Find the slope of the line containing the points ( 3, 4 ) and ( 3, - 6 ).

The number of DVDs sold in any day is one-third the number of DVDs sold the previous day three times the number of DVDs sold the following day.

The exponential function D(t) = 729(1/3)^t models the number of DVDs sold where t is the number of days since the release date and D(t) is the number of DVDs sold.

The definition of an exponential function is given as follows:

y = ab^x.

In which:

For this problem, the parameter values are given as follows:

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The statement that describes a key feature of function g if [tex]g(x)=e^x-7[/tex]  is Horizontal asymptote of y= -7.

A horizontal line that is not a part of a function's graph but is essential because it directs the graph's x values is known as a horizontal asymptote.

A horizontal line that a function's graph appears to coincide with but does not actually do so is said to be its horizontal asymptote.

A line that is asymptotically sloped, vertical, or both has the equation x = a, y = a, or y = ax + b

In this instance, the declaration that enumerates the primary property of the function g if g(x) = [tex]e^x[/tex] - 7 is that the horizontal asymptote of y = -7.

This can be seen from the equation given.

Therefore option (d) is correct

For more questions on asymptote

https://brainly.com/question/28032581

#SPJ4

Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

Avery can interpret 302 = 3 by understanding that 30 is the total amount of soup to be divided, and 2 represents the number of equal parts she wants to divide the soup into. This means that Avery can divide the 30 cups of soup into 3 equal containers, each containing 10 cups of soup.

Interpretation 1: Avery can divide the 30 number of cups of soup into 3 equal containers, each containing 10 cups of soup.

learn more about number here

https://brainly.com/question/10547079

#SPJ4

option:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

hope it helps!:D

The cost of Japan and Switzerland tickets are 17.15 dollars and 13.15 dollars respectively.

it would cost $77.75 to buy three tickets in Japan plus 2 tickets in Switzerland. Three tickets in Switzerland plus two tickets in japan would cost $73.75.

Using system of equation,

let

x = cost of each ticket in Japan

y = cost of each ticket in Switzerland

Therefore,

3x + 2y = 77.75

2x + 3y = 73.75

Multiply equation(ii) by 1.5

3x + 2y = 77.75

3x + 4.5y = 110.625

subtract the equations

2.5y = 32.875

y = 32.875 / 2.5

y = 13.15 dollars

Hence,

3x + 2y = 77.75

3x = 77.75 - 2y

3x = 77.75 - 2(13.15)

3x = 77.75 - 26.3

x = 51.45 / 3

x = 17.15 dollars

Therefore,

cost of Japan ticket = 17.15 dollars

cost of Switzerland ticket = 13.15 dollar

learn more on equation here: https://brainly.com/question/29652475

#SPJ1

The correct option is C. Length = 24 feet, width = 18 feet

To measure a rectangular room, use a tape measure, pencil and paper to record the length and width of the room. Then multiply these numbers to get the total area of the room.

The calculation is as follows:

Since 2cm = 6 feet

So,

The length is = 4(6) = 24 feet

And, the width be = 3(6) = 18 feet

Read more about length and width here:

https://brainly.com/question/15161439

#SPJ1

A scale drawing of Julie's living room is shown below:

A rectangle is shown. The length of the rectangle is labeled as length equal to 8 cm, and the width is labeled as width equal to 6 cm.

If each 2 cm on the scale drawing equals 4 feet, what are the actual dimensions of the room?

A)Length = 16 feet, width = 12 feet

B)Length = 10 feet, width = 8 feet

C)Length = 32 feet, width = 24 feet

D)Length = 14 feet, width = 12 feet

Utilize the following formula to convert metres to miles: m/1,609.344=mi (meters divided by 1,609.344 equals miles).

To learn more about metres refer to:

https://brainly.com/question/13329820

#SPJ4

Answer:

x=2

Step-by-step explanation:

undefined slope means the line is vertical

The 36.5 °C when converted to Fahrenheit it is equal to 97.7 °F.

