What is the solution of the system of equations?

An equation that could be used to find p, the base price of the pizza is: D. 7.15 = 1/3(p + 4.5).

In order to write a linear equation to describe this situation, we would assign a variable to the base price of the pizza, and then translate the word problem into a linear equation as follows:

Let the variable p represent the base price of the pizza.

Since this group of three (3) friends had a share of $7.15, which included the base price of the pizza, a linear equation that can be used to model this situation is given by;

7.15 = 1/3(p + 4.5)

21.45 = p + 4.5

p = 21.45 - 4.5

p = $16.95

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The perimeter of triangle WXY is (8a + 3b - 5) in

the perimeter of the polygon is (4a + 8b -1) in.

The perimeter of triangle WXY is solved using addition of sides

perimeter of triangle = (2b + a) in + (4a - 3) in. +  (3a + b - 2) in.

perimeter of triangle = 8a + 3b - 5 in

perimeter of polygon = perimeter  of triangle WYZ - (4a - 3) in + (2b + a) in + (3a + b - 2) in.

perimeter of polygon = (4a + 5b - 2) in - (4a - 3) in + (2b + a) in + (3a + b - 2) in.

perimeter of polygon = (4a + 8b -1) in.

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The given matrix is:

```

4  6  2

1  5 -3

-7 0  9

```

The dimensions of the matrix are 3 x 3 because it has 3 rows and 3 columns.

The indicated element is "a23", which is not present in the matrix. The correct element in the 2nd row, 3rd column is 9.

Therefore, the correct answer is (b) 3x3; 9, a23.

Step-by-step explanation:

- The matrix has 3 rows and 3 columns, so its dimensions are 3 x 3.

- The indicated element is a23, which does not exist in the matrix. However, the element in the 2nd row and 3rd column is 9.

- Therefore, the correct answer is (b) 3x3; 9, a23.

Therefore, the expression "four more than 5 times the cube of a number" is equivalent to 5x³ + 4.

Let the number be represented by x. Then, "5 times the cube of a number" can be written as 5x³. "Four more than 5 times the cube of a number" means we add 4 to this expression.

The phrase "the cube of a number" means that we raise the number to the third power, which is denoted by x³.

The phrase "5 times the cube of a number" means that we multiply the cube of the number by 5, which is denoted by 5x³.

The phrase "four more than 5 times the cube of a number" means we add 4 to 5x³, which is denoted by 5x³ + 4.

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Answer:

0.27

Step-by-step explanation:

Probability of picking a green is 0.27 (t nearest hundredth).

Answer:

the answer is B

Step-by-step explanation:

are you a make a wish kid

Because i would love for you to bounce that

The length of each side is 26 meters, 32.5 meters and 32.5 meters.

Let, ABC is an isosceles triangle BC is the base and AB and AC are two equal sides.

By the property of triangle, the perirmeter P is equal to the sum of all three sides.

Let the sides are 4x, 5x, 6x.

P = 4x + 5x + 5x

91 = 14x

x = 6.5

Substitute the values in the assumed sides,

A = 4 × 6.5 = 26

B = 5 × 6.5 = 32.5

C = 5 × 6.5 = 32.5

The base of triangle is 26 meters and the two equal sides are 32.5 meters.

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The measure of acute angle is π/7

The area of a sector of a circle is a fraction of the circle's total area, proportional to the measure of the central angle that subtends the sector.

The formula to calculate the area of a sector of a circle is:

=> A = (θ/360) × πr²

Where: A is the area of the sector

θ is the measure of the central angle in degrees

r is the radius of the circle

We can use this formula to calculate the area of the sector in the given problem

Here we have

Two distinct lines pass through the center of three concentric circles of radii 3, 2, and 1. The area of the shaded region in the diagram is 8/13 of the area of the unshaded region.

