What is the equation of the line that is parallel to the given line and passes through the point (−2, 2) ?

A. y=1/5x+4

B. y=1/5x+12/5

C. y=−5x+4

D. y=−5x+12/5

The solution is, the probability of picking a boat from Virginia is 3/8

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

The formula of probability is often given as

P = no. of favorable event/ no. of total outcome

In this case, our variables are

no. of favorable event=6

no. of total outcome =16

Let's proceed to input our values and solve

P = 6/16

  = 3/8

From the calculation above the probability of picking a boat from Virginia is 3/8

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Answer:

The domains are (1,4,9) Ranges are (-1,-2,-3)

Step-by-step explanation:

The domain is on the x-axis and the range is on the y-axis

Answer:

The rate at which the tank is being emptied is 25 gallons per minute, which means that the change in the amount of oil in the tank per minute is -25. Let's assume that the initial amount of oil in the tank is 2500 gallons and the capacity of the tank is 3000 gallons.

The equation that relates the amount of oil in the tank, V, and time, t, is given by:

V = 2500 - 25t

This equation represents a linear relationship between the amount of oil in the tank and time. As time increases, the amount of oil in the tank decreases linearly at a rate of 25 gallons per minute.

The capacity of the tank, c, is 3000 gallons, which means that the tank will be completely emptied after:

t = (3000 - 2500) / 25 = 20 minutes

After 20 minutes, the amount of oil in the tank will be:

V = 2500 - 25(20) = 2000 gallons

The numerator of the z-score test statistic measures the difference between the sample mean and the population mean (or the hypothesized population mean, depending on the context) in terms of the standard error of the mean.

It can use z- test only if the population standard deviation is known (or given) and the sample is large (more than 30 units)

If the mean and standard deviation is known, then the z-score is calculated using the formula.

z = (x - μ) / σ

where x is data;

μ is the mean and σ is the standard deviation.

Thus, the actual distance between a sample mean x and a population mean µ is measured by the numerator of z- score test statistic.

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The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.

E° is the complement of event E. It is the set of all outcomes that are not in event E and can be expressed as E° = {14, 15, 16, 17}.The probability of event E° is calculated by summing the probabilities of all outcomes in the event, P(E°) = P(14) + P(15) + P(16) + P(17). Since all outcomes in the sample space are equally likely, the probability of each outcome is 1/12. This means that the probability of event E° is calculated as follows:

P(E°) = 1/12 + 1/12 + 1/12 + 1/12 = 4/12 = 1/3.

Therefore, The complement of event E, E°, is {14, 15, 16, 17}. The probability of event E° is 1/3, as all outcomes in the sample space are equally likely, with a probability of 1/12.

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We can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

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, "%". The percentage can be calculated by dividing the value by the total value and then multiplying the result by 100.

a) To find the percentage of gas stations that sell regular gas for less than $1.973, we need to calculate the z-score corresponding to this value:

z = (1.973 - 2.05) / 0.47 = -0.164

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for less than $1.973 is approximately 44.38%.

b) To find the percentage of gas stations selling regular gas for at least $2.17, we can calculate the z-score corresponding to this value:

z = (2.17 - 2.05) / 0.47 = 0.255

Using a standard normal distribution table or calculator, we can find that the percentage of gas stations selling regular gas for at least $2.17 is approximately 40.86%.

c) To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can calculate the z-scores for each value:

z1 = (1.97 - 2.05) / 0.47 = -0.164

z2 = (2.05 - 2.05) / 0.47 = 0

Using a standard normal distribution table or calculator, we can find the probabilities corresponding to each z-score:

P(z < -0.164) = 0.4364

P(z > 0) = 0.5 - 0.5(0) = 0.5

To find the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05, we can add these probabilities:

P(z < -0.164 or z > 0) = P(z < -0.164) + P(z > 0) = 0.4364 + 0.5 = 0.9364

Therefore, the probability that a gas station sells regular gas for less than $1.97 or greater than $2.05 is approximately 93.64%.

d) To find the number of gas stations that sell regular gas for no more than $2.01, we can calculate the z-score corresponding to this value:

z = (2.01 - 2.05) / 0.47 = -0.085

Using a standard normal distribution table or calculator, we can find the probability corresponding to this z-score:

P(z < -0.085) = 0.4664

Multiplying this probability by the total number of gas stations (75), we can estimate the number of gas stations that sell regular gas for no more than $2.01:

0.4664 * 75 ≈ 35

Therefore, we can estimate that approximately 35 gas stations sell a gallon of regular gas for no more than $2.01.

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Complete question:

The price of a gallon of regular gasoline at 75 What percent of gasoline gas stations sell gallons of gas stations across the state is normally regular gas for less than $1.973 distributed with & a mean of $2.05 and a standard deviation of 47. b) What percent of gas stations sell a gallon? regular gas for at least $2.17? c) What is The probability that gas station sells gallons of regular gas for less than $1.97 or greater than $2.05? About how many stations sell a gallon of regular gas for no more than $2.01?

3/4 in a decimal, divide the denominator by the numerator to get 3/4 as a decimal 3/4 is 0.75.

We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.

3/4

3[1/2 x 1/2]

3 x [0.5 x 0.5]

3 x 0.25

0.75

To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.

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The steps to calculate the equilibrium concentration have been explained below.

Equilibrium concentration is a state in a chemical reaction, at which the rate of forward reaction becomes the same as the rate of backward reaction.

Calculating equilibrium concentration requires several steps depending on the type of equilibrium you are dealing with which are,

1)Write the balanced chemical equation for the reaction.

2)Write the equilibrium expression that describes the relationship between the concentrations of the reactants and products at equilibrium.

3)Determine the initial concentrations of the reactants and/or products

4)Determine the direction of the reaction by comparing the initial concentrations of the reactants and products with the equilibrium constant (Keq).

5)Calculate the change in concentration between the equilibrium concentration and the initial concentration.

6)Calculate the equilibrium concentration by adding the change in concentration to the initial concentration.

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The complex numbers calculators are Symbolab, Desmos, Wolfram Alpha etc.

There are many online calculators available for performing calculations involving complex numbers. Here are a few options :

Symbolab : Symbolab is a popular online math tool that includes a complex numbers calculator.

Desmos : Desmos is a powerful online graphing calculator that also includes support for complex numbers

Wolfram Alpha: Wolfram Alpha is a computational search engine that can perform a wide range of mathematical calculations, including those involving complex numbers

These are just a few options, but there are many other online calculators and resources available for performing calculations involving complex numbers.

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Answer:

A) 210 B) 0.18

Step-by-step explanation:

got it right

Period, which is a measure of how long an oscillation lasts, is constant. With L being the pendulum's length and g being the acceleration brought on by gravity, the formula for calculating a pendulum's period is T = 2π √L/g,

A simple pendulum is a machine whose point mass is suspended from a fixed support by a light, inextensible string. When a pendulum is displaced sideways from its resting position due to gravity, the equilibrium position is subjected to a restoring force that will accelerate it back toward the equilibrium position.

Only the length of the string affects a pendulum's period; the mass of the ball has no bearing. When two pendula are the same length but have different masses, their periods will be the same. The pendulum with the longer string will have a longer period if there are two of them, but their periods will differ.

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The solution of the inequality is x < -4 or x < 4

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4

An inequality can be expressed using one of several symbols, including < (less than), > (greater than), <= (less than or equal to), >= (greater than or equal to), and != (not equal to).

x² < 16

Take the square root of both sides:

x < ±√16

x < ±4

x < -4 or x < 4

Therefore, the solution is x < -4 or x < 4

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Therefore , the solution of the given problem of angle comes out to be

m∠QRP =  50 degree.

In Euclidean space, an angle is a structure that consists of two poles who split at its apex and apex, which are located in its centre. The sides or loops are the name given to these rays. Combining two rays could result in an inclination within the planes in that they are located. Two planes can be combined to form angles as well. These are referred to as dihedral angles. Two line rays at their end points can be arranged in many ways to produce patterns in two dimensions.

Here,

Given :

m∠RSP = 79 , m∠SPR = 40 and m∠QRS = 111

To find the angle m∠QRP

So,

First find the angle ∠SRP

Thus ,

it is a triangle

79 + 40 + ∠SRP = 180

=> ∠SRP  = 180 - 79 -40

=>∠SRP = 61 degree

and

=> m∠QRP = m∠QRS  - ∠SRP

=> m∠QRP =  111 - 61

=> m∠QRP =  50 degree.

Therefore , the solution of the given problem of angle comes out to be

m∠QRP =  50 degree.

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According to the conversion, 55 kg is equal to approximately 121.25 lbs.

In the world of mathematics, measurement plays a vital role in determining the quantity, weight, and size of any object. The standard units of measurement are different in various countries, and knowing how to convert from one unit to another is essential.

The question posed is, "What is 55 kg in lbs?" Here, 'kg' is a unit of mass, commonly used in the metric system, whereas 'lbs' stands for pounds, which is a unit of weight in the Imperial system. To convert from kg to lbs, we need to multiply the given value by a conversion factor.

1 kg is equal to 2.20462 pounds. Hence, we can use this conversion factor to convert 55 kg to lbs as follows:

55 kg x 2.20462 lbs/kg = 121.2542 lbs (rounded off to two decimal places)

In conclusion, understanding measurements and being able to convert from one unit to another is a fundamental aspect of mathematics. In this case, we used the conversion factor of 2.20462 lbs/kg to convert 55 kg to lbs.

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There are various online tools and calculators available to calculate Pythagorean triples, which are sets of three integers that satisfy the Pythagorean theorem a² + b² = c², with c being the hypotenuse of a right triangle.

To calculate Pythagorean triples online, you can use tools such as online Pythagorean triple calculators, which allow you to input the value of one of the sides of a right triangle and then automatically generate the values of the other two sides. Some online calculators also allow you to enter a range of numbers and generate a list of all the Pythagorean triples within that range.

Other tools include apps and software that can be downloaded onto your computer or mobile device. These tools are useful for solving problems in geometry, physics, and other fields that involve right triangles and the Pythagorean theorem.

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To multiply, flip (or invert) the divisor into a reciprocal, then start changing the division sign to a multiplication symbol. If you can, simplify your response.

1. Use a division sign to start writing the entirety and the mixed numbers as improper fractions.

2. Write this same divisor's mutual recognition as well as replace the division sign with a multiplication sign.

3. Simplify any common factors in which it actually occur.

4. To achieve the outcome, simply multiply the numerators and denominators together.

Let us try this: 3½ ÷ 2

Rewrite 3½  as an invalid fraction.

i.e, 7/2 ÷ 2/1

Write the reciprocal of the divisor and replace with, 7/2 × 1/2 = 7/4

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a. The coordinates after the rotation are: D(-5, 4) → D' (5, -4), E(3, 6) → E'(3, -6), and F(4, 2) → F'(4, -2) b. The general rule below that describes the rotation are: (x, y) → (x, -y).

According to the definition of a transformation in mathematics, a transformation is a geometric shape or formula that has been altered, mapping the shape or formula from its preimage, or initial position, to its image, or after-transformation position. Because transforming a function to a different space offers a fresh viewpoint on the issue, scientists and mathematicians employ transformations to simplify a problem. Scientists frequently shift a function, manipulate it, and then transform it back to its original place because this fresh perspective can make computations easier in the new space than in the old one.

a. The coordinates after the rotation are:

D(-5, 4) → D' (5, -4)

E(3, 6) → E'(3, -6)

F(4, 2) → F'(4, -2)

b. The general rule below that describes the rotation are:

(x, y) → (x, -y)

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Kilometers per hour (km/h) and miles per hour (mph) are both units of speed used to measure how fast something is moving.

Kilometers per hour are the standard unit of speed used in most countries that use the metric system, while miles per hour is more commonly used in the United States and other countries that use the imperial system.

To convert km/h to mph, you can multiply the speed in kilometers per hour by 0.621371. This conversion factor is based on the fact that one mile is equivalent to 1.60934 kilometers. Converting between these two units is a common task when traveling, driving, or using fitness trackers or GPS devices.

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The example of histogram is dataset of exam scores of 100 students, with scores ranging from 50 to 100

A histogram is a graphical representation of the distribution of a dataset. It is a way to visualize the frequency distribution of a set of continuous or discrete data. Here's an example of a histogram:

Suppose we have a dataset of exam scores of 100 students, with scores ranging from 50 to 100. We can create a histogram to visualize the distribution of scores. The histogram will have a vertical axis representing the frequency of scores and a horizontal axis representing the range of scores. We can divide the horizontal axis into equal intervals, called bins, and count the number of scores falling into each bin.

The histogram is shown in the figure

In this example, the histogram shows that most students scored between 70 and 80, with a few students scoring below 60 and above 90.

The histogram also shows that the distribution of scores is roughly symmetrical, with no outliers.

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Unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Income is the consumption and saving opportunity gained by an entity within a specified timeframe, which is generally expressed in monetary terms.

In 10 years, an individual's earned and unearned income may vary greatly depending on their career and investment choices, economic conditions, and personal circumstances.

Some individuals may see increases in earned income as they gain more experience or take on higher-paying positions, while others may see fluctuations or decreases in earned income due to changes in the job market.

Similarly, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

Hence, unearned income may vary depending on investment performance, interest rates, and changes in government policies.

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Based on angle relationship, the missing angles are:

1. Angle a = 108°; reason: alternate interior angles

2. Angle b = 43°; reason: corresponding angles

3. Angle c = 114°, reason: corresponding angles are congruent.

4. Angle d = 101°; reason: same-side interior angles .

5. Angle e = 82°, reason: alternate interior angles

angle f = 82°, reason: vertical angles

6.  Angle g = 67°, reason: corresponding angles

Angle h = 113°, reason: same-side interior angles

7. Angle i = 127°, reason: corresponding angles

Angle j = 53° [reason: linear pair angles]

8. k = = 156° [reason: supplementary angles]

l = 24° [reason: alternate exterior angles]

9. m = 72° [reason: alternate exterior angles]

10. n = 86° [reason: supplementary angles]

11. p = 25° [reason: supplementary angles]

12. q = r = 61° [reason: supplementary angles]

To calculate a missing angle in a figure using angle relationships, follow these steps:

Therefore:

1. Angle a = 108°, the reason is: alternate interior angles are congruent.

2. Angle b = 43°, the reason is: corresponding angles are congruent.

3. Angle c = 114°, the reason is: corresponding angles are congruent.

4. Based on the same-side interior angles theorem (angle relationship), we have:

d = 180 - 79

d = 101°

5. Angle e = 82°, the reason is: alternate interior angles are congruent.

angle f = 82°, because, vertical angles are congruent.

6.  Angle g = 67°, the reason is: corresponding angles are congruent.

Angle h = 180 - 67 = 113°, the reason is: same-side interior angles are supplementary.

7. Angle i = 127°, the reason is: corresponding angles are congruent.

Angle j = 180 - 127 = 53° [reason: linear pair angles]

8. k = 180 - 24 = 156° [reason: supplementary angles]

l = 24° [reason: alternate exterior angles are congruent]

9. m = 72° [reason: alternate exterior angles are congruent]

10. n = 180 - 94 = 86° [reason: supplementary angles]

11. p = 180 - 155 = 25° [reason: supplementary angles]

12. q = r = 180 - 119 = 61° [reason: supplementary angles]

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Answer:

The value of x can be 10

The value of y can be -4

Step-by-step explanation:

Assume the function is linear of the form
y = mx

When x = 5, y = -2

Simply multiply x by 2 and equivalently multiply -2 by 2

x = 5 x 2= 10

y = -2 x 2 = -4

The given inequality is x > (y – 2)2 – 4. To graph this inequality, we first need to plot the vertex of the parabola, which is (2, -4). This point is included in the shaded region because the inequality is "greater than" and not "greater than or equal to". Next, we need to determine whether the parabola opens upward or downward. Since the coefficient of the squared term is positive, the parabola opens upward.

Now, we need to decide which side of the parabola to shade. To do this, we can choose a test point that is not on the parabola and substitute its coordinates into the inequality. For example, the point (0,0) is a convenient test point. Substituting x=0 and y=0 into the inequality, we get:

0 > (0 – 2)2 – 4

0 > 0

Since 0 is not greater than 0, the point (0,0) is not in the shaded region. Therefore, we need to shade the side of the parabola that does not contain the point (0,0).

Among the given options, only the first one matches the graph described above. Therefore, the answer is: the graph that represents x > (y – 2)2 – 4 is the one where a parabola opens up and goes through (0, 0), has a vertex at (2, -4), and everything outside of the parabola is shaded.

The area of the play area is 8.74 square feet.

If Highwood Park has 420 feet of fencing, then we can use the formula f = 47(a + 9) – 16 to calculate the area of the play area.

This formula takes in account the area (a) of the play area, as well as the number of feet of fencing needed to enclose it (f).

In this equation, the number of feet of fencing (f) is equal to 47 multiplied by the area (a) plus 9, and then subtracted by 16.

Since we know that the amount of fencing is 420 feet, we can solve the equation for the area, a.

First, we need to subtract 16 from both sides of the equation. This leaves us with

=> 420 = 47a + 9.

Next, we subtract 9 from both sides of the equation, which gives us

=> 411 = 47a.

Finally, we divide both sides of the equation by 47, which gives us

=> a = 8.74.

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The supplied statement states that the clock will stop following 12 hours, or at 7.

The term clock has cognates in several European languages and is derived from the antique Latin word for "bell," "clocca." The Medieval Low German and Late Dutch words Klocke were used to create the English term clock, which was transmitted to England first from Low Countries.

Step 1: Discovering that connection

From 12 am to 12 pm it moves 360° ⇒12 hours

1° ⇒ 12/360 hours………(1)

Step 2: Determine where a clock's hands will stop using relation (1).

Right angles are 90° at one.

1° ⇒ 12/360 hours

90° ⇒ 12/360 * 90 hours = 12 hours

As a result, the clock will stop at 7 after 12 hours.

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Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

The area of a regular hexagon is calculated using the formula (3√3 / 2) × s^2, where s is the length of a hexagonal side. Given that we are talking about a regular hexagon, it is important to remember that all of the sides are the same length. The formula Area of the Hexagon = (3√3 / 2) × s^2, where's' is the length of the hexagonal side, can be used to determine the area of a regular hexagon when one of its sides is known.

All of the sides of the hexagon are the same length because it is a regular shape.

Therefore, each side has a length of 57 inches / 6 = 9.5 inches.

To find the area of the hexagon, we can use the formula:

Area = (3√3 / 2) × s^2

where s is  length of a side.

Substituting s = 9.5 inches, we get:

Area = (3√3 / 2) × (9.5 inches)^2

Area ≈ 244.3 square inches

Rounding to the nearest tenth, the area of the hexagon is 244.3 square inches.

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Using the formula 1 millilitre = 10⁻³ microliters, we can convert millilitres to microliters.

The volume unit is milliliters (mL). One microliter (uL) is likewise a volume unit, although it is a smaller unit.

We already know that Milli equals 10⁻³.

As a result, we may write the relationship using the unit conversion idea.

One microliter equals 10⁻³ milliliters.

For example, if we have 2 microliters, it is equal to 2 x 10⁻³ milliliters.

Thus, we now have a standard formula that we can use to calculate the time in microliters to milliliters and milliliters to microliters.

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Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.

For instance, to multiply 3/4 by 2:

Put 2 over 1, making it 2/1, to make it a fraction.

To get 1/2, invert 2/1.

To get 3/8, multiply 3/4 by 1/2.

Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.

Hence, 1/4 is equivalent to 3/4 when divided by 2.

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As a result of these entries, the revenue and expense accounts will have zero balances, and the net income of $19,500 will be transferred to the Retained Earnings account.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Based on the information provided in the image, here are the closing entries for the accounting period:

Close the revenue accounts:

Account Titles Debit Credit

Income Summary 34,000

Service Revenue           34,000

Close the expense accounts:

Account Titles Debit Credit

Salaries Expense 8,000

Rent Expense         6,000

Supplies Expense 1,500

Income Summary           15,500

Close the Income Summary account to the Retained Earnings account:

Account Titles Debit Credit

Income Summary          19,500

Retained Earnings 19,500

Therefore, As a result of these entries, the revenue and expense accounts will have zero balances, and the net income of $19,500 will be transferred to the Retained Earnings account.

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