How many solutions does the equation 2 + 6(x- 4) = 3x - 18 + 3x have?

Answer:

N+1

Step-by-step explanation:

It begins with = 2

then n+1=3

then n+2=4 and so on it is n+1

Answer: she bought 12  

Solution:

The surface area of the pyramid will be calculated below as

By substituting the values, we will have

Hence,

The final answer is

Answer:

16

Step-by-step explanation:

10/a = 15/24

Cross multiply.

15 × a = 10 × 24

15a = 240

Divide both sides with 15.

a = 240/15

a = 16

Answer:

a = 16

Step-by-step explanation:

=> \(\frac{10}{a} = \frac{15}{24}\)

Cross Multiplying

=> 10 * 24 = a * 15

=> 15a = 240

Dividing both sides by 15

=> a = 16

The directional derivative of the given function at P(1,2) in the direction of the unit vector U = ai+bj is given by Duf = (4/9)a + (2/9)√(1-a^2).Hence, the answer is more than 100 words.

Directional derivative of the function f(x,y)=ln(8x^2+2y^2) at the point P(1,2) in the direction of the unit vector U = ai+bj can be computed as follows:

Step-by-step explanation:

Firstly, we find the gradient of the function f(x,y) at the point P(1,2).\(∇f(x,y) = (∂f/∂x)i + (∂f/∂y)j\)

Here, \(∂f/∂x\) = 16x/(8x^2+2y^2) and

\(∂f/∂y\)= 4y/(8x^2+2y^2)

Therefore, at the point P(1,2),\(∇f(1,2)\)

= 16i/36 + 8j/36

= (4/9)i + (2/9)j.

Now, we have to compute the directional derivative of f at P in the direction of U. The formula for computing the directional derivative of f at P in the direction of U is given by:

Duf = \(∇f(P)\) . U where . represents the dot product.

So, Duf =\(∇f(1,2)\).

U = (4/9)i . a + (2/9)j . bWe know that U is a unit vector.

Therefore, |U| = \(√(a^2+b^2)\) = 1

Squaring both sides, we get a^2 + b^2 = 1

Hence, b =\(± √(1-a^2)\).

Taking b = √(1-a^2), we get

Duf = (4/9)a + \((2/9)√(1-a^2)\)

Thus, the directional derivative of the given function at P(1,2) in the direction of the unit vector U = ai+bj is given by

Duf = (4/9)a +\((2/9)√(1-a^2).\)

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Answer:

A) -3/4

B) 1/4

Step-by-step explanation:

A) m = y2-y1 / x2-x1

B) rise / run

Hope this helps. Pls give brainliest.

Answer: D

Step-by-step explanation: +2 would be an upwards translation

Answer:

slope: -3

y-intercept; (0,-2)

Step-by-step explanation:

i think its C :)

Her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

Let's assume that the total distance of the round trip is d kilometers and that she drove at a constant speed of v km/h for the entire trip. The time it takes for her to travel the entire distance at speed v is given by t = d/v.

Since she drove back home using the same path she took out to the university, her average speed for the entire trip must be equal to her speed on the way out and back. Therefore, the total time it took for her to complete the round trip is 2t = 2d/v.

Since the total time it took for her to complete the round trip is 7.1 hours, we can set up an equation:

2d/v = 7.1 hours

Converting hours to seconds and solving for v, we have:

v = 2d / (7.1 * 3600) km/s

Finally, converting to km/h, we get:

v = 2d / (7.1 * 3600) * 3600 km/h

Therefore, her average speed for the entire trip, in kilometers per hour, is equal to 2d / (7.1 * 3600) * 3600 km/h

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To determine the probability that the fourth person will be the first customer to enter the store, we can use the geometric distribution.

The geometric distribution models the number of trials needed to achieve the first success (entering the store in this case) in a series of independent Bernoulli trials (each potential customer walking by). The probability of success in each trial is given as 0.61.

