that the total cost of the house is:

600 plus the total cost of the lot on which it was built.

i.e.   The expression that represents the total cost of the house is:

                      $ 600+12x

Answer:

This is a perfect cube

The side length is [tex]9[/tex] centimeters

Taking the cube root of the volume will determine the side length

Step-by-step explanation:

we know that

The volume of a cube is equal to

[tex]V=s^{3}[/tex]

where

s is the length side of the cube

In this problem we have

[tex]V=729\ cm^{3}[/tex]

Solve for s-------> that means isolate the variable s

Find the length side of the cube s

[tex]s=\sqrt[3]{V}[/tex]

substitute the value of V

[tex]s=\sqrt[3]{729}=9\ cm[/tex] --------> a perfect cube

therefore

Statements

This is a perfect cube--------> Is true

The side length is [tex]9[/tex] centimeters -------> Is true

Taking the cube root of the volume will determine the side length ------> Is true

The side length of the cube is 9cm³ showing that the cube is a perfect cube

The formula for calculating the volume of a cube is expressed as:

V = s³

where:

s is the side length of the cube

Given the following

V = 729cm³

Substitute the given parameters into the formula

729 = s³

s³ = 729

s = 9cm

Hence the side length of the cube is 9cm³ showing that the cube is a perfect cube

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Jenna hikes 2 miles in 1 hour, as she covers 1/2 mile in each 1/4 hour and there are four 1/4 hours in a full hour.

Jenna hikes 1/2 mile every 1/4 hour. To determine how far she hikes in 1 hour, we need to calculate the distance she can cover in four such intervals since 1 hour is composed of four 1/4 hours.

So, the calculation would be:
1/2 mile in 1/4 hour

1/2 mile x 4 (since there are 4 quarters in a full hour) = 2 miles

Therefore, Jenna hikes 2 miles in 1 hour.