Let the area of the shaded part is 'S' and 'U' be the area of the unshaded part and the acute angle formed by the two lines be 'θ'

Hence, we can take => S + U = 9π

From the data, S = 8/13 U

=> 8/13 U + U = 9π

=>  21/13 U = 9π

=> 9π = 21/13 U

=> U = 117/21 π

=> U = 39π/7  and S = 24π/7

Now write the area of the shaded region in terms of θ

=> 2θ/2π · π + 2(π - θ)/2π (4π - π) + 2θ/2π (9π - 4π) = 24π/7

=> θ + 3π - 3θ + 5θ = 24π/7

=> 3θ + 3π = 24π/7  

=> 3θ = 24π/7 - 3

=> 3θ = 24π - 21π/7

=> 3θ = 3π/7  

=>  θ = π/7  

Therefore,

The measure of acute angle is π/7

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The unknown values in the line segment area s follows:

y = 9

GH = 66 units

HI = 22 units

GI =  88 units

The line segment is measured GI. Therefore, H is in between G and I.

Hence,

GH = 7y + 3

HI = 3y - 5

GI = 9y + 7

Let's find y as follows:

7y + 3 + 3y - 5 = 9y + 7

10y - 2 = 9y + 7

10y - 9y = 7 + 2

y = 9

Let's find the GH

GH = 7y + 3 = 7(9) + 3= 63 + 3 = 66 units

Let's find the HI

HI = 3y - 5 = 3(9) - 5 = 27 - 5 = 22 units

Let's find the GI

GI = 9y + 7 = 9(9) + 7 = 81 + 7 = 88 units

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The price of the used book in the bookstore is $7.50.

A price is amount of money that the buyer pays to seller in an exchange for a product, service, asset etc.

We are given that:

The owner of the bookstore buys a used book for $2.50.

He resells it for 300% of that price.

So, the price of the used book in this bookstore will be:

= $2.50 x 300%

= $2.50 x 3.00

= $7.50.

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The interquartile range (IQR) is better than the standard deviation as a measure of dispersion when dealing with skewed data or outliers.

The advantage of using IQR is that it is more resistant to outliers than standard deviation. Standard deviation measures the spread of data around the mean, and if there are outliers in the data, it can be heavily influenced by them.

On the other hand, IQR is calculated using the median and quartiles, which are not affected by outliers. This makes IQR a more robust measure of dispersion in such cases. Additionally, IQR provides information on the range of the middle 50% of the data, which can be more informative than the range of the entire dataset provided by the standard deviation.

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The equation that describes the translation is given as follows:

(x,y) -> (x - 4, y + 3).

The four translation rules are defined as follows:

If we look the corresponding vertex of each vertex, we have that the translations are given as follows:

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Town A is 8km far  apart from Town B.

Speed is measured as the ratio of distance to the time in which the distance was covered which does not give direction.

The formula = Distance/Time

How to determine this

Let d represent the distance covered

And let t represent the time covered

First,

To calculate the distance covered by the cyclist and Joggers

The cyclist and joggers travel the total distance at t hour

Distance = Speed * Time

The cyclist travels at 14t km

And Joggers at 10t km

So, d = 14t +10t

d = 24t

Then, the Cyclist meet the Jogger in 4 minutes i.e 4/60 hours = 1/15 hours and t + 1/15 until the cyclist meet the walker

So, using the formula Speed = Distance/Time

Distance = Speed * Time

The cyclist travels at 14(t + 1/15)

And the walker at 6(t + 1/15)

= 14(t + 1/15) + 6(t + 1/15)

= 20(t + 1/15)

So, when d = 24t and d = 20(t + 1/15)

24t = 20(t + 1/15)

24t = 20t + 20/15

24t - 20t = 4/3

4t = 4/3

12t = 4

t = 4/12

t = 1/3

Since t = 1/3 ,

d = 24t = 24(1/3)

d = 8km

Therefore, Town A is 8km far apart from Town B

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The three-decimals which are written in expanded form and are greater than 5.3 are (b) 5+0.3+0.001,  (d) (5×1)+(3×0.1)+(3×0.01)  and (e) (6×1)+(2×0.1)+(1×0.01).

A Decimal is a number system that uses a base of ten and a decimal point to separate the whole number from the fractional part. It represents numbers that are not whole or integers, but rather parts of a whole.

