A soup recipe requires 6 ounces of bouillon plus 2 ounces for each quart of water used.
This relationship is represented by the equation b = 2q +6, where b represents the
number of ounces of bouillon and q represents the number of quarts of water

The simplified form of the expression is -184.

To simplify the expression (46)(4-8), we can start by simplifying the parentheses.

(46)(4-8) can be rewritten as (46)(-4).

Next, we multiply 46 by -4:

(46)(-4) = -184.

We can start by simplifying the brackets in order to simplify the statement (46)(4-8).

You may write (46)(4-8) as (46)(-4).

Then we divide 46 by -4:

(46)(-4) = -184.

Starting with the brackets, we may begin to simplify the expression (46)(4-8).

(46)(4-8) is equivalent to (46)(-4).

Now let's multiply 46 by -4:

(46)(-4) = -184.

We may start by removing the brackets from the phrase (46)(4-8).

As (46)(-4), (46)(4-8) can be written.

After that, we multiply 46 by -4.

(46)(-4) = -184.

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Answer:

C

Step-by-step explanation:

We are given that:

\(\sin \theta +\csc \theta = 2\)

And we want to find the value of:

\(\sin^2\theta + \csc^2\theta\)

From the first equation, we can square both sides:

\((\sin \theta + \csc \theta)^2=(2)^2\)

Square:

\(\sin ^2\theta +2\sin\theta\csc\theta +\csc^2\theta =4\)

Let csc(θ) = 1 / sin(θ):

\(\displaystyle \sin ^2\theta +2\sin\theta\left(\frac{1}{\sin \theta}\right) +\csc^2\theta =4\)

Simplify:

\(\displaystyle \sin ^2\theta +2(1) +\csc^2\theta =4\)

Therefore:

\(\sin ^2\theta + \csc^2\theta =2\)

Our answer is C.

The most appropriate choice for remainder theorem will be given by-

Quotient = \(-x^3-2\)

Remainder = -3

What is remainder theorem?

When f(x) is divided by (x-a), the remainder will be f(a).

If the remainder is zero, (x-a) will become a factor of f(x)

Expression to be divided is called dividend, expression by which dividend is divided is called divisor, expression obtained on division is called Quotient and the other part is the remainder.

There is also a well known formula

Divisor x Quotient + Remainder = Dividend

Here,

P(x) = \(-x^4 +3x^3 -2x+3\)

P(3) =  \(-(3)^4+3(3)^3-2(3)+3\)

      = \(\\-81+81-6+3\)

      = -3

So by Remainder theorem, remainder is P(3)

So, Remainder = -3

Let the quotient be q(x)

divisor = \(x - 3\)

We know,

Divisor x Quotient + Remainder = Dividend

\((x-3) \times q(x) +(-3) = -x^4 +3x^3 -2x+3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+3 +3\\(x-3) \times q(x) = -x^4 +3x^3 -2x+6\\q(x) = \frac{-x^4 +3x^3 -2x+6}{x -3}\\q(x) =\frac{ -x^3(x-3)-2(x-3)}{x-3}\\q(x) = \frac{(x-3)(-x^3-2)}{x-3}\\q(x) = -x^3-2\)

So, Quotient = \(-x^3-2\)

Remainder = -3

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Answer:

24

Step-by-step explanation:

I will assume this is a right triangle with the information given

a^2+b^2 = c^2 is the Pythagorean theorem

18^2 + b^2 = 30^2

Subtract 18^2 from each side

18^2  - 18^2+ b^2 = 30^2 -18^2

b^2 =900 -324

b^2 =576

Take the square root of each side

sqrt(b^2) = sqrt(576)

b =24

Answer:

gggg

Step-by-step explanation:

bfdrfgnhtrh

The value of x from the given equation is -2

Equations are expressions separated by an equal sign.

Given the expression

x/2 - (5x-3)/12 = 1/3 x - 0.75

Find the LCM

6x-(5x-3)/12 = 1/3 x - 0.75

(x+3)/12 = 1/3 x - 0.75

(x+3)/12 - x/3 = -0.75

(x+3-4x)/12 = 0.75

-3x +3 = 9

Subtract 3 from both sides

-3x = 9 - 3

-3x = 6

x = -2

Hence the value of x from the given equation is -2

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Answer:

\(18\sqrt{3} + 55\sqrt{3} = 73\sqrt{3}\)

Step-by-step explanation:

27= 3 * 3 * 3

75 = 3 * 5*5

18 sqr 3 + 55 sqr 3 = 73 sqr 3

Hello!

Answer:

B. <DEF

Step-by-step explanation:

The vertex is the common endpoint, which is always in the middle of an angle. So E will be in the middle.

Hope this helps!

Answer:

Angle DFE

Step-by-step explanation:

A vertex is a point where two or more curves, lines, or edges meet.

Therefore, it would be the end point.

Answer:

(0,3)

Step-by-step explanation:

Answer:

0, 3

Step-by-step explanation:

first find the x axis variable, (0), then find the y axis variable, (3).

Answer:

-m

Step-by-step explanation:

2m+3m+(-6m)=2m+3m-6m

                      =5m-6m

                      =-m

Answer:

-m

Step-by-step explanation:

2m+3m+(-6m)​

Remove parentheses.

2m+3m-6m

Add and subtract.

-1m or -m

Hope this helps :)

The expression that defines sn is the limit of 7 over 9 times (1/3) to the power of n as n approaches infinity.

In this given series, each term is obtained by taking the previous term and multiplying it by 7 over 3. As n approaches infinity, the exponent of (1/3) becomes larger, and the value of (1/3) to the power of n approaches zero. Thus, the entire expression approaches the value of 7 over 9 times zero, which is equal to zero. Therefore, the limit of 7 over 9 times (1/3) to the power of n as n approaches infinity is zero.

In simpler terms, as n gets larger and larger, each term in the series becomes exponentially smaller because the base (1/3) is less than 1. Consequently, the sum of an infinite number of such terms becomes infinitesimally close to zero. This behavior is characteristic of geometric series with a common ratio between -1 and 1, and it allows us to determine the limit of the series by examining the behavior of the terms as n tends to infinity. In this case, the limit is zero.

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Answer: The items cost as follows;

(a) Brush = $3.50, (b) Sketchbook = $21 and (c) Paint set = $28

Step-by-step explanation: First of all we shall assign letters to the unknown variables, hence we shall call the brush x, the sketchbook y, and the paint set we shall call z.

The total amount spent by Corey was $52.50 because after buying all he needed, he had $2.00 left out of a total of $54.50. This means his transaction can be expressed as follows;

x + y + z = 52.50

However, we know that the brush was 1/6 as much as the sketchbook, that is, if the sketchbook is y, then the brush which is x shall be 1/6 of y. Simply put, x = 1/6y or x = y/6.

Similarly, the sketchbook cost 3/4 of the paint set. If the paint set is z, that means y = 3/4z or y = 3z/4.

Note however that, if y = 3z/4, then by cross multiplication,

4y = 3z

4y/3 = z

Having derived that x = y/6 and z = 4y/3, we can substitute for the values of x and z into the original equation

x + y + z = 52.50

y/6 + y + 4y/3 = 52.5

using a common denominator which is 6, you now have;

(y + 6y + 8y)/6 = 52.5

By cross multiplication, you now have

15y = 52.5*6

15y = 315

Divide both sides of the equation by 15

y = 21

Therefore, if the sketchbook is y, then the sketchbook costs $21.

Also if the brush is x, then the brush costs

x = y/6

x = 21/6

x = 3.50 (The brush costs $3.50)

Also if the sketchbook costs 3/4 of the paint set, then

y = 3z/4

21 = 3z/4

21*4 = 3z

84 = 3z

Divide both sides of the equation by 3

28 = z (The paint set costs $28)

The problem where the professor states that the average age of students in the university is 21 years is an example of statistical inference.

Statistical inference is the process of using data from a sample to make inferences or conclusions about a population. It allows us to draw conclusions about a larger group of individuals or objects based on information from a smaller sample. It is a fundamental part of statistical analysis and is used in many fields, including research, business, and government.

Statistical inference includes two main types: estimation and hypothesis testing.

Estimation: This involves using sample data to make estimates about population parameters. For example, using the sample mean to estimate the population mean or the sample proportion to estimate the population proportion.

Hypothesis testing: This involves using sample data to test a claim or hypothesis about a population parameter. For example, testing the claim that a coin is fair, based on the proportion of heads in a sample of coin flips.

The goal of statistical inference is to use the information from a sample to make informed decisions or predictions about a population. It allows us to draw general conclusions from a specific set of data, and it is an essential tool for making sense of data in many fields.

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Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

According to the statement seen in this question, the line segments RT and  ST are collinear to each other. Mathematically speaking, the length of the line segment ST can be found by using the following formula:

RT = RS + ST

ST = RT - RS

ST = 19 - 6

ST = 13

Under the consideration of collinearity of two line segments, the length of the line segment ST is equal to 13.

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Answer:

−590+5√5

^-^hope this helped^-^

Answer:

D

Step-by-step explanation:

Trust me

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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Answer:3(3m−2)=2(3m+3)

Use the distributive property to multiply 3 by 3m−2.

9m−6=2(3m+3)

Use the distributive property to multiply 2 by 3m+3.

9m−6=6m+6

Subtract 6m from both sides.

9m−6−6m=6

Combine 9m and −6m to get 3m.

3m−6=6

Add 6 to both sides.

3m=6+6

Add 6 and 6 to get 12.

3m=12

Step-by-step explanation:

The correct option is B• "The LP has multiple optimal solutions". Because  feasible region, intersects with the objective function in multiple points.

The given linear programming (LP) problem consists of two constraints and two decision variables, x1 and x2. The objective function to be minimized is x1 + 2x2.

To determine the nature of the LP problem, we need to analyze its feasible region and objective function.

The first constraint, x1 + x2 ≤ 4, defines a region in the xy-plane that lies below the line x1 + x2 = 4. The second constraint, x1 - x2 ≥ 5, defines a region that lies to the right of the line x1 - x2 = 5. The feasible region is the intersection of these two regions.

By analyzing the feasible region, we can determine the potential optimal solutions. Since the feasible region is a bounded region, there are finite points within it. The objective function, x1 + 2x2, represents a straight line in the xy-plane with a positive slope. As long as this line intersects the feasible region, there will be multiple points of intersection, each representing a potential optimal solution.

Therefore, the LP problem has multiple optimal solutions because there are multiple points of intersection between the objective function and the feasible region.

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Answer:

46,656

Step-by-step explanation:

6^2x3=

6^6=

6x6x6x6x6x6=

46,656

Hope that helps!

Answer:

1458

Step-by-step explanation:

2×3^6 that is d answer

Answer:

500

Step-by-step explanation:

Umm I dont know how to explain but im 100% sure

I got it right on my quiz so...

Answer: 500

Step-by-step explanation:

the first one

Answer:

Area ~= 52.4 m^2

OR (see image why)

Area ~= 52.3 m^2

Step-by-step explanation:

Use A = pi•r^2 to find the area of the whole circle. For a sector, times that by degrees/360.

Your problem has a 60° sector. 60/360 is 1/6.

Use either, 60/360 or 1/6 times 100pi.

If you use the pi button on the calculator the answer is .1 different than if you use 3.14 for pi in your calculation. The pi button answer is more accurate. See image.

a) The nth derivative for f(x) = xⁿ is n!.

b) The nth derivative for expression f(x) is (-1)^(n+1) * n! / x^(n+1).

(a) f(x) = xⁿ:

To find the nth derivative of f(x) = xⁿ, we can start by calculating the first few derivatives and looking for a pattern:

f(x) = xⁿ

f'(x) = n x^(n-1)

f''(x) = n(n-1)x^(n-2)

f'''(x) = n(n-1)(n-2)x^(n-3)

...

From this pattern, we can observe that the nth derivative of f(x) is given by:

f ⁿ(x) = n(n-1)(n-2)...(n-(n-1)) x^(n-n)

f ⁿ(x) = n!

Therefore, the nth derivative of f(x) = xⁿ is n!.

(b) f(x) = 1/x:

To find the nth derivative of f(x) = 1/x, we can again start by calculating the first few derivatives and observing the pattern:

f(x) = 1/x

f'(x) = -1/x^2

f''(x) = 2/x^3

f'''(x) = -6/x^4

f''''(x) = 24/x^5

...

From this pattern, we can observe that the nth derivative of f(x) alternates between positive and negative values, and is given by:

f ⁿ(x) = (-1)^(n+1) * n! / x^(n+1)

Therefore, the nth derivative of f(x) = 1/x is (-1)^(n+1) * n! / x^(n+1).

In summary, to find the nth derivative of a function, we can start by calculating the first few derivatives and looking for a pattern. Once we have identified the pattern, we can use it to derive a formula for the nth derivative of the function.

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The total surface area of the triangular prism is: 111 ft²

To find the total surface area of the given triangular prism, we will find the area of all the surfaces and add it up.

Formula for the area of a rectangle is:

Area = Length * Width

Area of a triangle is:

Area = ¹/₂ * base * height

Thus:

Total Surface area = 2(¹/₂ * 3 * 7) + (7 * 5) + (8 * 5) + (3 * 5)

Total Surface area = 21 + 35 + 40 + 15

Total Surface area = 111 ft²

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Answer:

\(40-50d\)

Step-by-step explanation:

Use the distributive property:

\(10(4-5d)\\\\10(4)-10(5d)\\\\40-50d\)

Since these are not like terms, they can't be further simplified.

:Done

Answer:

pre-image also means domain

so the value of X is 5

so 5x = 5×5

the answer is 25

The solution of the given equation is x = 4i-3.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equation is  x² + 6x + 13 = 0. The solution of the equation will be done as,

x² + 6x + 13 = 0

( x + 3 )² - 3² + 13 = 0

( x + 3 )² - 9 + 13 = 0

( x + 3 )² = -4

( x + 3 ) = √-4

( x + 3 )²  = 4i

x = 4i - 3

Therefore, the solution of the given equation is x = 4i-3.

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The height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

In geometry, it is defined as the three-dimensional shape having two circular shapes at a distance called the height of the cylinder.

We know the volume of the cylinder is given by:

\(\rm V = \pi r^2 h\)

We have:

Volume of the cylinder = 12π cubic inches

Dimeter of the cylinder = 4 inches

Radius of the cylinder = 2 inches

Here no other information is given in the question, Let suppose it is required to find the height of the cylinder

12π = π(2)²h

12  = 4h

h = 3 inches

Thus, the height of the cylinder is 3 inches if the cylinder has a volume of 12π cubic inches and a diameter of 4 inches.

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The type of influence on wellness that this represents is given as follows:

A. Social.

An influence on wellness is an activity that improves the morale of certain aspect of our lives.

The aspect improved in this problem is the social aspect, along with the physical aspect, as follows:

Since this is an example of social bonding, option A gives the correct option regarding which type of influence on wellness this is an example of.

For example, reading a book would be intellectual influence, while recycling would be environmental influence.

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therer sorry for the cropped pic btw lol