If A:B=6:7 and B:C=14:9, then what is A:C in its simplest form

Answer:

40

Step-by-step explanation:

1. List all the multiples

10,20,30,40

8,16,24,32,40

The first set in the list that describes the number 22 is the set of natural numbers.

The natural numbers, also known as counting numbers, are the set of positive integers starting from 1 and extending infinitely. In this set, we have numbers like 1, 2, 3, 4, and so on. Since 22 is a positive whole number, it falls within the set of natural numbers.

To provide some context, the other sets mentioned in the list are as follows:

Whole numbers: The set of natural numbers including zero (0). It includes numbers like 0, 1, 2, 3, and so on.

Integers: The set of whole numbers including their negatives. It includes numbers like -3, -2, -1, 0, 1, 2, 3, and so on.

Rational numbers: The set of numbers that can be expressed as a fraction, where the numerator and denominator are integers. Examples include 1/2, 3/4, -5/6, and so on.

Real numbers: The set of all numbers, including rational and irrational numbers. It includes numbers like pi (π), square roots of non-perfect squares, and any other number that can be expressed on the number line.

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a. There are 28 different 2-drug combinations possible.

b. There are 56 different 3-drug combinations possible.

c. There are 56 different 5-drug combinations possible.

d.  There are 28 different 6-drug combinations possible.

e.  There were 248 different combinations of the eight drugs tested as treatments.

a. The number of 2-drug combinations of the eight drugs can be calculated using the combination formula:

C(n, k) = n! / (k!(n - k)!)

In this case, we have n = 8 (eight drugs) and k = 2 (2-drug combinations). Plugging the values into the formula:

C(8, 2) = 8! / (2!(8 - 2)!)

= 8! / (2! * 6!)

= (8 * 7 * 6!) / (2! * 6!)

= (8 * 7) / (2 * 1)

= 28

Therefore, there are 28 different 2-drug combinations possible.

b. Similar to part a, the number of 3-drug combinations can be calculated using the combination formula:

C(8, 3) = 8! / (3!(8 - 3)!)

= 8! / (3! * 5!)

= (8 * 7 * 6 * 5!) / (3! * 5!)

= (8 * 7 * 6) / (3 * 2 * 1)

= 56

Hence, there are 56 different 3-drug combinations possible.

c. Following the same approach, the number of 5-drug combinations can be calculated as:

C(8, 5) = 8! / (5!(8 - 5)!)

= 8! / (5! * 3!)

= (8 * 7 * 6 * 5 * 4 * 3!) / (5! * 3!)

= (8 * 7 * 6 * 4) / (4 * 3 * 2 * 1)

= 56

Therefore, there are 56 different 5-drug combinations possible.

d. Similarly, the number of 6-drug combinations can be calculated as:

C(8, 6) = 8! / (6!(8 - 6)!)

= 8! / (6! * 2!)

= (8 * 7 * 6!) / (6! * 2)

= (8 * 7) / 2

= 28

Hence, there are 28 different 6-drug combinations possible.

e. To find the total number of different combinations tested as treatments, we need to consider all possible combinations ranging from 1-drug to 8-drug combinations, including the control treatment with no drugs.

The total number of combinations is the sum of the combinations from each category:

C(8, 1) + C(8, 2) + C(8, 3) + C(8, 4) + C(8, 5) + C(8, 6) + C(8, 7) + C(8, 8)

Using the combination formula for each category and summing the values:

1 + 28 + 56 + 70 + 56 + 28 + 8 + 1 = 248

Therefore, there were 248 different combinations of the eight drugs tested as treatments.

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Answer:

D

Step-by-step explanation:

At least = Less than sign

At most = Greater than sign

Both include the -6 and 9. (Closed dots)

Answer:

Wind and biofuel

Step-by-step explanation:

The other are all nonrenewable.

Hope this helps. Also will you friend me so I know if you need any more help I can help you.

Answer:

The formula is V = r²h for the volume of a cylinder, we need to first find the radius of the cylinder:

The diameter of the cylinder is 7 feet, so the radius is half of that cylinder, so you have to divide by 2 to get half of the diameter:

r = 7/2

= 3.5 feet.

V = π(3.5)²(12)

V = π(12.25)(12)

V = 147π

Therefore, the volume of the cylinder is 147π cubic feet.

Answer:

B For each x increase of 1, the y increases by a common factor of 3

Step-by-step explanation:

so it means that y is adding 3 every time x adds 1

Answer:D

The last one explanation of that graphic line is correct answer.

Answer:

(5,7)



x = 5

y = 7

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

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

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

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer: A = (1m/3)^2 or A= (1/3)^2 m

Or A= (1/3)(1/3)

Step-by-step explanation:

No choices given, but it will look like one these answers.

The area of a square that has a side length of 1/3 meter is 1/9 square meter.

I hope this helps you.

Answer:

a= (1/3)(1/3)

Step-by-step explanation:

Answer:

I believe that X = 16/9 is the answer

Answer:

x = 7, -11

Step-by-step explanation:

(x + 2)^2 = 81

(7 + 2)^2 = 81      Take one value of x

9^2 = 81              Solve for the exponent

81 = 81                Final Answer

(x + 2)^2 = 81

(-11 + 2)^2 = 81   Take one value of x

9^2 = 81             Solve for the exponent

81 = 81

Understandings:

Understand how to solve for exponents

For example the ones that we used in this situation, in order to solve for an exponent, multiply the number by itself twice = 9 x 9 = 9^2 = 81

Answer:

x = 7 , x = - 11

Step-by-step explanation:

\((x+ 2)^2 = 81\\\\(x+2) = \sqrt{81}\\\\(x+2) = \pm 9\\\\x + 2 = 9 \ , \ x + 2 = - 9\\\\x = 9 - 2 \ , \ x = - 9 - 2\\\\x = 7 \ , \ x = -11\)

Based on the text, the primary source of primate endangerment today is habitat destruction.

Habitat destruction is considered the primary source of primate endangerment based on various factors mentioned in the text. Primates, like many other species, heavily rely on their natural habitats for survival, including food, shelter, and breeding. However, human activities such as deforestation, urbanization, and land conversion for agriculture or infrastructure development have significantly reduced and fragmented primate habitats.

Habitat destruction leads to the loss of critical resources and disrupts the ecological balance necessary for primate populations to thrive. As their habitats shrink, primates face increased competition for limited resources, reduced access to food and water sources, and decreased opportunities for successful reproduction and rearing of offspring. This loss of habitat also exposes primates to increased vulnerability to predation, disease transmission, and human-wildlife conflicts.

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Answer:

7/66

Step-by-step explanation:

Given problem,

→ (7/10) × (1/3) × (5/11)

Let's solve the given problem,

→ (7/10) × (1/3) × (5/11)

→ (7 × 1 × 5)/(10 × 3 × 11)

→ 35/330

→ 7/66

Hence, the answer is 7/66.

To show that for any string w ∈ L(G) of length n ≥ 1, exactly 2n − 1 steps are required for any derivation of w in a context-free grammar (CFG) in Chomsky normal form (CNF), we can prove it by induction.

First, let's consider the base case when n = 1. In this case, w consists of a single terminal symbol. Since the CFG is in CNF, the derivation for w will consist of a single production rule that directly produces the terminal symbol. Thus, in this case, exactly 1 step is required, which is equal to 2n − 1 = 1.

Now, let's assume that for any string of length k < n, the number of steps required for its derivation is 2k − 1. We will prove that for a string w of length n, the number of steps required for its derivation is 2n − 1.

Since the CFG is in CNF, any production rule in the derivation can either introduce two non-terminals or substitute a non-terminal with a terminal symbol.

Therefore, for a string of length n, the total number of steps required for its derivation is n + (n - 1) = 2n - 1.

By induction, we have shown that for any string w ∈ L(G) of length n ≥ 1 in a CFG in CNF, exactly 2n − 1 steps are required for any derivation of w.

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A vector space is an abstract mathematical concept that is used to describe a collection of elements, known as vectors.

Vector is a mathematical object that has both magnitude and direction. It can be represented graphically by a line segment with a starting point and an endpoint. Vectors are used in physics, engineering, and mathematics to represent physical quantities such as force, velocity, and acceleration. They can also be used to represent geometric figures such as lines, points, and planes. Vectors are important in many applications, such as navigation, graphics, and robotics.

It is an important concept in linear algebra, and is used to describe the behavior of linear equations and systems.

A vector space is made up of a set of vectors, which can be seen as elements of the space. Each vector is a combination of scalar numbers, called components, and the space is made up of all possible combinations of these components. The components can be real numbers, complex numbers, or even functions.

The vector space is defined by certain operations, called vector addition and scalar multiplication. Vector addition is the process of adding two vectors together, and scalar multiplication is a process of multiplying a vector by a scalar number. Using these operations, the vector space can be used to solve linear equations and systems of equations.

The vector space is also used to describe the geometry of the space. It is used to describe dimensions, angles, and distances between vectors. It is also used to describe shapes and objects within the space, and to describe how they interact with each other.

Finally, the vector space is used to represent linear transformations, which are important in physics and engineering. A linear transformation is a process of mapping a vector to another vector, and is used to describe the behavior of physical systems. This can be used to solve complicated equations and systems of equations.

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By solving the LP formulation using Solver in Excel, you will obtain the optimal values for the decision variables x1, x2, x3, x4 that maximize the objective function Z.

To solve the given linear programming problem in Excel, you can use the Solver add-in. Here are the steps to set up and solve the LP formulation:

Step 1: Set up the Excel spreadsheet with the following columns:

Column A: Variables (x1, x2, x3, x4)

Column B: Coefficients of the objective function (300, 90, 400, 150)

Column C: Constraint coefficients for the first constraint (35000, 10000, 25000, 90000)

Column D: Constraint coefficients for the second constraint (4, 2, 7, 3)

Column E: Constraint coefficients for the third constraint (1, 1, 0, 0)

Column F: RHS values for the constraints (120000, 12, 1)

Column G: Variable type (0 or 1)

Column H: Variable names (optional)

Cell J2: Objective function (formula: =SUMPRODUCT(B2:B5, G2:G5))

Step 2: Set up the Solver add-in:

Go to the "Data" tab and click on "Solver" in the "Analysis" group.

In the Solver Parameters dialog box, set the following:

Set Objective: Cell J2

To: Max

By Changing Variable Cells: Range G2:G5

Subject to the Constraints: Range C2:F4

Click on the "Add" button to add each constraint.

Click on the "Solve" button to solve the LP problem.

Note: Before running the Solver, make sure you have the Solver add-in enabled. You can enable it by going to "File" -> "Options" -> "Add-Ins" -> "Excel Add-Ins" -> "Solver Add-in" -> "OK".

By solving the LP formulation using Solver in Excel, you will obtain the optimal values for the decision variables x1, x2, x3, x4 that maximize the objective function Z.

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Answer:

the first one's answer is y > x

the first second one's answer is y < 6.5x i believe, sorry if im wrong

Step-by-step explanation:

Answer:

6x-12

Step-by-step explanation:

3*2x-3*4

6x-12

Hope this helps plz hit the crown :D

The general relationship between the sample size and the margin of error is that they are inversely proportional.

As the sample size increases, the margin of error decreases, and vice versa. In other words, a larger sample size leads to a smaller margin of error, providing more accurate and reliable results. This occurs because larger samples are more likely to represent the entire population, reducing the chance of random sampling errors.

Conversely, a smaller sample size may not fully represent the population, leading to a higher margin of error and less accurate results. In conclusion, to obtain more precise and reliable findings, it's essential to choose an appropriate sample size that minimizes the margin of error while considering factors like population size, variability, and desired confidence level.

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Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

The linearization of the function f(x) = x + cos(x) at x = 0 is: A) L(x) = x + 1The linearization of a function at a given point is the equation of the tangent line to the graph of the function at that point.

The linearization of a function at a given point is the equation of the tangent line to the graph of the function at that point. To find the linearization, we need to evaluate the function and its derivative at the given point.

Given function: f(x) = x + cos(x)

First, let's find the value of the function at x = 0:

f(0) = 0 + cos(0) = 0 + 1 = 1

Next, let's find the derivative of the function:

f'(x) = 1 - sin(x)

Now, we can construct the equation of the tangent line using the point-slope form:

L(x) = f(0) + f'(0)(x - 0)

L(x) = 1 + (1 - sin(0))(x - 0)

L(x) = 1 + (1 - 0)(x - 0)

L(x) = 1 + x

The linearization of the function f(x) = x + cos(x) at x = 0 is L(x) = x + 1. This means that for small values of x near 0, the linearization provides a good approximation of the original function.

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Answer:

not linear since all first differences are not equal

Step-by-step explanation:

To find the first differences, subtract each y value from the next y value.

Use only y values.

here are the 4 first differences you need to calculate.

1 - 0 = 1

4 - 1 = 3

9 - 4 = 5

16 - 9 = 7

Now you place them in the appropriate column in the table.

x   y      first difference

0   0       1

1   1         3

2   4       5

3   9       7

4   16

If the first differences were all equal, the function would be a linear function.

In this case, the first differences are all different, 1, 3, 5, 7, so the function is not linear.

Answer:

i) Her claim is incorrect

ii) see below

iii)  44 cm

Step-by-step explanation:

Given:

If the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:

Area of rectangle = width × length

⇒ Area of poster = (3x) × 3(x + 4)

                             = 9x(x + 4)

                             = 9x² + 36x  cm²

Inputting x = 31 into the area of poster formula found above:

⇒ 9(31)² + 36(31)

= 8649 + 1116

= 9765 cm²

Therefore, as 9765 ≠ 1053 her claim in incorrect.

Using the formula for the area of poster found in part (i).

Area of poster = 1053 cm²

⇒ 9x² + 36x = 1053

⇒ 9x² + 36x - 1053 = 0

⇒ 9(x² + 4x - 117) = 0

⇒ x² + 4x - 117 = 0

First find x by solving the equation from part (ii):

⇒ x² + 4x - 117 = 0

⇒ x² + 13x - 9x - 117 = 0

⇒ x(x + 13) - 9(x + 13) = 0

⇒ (x - 9)(x + 13) = 0

⇒ x = 9,  x = -13

As width cannot be negative, x = 9 only

Perimeter of picture = 2(width + length)

                                 = 2(x + x + 4)

                                 = 2(2x + 4)

                                 = 4x + 8

Input found value of x into the expression for the perimeter:

⇒ Perimeter of picture = 4(9) + 8

                                      = 36 + 8

                                      = 44 cm