Which system of equations is equivalent to this system?

2 equations. 3 times (p minus q) = 2 times p + 11. 4 times p + q = p + 3. CLEAR CHECK

p−3q=113p+q=3

p−3q=333p+q=3

3p−q=113p+q=3

5p−3q=113p+q=3

The decimal fraction 3.003 can be expressed as the sum of fractions 3,003/1,000.

To express the decimal fraction 3,003 as a sum of fractions with a denominator that is a power of 10, we first need to determine the number of decimal places in the fraction. In this case, there are three decimal places, so we can write:

3,003 = 3 + 0.0 0 3

To express 0.003 as a fraction, we can write it as:

0.003 = 3/1000

So, we can write:

3,003 = 3 + 3/1000

To express this as a fraction with a denominator that is a power of 10, we can write:

3,003 = 3,000/1,000 + 3/1,000

Simplifying this expression, we get:

3,003 = 3,000/1,000 + 3/1,000 = (3,000 + 3)/1,000 = 3,003/1,000

Therefore, the decimal fraction 3,003 can be expressed as a sum of fractions with a denominator that is a power of 10 as 3,003/1,000.

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K Co Ltd's capital structure, stock dividend, and the arising number of new ordinary shares.
1) To compute the number of new ordinary shares arising out of the 10% stock dividend on K Co Ltd's ordinary shares, follow these steps:

Step 1: Identify the current number of ordinary shares outstanding in K Co Ltd's capital structure.
Step 2: Calculate the 10% stock dividend by multiplying the current number of ordinary shares by 0.1 (10%).
Step 3: The result from Step 2 will give you the number of new ordinary shares arising from this stock dividend issue.

2) To show the new capital structure after this stock dividend issue, follow these steps:
Step 1: Add the number of new ordinary shares (calculated in step 3 of the previous part) to the existing number of ordinary shares.

Step 2: Update the capital structure to reflect the new total number of ordinary shares.
Step 3: If there are any changes in other parts of the capital structure, such as preferred shares or debt, update those as well to reflect the new capital structure.

In summary, K Co Ltd intends to declare a 10% stock dividend on its ordinary shares, which will result in an increase in the number of ordinary shares arising from this issue. By calculating the number of new shares and updating the capital structure, you will be able to see the new capital structure after this stock dividend issue.

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The resultant component of the vector addition is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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Answer:

Step-by-step explanation:

Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.

I think sorry if I’m wrong

The height of a 16-year-old boy in the 96th percentile is approximately 73.8 inches. Rounded to the nearest inch, the answer is 74 inches.

To find the z-score associated with the 96th percentile, we need to use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can convert the given distribution to a standard normal distribution by using the formula:

z = (x - μ) / σ

where z is the z-score, x is the value we want to convert, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, we want to find the z-score associated with the 96th percentile. The 96th percentile is the value below which 96% of the observations fall. We can find this value by using a standard normal table or a calculator. Using a calculator, we get:

invNorm(0.96) ≈ 1.75

This means that the z-score associated with the 96th percentile is 1.75.

To find the height of a 16-year-old boy in the 96th percentile, we can use the formula:

x = μ + z * σ

where x is the value we want to find, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the z-score we just found.

In this case, we have:

x = 68.3 + 1.75 * 2.9 ≈ 73.8

Thus, 74 inches is the conclusion.

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a) equation will be 0.5x + 3 = 18.50

b)  equation will be (0.75x - 0.10x) + 3 = 21.00

a) Sydney made $18.50 selling lemonade.

she sold each cup for $0.50 and received a $3 tip from a neighbor.

let x be the cost of cup she sold.

equation will be 0.5x + 3 = 18.50

b) Daria made a profit of $21.00 selling lemonade

she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.

equation will be (0.75x - 0.10x) + 3 = 21.00

c) Sydney don't have to pay for the cups used while Daria paid.

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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.

B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.

C. The equations differ in the fact that one accounts for the cost per cup while the other does not.

In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.

Part A: Let x be the number of cups of lemonade sold.

Then, the total amount of money Sydney made is given by:

Total money = (selling price per cup) × (number of cups sold) + tip

Substituting the given values, we get:

18.50 = (0.50) x + 3

Part B: Let y be the number of cups of lemonade sold.

Then, the total profit made by Daria is given by:

Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)

Substituting the given values, we get:

21.00 = (0.75) y - (0.10) y + 3

Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.

On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.

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Complete question is

Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.

Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.

Part C: Explain how the equation from part A and part B differ.

The mean is 35 minutes and the median is 34 minutes.

let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.

Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)

Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes

Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)

Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.

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The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.

Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.

That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.

And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.

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The total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.