To determine which decimals written in expanded-form are greater than 5.3, we simply add up the values of each place value.

The decimals that are greater than 5.3 will have a sum greater than 5.3.

Option (a) : 5+0.3+0.00

= 5 + 0.3,

= 5.3, which is not-greater than 5.3.

Option (b) : 5+0.3+0.001

= 5.3 + 0.001,

= 5.301, which is greater than 5.3.

Option (c) : (5×1)+(2×0.1)+(9×0.01)

= 5 + 0.2 + 0.09,

= 5.2 + 0.09,

= 5.29, which is not greater than 5.3.

Option (d) : (5×1)+(3×0.1)+(3×0.01)

= 5 + 0.3 + 0.03,

= 5.3 + 0.03,

= 5.33, which is greater than 5.3.

Option (e) : (6×1)+(2×0.1)+(1×0.01)

= 6 + 0.2 + 0.01,

= 6.2 + 0.01

= 6.21, which is greater than 5.3.

Therefore, the decimals that are greater than 5.3 are options (b), (d), and (e).

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The given question is incomplete, the complete question is

Which decimals written in expanded form are greater than 5.3 ?

Select three options.

(a) 5+0.3+0.00

(b) 5+0.3+0.001

(c) (5×1)+(2×0.1)+(9×0.01)

(d) (5×1)+(3×0.1)+(3×0.01)

(e) (6×1)+(2×0.1)+(1×0.01)

The perimeter of triangle ABC with point A(-2,1) , B(-6,-3) and C(-4,4)  is 4√2 + √53 + √13

To find the perimeter of triangle ABC, we need to find the distance between its three vertices.

Using the distance formula, we can find the length of each side of the triangle.

AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-6 - (-2))² + (-3 - 1)²]

= √[(-4)² + (-4)²]

= √32

= 4√2

BC = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - (-6))² + (4 - (-3))²]

= √[2² + 7²]

= √53

AC = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - (-2))² + (4 - 1)²]

= √[2² + 3²]

= √13

Therefore, the perimeter of triangle ABC is:

Perimeter = AB + BC + AC

= 4√2 + √53 + √13

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The shape formed is rectangle. Length of AD is 5. Perimeter of ABCD is 20. Area of BCD is  [tex]\sqrt{65}[/tex] .

a) The shape formed is a rectangle.

b) The length of AD can be found using the distance formula:

AD = [tex]\sqrt{(3-(-2))^{2}+(-3-(-3))^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

Therefore, the length of AD is 5.

c) The perimeter of ABCD can be found by adding up the lengths of all four sides:

AB = [tex]\sqrt{(-2-(-2))^{2}+(2-(-3))^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

BC = [tex]\sqrt{(3-(-2))^{2}+(2-2)^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

CD = [tex]\sqrt{(3-3)^{2}+(-3-2)^{2} }[/tex]

     = [tex]\sqrt{5^{2}}[/tex]

     = 5

DA = [tex]\sqrt{(-2-3)^{2}+(-3-(-3))^{2} }[/tex]

      = [tex]\sqrt{5^{2}}[/tex]

       = 5

Perimeter = AB + BC + CD + DA

                 = 5 + 5 + 5 + 5

                 = 20

Therefore, the perimeter of ABCD is 20.

d) Now join points B and D to form line segment BD. The area of triangle BCD can be found using the formula for the area of a triangle:

Area of BCD = (1/2) * base * height

The base is BD, which has length:

BD = [tex]\sqrt{(3-(-2))^{2}+(-3-2)^{2} }[/tex]

     = [tex]\sqrt{65}[/tex]

To find the height, we need to draw a perpendicular line from C to line BD:

The height is the length of the perpendicular line from C to line BD. Since C and D have the same x-coordinate, this perpendicular line will be vertical and have length 2 units (the difference between the y-coordinates of C and D).

Therefore, the height is 2.

Area of BCD = (1/2) * BD * height

                     = (1/2) *  [tex]\sqrt{65}[/tex] * 2

                     =  [tex]\sqrt{65}[/tex]

Therefore, the area of BCD is  [tex]\sqrt{65}[/tex] square units.

