X - 3y = 6*
Your answer
solve for y

The Slope of the line q is 7/3

Given that  a line “p” has a slope \(\frac{7}{3}\) , another line “q” is given which is parallel to line “p”, and asked the slope of line “q”

Parallel lines:

Parallel lines are two or even more lines that lie on the same plane but never intersect. They are equal in distance and have the same slope.

The slope of parallel lines are equal so, the slope of line “p” is equal to the slope of line “q”

The slope of line “p”=slope of line “q”

Given that the slope of line “P”=\(\frac{7}{3}\)

therefore, The slope of the line q is \(\frac{7}{3}\)

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The Solution:

Given:

We are required to use the logarithm property to find an equivalent for the given expression.

By logarithm Property:

Therefore, the correct answer is:

The constant percent rate of change of f(x) with respect to x so, the answer is 45% growth.

What is the percentage?

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

The constant percent rate of change of f(x) with respect to x is equal to the exponent in the function, which is 1.45.

The constant 1.45 represents the rate of growth or decay of the function.

If 1.45 is greater than 1, then the function grows exponentially, indicating growth.

If 1.45 is less than 1, then the function decreases exponentially, indicating decay.

In this case, 1.45 is greater than 1, so the function grows exponentially.

This means that the constant percent rate of change of f(x) with respect to x is 45% growth.

Hence, the constant percent rate of change of f(x) with respect to x so, the answer is 45% growth.

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Applying the definition o a supplement of an angle, the measure of angle P in degrees is: 105°.

The supplement of an angle is defined as the angle measure that is added to the angle to give a sum of 180 degrees.

For example, the supplement of angle X is 180 - measure of angle X.

Given the following:

Supplement of angle P = 180 - measure of angle P

Measure of angle P = (180 - measure of angle P) + 30 degrees

Therefore:

(180 - m<P) + [(180 - m<P) + 30] = 180

Open the parentheses:

180 - m<P + 180 - m<P + 30 = 180

Combine like terms:

390 - 2(m<P) = 180

390 - 180 = 2(m<P)

210 = 2(m<P)

210/2 = 2(m<P)/2

105 = m<P

m<P = 105°

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Among the following statements, "the interquartile range is better than the standard deviation to describe skewed data sets" is true because it is not affected by extreme values or outliers in the dataset.

The interquartile range (IQR) is a measure of variability that describes the spread of the central 50% (not 75%) of the data. It is a robust measure, meaning it is not affected by extreme values or outliers in the dataset, which can make it more appropriate for skewed datasets or datasets with outliers.

The standard deviation, on the other hand, is a measure of variability that describes the average distance of the data points from the mean. It is a more sensitive measure, meaning it is affected by extreme values and outliers in the dataset, which can make it less appropriate for skewed datasets or datasets with outliers.

The range is found by subtracting the minimum value from the maximum value, which makes the other two statements false.

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a. To find the Maclaurin series for f(x) = 5e^-2x, we first need to find the derivatives of the function.

f(x) = 5e^-2x

f'(x) = -10e^-2x

f''(x) = 20e^-2x

f'''(x) = -40e^-2x

The Maclaurin series for f(x) can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

The first four nonzero terms of the Maclaurin series for f(x) are:

f(0) = 5

f'(0) = -10

f''(0) = 20

f'''(0) = -40

So the Maclaurin series for f(x) is:

f(x) = 5 - 10x + 20x^2/2! - 40x^3/3! + ...

b. The power series using summation notation can be written as:

f(x) = Σ (n=0 to infinity) [f^(n)(0)/n!] x^n

f(x) = Σ (n=0 to infinity) [(-1)^n * 10^n * x^n] / n!

c. To determine the interval of convergence of the series, we can use the ratio test.

lim |(-1)^(n+1) * 10^(n+1) * x^(n+1) / (n+1)!| / |(-1)^n * 10^n * x^n / n!|

= lim |10x / (n+1)|

As n approaches infinity, the limit approaches 0 for all values of x. Therefore, the series converges for all values of x.

The interval of convergence is (-infinity, infinity).

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The probability of selecting two girls at random is 0.178

A probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. The sample space is the entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment. The likelihood of occurrence of an event is known as probability. The probability of occurrence of any event lies between 0 and 1.

sample space = 6 girls + 7 boys = 13 students

probability of boys = 7 / 13

probability of girls = 6/13

The probability of two girls = (6 / 13) * (5 / 13) = 0.178

The probability of two girls is 0.178

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Answer:

The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.

Answer:

$1,640

Step-by-step explanation:

Total  Amount = Principal Amount + Interest Earned

Interest Earned = Principal * Interest Rate (as a decimal) * time (in years)

Interest = 1000(.04)(16) which equals $640

Add $640 to the principal of $1000 and  George will receive $1,640 on his 16th birthday

Answer: 2h=24

Step-by-step explanation:

u can add lines to split the figure into a triangle and two rectangles.

