Type the expression that results from the following series of steps:
Start with
n
, add 5, multiply by 4, then subtract 7.

The ways the system of equations 9x - 2y = 43x+8y=12can be solved are:

A) Multiply the first equation by 4, then add the equations.

D) Multiply the second equation by 3, then subtract the equations.

From the given equations,9x - 2y = 43x+8y=12we need to use wyas of solving simultaneous equation to solve it.

Then if we Multiply the first equation by 4,  thge we can then perform addition to the second equation like

9x - 2y = 4

36x - 8y = 4

3x+8y=12

then if we add to equation 2 we have

39x =12

then we can solve x = 12/39

The same can be done with equation D .

Therefore, option A and D are correct.

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Answer:

Step-by-step explanation:

To solve the system of equations:

9x - 2y = 4 ...(1)

3x + 8y = 12 ...(2)

We can use elimination method by adding or subtracting the equations in a way that one variable is eliminated.

Here are the possible ways to solve the system:

A) Multiply the first equation by 4, then add the equations.

Multiplying the first equation by 4 gives:

36x - 8y = 16

Adding the resulting equation to the second equation gives:

36x - 8y + 3x + 8y = 16 + 12

Simplifying the equation:

39x = 28

x = 28/39

Substituting x in equation (1) gives:

9(28/39) - 2y = 4

Solving for y gives:

y = -155/78

Therefore, the solution is (x,y) = (28/39, -155/78).

B) Multiply the second equation by 3, then add the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Adding the resulting equation to the first equation gives:

9x - 2y + 9x + 24y = 4 + 36

Simplifying the equation:

18x + 22y = 40

Dividing the equation by 2 gives:

9x + 11y = 20

Substituting 9x from equation (2) gives:

3x + 8y = 12

Solving for x gives:

x = (12 - 8y)/3

Substituting x in equation (3) gives:

9[(12-8y)/3] + 11y = 20

Solving for y gives:

y = 16/39

Substituting y in equation (2) gives:

3x + 8(16/39) = 12

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

C) Multiply the first equation by 3, then add the equations.

Multiplying the first equation by 3 gives:

27x - 6y = 12

Adding the resulting equation to the second equation gives:

27x - 6y + 3x + 8y = 12 + 12

Simplifying the equation:

30x = 24

x = 4/5

Substituting x in equation (1) gives:

9(4/5) - 2y = 4

Solving for y gives:

y = -23/10

Therefore, the solution is (x,y) = (4/5, -23/10).

D) Multiply the second equation by 3, then subtract the equations.

Multiplying the second equation by 3 gives:

9x + 24y = 36

Subtracting the second equation from the first equation gives:

6x - 26y = -8

Solving for x gives:

x = (26y - 8)/6

Substituting x in equation (2) gives:

3[(26y-8)/6] + 8y = 12

Solving for y gives:

y = 16/39

Substituting y in equation (1) gives:

9x - 2(16/39) = 4

Solving for x gives:

x = 28/39

Therefore, the solution is (x,y) = (28/39, 16/39).

a) Fluke has 5 letters. b) Propose has 7 letters. c) Mississippi has 11 letters  d) Arrange has 7 letters

We have been given that child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue.

Since, the number of different letter arrangements can be made from the letters Fluke is 5! = 120.

b)  the number of different letter arrangements that can be made from the letters Propose is 7! = 5040.

Therefore, Propose has 7 letters.

c) the number of different letter arrangements can be made from the letters Mississippi is

11!/(4!4!) = 34650.

Thus Mississippi has 11 letters, and it has 4 S's and 4 I's

d) the number of different letter arrangements that can be made from the letters Arrange,

7!/(2!2!) = 1260.

Thus Arrange has 7 letters, and it has two Rs and two Es.

Then, the number of arrangements that can be made is; 12!/[(6!)(4!)(1!)(1!)] = 27720 arrangements.

Therefore, the child can make 27720 arrangements with 12 blocks.

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Answer:

2

Step-by-step explanation:

Use order of operations PEMDAS

3^2 = 9 * 2 = 18

20-18= 2

The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

"Information available from the question"

In the question:

The mean of the quantitative variable of interest in the population is called the

Now, According to the question:

Let's know:

Sample Mean:

A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.

The mean of the quantitative variable of interest in the sample is called the. Sample Mean. The standard deviation of the quantitative variable of interest in the population is called the. Population Standard Deviation.

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Answer:

52.30472

Step-by-step explanation:

A=πr(r+h2+r2)=

π·2·(2+62+22)≈

52.30472

The statement that best explains both students approach to the sequence is that; They are both correct.

According to Julia,

AP = -5.5, 11, ...

First term; a = 5.5

common difference; d= 11 - (-5.5)

d = 16.5

Thus;

a₃ = a₂ + d

a₃ = 11 + 16.5

a₃ = 27.5

a₄ = 27.5 + 16.5

a₄ = 44

According to Taquan;

First term; a = -5.5

common ratio; r = 110/-5.5

r = -2

a₃ = -2(11) = -22

a₄ = -2(-22) = 44

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Answer :a₄ = -2(-22) = 44

Good luck it just get harder but keep trying

Answer:

Yes, the measurements 3cm, 4cm and 5cm are possible to create a triangle!

Step-by-step explanation:

Answer:

\(Ran(f)=[4,\infty)\)

Step-by-step explanation:

The parent function of the absolute value function is \(|x|\)

The function given is shifted vertically to \(x=4\), therefore, we are working in the function \(f\), such as

\(f(x)=|x|+4\)

\(Dom(f)=(-\infty, \infty) = \mathbb{R}\)

The range/image represents all the possible outputs of the function. It is shown in the y-axis.

Therefore,

\(Ran(f)=[4,\infty)\)

If two expressions have the same coefficients of the variable, then the variable can be any number

For the first choice

3(3r + 3) = 9r + 9 === 1st expression

6r + 6 ===== 2nd expression

If we equate them

9r + 9 = 6r + 6

If we solve the equation we will find just one value of r

9r + 9 - 6r = 6r - 6r + 6

3r + 9 = 6

3r + 9 - 9 = 6 - 9

3r = -3

r = -1

But in the other choices, the two expressions have the same coefficients of r

Then when we equate them they will cancel each other

Then r can be any value

Because it does not affect the equation

Using slope and y - intercept, the equation of the line is y = -14x + 63

The equation of a straight line is a mathematical equation that gives the relation between the coordinate points lying on that straight line. It can be written in different forms and tells the slope, x-intercept, and y-intercept of the line.

The slope-intercept form of equation of a line is written as;

y = mx + c

From the two points given, we can find the slope of the line

slope (m) = y₂ - y₁ / x₂ - x₁

m = -7 - 7 / 5 - 4

m = -14/ 1

m = -14

The slope is -14 and we can use this to find the y - intercept

y = mx + c

7 = -14(4) + c

7 = -56 + c

c = 56 + 7

c = 63

The equation of the line is y = -14x + 63

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The most appropriate design would be experiment. Implementation of the design would be by selection of trees, then the application of fertilizer, followed by data collection and statistical analysis.

a) Most appropriate design: Experiment

The orchard owner wants to determine if a new formula of fertilizer produces more apples per tree compared to a current popular brand. To make a causal conclusion, an experiment would be the most appropriate design. In an experiment, the orchard owner would randomly assign the trees to receive either the new fertilizer formula or the current popular brand and then compare the number of apples produced. This allows the orchard owner to control for other variables and isolate the effect of the fertilizer on the number of apples produced.

b) Implementation:

Selection of trees: The orchard owner would randomly select a sample of trees from their orchard and divide them into two groups: the experimental group (receiving the new fertilizer formula) and the control group (receiving the current popular brand).

Application of fertilizer: Both the experimental and control groups would receive the same amount of fertilizer, but the experimental group would receive the new formula while the control group would receive the current popular brand.

Data collection: The orchard owner would measure the number of apples produced by each tree in both the experimental and control groups.

Statistical analysis: The orchard owner would use appropriate statistical tests to compare the number of apples produced by each group and determine if there is a significant difference between the two.

c) Benefit:

One benefit of this experimental design is that it allows the orchard owner to determine causality. By randomly assigning the trees to receive either the new fertilizer formula or the current popular brand, the orchard owner can be confident that any difference in the number of apples produced is due to the fertilizer and not other factors. This is important for making decisions about which fertilizer to use in the future.

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Since the z-score for the male weighing 1700 g is -2.78 and the z-score for the female weighing 1700 g is -0.92, the male has the weight that is more extreme.

The z-score measures how many standard deviations a data point is away from the mean. We can calculate the z-scores as follows:

For the male weighing 1700 g:

z_male = (1700 - 3201.5) / 714.3

For the female weighing 1700 g:

z_female = (1700 - 3081.19) / 512.8

To determine who has the weight that is more extreme, we compare the absolute values of the z-scores. The data point with the larger absolute z-score is considered more extreme relative to its respective group. Therefore, we compare |z_male| and |z_female|.

If |z_male| > |z_female|, then the male weighing 1700 g is more extreme.

If |z_male| < |z_female|, then the female weighing 1700 g is more extreme.

By calculating the z-scores and comparing their absolute values, we can determine which individual's weight is more extreme relative to their respective group.

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Answer:

its pr

Step-by-step explanation:

because im smart

Equation:

c = 20.00 - d

Solution:

c = 20.00 - 8.49

c = 11.51

The coordinates (w, y) of a point in R where f(x, y) has the maximum value are (0, 14).

To find the maximum value of the function f(x, y) = -3x + y on the convex region R, we can use the method of linear programming.

The given region R is defined by the following inequalities:

6x + 3y ≤ 42

2x + 4y ≤ 32

x ≥ 0

y ≥ 0

We need to maximize the function f(x, y) = -3x + y subject to these constraints.

To solve this linear programming problem, we can use graphical methods or linear programming algorithms. Here, we'll solve it using graphical methods.

First, let's graph the feasible region R by plotting the boundary lines and shading the region that satisfies all the given inequalities.

The graph of 6x + 3y = 42 is a straight line passing through the points (0, 14) and (7, 0).

The graph of 2x + 4y = 32 is a straight line passing through the points (0, 8) and (16, 0).

The feasible region R is the intersection of the shaded region below and to the right of these lines.

Next, we evaluate the objective function f(x, y) = -3x + y at the vertices of the feasible region R.

Let's label the vertices of R as A, B, C, and D. Using the coordinates of these vertices, we can calculate the value of f(x, y) at each vertex:

Vertex A: (0, 0)

f(0, 0) = -3(0) + 0 = 0

Vertex B: (0, 14)

f(0, 14) = -3(0) + 14 = 14

Vertex C: (7, 0)

f(7, 0) = -3(7) + 0 = -21

Vertex D: (4, 4)

f(4, 4) = -3(4) + 4 = -8

Finally, we determine the maximum value of f(x, y) by comparing the values at the vertices:

Maximum value of f(x, y) = 14

The maximum value of the function f(x, y) = -3x + y is 14.

To find the coordinates (w, y) of a point in R where f(x, y) has the maximum value of 14, we can observe that this maximum value is achieved at the vertex B: (0, 14).

Therefore, the coordinates (w, y) of a point in R where f(x, y) has the maximum value are (0, 14).

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Step-by-step explanation:

f(-1) = 4(2)^-1 ≈ 4 × 1/2 = 2

(x, f(x)) = (-1, 2)

f(0) = 4(2)⁰ = 4×1 = 4

(x, f(x)) = (0, 4)

f(1) = 4(2)¹ = 4×2 = 8

(x, f(x)) = (1, 8)

f(2) = 4(2)² = 4×4 = 16

(x, f(x)) = (2, 16)

.Explanation

The question wants us to get the growth rate of the sum invested

To do this,

We have to use the general equation

The given equation is

To get the percentage growth rate, we will have to compare with the general formula

We will find out that

Answer:

Answer option 2

Step-by-step explanation:

When a shape is rotated counterclockwise by 90°, each point of the shape is moved in a circular motion in the counterclockwise direction by 90° around the fixed point of rotation.

As the triangle is rotated about point O, the position of point O does not change (i.e. it is "fixed").

Line segment OA is horizontal in the original figure. When it is rotated 90° counterclockwise, it becomes vertical, where A is above O.

Line segment BA is vertical in the original figure. When it is rotated 90° counterclockwise, it becomes horizontal, where B is to the left of A.

Therefore, the figure that represents the image after the given rotation is the second answer option.

Answer:

Answer option number two.

The product of the factors also has real coefficients and is equal to the polynomial. Given P(x) P(x) = = 9x5 +24x4 - 68x³ - 94x² + 21990, we can factor the polynomial in order to write it in factored form.

Given P(x) P(x) = = 9x5 +24x4 - 68x³ - 94x² + 21990, we can factor the polynomial in order to write it in factored form. Here’s how:

Step 1: Take out the greatest common factor

The greatest common factor of the terms is 1. Therefore, we cannot take out any common factor.

Step 2: Check for sum or difference of two cubes

This polynomial cannot be factored using the sum or difference of two cubes.

Step 3: Check for quadratic form

The polynomial can be expressed in a quadratic form. We can factor it using the quadratic formula.

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Here, a = 9, b = 24, c = 21990

The discriminant is D = b^2 - 4acD = (24)^2 - 4(9)(21990)

D = -1740768

Since the discriminant is negative, there are no real solutions. Therefore, the polynomial cannot be factored in the real number system.

However, we can still write the polynomial in factored form using imaginary numbers.  This is P(x) = (3x - 10i)(x - 2i)(x + 2i)(x + 5)(3x - 10), where i = sqrt(-1)

Note that each complex conjugate (3x - 10i)(3x + 10i) and (x - 2i)(x + 2i) produce a quadratic polynomial that has real coefficients and the other factors (x + 5) and (3x - 10) are both linear factors with real coefficients. Therefore, the product of the factors also has real coefficients and is equal to the polynomial.

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The conditional probability of an even number occurring on both dice given that the sum of the numbers equals eight is 2/5 or 0.4

To solve this problem, we need to first determine the sample space of all possible outcomes for rolling two dice with a sum of eight. The possible outcomes are (2, 6), (3, 5), (4, 4), (5, 3), and (6, 2).

Next, we need to determine the number of outcomes where both dice show an even number. There are only two possible outcomes for this case, which are (4, 4) and (6, 2).

Therefore, the probability of an even number occurring on both dice given that the sum of the numbers equals eight is 2/5 or 0.4.

We can also calculate this probability using conditional probability. The conditional probability of an even number on both dice given that the sum is eight is the probability of getting an even number on both dice AND a sum of eight divided by the probability of getting a sum of eight.

The probability of getting an even number on both dice AND a sum of eight is 2/36 or 1/18, as there are only two ways to get both dice to show an even number, and only one way to get a sum of eight with each of those outcomes.

The probability of getting a sum of eight is 5/36, as there are five ways to get a sum of eight out of 36 possible outcomes.

Thus, the conditional probability of an even number occurring on both dice given that the sum of the numbers equals eight is (1/18) / (5/36) = 2/5 or 0.4, which is the same as our previous answer.

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The Labοr Time cοnstraint is a resοurce availability cοnstraint. If the right-hand side fοr this cοnstraint increases tο 750, the dual value (shadοw price) will be less negative. Optiοn(e) is cοrrect.

Resοurce availability cοnstraints imply a scarcity οf resοurces. The limiting factοr is that these cοnstraints limit the prοductiοn οr οutput οf an οrganizatiοn. Cοnstraints οf resοurce availability are represented as linear equatiοns in οptimizatiοn prοblems, which must be fulfilled. These cοnstraints specify the maximum number οf resοurces that can be used in prοductiοn, the minimum amοunt οf prοductiοn that must be achieved, and the availability οf specific resοurces within the plant, amοng οther things.

The allοwable increase and decrease in the right-hand side οf the cοnstraint οf labοr time are 100 and 200, respectively.

The allοwable increase is 50. Therefοre, the shadοw price will be less negative. As a result, the cοrrect οptiοn is (e) It will be less negative.

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Complete question:

Consider a partial output from a cost minimization problem that has been solved to optimality. name Final value shadow price constraint R.H side allowable increase allowable desrease

labor time 700 -6 700 100 200

The Labor Time constraint is a resource availability constraint. What will happen to the dual value (shadow price) if the right-hand-side for this constraint increases to 750 ?

a. It will be zero.

b. It will be positive.

c. It will remain at −6.

d. It will be more negative.

e. It will be less negative.

To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.

The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.  

The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.

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The probability of choosing a 5 and then a 6 is 1/49

From the question, we have the following parameters that can be used in our computation:

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

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Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

Answer:

A=94

Step-by-step explanation:

Length: 5

Width: 4

Height: 3

Shape: Rectangle prism

Solved for surface area

Formula: A=2(wl+hl+hw)

Formula: L*W*H

Answer: A=94

Hope this helps.

Answer:

Step-by-step explanation:

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

Let's say that the very first figure is x and the next is y.

x - y = 3 -----> y=x-3 .........(i)

xy=88 .......(ii)

Substitute (i) to (ii)

xy=88

x(x-3)=88

x\(x^{2} - 3x = 88\\x^{2} - 3x - 88 = 0\)

(x+8)(x-11)=0

x+8=0 or x-11=0

x=-8 or x=11

Substitute x=-8 to (i)

y=x-3

y=-8-3=-11

Substitute x=11 to (i)

y=x-3

y=11-3=8

Thus, x = -8 and y =- 11 or x = 11 and y = 8

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

A 2nd equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0.  For instance, if school administration decides to build a chapel with a floor size of 400 sq metres and a length that is two meters longer than its width, we will need the aid of a quadratic equation to determine the length and breadth. 

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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a) The corresponding z-score is 0.5 and the direction is to the right.

b) The percentage of adult spiders that have carapace lengths exceeding 19 mm is 30.85%.

If the area under the standard normal curve that lies to the right of nothing is 50%, then the z-score corresponding to this area is 0.

To find the z-score and direction that corresponds to the percentage of adult spiders that have carapace lengths exceeding 19 mm, we need to determine the area under the standard normal curve to the right of 19 mm and then find the corresponding z-score using a standard normal distribution table or calculator.

Assuming a normal distribution of carapace lengths of adult spiders, we need to standardize the value of 19 mm by subtracting the mean and dividing by the standard deviation. If we assume that the mean carapace length of adult spiders is 18 mm with a standard deviation of 2 mm, we can calculate the z-score as follows

z = (19 - 18) / 2 = 0.5

This means that a carapace length of 19 mm is 0.5 standard deviations above the mean. To find the area under the standard normal curve to the right of 19 mm, we can use a standard normal distribution table or calculator, which gives us an area of 0.3085.

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