What is the value of x?

-36 + (-3x) = 0

Answer:

8

Step-by-step explanation:

2 1/5 + 5 4/5 =

2 + 5 = 7

1/5 + 4/5 = 1

1 + 7 = 8

Answer: y = -9/2x + 12

Step-by-step explanation: So, the slope of the line is 9/2 since the change in y is -9 and the change in x is a positive 2. That can be written as 9/2. The y intercept is 12, since when x = 0, y = 12. We can insert these numbers in the equation and get the answer

We know that it took 18 hours to drive 666 miles. If we divide the distance by the hours (666 miles)/(18 hours)

We find that 666/18= 37 miles per hour . which means we travel 37 miles each hour.

So, we can estimate that driving 37 miles it will take 1 hour (the distance to Chicago).

Answer:

666/18=37miles/hour

it would take 1 hour to drive 37 miles

1.Each method works differently the angles inside them is what matters.

2. Manipulating algebra tiles can help people solve linear equations

3.Distribute each term of the first polynomial to every term of the second polynomial. Remember that when you multiply two terms together you must multiply the coefficient (numbers) and add the exponents. But with Integers you multiply two integers with different signs

4.So you know how

A monomial is a number, a variable or a product of a number and a variable.

multiply each term in one polynomial by each term in the other polynomial

The exponential function that fits the given data can be represented by the equation:

y = a * e^(bx)

Where y represents the number of women graduating from 4-year colleges, x represents the year, a represents the initial value (number of women graduating in 1930), and b represents the growth rate.

To find the values of a and b, we can use the data points given:

(1930, 48,752) and (2009, 764,000)

Using the first data point, we have:

48,752 = a * e^(b*1930)

Using the second data point, we have:

764,000 = a * e^(b*2009)

To solve these equations, we need to eliminate a. We can divide the two equations:

(764,000 / 48,752) = (a * e^(b*2009)) / (a * e^(b*1930))

Simplifying the equation:

15.66 = e^(b*(2009-1930))

Now, we can take the natural logarithm of both sides to solve for b:

ln(15.66) = b * (2009-1930)

ln(15.66) = b * 79

Dividing both sides by 79:

b = ln(15.66) / 79

Using the value of b, we can substitute it back into either of the initial equations to solve for a. Let's use the first equation:

48,752 = a * e^(b*1930)

Substituting the value of b:

48,752 = a * e^((ln(15.66)/79)*1930)

Now, we can solve for a:

a = 48,752 / e^((ln(15.66)/79)*1930)

Calculating these values will give you the exponential function that fits the data and the exponential growth rate.

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Close ties between the members of the group typically are formed during the norming stage of group development.

The norming stage of group development is the third stage, where the group begins to establish a sense of cohesion and unity. During this stage, members start to accept each other's ideas and opinions, develop relationships with one another, and establish patterns of communication and interaction. As a result of these positive developments, close ties between the members of the group often begin to form.

In the norming stage, group members also start to identify common goals and work together to achieve them. This shared sense of purpose can further strengthen the bonds between group members and contribute to the formation of close ties.

Overall, the norming stage is an important period of transition for groups as they move from the early stages of forming and storming to a more cohesive and productive group dynamic. The close ties formed during this stage can help to foster a supportive and collaborative environment that benefits the group as a whole.

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the rate of change of the radius at the instant the volume equals 36π cm³ is 7 / (36π) cm/sec.

The volume V of a sphere with radius r is given by the formula V = (4/3)πr³. We are given that the rate of change of the volume is 7 cm³/sec. Differentiating the volume formula with respect to time, we get dV/dt =(4/3)π(3r²)(dr/dt), where dr/dt represents the rate of change of the radius with respect to time.