                                  = 97.7

To learn more about unit conversion refer to :

https://brainly.com/question/30395559

#SPJ4

The solution of the initial value problem is [tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

A differential equation is a mathematical equation that relates a function and its derivatives to some independent variables.

In this case, the differential equation is given by:

dy/dt = t² + 1, t ≥ 0

with the initial value y = 6 when t = 0.

To solve this initial value problem, we can use the method of integrating factor.

We can find the integrating factor for this differential equation by using the formula:

[tex]= > e^{\intP(t)dt,[/tex]

where P(t) = t² + 1

So,

[tex]= > e^{\int P(t)dt} = e^{t^3/3 + t}[/tex]

By the product rule, we have:

[tex]= > d/dt(e^{t^3/3 + t)y} = d/dt(e^{t^3/3 + t)(t^2 + 1)})[/tex]

We can evaluate the integral on the right side using standard integration techniques, and we get:

[tex]= > e^{t^3/3 + t}y = e^{(t^3/3 + t)(t^3/3 + t^2 + t + C)[/tex]

Finally, we can isolate y by dividing both sides of the equation by e^(t^3/3 + t):

[tex]= > y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

To find the value of C, we can use the initial value y = 6 when t = 0:

6 = Ce⁰

So, C = 6.

Therefore, the solution to the initial value problem is:

[tex]y = (t^3/3 + t^2 + t + 6)e^{(t^3/3 + t)}[/tex]

To know more about differential equation here.

https://brainly.com/question/30074964

#SPJ4

To add or subtract mixed numbers with like denominators, follow these steps:

For example, Add: 1 ¾ + 1 ½

Convert to improper fractions:

1 ¾ = 7/4

1 ½ = 3/2 = 6/4

Add the numerators and keep the denominator the same:

7/4 + 3/2 = (7 + 6) / 4 = 13/4

Convert the result back to a mixed number:

13/4 = 3 1/4

So the answer is 3 1/4.

Learn more about mixed number on:

https://brainly.com/question/1746829

#SPJ1

The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

To learn more about the distance, visit:

brainly.com/question/15256256

#SPJ4

The speed of the passenger train is 80 mph.

Let's call the speed of the passenger train "p" and the speed of the freight train "f". We know that "p" = "f" + 14, and that the time it takes for the two trains to cover their respective distances is the same.

Therefore, we can write the equation:

400/p = 330/f

Expanding the second term and substituting "p" for "f" + 14:

400/p = 330/(p - 14)

Cross multiplying and simplifying:

400 * (p - 14) = 330 * p

Expanding both sides:

400p - 5600 = 330p

Subtracting 330p from both sides:

70p = 5600

Dividing both sides by 70:

p = 80 mph

So the speed of the passenger train is 80 mph.

To learn more about Distance

brainly.com/question/15256256

#SPJ4

The length of each piece to the nearest inch is 16 inches.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Total length of the board = 2 meters

Gillian cuts the board into 5 equal pieces.

Length of each piece of the board in meters = 2 / 5 = 0.4 meter

We know that,

1 meter = 39.37 inches

0.4 meter = 39.37 × 0.4

                = 15.748 inches

                ≈ 16 inches

Hence the length of each piece of the board is approximately 16 inches.

Learn more about Division here :

https://brainly.com/question/21416852

#SPJ1

The time that Nagma takes to complete five rounds is 0.4 hours or 24 minutes.

Travel time is the total time required to pass a certain length of road.

Given,

Length = 180m

Width = 120 m

Speed = 7.5 km/hr

Time of five rounds?

Steps,

The first step that must be done is to find the travel time for one round

Distance of one round = 2(length + width)

Distance of one round = 2(180 + 120)

Distance of one lap = 3 (300)

Distance of one round = 600 m = 0.6 km

Time needed to reach 5 rounds

Time = 5 (distance : speed)

Time = 5 (0.6 : 7.5)

Time = 0.4 hours = 24 minutes

So, the time needed to complete five rounds is 0.4 hours or 24 minutes.

Learn more about time here: https://brainly.com/question/17146782

#SPJ4

The given equation does not represent y as a function of x.

A relation is a function if for every unique x value, there exists only one unique y value. The equation 5x³y = 15 does not define a unique value for y for a given value of x, and therefore does not represent y as a function of x.

The equation 5x³y = 15 does not represent y as a function of x. A function must have exactly one output value for each input value, but this equation doesn't have the unique output restriction.

The equation 5x³y = 15 represents a 3-dimensional surface in the x-y-z plane, where z = 5x³y. It does not define y as a function of x, because for a given x there can be multiple values of y that satisfy the equation. To define y as a function of x, additional information, such as an equation that relates y and x in a one-to-one manner, is needed.

Learn more about Function Of X, Y Output here:

https://brainly.com/question/11135014

#SPJ4

The value of p is obtained as follows:

p = 18%.

The value of p is obtained applying the proportions in the context of this problem.

A proportion is applied as a percentage is given by the division of the number of desired outcomes by the number of total outcomes, which is then multiplied by 100%.

The outcomes for this problem are given as follows:

Hence the percentage is given as follows:

p = 137/750 x 100%

p = 18%.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:  

Step-by-step explanation:

4564.  2 75444214///4222.-112

The fully simplified form of the expression is [tex]\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]

A quadratic equation is a type of polynomial equation that has the general form ax^2 + bx + c = 0, where a, b, and c are coefficients and x is an unknown variable. The equation has two solutions, which can be found using the quadratic formula x = (-b ± √(b^2 - 4ac)) / 2a, where the ± symbol indicates that there are two possible solutions.

Quadratic equations are used to model a variety of real-world phenomena, such as the motion of objects under the influence of gravity, the path of a projectile, and the growth of a population over time. They are also used to describe the parabolic shape of curves and to solve optimization problems, such as finding the maximum or minimum value of a function

We can simplify the expression as follows:

[tex]\frac{3}{2x+12} =\frac{x-15}{x^{2} -2x-48}[/tex]

First, we'll simplify the denominators. To do this, we can factor the quadratic expression x² - 2x - 48:

x² - 2x - 48 = (x - 8)(x + 6)

Now we can rewrite the denominators:

[tex]\frac{3}{2x+12}-\frac{x-15}{(x-8)(x+6)}[/tex]

Next, we'll simplify the fraction in the second term using partial fraction decomposition:

[tex]\frac{x-15}{(x-8)(x+6)} =\frac{A}{x-8}+\frac{B}{x+6}[/tex]

where A and B are constants that we can find by multiplying both sides by (x - 8)(x + 6) and equating the numerators:

x - 15 = A(x + 6) + B(x - 8)

Expanding both sides:

x - 15 = Ax + 6A + Bx - 8B

Comparing coefficients:

-15 = Ax + 6A + Bx - 8B

1 = A + B

8B = Ax + 6A + 15

-6A = -15 - Ax - 8B

-6A = -15 - (A + B)x - 8B

-6A = -15 - x + 7x

-6A = -15 - x + 7x

-6A = -15 + 6x

Solving for A and B, we have:

A = -3

B = 4

So, the second term can be written as:

[tex]\frac{x-15}{(x-8)(x+6)} =\frac{-3}{x-8}+\frac{4}{x+6}[/tex]

Putting everything together, we have:

[tex]\frac{3}{2x+12} -\frac{x-15}{(x-8)(x+6)} =\frac{3}{2x+12}-\frac{-3}{x-8} +\frac{4}{x+6}[/tex]

which is the fully simplified form of the expression.

To know more about expression visit:

https://brainly.com/question/29176690

#SPJ4

The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4)

What is center of dilation?

A dilation's center is a fixed point in the plane around which all points expand or shrink. Under a dilation (k 1), the sole invariant (not changing) point is the center, which might be within, outside, or on a figure.