Area of the figure

= (12x15)/2 + 6x4 + 2x5

=124 yd^2

Responder:

$ 555,911.5

Explicación paso a paso:

Dado

Principal = $ 545,680

Interés = 2,25%

Tiempo = 10 meses = 10/12 años

Debemos buscar la cantidad después de 10 meses.

Monto = Principal + Intereses

Interés = PRT / 100

Interés = 545,680 * 2,25 * 10/1200

Intereses = 12,277,800 / 1200

Interés = 10.231,5

Cantidad = 545,680 + 10,231.5

Cantidad = 555,911.5

por lo tanto, la cantidad después de 10 meses es $ 555,911.5

Answer:

288q-185=236q-245

Answer:  288q - 185 = 236q - 245

Explanation:

A product is the result of multiplying. So "product of 288 and q" means "288 times q" or "288*q" or simply "288q".

The rest of the sentence your teacher gave you is probably self explanatory, so there's not much else to mention.

Answer:

Orange juice

Step-by-step explanation:

The bottle of apple juice costs 3 dollars for 2 liters, and the bottle of orange juice costs 3.99 dollars for 3 liters. To see which bottle has the better deal, we need to make the liters the same so we can compare them.

We can divide the 2 liters for 3 dollars ratio by 2 to get that 1 liter of apple juice costs 1.5 dollars, and we can divide the orange juice ratio by 3 to get that 1 liter of orange juice costs 1.33 dollars. We see that for 1 liter, orange juice is cheaper, so it is the better deal.

The mean number of individuals with 20/20 vision is 23.

To find the mean number of individuals with 20/20 vision, we can use the formula for the expected value of a binomial distribution. In this case, the probability of an individual having 20/20 vision is p = 0.33, and the number of trials (i.e. individuals selected) is n = 70.
The formula for the expected value of a binomial distribution is:
E(X) = np
Substituting in our values, we get:
E(X) = 70 x 0.33
E(X) = 23.1
So, the mean number of individuals with 20/20 vision out of 70 selected at random from the population is approximately 23.1. However, since we can't have a fraction of a person, we should round our answer to the nearest whole number.
Therefore, the mean number of individuals with 20/20 vision is 23.

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Answer:

p(-2) = -11

p(0) = -3

p(5) = 17

Step-by-step explanation:

Think of p(x) as a y.  Just substitute the x values into the equation, and with some basic algebra, you should get your answer

p(-2) = -3 + (-8) = -11

p(0) = -3 + 0 = -3

p(5) = -3 + 20 = 17

Answer:

6 grapes.

Step-by-step explanation:

If she already had 9 grapes, subtract 15 and 9 to get 6.

Answer:

6 grapes

Step-by-step explanation:

take 15 subtract 9 to get 6

Answer:

That a sloth will walk 12 feet in 2 minutes

Step-by-step explanation:

Answer:

it's the last one in the lower right corner.

we found that the distance from the digital camera's lens to the image that it forms is \(10.125 m\).

A certain digital camera having a lens with focal length \(7.50 cm\) is focused on an object of height \(1.45 m\) that is at a distance of \(4.35 m\) from the lens.

The question demands the distance from the digital camera's lens to the image that it forms.

This distance can be calculated by using the lens equation:

\($$\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}$$Where \(f\) is the focal length, \(d_{o}\)\) is the distance of the object from the lens, and \(\(d_{i}\)\) is the distance of the image from the lens. It can also be calculated using magnification formula:

\($$M=-\frac{d_{i}}{d_{o}}$$\) We can use the magnification formula, to find the distance of the image:

\($$M=\frac{h_{i}}{h_{o}}$$$$-1=\frac{h_{i}}{h_{o}}$$$$h_{i}=-h_{o}$$$$h_{i}=-1.45 m$$\)

Now, using the lens formula, we get:

\($$\frac{1}{f}=\frac{1}{d_{o}}+\frac{1}{d_{i}}$$$$\frac{1}{7.50 cm}=\frac{1}{4.35 m}+\frac{1}{d_{i}}$$\)

We can now solve for the unknown value:\(\[\frac{1}{d_{i}}=\frac{1}{7.50}-\frac{1}{4.35}\]\[\frac{1}{d_{i}}=\frac{1}{10.125}\] $$d_{i}=10.125 m $$\)

Thus, the distance from the digital camera's lens to the image that it forms is \(10.125 m\). The main answer is $10.125 m$ .

The distance from the digital camera's lens to the image that it forms is \(10.125 m\).

A certain digital camera having a lens with focal length \(7.50 cm\) is focused on an object of height \(1.45 m\) that is at a distance of \(4.35 m\) from the lens.

The distance from the digital camera's lens to the image that it forms can be calculated by using the lens equation or magnification formula. Here, we used the magnification formula to find the distance of the image, which is -1.45 m, as the image is inverted.

Then, we used the lens formula to solve for the unknown value. