Given (6) = 8.1 (6) = 17. g(6) = -11, and g'6) = 16, find the value of W(6) based on the function below. h(x) = f(x).g(x) Answer h'(6) = ____

The 2 given lines with the given coordinates when analyzed are seen to be; Parallel

The formula to find the slope of a line passing through two coordinates is;

m = (y2 - y1)/(x2 - x1)

Slope of Line 1 which has coordinates of (-1, 9) and (-6, -6) is;

m1 = (-6 - 9)/(-6 - (-1))

m1 = -15/-5

m1 = 3

Slope of Line 2 which has coordinates of (-7, -23) and (0, -2) is;

m2 = (-2 - (-23))/(0 - (-7))

m2 = 21/7

m2 = 3

Now the slopes of both lines are the same and as such we can say that they are parallel. It should be noted that if the were perpendicular, then their slopes will be negative reciprocals of each other.

Read more about Slope of Line at; https://brainly.com/question/3493733

#SPJ1

False. The correlation coefficient can vary between -1 and 1, and it can be negative.

The correlation coefficient is a statistical measure that quantifies the strength and direction of the relationship between two variables. It ranges from -1 to 1, inclusive. A value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other variable increases proportionally. A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases proportionally. A correlation coefficient of 0 indicates no linear relationship between the variables.

Therefore, the statement that the correlation coefficient varies between 0 and 1 and can never be negative is false. The correlation coefficient can indeed be negative, indicating a negative relationship between the variables. It is important to note that the correlation coefficient only measures the strength and direction of the linear relationship between the variables and does not capture other types of relationships, such as non-linear or causal relationships.

Learn more about correlation coefficient here:

brainly.com/question/29978658

#SPJ11

Answer:

The answer is A.

Step-by-step explanation:

The only option is A. since an intercept of (-5,0)

Option B has y-int: (0,-5)
Option C has y-int: (0,5)

Option D has x-int(5,0)

Answer: The area of the square pizza box is 324 square inches.

Step-by-step explanation:

The area of the square pizza box is 18 inches x 18 inches = 324 square inches. The area of the circular pizza is π x (8 inches)^2 = 201.06 square inches. The difference between the area of the box and the pizza is 324 square inches - 201.06 square inches = 122.94 square inches. (rounded to the nearest hundredth).

Answer:

no. c is the correct answer

Answer: 12 m

Step-by-step explanation:he path of a football has been modeled by the equation:

Probability that he will make the next free throw is 0.89% if larry bird made approximately 89% of all free throws during his nba career.

During nba career he made approximate 89% of all free throws.

To calculate the probability of the next 10 free throws given which will be

= No. of possible outcome / Total no. of outcome

= 89 / 100

= 0.89 %

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcome like how likely they are.

P(A) = (# of ways A can happen) / (Total number of outcomes)

which means that Probability that he will make the next free throw is 0.89 %

To learn more about probability

https://brainly.com/question/9653825

#SPJ4

Hence, the power series representation of the function is 2arctan(2/π) = Σ n*(an)*(x-a)^(n-1). And the radius of convergence and interval of convergence for the power series is respectively, 3*(1+(2/π)^2)^2/π^2 and (-[3*(1+(2/π)^2)^2/π^2], [3*(1+(2/π)^2)^2/π^2]).

The given function is :

f(x) = e^(-2x)/2. And, the function is the power series representation of this form f(x) = Σ an(x-a)^n.Let's derive the power series representation for f(x) = 2arctan(2/π)Solution:

Consider the function f(x) = 2arctan(2/π)This function is the power series representation of this form f(x) = Σ an(x-a)^n.The derivative of the function is :

f'(x) = 2/(1+(2/π)^2) * (1/1+x^2 ) .Power series representation of the derivative is :

f'(x) = Σ n*(an)*(x-a)^(n-1)Now, let's evaluate the first few coefficients using the above formula.(a0)' = f'(0) = 2/(1+(2/π)^2) * 1 = π/2(1/1^2) = π/2(a1)' = 0a2 = (a2)'/(2!) = 0a3 = (a3)'/(3!) = (π/2)/(3!(1+(2/π)^2)^2) * 6π = π^2/(3*(1+(2/π)^2)^2)a4 = (a4)'/(4!) = 0a5 = (a5)'/(5!) = -(π^4)/(5*3!(1+(2/π)^2)^4)The power series representation of f(x) = 2arctan(2/π) is :

f(x) = Σ an(x-a)^n = 2arctan(2/π)f'(x) = Σ n*(an)*(x-a)^(n-1)Let's use this to evaluate the radius of convergence of the power series representation of f(x).a = 0an = π^2/(3*(1+(2/π)^2)^2) . For the given series, radius of convergence is given by R = 1/L.

Hence, R = 1/L = 1/ lim sup |an|^(1/n) = 1/[(π^2/(3*(1+(2/π)^2)^2))]^(1/n)Taking limit, we get,R = 3*(1+(2/π)^2)^2/π^2Now, let's evaluate the interval of convergence.IOC = (-R, R)Let's substitute the value of R in the above equation to get the interval of convergence.IOC = (-[3*(1+(2/π)^2)^2/π^2], [3*(1+(2/π)^2)^2/π^2])

Hence, the power series representation of the function is 2arctan(2/π) = Σ n*(an)*(x-a)^(n-1). And the radius of convergence and interval of convergence for the power series is respectively, 3*(1+(2/π)^2)^2/π^2 and (-[3*(1+(2/π)^2)^2/π^2], [3*(1+(2/π)^2)^2/π^2]).

learn more about convergence in this link:

https://brainly.in/question/3422448

#SPJ11

V is at its maximum when \(a = b\ \pi x\),  \(V = \pi x2h\), and \(c = a x2 + b\ \pi xh\).

This question uses the principles of geometry, specifically the formulas for the area of a circle and the area of a curved surface. In addition, the concept of cost maximization is used to determine the cost of the tank when the volume is at its maximum.

Given,

\(c = a x2 + b\ \pi xh\)

This equation states that the cost of the tank is equal to the cost of the base plus the cost of the curved surface.

The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.

The area of the curved surface is equal to πxh, where h is the height of the tank.

Combining these two equations gives the equation for c.

\(V = \pi x2h\)

This equation states that the volume of the tank is equal to the area of the base multiplied by the height.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The height of the tank is h. Combining these two equations gives the equation for V.

V is at its maximum when \(a = b\pi x\)

This equation states that the volume of the tank is maximized when the cost of the base is equal to the cost of the curved surface.

The cost of the base is equal to the area of the base multiplied by the cost per square metre, which is a.

The area of the base is equal to \(\pi x2\), where x is the radius of the base. The cost of the curved surface is equal to the area of the curved surface multiplied by the cost per square metre, which is b.

The area of the curved surface is equal to πxh, where h is the height of the tank.

Setting a equal to bπx gives the equation for the maximum volume.

To learn more about principles of geometry, visit

brainly.com/question/10178782

#SPJ1

Multiplication is the process of multiplying. The products that have the same sign as the product of -2 3/7 and -6/11 are B and D.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The product of two positive numbers and the product of two negative numbers both are positive while the product of a negative number and a positive number is negative. Therefore, the product of -2 3/7 and -6/11 is positive, since both are negative.

A.) 3/8 × (-6/7) = Negative

B.) 1 2/9 × 2 6/17 = Positive

C.) -9/20 × 3 4/5 = Negative

D.) -1/3 × -2/3 = Positive

Hence, the products that have the same sign as the product of -2 3/7 and -6/11 are B and D.

Learn more about Multiplication:

https://brainly.com/question/14059007

#SPJ1

Which products have the same sign as (Negative 2 and StartFraction 3 over 7 EndFraction) (Negative StartFraction 6 over 11 EndFraction)? Check all that

The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19

The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7

The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below

f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3

When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343

Then

f[g(x)] = - 64x³ - 336x² - 588x - 340

Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;

g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g

[f(x)] = -4x³ + 19

Therefore,

f[g(x)] = - 64x³ - 336x² - 588x - 340

g[f(x)] = -4x³ + 19

Learn more about the function at

https://brainly.com/question/32520165

#SPJ11

The values of \(A\) and \(B\), we can write \(Y(s)\) as \[Y(s) = \frac{A}{s-9} + \frac{B}{s+3}\]. for the initial value problem: \(y'' + 4y' + 8y = \delta(t-2), \quad y(0) = 0, \quad y'(0) = 0\), we follow the same steps as in part a) to find the solution \(y(t)\).

To solve the given initial value problem using the Laplace transform, we will follow the standard procedure of taking the Laplace transform of the differential equation, solving for the Laplace transform of the unknown function, and then finding the inverse Laplace transform to obtain the solution.

Let's solve each problem separately:

a) For the initial value problem: \(y'' - 6y' - 27y = \delta(t-4), \quad y(0) = 0, \quad y'(0) = 0\).

Taking the Laplace transform of the differential equation, we get:

\[s^2Y(s) - sy(0) - y'(0) - 6sY(s) + 6y(0) - 27Y(s) = e^{-4s}\]

Substituting the initial conditions, we have:

\[s^2Y(s) - 6sY(s) - 27Y(s) = e^{-4s}\]

Simplifying, we get:

\[(s^2 - 6s - 27)Y(s) = e^{-4s}\]

To solve for \(Y(s)\), we divide both sides by \((s^2 - 6s - 27)\):

\[Y(s) = \frac{e^{-4s}}{s^2 - 6s - 27}\]

Now, we need to find the inverse Laplace transform of \(Y(s)\) to obtain the solution \(y(t)\). Since the denominator factors as \((s-9)(s+3)\), we can write \(Y(s)\) in partial fraction form:

\[Y(s) = \frac{A}{s-9} + \frac{B}{s+3}\]

Multiplying both sides by \((s-9)(s+3)\) to clear the fractions, we have:

\[e^{-4s} = A(s+3) + B(s-9)\]

To find the values of \(A\) and \(B\), we can equate coefficients of the corresponding powers of \(s\). By substituting \(s = 9\) and \(s = -3\) into the equation, we can solve for \(A\) and \(B\).

After finding the values of \(A\) and \(B\), we can write \(Y(s)\) as:

\[Y(s) = \frac{A}{s-9} + \frac{B}{s+3}\]

Finally, taking the inverse Laplace transform of \(Y(s)\) will give us the solution \(y(t)\).

b) Similarly, for the initial value problem: \(y'' + 4y' + 8y = \delta(t-2), \quad y(0) = 0, \quad y'(0) = 0\), we follow the same steps as in part a) to find the solution \(y(t)\).

Learn more about initial value here

https://brainly.com/question/10155554

#SPJ11

\(\[s^2Y(s) - sy(0) - y'(0) - 6sY(s) + 6y(0) - 27Y(s) = e^{-4s}\]\)

Answer:

-7

Step-by-step explanation:

We are given the following sequence:

\( \displaystyle \large{6,5,4,3,2,...}\)

Checking if the sequence is arithmetic by using the following formula:

\( \displaystyle \large{a_{n + 1} - a_n = d}\)

where d is a common difference. Common Difference means that these sequences must have same difference.

Let's check!

5-6 = -1

4-5 = -1

3-4 = -1

2-3 = -1

Since they are the same, the sequence is arithmetic.

General Term of Arithmetic Sequence

\( \displaystyle \large{a_n = a_1 + (n - 1)d}\)

We know that a1 is 6 since 6 is the first term.

d is -1.

Our goal is to find a14. Therefore,

\( \displaystyle \large{a_{14} = 6 + (14 - 1)( - 1)} \\ \displaystyle \large{a_{14} = 6 + (13)( - 1)} \\ \displaystyle \large{a_{14} = 6 - 13} \\ \displaystyle \large{a_{14} = - 7}\)

Therefore, the 14th term of sequence is -7.

Answer:

(21)(21)

Step-by-step explanation:

21x21=441

21²

r = 88.5

y = 3/4

Step-by-step explanation:

From the lower triangle,

97 - 2x = 4x -2

Collecting all similar terms, we get

6x = 99 or x = 16.5

From the upper triangle, we can see that

5x + 6 = r ---> 5(16.5) + 6 = r or r = 88.5

Since the sum of all the interior angles of a triangle is equal to 180, we can write

4y + (5x + 6) + r = 180 ---> 4y + 5(16.5) + 6 + 88.5 = 180

4y = 3 or y = 3/4

Answer: i agree with the other guy ↑

Answer:

varied

square root of number never result negative number

Step-by-step explanation:

There will only be one real solution.

If \(x\) is a real number, the square root function \(\sqrt x\) will only have real solutions when \(x\ge0\).

For \(x<0\), we get imaginary solutions.

Also, when \(\sqrt x> 0\), \(x>0\)

In other words, when the square root of \(x\) is a positive real number,  \(x\) will be a unique positive number.

We can see this when trying to solve the equation given in the question

So, the equation

\(\sqrt x=c\)

where \(c>0\), when solved, will give

\(\sqrt x=c\\(\sqrt x)^2=c^2\\x=c^2\)

We will have a unique solution because squaring a positive real number gives a single result.

Learn more here: brainly.com/question/24117016

Answer:

2x + 25

Step-by-step explanation:

Let that number be x.

Step 1 : Multiply x and 2.

x * 2 = 2x

Step 2 : Add 25 and 2x.

2x + 25

Hence,

25 is added to the product of a number and 2 is 2x + 25.

The solution  \(P(x \leq 4),p{x= 3), p(2 \leq * \leq 4)\)  is mathematically given as

Generally, the equation for the Probability of P(X=3) is mathematically given as

b)

\(P(X=3) = P(X \leq 3)-P(X\leq 2)\)

Therefore

\(P(X=3)= 0.65-0.48\)

P(X=3)= 0.17

c)

\(P(2\leq X\leq 4) = P(X\leq 4)-P(X\leq 1)\\\\\\P(2\leq X\leq 4) = 0.84-0.31'\)

\(P(2 < =X\leq 4)=0.53\)

a)

\(P(2\leq X\leq 4)=0.84\)

Read more about cumulative probability distribution.

https://brainly.com/question/19884447

#SPJ1

The null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

What is the null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Here,

We have to find out the slope of the line predicted by the null hypothesis if we are doing a linear regression.

We concluded that the null hypothesis states that the slope is equal to zero, and the alternative hypothesis states that the slope is not equal to zero.

Hence, the null hypothesis is that the linear regression model does not exist. This essentially means that the value of all the coefficients is equal to zero.

To learn more about the null hypothesis from the given link

https://brainly.com/question/13135308

#SPJ4

Two methods are used to compute the value of D, which is the determinant of a 3x3 matrix. Both methods yield the same result, D = 1.

In the given problem, we need to compute the value of D using two different methods. The value of D is given by the determinant of a 3x3 matrix.

Method 1: Using the formula for the determinant of a 3x3 matrix

We can directly compute the determinant of the given matrix using the formula:

D = | 1 1 1 |

   | 1 1 -1 |

   | 1 -1 1 |

Expanding the determinant along the first row, we have:

D = 1 * | 1 -1 | - 1 * | 1 -1 | + 1 * | 1 1 |

       | 1 1 |         | 1 1 |       | -1 1 |

Simplifying further, we get:

D = (1 * (1 * 1 - (-1) * 1)) - (1 * (1 * 1 - (-1) * 1)) + (1 * (1 * (-1) - 1 * (-1)))

D = 1 - 1 + 1 = 1

Therefore, the value of D is 1.

Method 2: Using row operations

Another method to compute the determinant is by using row operations to transform the matrix into an upper triangular form. Since the given matrix is already upper triangular, the determinant is the product of the diagonal elements:

D = 1 * 1 * 1 = 1

Again, the value of D is 1.

Both methods yield the same result, which is D = 1.

To learn more about row operations click here: brainly.com/question/28173301

#SPJ11

9514 1404 393

Answer:

Step-by-step explanation:

Let a, b, c represent the quantities of 20%, 35%, and 55% solutions, respectively. Then for the given mix, we have ...

  a + b + c = 108 . . . . . total number of liters

  .20a +.35b +.55c = 0.40·108 . . . . . liters of acid

  0a - 3b + c = 0 . . . . . 55% solution was 3 times 35% solution

__

Solving these three equations by your favorite method gives ...

  (a, b, c) = (36, 18, 54)

The chemist used 36 liters of 20%, 18 liters of 35%, and 54 liters of 55%.

_____

Comment on alternate approach

Since the ratio of 55% to 35% is 3 : 1, that mix will have an acid content of ...

  (3(.55) +1(.35))/4 = 0.50 = 50%

So, the final mix is equivalent to some quantity of 50% mix being added to some quantity of 20% mix. The fraction that is 50% mix* will be (40-20)/(50-20) = 2/3 of the total, or (2/3)(108 L) = 72 L.

Now we know that (1/3)(108 L) = 36 L of 20% solution is needed and (1/4)(72 L) = 18 L of 35% solution is needed. 3 times that is 54 L of 55% solution.

__

* After you work a few mixture problems, you can see the pattern. If we start with an equation for x = fraction of 50% to use with 20% to make 40%, we get ...

  x(50%) +(1 -x)(20%) = 40%

  x(50% -20%) = 40% -20% . . . . . subtract 1(20%) and factor out x

  x = (40% -20%)/(50% -20%)

The key here is to see where the numbers 20%, 40%, and 50% show up in the fraction.

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

To find a polynomial function with integer coefficients that has the given zeros, we can use the factor theorem and the zero-product property. Therefore, the function is f(x) = (x + 2)(x - 1)(x - 3) = x^3 - 2x^2 - 5x + 6 .

In summary, to find a polynomial function with integer coefficients that has the given zeros, we can use the factor theorem and the zero-product property to obtain the factors of the polynomial, and then multiply them together to get the polynomial function.

For example, suppose we want to find a polynomial function with integer coefficients that has zeros at -2, 1, and 3. We can start by using the factor theorem to obtain the factors of the polynomial:

(x + 2)(x - 1)(x - 3)

We can then multiply these factors together to obtain the polynomial function:

f(x) = (x + 2)(x - 1)(x - 3) = x^3 - 2x^2 - 5x + 6

This is a polynomial function with integer coefficients that has zeros at -2, 1, and 3. Note that we can also check this by using the zero-product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero. We can plug in each of the zeros (-2, 1, and 3) into the polynomial function and verify that the result is zero, which confirms that these are indeed the zeros of the polynomial.

To learn more about polynomial  click here, brainly.com/question/11536910

#SPJ11

Answer:

64

Step-by-step explanation: 7^4=2401   4^4=256     2401/256= 64

Statement is true because the corresponding sides are congruent. The answer is: BA = LN.

What is Triangle?

A triangle is a closed, two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and is used in many areas of mathematics, science, and engineering.

Since triangle ABC and triangle LMN have congruent corresponding sides, we know that they are similar triangles. This means that their corresponding angles are also congruent.

We are given that angle BAC is 58 degrees and angle MLN is 78 degrees. Since corresponding angles are congruent, this means that angle BAC is congruent to angle MLN.

Therefore, triangle ABC and triangle LMN are similar triangles with two pairs of corresponding congruent angles. This means that all corresponding sides are proportional.

Since AC = LN and BA = ML, we know that the ratio of the lengths of corresponding sides is:

AC / LN = BA / ML

Substituting the given values, we get:

1 = 1

This statement is true because the corresponding sides are congruent.

Therefore, the answer is: BA = LN.

Learn more about Triangle

https://brainly.com/question/17335144

#SPJ1

Answer:

True

Step-by-step explanation:

When displaying any sort of data, it is important to make the table or chart as easy to understand and read as possible without compromising the data. In this case, it is simpler to understand the pie chart if we use as few slices as possible that still makes sense for displaying the data set.

Answer:

There are 1,883 calories in 2 pounds