The probability that the fourth person will be the first customer to enter the store is equal to the probability of three consecutive failures (the first three people not entering the store) followed by a success (the fourth person entering the store).

The probability of failure in each trial is given by (1 - 0.61) = 0.39.

So, the probability that the fourth person will be the first customer to enter the store is calculated as follows:

P(fourth person is the first customer) = P(failure) * P(failure) * P(failure) * P(success)

= 0.39 * 0.39 * 0.39 * 0.61

≈ 0.0602

Therefore, the probability that the fourth person will be the first customer to enter the store is approximately 0.0602, or 6.02%.

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Answer:

um all you do is multiply 21 as the length by 14 was the width (LxW)  

Step-by-step explanation:

=294 is your answer    I think ...

The contractor does not have enough concrete to finish the job. The conical pile of concrete mix has a volume of approximately 183.17 cubic yards, which is less than the required 78 cubic yards.

To determine if the existing conical pile of concrete contains enough material, we need to calculate the volume of the pile and compare it to the required volume of 78 cubic yards.

The volume of a cone can be calculated using the formula V = (1/3)πr²h, where V is the volume, π is approximately 3.14159, r is the radius of the base, and h is the height of the cone.

Given that the diameter of the pile is 22 feet, the radius is half the diameter, which is 11 feet. The height of the pile is 12 feet.

Using the formula, we can calculate the volume of the pile:

V = (1/3) * 3.14159 * (11^2) * 12

V ≈ 1664.71 cubic feet

To convert the volume to cubic yards, we divide by 27 (since there are 27 cubic feet in a cubic yard):

Volume in cubic yards = 1664.71 / 27 ≈ 61.65 cubic yards

Since the volume of the existing conical pile is approximately 61.65 cubic yards, it is not enough to meet the required volume of 78 cubic yards. Therefore, the contractor needs additional concrete to complete the construction job.

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The maximal amount of medically unsupervised weight loss that an adult should aim for in one week is generally 1-2 pounds (0.5-1 kg). This is because losing weight too quickly can be harmful to your health and lead to a number of negative side effects, such as muscle loss, fatigue, dehydration, and gallstones.

It's important to note that the amount of weight an individual can lose in a week can vary depending on factors such as their starting weight, body composition, and overall health. In some cases, a doctor or other medical professional may recommend a faster rate of weight loss under close supervision, but this is generally reserved for people who are severely overweight or have medical conditions that require rapid weight loss.

Ultimately, it's important to approach weight loss in a healthy and sustainable way, with a focus on making long-term lifestyle changes rather than relying on quick fixes or fad diets. A balanced diet, regular exercise, and a consistent sleep schedule are all important components of a healthy weight loss plan.

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Answer:            x = 2.5214

Step-by-step explanation:

log(4x+10) = 3

e^(log(4x+10)) = e^3

E^ log cancels out and equals one so

4x + 10 = e^3

       4x = e^3 -10

         x = (e^3 - 10)/4

         x = 2.5214

Answer:

7/20

Step-by-step explanation:

So first we know that there are a total od 25 students

15+10=25

And the probability of choosing the first girl is 15/25 or 3/5 simpler terms.

Now to be able to choose another girl in a row just multiply the then probability

So we started off with 25, if a girl was choosen, the population would b 24

and with 24, there is a missing girl so instead of 15 it is 14

now 14/24 or 7/12 simplified

multiply the two

7/12*3/5=21/60

Simplified

7/20

Answer:

100 because  it is corresponding angels ...