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Answer:

Step-by-step explanation:B

For the first problem, using the monthly payment formula monthly deposit needed is $118.69. For the second problem, using the same formula the monthly payment is $1029.73.

We have the following variables

P = Monthly payment

r = Annual interest rate = 3.7% = 0.037/12 per month

n = Number of payments = 15 months

A = Amount to be saved = $1800

Using the monthly payment formula

P = (r * A) / (1 - (1 + r)⁻ⁿ)

Substituting the given values

P = (0.003083 * 1800) / (1 - (1 + 0.003083)⁻¹⁵)

P ≈ $118.69

Therefore, you should deposit approximately $118.69 each month to save $1800 in 15 months, assuming an APR of 3.7%, compounded monthly.

We have the following variables

P = Monthly payment

r = Annual interest rate = 9.1% = 0.091/12 per month

n = Number of payments = 30 years * 12 months = 360 months

A = Mortgage amount = $127,000

Using the monthly payment formula

P = (r * A) / (1 - (1 + r)⁻ⁿ)

Substituting the given values

P = (0.007583 * 127000) / (1 - (1 + 0.007583)⁻³⁶⁰)

P ≈ $1029.73

Therefore, the monthly payment for a shack mortgage of $127,000 with a fixed APR of 9.1% for 30 years would be approximately $1029.73.

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Standardize every test score from Mr. Bowman's class, the new mean would be 0, the new standard deviation would be 1, and the shape of the distribution would remain the same as before.

Let's first understand what standardizing means.
Standardizing test scores involves transforming the original scores to a new scale, called z-scores.

This process is done by subtracting the mean (average) score from each test score and dividing the result by the standard deviation of the scores. The formula for finding the z-score is:
z = (X - μ) / σ
X is the original test score, μ is the mean, and σ is the standard deviation.
Now, let's discuss the properties of the standardized scores:
New mean:

Standardize the test scores, the new mean (average) of the z-scores will always be 0.

This occurs because we subtract the mean from each test score, making the sum of the differences equal to 0.
New standard deviation:

After standardization, the standard deviation of the z-scores will always be 1.

This is because we divide each score by the original standard deviation, results in the new standard deviation being equal to 1.
Shape of the distribution:

The shape of the distribution (i.e., the pattern of the scores) will not be affected by standardization.

If the original scores followed a bell-shaped curve, the standardized scores would maintain the same bell shape.

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a. The random variable X is the number of California residents in a sample of 11 who have adequate earthquake supplies.

b. X may take on the values 0, 1, 2, ..., 11, since it is possible that none or all of the residents have adequate earthquake supplies.

c. X ~ Binomial(11, 0.3), since we have a fixed number of trials (n=11) and each trial is either a success (having adequate earthquake supplies) or a failure (not having adequate earthquake supplies), and the probability of success (p=0.3) is constant for each trial.

d. To find the probability that at least eight have adequate earthquake supplies, we can use the binomial probability formula or a calculator. Using a calculator, we get P(X >= 8) = 0.0512.

e. It is more likely that none of the residents surveyed will have adequate earthquake supplies.

f. The expected value of X is E(X) = np = 11 x 0.3 = 3.3. So we can expect about 3 or 4 residents out of the 11 to have adequate earthquake supplies on average.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

a. The random variable X is the number of California residents in a sample of 11 who have adequate earthquake supplies.

b. X may take on the values 0, 1, 2, ..., 11, since it is possible that none or all of the residents have adequate earthquake supplies.

c. X ~ Binomial(11, 0.3), since we have a fixed number of trials (n=11) and each trial is either a success (having adequate earthquake supplies) or a failure (not having adequate earthquake supplies), and the probability of success (p=0.3) is constant for each trial.

d. To find the probability that at least eight have adequate earthquake supplies, we can use the binomial probability formula or a calculator. Using a calculator, we get P(X >= 8) = 0.0512.

e. It is more likely that none of the residents surveyed will have adequate earthquake supplies. This is because the probability of success (having adequate earthquake supplies) for each resident is only 0.3, which means the probability of all 11 residents having adequate supplies is very low [tex]0.3^{11}[/tex], while the probability of none of them having adequate supplies is much higher [tex](0.7^{11})[/tex].

f. The expected value of X is E(X) = np = 11 x 0.3 = 3.3. So we can expect about 3 or 4 residents out of the 11 to have adequate earthquake supplies on average.

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Yes, it is possible to create two 6-sided dice with different numbers than the standard dice

What is probability?

The probability formula involves dividing the number of favorable outcomes by the total number of possible outcomes to determine the probability of an event. The probability of an event ranges from 0 to 1, as the number of favorable outcomes cannot exceed the total number of outcomes.

One example of such a pair of dice is:

Die 1: 1, 1, 2, 3, 3, 4

Die 2: 1, 2, 2, 3, 4, 4

The probabilities of getting each sum with these dice are:

Sum 2: 1/36

Sum 3: 2/36

Sum 4: 3/36

Sum 5: 4/36

Sum 6: 5/36

Sum 7: 6/36

Sum 8: 5/36

Sum 9: 4/36

Sum 10: 3/36

Sum 11: 2/36

Sum 12: 1/36

These probabilities match the probabilities of getting each sum with standard dice, even though the numbers on these dice are different.

Hence, Yes, it is possible to create two 6-sided dice with different numbers than the standard dice

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Based on the provided list, the four true statements regarding confidence intervals for a population mean are:

1. If a confidence interval for the population mean is constructed from a sample of size n=30, that interval must contain the sample mean.

2. If a particular 91% confidence interval captures the population mean, then for the same sample data, the population mean will also be captured at the 87% confidence level.

3. Increasing the confidence level will increase the width of the confidence interval.

4. For the same sample data, a 95% confidence interval will be narrower than a 99% confidence interval.

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Letters x, y, and z are angle measures. The following equations would ensure that lines p and q are parallel: x = z ; x + y = 180°

A Equation is a numerical explanation that is comprised of two articulations associated by an equivalent sign. In its simplest form in algebra, an equation is a statement that demonstrates that two mathematical expressions are equal.

The image with the angles x, y, and z, as well as the lines p and q, can be found in the link at the answer's conclusion.

Using the image provided;

We can see that the two parallel lines p and q are divided by a transverse line. As a result,

We can say that because we can see that x and z are angles that correspond to one another; Second, we can see that y and z are supplementary angles due to the fact that they form a straight line and that the sum of straight angles is 180 degrees.

therefore; We can say that, using the negotiation property of equivalency, y + z = 180° because x = z.

x + y = 180°

Question:

Angle measures are represented by x, y, and z. Which conditions could ensure that lines p and q are equal? Select all relevant options.

x = z, x + y = 180°, x = y, and z = 180°

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Answer:The number line should look like this:

<-----o----->

-3

Step-by-step explanation:

To solve the inequality x - 2 ≤ -5, we can follow these steps:

Add 2 to both sides of the inequality to isolate x on one side:

x - 2 + 2 ≤ -5 + 2

x ≤ -3

The solution to the inequality is x ≤ -3, which means that x is less than or equal to -3.

To plot the solution on a number line, we can place a closed dot on -3 to represent the "less than or equal to" condition, indicating that -3 is included in the solution set.

The number line should look like this:

<-----o----->

-3

The closed dot on -3 indicates that -3 is included in the solution set.

An example of what the crosstab and column chart might look like, and the associated column chart might look like in the attached figure.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

how to create a crosstab and an associated column chart for gender versus opinion, expressed as percentages.

To create a crosstab, you would need to have a dataset with two variables: gender and opinion.

Each row in the dataset should contain the gender and opinion of a respondent.

You can then create a crosstab by counting the number of respondents for each combination of gender and opinion.

To express the counts as percentages, you would need to divide each count by the total number of respondents for each gender (i.e., the sum of counts for that gender) and multiply by 100.

This will give you the percentage of respondents with each opinion for each gender.

Once you have the crosstab with the percentages, you can create an associated column chart by plotting each percentage as a column for each opinion and gender combination.

You can label the x-axis with the opinion categories and the y-axis with the percentage values, and use different colors or patterns to distinguish between male and female respondents.

Hence, an example of what the crosstab and column chart might look like, and what the associated column chart might look like in the attached figure.

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The integral that gives the length of the parametric curve x(t) = 2t², y(t) = t, 0 ≤ t ≤ 8 is: ∫₀⁸ √(16t² + 1) dt

To find the length of the parametric curve

[tex]x(t) = 2t^2, y(t) = t, 0 ≤ t ≤ 8[/tex]

, we need to evaluate the integral:

[tex]∫√[(dx/dt)² + (dy/dt)²]dt[/tex]

where dx/dt and dy/dt are the first derivatives of x(t) and y(t) with respect to t, respectively.

Step 1: Compute dx/dt ,

[tex] dx/dt = d(2t^2)/dt = 4t dy/dt = d(t)/dt =1[/tex]

Step 2: Compute the square of the derivatives and sum them

(4t)² + (1)² = 16t² + 1

Step 3: Find the square root of the sum √(16t² + 1) Step 4: Set up the integral and evaluate it over the given interval [0, 8] Length = ∫₀⁸ √(16t² + 1) dt

Thus, the integral that gives the length of the parametric curve x(t) = 2t², y(t) = t, 0 ≤ t ≤ 8 is: ∫₀⁸ √(16t² + 1) dt

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Correct answer is "Examine the following integral gives the length of the parametric curve or not x(t) = 2t², y(t) = t, 0 ≤t≤8"

There are three possible 1-digit ternary sequences

There are eight possible 2-digit ternary sequences

f(n) be the number of n-digit ternary sequences in which no 1 appears anywhere to the right of any 2. We can find a recursive formula for f(n)as follows:

Consider any such n-digit sequence. There are two cases to consider for the leftmost digit:

The leftmost digit is 0: In this case, we can append any valid (n-1)-digit sequence to the right, which gives us f(n-1)possibilities.

The leftmost digit is 2: In this case: f(n)=f(n−1)+f(n−2)as the second digit must be 0 (since no 1 can appear to the right of any 2). After the second digit, we can append any valid (n-2)-digit sequence to the right, which gives us[tex]$f(n-2)$[/tex] possibilities.

Therefore, we have the recurrence r

with initial values f(1) = 3(since there are three possible 1-digit ternary sequences: 0, 1, or 2) and f(2) = 8 (since there are eight possible 2-digit ternary sequences: 00, 01, 02, 20, 21, 22, 10, 12).

A recurrence relation is an equation which represents a sequence based on some rule. It helps in finding the subsequent term (next term) dependent upon the preceding term (previous term). If we know the previous term in a given series, then we can easily determine the next term.

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In this scenario, the correct options would be:

Part 2: A. Increase the money supply.

Part 3: B. Output will decline.

In the field of economics, inflation (or less frequently, price inflation) is the overall rise in an economy's price level over time.

Part 2: In the given scenario where the country's currency is undervalued due to a fixed exchange rate, I would recommend the following course of action:

A. Increase the money supply: This option can help stimulate the economy and address the undervaluation of the currency. By increasing the money supply, the government can inject more liquidity into the economy, which can lead to increased spending and investment. This increased economic activity can help strengthen the currency's value.

Part 3: If the country increases the money supply too much, the likely outcome would be:

B. Output will decline: When the money supply is increased excessively, it can lead to inflationary pressures. Inflation erodes the purchasing power of money, causing a decline in real output. Businesses may face rising costs, and consumers may experience reduced purchasing power. Consequently, this can negatively impact production and economic growth.

Therefore, in this scenario, the correct options would be:

Part 2: A. Increase the money supply.

Part 3: B. Output will decline.

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[tex]\sin( 30^o )=\cfrac{\stackrel{opposite}{AB}}{\underset{hypotenuse}{16}} \implies 16\sin(30^o)=AB \implies 8= AB[/tex]