We are looking for the rate of change of the radius, dr/dt, when the volume equals 36π cm³. Substituting the values into the equation, we have: 7 = (4/3)π(3r²)(dr/dt)

7 = 4πr²(dr/dt) To find dr/dt, we rearrange the equation: (dr/dt) = 7 / (4πr²) Now, we can substitute the volume V = 36π cm³ and solve for the radius r: 36π = (4/3)πr³

36 = (4/3)r³

27 = r³

r = 3  Substituting r = 3 into the equation for dr/dt, we get: (dr/dt) = 7 / (4π(3)²)

(dr/dt) = 7 / (4π(9))

(dr/dt) = 7 / (36π)

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Answer: i believe its 15.12

Step-by-step explanation:

The given integral can be transformed into polar coordinates to evaluate it more conveniently.  The evaluated integral is 0.

To change the given integral to polar coordinates, we need to express the differential area element dA in terms of polar coordinates. In polar coordinates, we have dA = r dr dθ, where r represents the radial distance from the origin and θ represents the angle. The limits of integration also change accordingly. Since D is the top half of the disk, the range of θ is from 0 to π, and the range of r is from 0 to 5 (the radius of the disk).

After converting to polar coordinates, the integral becomes ∫∫D 5r^2 cos(θ) dr dθ. The integration is now separated into two parts: an integration with respect to r and an integration with respect to θ. The inner integral with respect to r can be evaluated as (5/3) r^3 cos(θ) evaluated from 0 to 5. This simplifies to (125/3) cos(θ). The outer integral with respect to θ is then evaluated as ∫₀^π (125/3) cos(θ) dθ. This integration yields (125/3) sin(θ) evaluated from 0 to π, resulting in a final answer of 0.

Therefore, the evaluated integral is 0. By converting to polar coordinates, we transformed the integral into a simpler form that allowed us to evaluate it more easily.

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Answer:

I guess option (C)

Step-by-step explanation:

Hope it helps!!!!

3) \(\angle B \cong \angle Y\)

4) \(\triangle ABC \sim \triangle ZYX\) by the SAS similarity theorem

ΔABC is similar ΔZYX by the SAS similarity theorem. Therefore, option B is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

1. AB/ZY = BC/YX = 2

2. ∠B and ∠Y are right angles

3. ∠B=∠Y

4. ΔABC is similar ΔZYX by the SAS similarity theorem.

Therefore, option B is the correct answer.

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Answer:

\(\sin(50^o) = \frac{3}{c}\)

Step-by-step explanation:

Given

See attachment for triangle

Required

Expression to solve c

To solve for c, we simply calculate the sine of angle at B

i.e.

\(\sin(50^o) = \frac{Opposite}{Hypotenuse}\)

This gives:

\(\sin(50^o) = \frac{3}{c}\)

Make c the subject

\(c = \frac{3}{\sin(50^o)}\)

The statement "the first step in the sampling design process is to determine the sample size" is false because according to the text, the first step in the sampling design process is to clearly define the target population.

The first step in the sampling design process is typically to define the target population and the research objectives.

This involves specifying the characteristics of the population under study and identifying the specific research questions or objectives that the sampling will address.

Once the target population and research objectives are established, the next steps in the sampling design process typically involve determining the appropriate sampling method (such as random sampling, stratified sampling, or cluster sampling) and selecting the sampling frame (the list or source from which the sample will be drawn).

After these initial steps, researchers can then consider factors such as the desired level of precision, confidence level, and variability in the population to determine the appropriate sample size.

The determination of the sample size usually comes after clarifying the research objectives and selecting the appropriate sampling method.

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Answer:

radius: 8.4   Area: 221.5

Step-by-step explanation:

16.8 divided by 2 = 8.4

The Formula for finding the area of circle= R₂ (radius squared: radius times itself) Multiplied by pi. pi = 3.14

8.4₂ multiplied by 3.14

Answer: Maximum area = 200m

Dimensions:

Length = 10m

Width = 20m

Such that there is only one side of 20m fenced because the other side of 20m is against the rock wall.

Step-by-step explanation:

We have the next problem.

Suppose that the vegetable area is a rectangle of length L and width W.