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

y = 6/x is not  an example of a linear function

Option B is correct

A linear function can be written in the form ax + by = c

Let us consider the options given and see which of them cannot be expressed in the form ax + by + c

For y  =   9  -  2x

This can also be expressed as

-2x + y  =  9

For y  =  x/2  +  9

This can also be expressed as:

x  -  2y  =  - 18

For y  =  5/6 x - 8

This can also be expressed as:

-5x  +  6y  =  -48

Only y = 6/x cannot be expressed in the form ax + by = c. Therefore, y  = 6/x is not an example of a linear function

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The each type of program was scheduled is,

A television network is creating a weekly comedies program schedule = 1.36

A television network is creating a weekly dramas program schedule = 3.15

There are two types of programs :

one is comedies and

another one is dramas

Let us assume,

x = comedy program = 30 minutes

y = drama programs = 60 minutes

The network schedules 230 programs total for the week

So,

We can write,

30x + 60y = 230            (Equation 1)

30x = 230 - 60y

We can solve it,

x = (230 - 60y) / 30

But,

The network needs to schedule 168 hours of programs to fill the week.

So,

We can get,

168 hours ⇒ one week

230 programs ⇒ x

Then,

x (168) = 230

x = 230/168

x = 1.36 hours

We can substitute x value in equation 1,

30x + 60y = 230  

30(1.36) + 60y = 230

We can multiply the products,

40.8 + 60y = 230

60y = 230-40.8

We can sum or difference the products,

60y = 189.2

y = 189.2/60

We can divide the products,

y = 3.15 hours

Then x and y values are substitute in equation 1,

We can write,

30x + 60y = 230  

30(1.36) + 60(3.15) = 230

We can multiply the products,

40.8 + 189 = 230

We can sum or difference the products,

229.8 ≅ 230

Therefore,

x = comedy program = 1.36 hours

y = drama programs = 3.15 hours

A television network is creating a weekly comedies program schedule = 1.36

A television network is creating a weekly dramas program schedule = 3.15

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The number of plastic tubing needed to fit around the edge of the pool is 423.3 ft².

The number of plastic tubing needed to fit around the area is calculated from the difference between the area of the rectangle and area of the circular pool.

Area of the circular pool is calculated as;

A = πr²

where;

A = π (15 ft / 2)²

A = 176.7 ft²

The area of the rectangle is calculated as follows;

A = length x breadth

A = 20 ft x 30 ft

A = 600 ft²

The number of plastic tubing needed to fit around the edge of the pool is calculated as;

The difference in the area = 600 ft² - 176.7 ft² = 423.3 ft²

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The number of different spanning trees for each graph is: a) K3: 1, b) K4: 4, c) K2,2: 2 and d) C5: 5.

a) The complete graph K3 consists of 3 vertices, and in a spanning tree, we need to have exactly 3 vertices connected without forming any cycles. Therefore, K3 has only one possible spanning tree.

b) The complete graph K4 has 4 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. K4 can be thought of as a tree with 4 branches extending from a central vertex. Each branch can be connected to any of the other vertices. Hence, there are 4 possible spanning trees for K4.

c) The complete bipartite graph K2,2 consists of 4 vertices divided into two sets, each containing 2 vertices. To form a spanning tree, we need to connect all 4 vertices without creating any cycles. Since there are only two possible edges between the two sets, there are only two possible spanning trees for K2,2.

d) The cycle graph C5 consists of 5 vertices arranged in a circular shape. To form a spanning tree, we need to connect all 5 vertices without creating any cycles. Removing any one of the edges from the cycle will result in a tree. Therefore, C5 has 5 different spanning trees.

Therefore, the number of different spanning trees for each graph is:

a) K3: 1

b) K4: 4

c) K2,2: 2

d) C5: 5  

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Answer:

-1

Step-by-step explanation:

I know that i^4 = 1

i^10 = i^4 * i^4 * i^2

     = 1 * 1 * i^2

We know that i^2 = -1

    =1 *1 *-1

    = -1

Answer:

Step-by-step explanation:

Correct answer:

x =  455

Step-by-step explanation:

C

12

​

(15)=(

12

15

​

)=

12!(15−12)!

15!

​

=

3⋅2⋅1

15⋅14⋅13

​

=455

n=4

k=12

m=n+k−1=4+12−1=15

x=(

k

m

​

)=455

The statement that best describes the composition of most foods is: "They contain mixtures of the three energy nutrients, although only one or two may predominate."

Most foods contain mixtures of the three energy nutrients, namely carbohydrates, proteins, and fats. However, the relative proportions of these nutrients can vary significantly from one food to another. In some foods, one or two of these nutrients may predominate, while others may contain relatively equal amounts of all three.

Carbohydrates are a primary source of energy for the body and can be found in various forms such as sugars, starches, and fibers. Foods like grains (e.g., rice, wheat, oats), fruits, vegetables, and legumes tend to be rich in carbohydrates. However, the specific types and amounts of carbohydrates can vary widely.

Proteins are crucial for building and repairing tissues, as well as for various metabolic functions. Foods like meat, poultry, fish, eggs, dairy products, legumes, nuts, and seeds are excellent sources of protein. Again, the protein content in different foods can vary.

Fats, also known as lipids, are an important energy source and provide essential fatty acids. Foods such as oils, butter, avocados, nuts, and fatty meats are high in fats. Like carbohydrates and proteins, the fat content in foods can differ significantly.

It's worth noting that some foods may predominantly consist of one specific nutrient. For example, pure sugar is almost entirely composed of carbohydrates, while pure oil is almost entirely composed of fats. However, most whole foods, such as fruits, vegetables, grains, meats, and dairy products, contain a mixture of these energy nutrients.

Furthermore, a balanced diet typically includes a combination of these nutrients in appropriate proportions. A varied diet that incorporates a range of foods from different food groups helps ensure an adequate intake of carbohydrates, proteins, and fats, along with other essential nutrients required for optimal health.

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Answer:

The parent graph has been horizontally shifted '2' units to the left, and vertically shifted 5 units down.

Hence, option (a) is true.

Step-by-step explanation:

Horizontal traslation of f(x) is of the form

\(f(x-h)\)

It means if the constant 'h' is negative, it means the the parent graph is shifted 'h' units to the left.

Vertical traslation of f(x) is of the form

\(f(x)+k\)

It means if the constant 'k' is subtracted from the output, the parent graph  vertically shifted 'k' units down.

Given

y = |x|

So, after y =  |x+2| -5, we conclude that the parent graph has been horizontally shifted '2' units to the left, and vertically shifted 5 units down.

Please also check the attached diagram.

Hence, option (a) is true.

True. The Precedence Diagramming Method (PDM) is a network diagramming technique in which activities are represented by arrows and connected at points called nodes.

The Precedence Diagramming Method (PDM) is a type of network diagramming technique commonly used in project management. It represents project activities as nodes connected by arrows to show their dependencies and sequence. PDM identifies the start and end dates of each activity and determines which activities can occur simultaneously and which need to be completed before others can start.

The nodes represent events, which indicate the start or end of an activity. The arrows represent the activities, and the direction of the arrow indicates the flow of the project. By using PDM, project managers can effectively visualize the project plan, identify critical paths, and determine the amount of time needed to complete the project.

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A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.

B. In this case, the overall cost of the sofa would be approximately $2,284.08

To find the initial value of the home when Zahir purchased it, we can use the compound interest formula:

Future Value = Initial Value * (1 + (interest rate))^years

Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.

548,900 = P * (1 + 0.048)^15

Now, we'll solve for P:

P = 548,900 / (1 + 0.048)^15

P ≈ 305,113.48

a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)

Initial Value = $1,791.99

Interest Rate = 27.93% (0.2793)

Number of periods = 12 (monthly)

Years = 1

Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)

Future Value ≈ 2284.33

Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.

b.  interest were compounded annually:

Future Value = Initial Value * (1 + interest rate)^years

Future Value = 1,791.99 * (1 + 0.2793)^1

Future Value ≈ 2284.08

In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).

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