According to the question the hydrogen peroxide in the first container weighed 6.4 ounces, and the hydrogen peroxide in the second container weighed 4.07 ounces.

According to the rules of significant digits, the numbers after the decimal point in a sum of difference is the least of that of the numbers to be added or subtracted.

This means that when 6.4 and 4.07 is added, then we will see numbers of decimal places in each number. 6.4 has 1 number after decimal point and 10.47 has 2.

Hence the result of 6.4 + 10.47 will have a minimum of 2 which is 1 decimal place.

Now, 6.4 + 4.07

= 10.47

Rounding it off from the above-mentioned criteria gives us 10.5 ounces.

Therefore, the total number of ounces of hydrogen peroxide, rounded to up to 1 significant digit after the decimal point, is 10.5 ounces.

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Denise can drive at most 80 miles to stay within her budget of $55.

Let's assume that Denise drives x miles during the rental period. Then the total cost of the rental will be:

Total cost = $35 (flat rate for the day) + $0.25 per mile x (number of miles driven)

We want to find the greatest number of miles that Denise can drive and still stay within her budget of $55, so we can set up an inequality as follows:

Total cost ≤ $55

$35 + $0.25x ≤ $55

Subtracting $35 from both sides

$0.25x ≤ $20

Dividing both sides by $0.25

x ≤ 80

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Jade rides 1.275 miles before stopping for a water break.

To solve this problem, we need to multiply the length of the trail by the fraction representing the portion of the trail that Jade rides.

First, we need to convert the mixed number 5 1/10 into an improper fraction. We do this by multiplying the whole number (5) by the denominator of the fraction (10) and adding the numerator (1). This gives us 51/10.

Next, we multiply 51/10 by 1/4 to find the fraction of the trail that Jade rides before stopping for a water break:

(51/10) x (1/4) = 51/40

To convert this fraction into a decimal, we divide the numerator by the denominator:

51 ÷ 40 = 1.275

Therefore, Jade rides 1.275 miles before stopping for a water break.

In summary, to find how many miles Jade rides before stopping, we convert the mixed number representing the length of the trail into an improper fraction, multiply it by the fraction representing the portion of the trail that Jade rides, and then convert the resulting fraction into a decimal to get our answer.

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The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.

To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:

1. Determine the function: In this case, the function is y=sin(x).

2. Identify the interval: The interval is from x=0 to x=4pi.

3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.

∫(sin(x) dx) from 0 to 4pi.

4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).

-∫(cos(x) dx) from 0 to 4pi.

5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).

[-cos(4pi)] - [-cos(0)]

6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.

[-1] - [-1]

7. Determine the area: The area is the difference between the values calculated in step 6.

[-1 - (-1)] = 0

The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.

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Answer:

w ≈ 68,3

Step-by-step explanation:

Use trigonometry:

[tex] \sin(42) = \frac{w}{102} [/tex]

Cross-multiply to find w:

[tex]w = 102 \times \sin(42°) ≈68.3[/tex]

Approximately 37.71 lbs of butter would be used to make 132 cookies.

we can use a proportion:

[tex]2 lbs of butter / 7 dozen cookies = x lbs of butter / 132 cookies\\[/tex]

To find x, we can cross-multiply and solve for x:

[tex]2 lbs of butter * 132 cookies = 7 dozen cookies * x lbs of butter264 lbs of cookies = 7xx = 264 / 7x = 37.71[/tex]

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We can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.

To find out how many people out of 1750 visitors to the Metropolitan Museum of Art would be expected to buy food at the cafeteria, follow these steps,
1. Determine the proportion of people who bought food in the random sample of 150 visitors: 45 people bought food, so the proportion is 45/150.
2. Simplify the proportion: 45/150 = 0.3 or 30%.
3. Apply this proportion to the total number of 1750 visitors: 1750 * 0.3 = 525.

So, based on the survey results, we can expect that approximately 525 people out of 1750 visitors to the museum would buy food at the cafeteria.

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The factorization of the given algebraic expression will give us:

4πr²(1 + ¹/₃r)

In order for us to factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression would first be found and then we will group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is referred to as  its factorization.

We are given the algebraic expression as:

4πr² + ⁴/₃πr³

Now, we want to factor 4πr² from both terms and this will give us:

4πr²(1 + ¹/₃r)

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Answer:

make me brainalist

Step-by-step explanation:

34.16

[tex] \frac{3416}{100} [/tex]

Answer:

To find the face value (p) of the note, we need to use the formula for simple interest:

I = P * r * t

where:

I = interest

P = principal or face value

r = interest rate per year

t = time in years

Since the note has a 6% interest rate and a 150-day term, we need to convert the time to years:

t = 150 / 365

t = 0.41096 years

Now we can solve for the face value:

I = P * r * t

2550 = P * 0.06 * 0.41096

2550 = 0.0246576P

P = 2550 / 0.0246576

P = 103364.99

So the face value (p) of the note is $103,364.99.

To find the interest (i), we can subtract the face value from the balloon payment:

i = 2550 - 103364.99

i = -100814.99

The negative interest result may seem strange, but it's because the balloon payment was higher than the face value of the note. In other words, Averi paid more than the note was worth in order to fully pay off the principal and interest.

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The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.

An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:

(x, y)                               →              (-x, y)

Coordinate = (-1, 1/10)   →  Coordinate A' = (-(-1), 1/10) = (1, 1/10).

Furthermore, the transformation rule for the translation of a point by k units up is given by;

(x, y + k)         →  (x', y')

(1, 1/10 + k)       →  E(1, 4 1/10)

1/10 + k = 4 1/10

k = 4 1/10 - 1/10

k = 4.

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Samantha is doing two things wrong: she is breaking the law and it is unsafe to handle a firearm while fishing.

Samantha is breaking the law by possessing a firearm while fishing at the pier. Most fishing piers are considered public places and carrying a firearm in public places is usually prohibited unless the person has a valid permit or is a law enforcement officer. It could cause panic among other people around her. It is important to follow local laws and regulations regarding firearms and to prioritize safety when in public spaces.

Additionally, it is unsafe and irresponsible to handle a firearm while fishing as it can cause accidents or injuries to oneself or others. She should not hold her fishing rod with both hands if she needs to be prepared to use her gun for self-defense. It would be difficult to access and use the gun effectively while holding the rod with both hands.

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The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..

The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.

Substituting the value of the radius in the formula, we get:

A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)

Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.

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Answer:

Hello! I'd be happy to help you with your math question. Based on the information you've provided, the aircraft flying in a north easterly direction turned through one whole number 2 over 3 right angle to the right of its path. To determine its new course, we need to know the original course of the aircraft. Do you happen to have that information? Once we have that, we can use some trigonometry to calculate the new course. Let me know and I'll be happy to guide you through the process.

Answer:

hope it helps________________

Step-by-step explanation:

If sales increase by 66,000, income will increase by 220,000.00

Net operating income 37,200.00

The margin of safety is 14.01%

Statement showing Computations  

particulars Amount Per unit

Sales 628,000.00 40.00

Variable Expenses 439,600.00 28.00

Contribution Margin 188,400.00 $ 12.00

Fixed Expenses 151,200.00

Net operating income 37,200.00

'

1)  BEP in unit sales = 151,200/12 12,600.00

.BEP in sales $ = 12,600 * 40 504,000.00

2)  Total Contribution margin at BEP = Fixed costs 151,200.00

3)a Target Profit $ 64,800.00

Fixed Expenses 151,200.00

Desired Contribution 216,000.00

3b. No of units to be sold = 216,000/12 18,000.00

Sales 720,000.00

Variable Expenses 504,000.00

Contribution Margin 216,000.00

Fixed Expenses 151,200.00

Net operating income 64,800.00

4)  Margin of safety = 628,000.00-540,000.00 88,000.00

MOS in % = 88,000/6280001 14.01%

5)CM Ratio = 188,400/628,000 0.3

If sales increase by 66,000, income will increase by 220,000.00

66,000/0.3

=220,000.

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If lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport, the distance between Lakeside and Seaside is approximately 8.6 miles.

To find the distance between Lakeside and Seaside, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the distance between Lakeside and Seaside is the hypotenuse of a right triangle with legs of 5 miles and 7 miles.

To apply the Pythagorean theorem, we can square the lengths of the legs and then take the square root of their sum:

distance = √(5² + 7²)

distance = √(25 + 49)

distance = √74

distance ≈ 8.6 miles (rounded to the nearest tenth)

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The independent variable is 't' and the dependent variable is 'd' while the rate of change is '3' and the initial value is '1'.

In the given function d=3t+1:

The independent variable here is 't' which represents time in seconds.

whereas the dependent variable is 'd' and it represent the distance traveled by a car in some unit. The rate of change is 3, and it represents the constant speed of the car in units of distance per unit of time.

While the initial value is 1, which represents the distance traveled by the car when time is 0.

Hence this function can be interpreted as if the car is travelling at a constant speed of 3 units of distance and has already travelled 1 unit of distance at the start of the journey.

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The square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.

Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.

Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

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Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.

Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.

The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.

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Answer:

y = (x+5)/3

Step-by-step explanation:

Isolate y

x = 3y - 5

x + 5 = 3y

(x+5)/3 = y