Such that the width side coincides with the rock wall, then we have that:

The perimeter is:

P = 2*L + 2*W

But because one of the width sides coincides with the wall, the amount of fence needed will be:

P = 2*L + W = 40m

And the area can be written as:

A = W*L

We want to find the maximum area that we can have.

First, write our two equations:

40m = 2*L + W

A = W*L

First we must isolate one of the variables in the first equation, and replace it into the second equation:

40m - 2*L = W.

then:

A = (40m - 2*L)*L = 40m*L - 2*L^2

We can write this as a quadratic equation:

A(L) = -2*L^2 + 40m*L

Now, notice that it has a leading coefficient negative, then the maximum of the area function will be at the vertex of the quadratic equation.

For a quadratic equation:

f(x) = a*x^2 + b*x + c

The vertex is at:

x = -b/2a

and the point is (-b/2a, f(-b/2a))

In this case we have:

b = 40m

a = -2

Then:

we must evaluate the area function in:

L = -40m/(-2*2) = 10m

A(L) = -2*L^2 + 40m*L

A(10m) = -2*100m^2 + 400m = 200m

Now we can find the width using one of the above equations:

W = 40m - 2*L = 40m - 2*10m = 20m

Then the dimensions that the farmer should use are:

Two sides of length 10m, and one side of length 20m

Answer:

Volume is 8 inches

Step-by-step explanation:

Formula for Volume is

   V = L× W × H = 4 ×0.25 ×8 = 8 inches

For the given arithmetic sequence 313, 307, 301, ..., the 42nd term of the sequence is -391.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.

It is given that,

The following sequence is,

313, 307, 301, ...

The given sequence is in the arithmetic progression the common difference of the series is,

d = 307 - 313 = 301 -307

d = -6

The nth term of the arithmetic progression is,

aₙ = a + (n – 1)d

a₄₂= - 307 + (42 -1)-6

a₄₂= -307 + 41(-6)

a₄₂= -307 +(-84)

a₄₂= -307 -84

a₄₂= -391

Thus, for the given arithmetic sequence 313, 307, 301, ..., the 42nd term of the sequence is -391.

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Answer: 14 - \(5x^{2}\)

Step-by-step explanation:

So what I would do is remove those parentheses so you would have

8 + \(6x^{2}\) + 6 - \(x^{2}\)

Then you are going to combine like terms that would look like

14 - \(5x^{2}\)

Hope that is correct

Answer:

Step-by-step explanation:

In this question we have to find the share of each person

First we have to find the sum of all the ratios,

\(2 + 3 + 5 \\ = 10\)

Then we have to represent their share as a fraction and then multiply it by the total value,

The share of first person:-

\( \frac{2}{10} \times 450000 \\ = 2 \times 45000 \\ = 90000\)

So the first person share is $90,000

The share of second person:-

\( \frac{3}{10} \times 450000 \\ = 3 \times 45000 \\ = 135000\)

So the second person share is $135,000

The share of third person:-

\( = 450000 - (135000 + 90000) \\ = 450000 - 225000 \\ = 225000\)

So the third person share is $225,000

(This is your answer hope it helps :))

In the grating equation nλ=d sin θ, the quantity θ will be determined in the lab by using meter sticks and geometry/trigonometry

The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign

Here we have given that the grating equation nλ=d sin θ, the quantity θ will be determined in the lab.

The term grating equation in math states that d = 1/N where N is the grating constant, and it is the number of lines per unit length and n is the order of grating, which is a positive integer, representing the repetition of the spectrum.

And the term trigonometry is defined as a branch of mathematics concerned with relationships between angles and ratios of lengths.

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Answer:

In a bubble sort, on each pass through the list that must be sorted, the largest value "bubbles" to the end of the list. Therefore, after each pass, the end of the list is guaranteed to be sorted. This means that we can stop making pair comparisons one comparison sooner, which is option B.