The center of dilation is the origin, so to find the new coordinates of each vertex, we need to multiply the original coordinates by the scale factor of 2.

A(2, 2) becomes A'(2 * 2, 2 * 2) = A'(4, 4)

B(4, 4) becomes B'(4 * 2, 4 * 2) = B'(8, 8)

C(-4, 2) becomes C'(-4 * 2, 2 * 2) = C'(-8, 4)

So, The new vertices of ΔA'B'C' are A'(4, 4), B'(8, 8), and C'(-8, 4).

To know more about center of dilation visit,

https://brainly.com/question/13173812

#SPJ1

Answer:

b. stratosphere

Step-by-step explanation:

The ozone layer, located in the stratosphere is responsible for absorbing the most UV radiation. This is because the ozone molecule (O3) is able to absorb UV radiation due to its molecular structure, specifically the presence of three oxygen atoms which allows it to efficiently absorb the UV-C radiation (the most damaging to living organisms). This protects life on Earth from harmful effects of UV radiation, such as DNA damage, skin cancer and other harmful impacts on plants and marine life.

"He did not apply the order of operations correctly. He should have performance the subtraction before the division. The correct answer is 23, not 7."

Bob did not apply the order of operations correctly. He should have performed the subtraction (3 - 3) before the division (÷ 3). The correct order of operations is to perform any calculations inside parentheses first, then perform any exponents, then perform any multiplication or division (from left to right), and finally perform any addition or subtraction (from left to right).

Applying the correct order of operations to the expression 3m - 3 ÷ 3, we get:

Therefore, the correct answer is 23, not 7.

It is important to always apply the order of operations correctly in mathematical expressions to ensure that the correct answer is obtained. Failure to follow the correct order of operations can lead to incorrect answers and misunderstandings.

This question should be provided as:

Bob used these steps to evaluate 3m - 3 ÷ 3 for m = 8. Complete the explanation about his error.

He did not apply the order of operations correctly. He should have performance the _______ before the ______. The correct answer is _____, not 7.

Learn more about parentheses here: brainly.com/question/172904

#SPJ4

on july 1 a one year non interest bearing note for 110250 was accepted in exchange for an unpaid accounts receivable for 105000 time was5%

The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis  0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

= [tex]98^{2}[/tex] (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

To learn more about Sample visit:

brainly.com/question/28223620

#SPJ4

The minimum sample size required will be 231.

What is Sample Size?

The act of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. The sample size is an important aspect of any empirical study whose purpose is to draw conclusions about a population from a sample.

The sample size(n) is 2558.

p = 46%

= 0.46 sample fraction of US adults who had experienced with substance misuse in their relatives

1) Where, 0.05/2 (n is the crucial value of z for two tailed test at 0.05 level of significance = 1.96) is the 95% CI for the population proportion of adults in the United States who had dealt with substance misuse in their family (P). (This can be acquired from the z table by locating the z that corresponds to an area close to 0.05/2).

Hence, the confidence interval is given by

= [0.46 ± 0.02]

= [0.44, 0.48]

As a result, we are 95% confident that the population share of US individuals who have experienced substance misuse in their relatives will fall between 0.44 and 0.48

2) Margin of error = E

= 0.02

3) Null hypothesis 0.4 percent of US people have dealt with substance misuse in their families.

P = 4/10

= 0.4

Alternative hypothesis  More than 0.5 percent of US individuals have dealt with substance misuse in their relatives.

P > 0.4

95% confidence interval is - [0.44, 0] 48]

We may reject the null hypothesis since the confidence interval does not include the null value of population proportion (0.4)

As a result, we have enough evidence that more than four out of every ten US adults have dealt with substance misuse in their families.

As a result, the newspaper could make the assertion.

4) According to the Gallop Poll poll of 2558 US individuals, more than four out of ten US citizens have dealt with substance misuse in their families.

5) The required minimum sample size is given by:

P is the specified value of population proportion under the null hypothesis = 0.4

= (1.96/0.02)²  (0.4) (1 - 0.4)

=  (0.4) 0.6

= 230.5

So, the minimum sample size required will be 231.

Since, the sample size taken in survey (2558) is more than 231, the sample size taken is not too small.

To learn more about Sample visit:

brainly.com/question/28223620

#SPJ4

The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

So, the value of θ is approximately equal to 0.92729522.

To know more about function visit:

brainly.com/question/28303908

#SPJ4

The value of θ is approximately equal to 0.92729522.

The sine function is a basic trigonometric function used in mathematics to describe the relationship between the lengths of sides of a right triangle and its angles. The sine function is denoted by the symbol sin and is defined as the ratio of the side opposite a given angle to the hypotenuse of the triangle.

The sine function is periodic, meaning that it repeats its values over a certain interval, and its values range from -1 to 1.

If sin (θ)=8/17, where 0 < θ < pi/2 and cos (θ)=5/13, then θ can be found using the inverse sine function.

θ = sin⁻¹ (8/17) = sin⁻¹ (5/13) = arctan(8/5).

Therefore, the value of θ is approximately equal to 0.92729522.

To know more about function visit:

brainly.com/question/28303908

#SPJ4

The team is predicted to win 56.2% of its games this season.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. The probability can also be expressed as in form of a percentage as we multiply it by 100.

It's the middle of a season, and Bill James has calculated the Pythagorean Winning Percentage (W%) of a team as .562.

To convert, the probability to percentage just multiply by 100 =.562*100

= 56.2%.

Hence The team is predicted to win 56.2% of their games this season.

Learn more about probability, by the following link.

brainly.com/question/24756209

#SPJ1

The unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).

Given vectors:

A = (2, 3, 4)

B = (1, -1, 4)

A unit vector is a vector with a magnitude of 1. Two vectors are orthogonal if the angle between them is 90 degrees. In order to find unit vectors orthogonal to both A and B, we must first compute the cross product of A and B. The cross product of two vectors is a vector perpendicular to both of the given vectors and can be denoted by A × B.

The cross product of A and B is given by:

A × B = (3, -12, 2)

To normalize this vector and find the unit vector, we must divide the vector by its magnitude. The magnitude of the vector A × B is equal to the square root of the sum of the squares of its components. We can write this as:

|A × B| = √(3^2 + (-12)^2 + 2^2) = √(169) = 13

Therefore, the unit vector orthogonal to both A and B is given by:

A × B/|A × B| = (3/13, -12/13, 2/13)

This vector can also be written in terms of its unit components, as:

u = (0.23, -0.92, 0.15)

Therefore, the unit vector orthogonal to both A and B is u = (0.23, -0.92, 0.15).

Learn more about unit vector here:

https://brainly.com/question/28028700

#SPJ4

The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

(x^2 + 4x + 8)(2x - 1)

now, we know,

(a+c)*b = ab+cb

so, we get,

⇒2x^3+8x^2+16x-x^2-4x-8

⇒2x^3+7x^2+12x-8

Hence, The solution of (x^2 + 4x + 8)(2x - 1) is, 2x^3+7x^2+12x-8.

To learn more on multiplication click:

brainly.com/question/5992872

#SPJ1

Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.

To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:

1. We must make a rule of three to find the exact amounts of each ingredient as shown below:

According to the above, the following ingredients are needed for this recipe:

Note: This question is incomplete because there is some information missing. Here is the complete information:

120g strawberry jelly

8 sponge fingers

420ml custard

180 g tinned fruit

Learn more about recipes in: https://brainly.com/question/1320828

#SPJ1

Answer:

8

Step-by-step explanation:

Since the two horizontal lines are parallel, we have that triangle CDG and triangle CEF are similar (corresponding points in that order). Therefore, using similarity, CD/CG = CE/CF. Therefore 3/4 = 9/(4+x).

So 12 = 4+x, and x = 8.

Answer:

this can be solved using trigonometry