Step-by-step explanation:

Bubble sort works by repeatedly comparing and swapping adjacent elements in the list if they are in the wrong order. During each pass through the list, the largest unsorted element "bubbles up" to its correct position. As a result, after the first pass, the largest element is in its correct position, after the second pass, the two largest elements are in their correct positions, and so on.

Therefore, with each subsequent pass, you can stop making pair comparisons one comparison sooner because the elements at the end of the list are already sorted.

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The width of the rectangular garden is 21 feet.

A rectangle is a plane shape that have pair of opposite sides equal and parallel.

To calculate the width of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Hence, the right option is D. 21 feet.

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a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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(D) "Every real number is either 0 or less" best describes the range of the function.

The collection of potential output values for a function is known as its range.

For instance, the range is the non-negative real numbers for the function f(x)=x2 on the domain of all real numbers (x∈R), which may be represented as f(x)≥0 (or [0,∞) using interval notation).

So, every y-coordinate in a function is negated when it is reflected across the x-axis.

Our y-values in the initial function will all be positive.

All of the y-values will be negative when this is reflected across the x-axis, resulting in a range of y-values that are less than or equal to 0.

Therefore, (D) "every real number is either 0 or less" best describes the range of the function.

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Complete question:
Which best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis?

A. all real numbers

B. all real numbers less than 0

C. all real numbers greater than 0

D. all real numbers less than or equal to 0

The correct answer is "all real numbers less than or equal to 0."

What is Range of function?

The range of a function is the set of all possible output values that the function can produce. When a function is reflected over the x-axis, the sign of its output values (i.e., positive or negative) is reversed.

For the function f(x) = Two-thirds(6)x, the range consists of all real numbers greater than or equal to 0.

When this function is reflected over the x-axis, the range will consist of all real numbers less than or equal to 0.

Therefore, The correct answer is "all real numbers less than or equal to 0."

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Complete Question -

Which best describes the range of the function f(x) = 2/3(6)x after it has been reflected over the x-axis?

A. all real numbers

B. all real numbers less than 0

C. all real numbers greater than 0

D. all real numbers less than or equal to 0

After plotting all the three points, we get the parabolic equation in the form is 2(x - 1)²-34.

Any point on a parabola, which has the shape of a U, is situated at an equal distance from the focus, a fixed point, and the directrix, a fixed line.

General equation of the quadratic equation,

Y = ax² + bx +c

Given points,

(-2, 0),

(-1, -10),

(4, 0).

Putting the points in the general equation,

Putting (-2, 0), we get

0 = 4a - 2b + c

Putting (-1, -10), we get

-10 = a - b +c

Putting (4, 0), we get

0 = 16a + 4b +c

Solving all equations we get,

a = 2 , b = -4 , c = -16

After putting the values,

Y = 2x²- 4x- 16

2(x² - 2x - 8)

2(x²- 2x + 1 - 1 - 16)

=2(x - 1)²-34

Hence we get the required equation in the parabolic form.

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Answer:

B:25    

Plug it in to check                

Answer:

435

Step-by-step explanation:

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30*0.0= 435

Answer:

the answer is: 435

Step-by-step explanation:

Answer:

so for the first graph, there was a total of 49 rewards given out and 79 for the second graph. I believe it is a total difference of 30 rewards.

Step-by-step explanation:

Answer:

The answer is 3 11/21

Step-by-step explanation:

Answer:

              \(\underlie{\bold{\ 3\frac{11}{21}\ }}\)

Step-by-step explanation:

\(2\frac7{15}\cdot1\frac37=\frac{2\cdot15+7}{15}\cdot\frac{1\cdot7+3}{7}=\frac{37}{15}\cdot\frac{10}{7}=\frac{37}{3}\cdot\frac{2}{7}=\frac{37\cdot2}{3\cdot7}=\frac{74}{21}=\frac{3\cdot21+11}{21}=3\frac{11}{21}\)

(1.1) A matrix equation b = [√11+e, 0, √2, √2]²T 2) a)  Gaussian elimination without pivoting does not provide unique solution. b) Gaussian elimination with scaled partial pivoting cannot provide a unique solution.(c) Basic LU decomposition is x = [0.788, -3.12, 0.167, 4.55]²T.

The given linear system can be written in matrix form as:

A × x = b

where A is the coefficient matrix, x is the column vector of variables (x1, x2, x3, x4), and b is the column vector on the right-hand side.

The coefficient matrix A is:

A = [[0, -e, √2, -√3],

[π², e, -e², 3/7],

[√5, -√6, 1, -√2],

[π³, e², -√7, -1/9]]

The variable vector x is:

x = [x1, x2, x3, x4]²T

The right-hand side vector b is:

b = [√11+e, 0, √2, √2]²T

(1.2) Solving the system using:

(a) Gaussian elimination without pivoting:

To solve the system using Gaussian elimination without pivoting, we perform row operations on the augmented matrix [A | b] until it is in row-echelon form. Then back-substitute to find the values of x.

The augmented matrix [A | b] is:

[0, -e, √2, -√3 | √11+e]

[π², e, -e², 3/7 | 0]

[√5, -√6, 1, -√2 | √2]

[π³, e², -√7, -1/9 | √2]

Performing row operations, the row-echelon form:

[π², e, -e², 3/7 | 0]

[0, -e, √2, -√3 | √11+e]

[0, 0, 0, 0 | 0]

[0, 0, 0, 0 | 0]

From the row-echelon form, that the system is underdetermined, with two free variables. Therefore, Gaussian elimination without pivoting cannot provide a unique solution.

(b) Gaussian elimination with scaled partial pivoting:

To solve the system using Gaussian elimination with scaled partial pivoting, row operations with partial pivoting until the augmented matrix [A | b] is in row-echelon form. Then back-substitute to find the values of x.

The augmented matrix [A | b] is:

[0, -e, √2, -√3 | √11+e]

[π², e, -e², 3/7 | 0]

[√5, -√6, 1, -√2 | √2]

[π³, e², -√7, -1/9 | √2]

Performing row operations with scaled partial pivoting, the row-echelon form:

[π³, e², -√7, -1/9 | √2]

[0, -e, √2, -√3 | √11+e]

[0, 0, -0.03, -1.02 | 0.027]

[0, 0, 0, 0 | 0]

From the row-echelon form that the system is underdetermined, with two free variables. Therefore, Gaussian elimination with scaled partial pivoting cannot provide a unique solution.

(c) Basic LU decomposition:

The system using LU decomposition, factorize the coefficient matrix A into the product of lower triangular matrix L and upper triangular matrix U. Then we solve the equations L × y = b for y using forward substitution, and U × x = y for x using back-substitution.

The coefficient matrix A is:

A = [[0, -e, √2, -√3],

[π², e, -e², 3/7],

[√5, -√6, 1, -√2],

[π³, e², -√7, -1/9]]

Performing LU decomposition,

L = [[1, 0, 0, 0],

[π², 1, 0, 0],

[√5, 0.3128, 1, 0],

[π³, 4.3626, 2.4179, 1]]

U = [[0, -e, √2, -√3],

[0, e + π², -e² + e × π², 3/7 - e × √2],

[0, 0, 0.9693, -0.3651],

[0, 0, 0, -2.2377]]

Solving L × y = b for y using forward substitution:

[1, 0, 0, 0] ×y = √11+e

[π^2, 1, 0, 0] × y = 0

[√5, 0.3128, 1, 0] × y = √2

[π^3, 4.3626, 2.4179, 1] × y = √2

Solving the above equations,

y = [0.788, -3.12, 0.167, 4.55]²T

Now, solving U × x = y for x using back-substitution:

[0, -e, √2, -√3] × x = 0.788

[0, e + π², -e² + e × π², 3/7 - e ×√2]× x = -3.12

[0, 0, 0.9693, -0.3651] ×x = 0.167

[0, 0, 0, -2.2377] ×x = 4.55

Solving the above equations,

x = [0.788, -3.12, 0.167, 4.55]²T

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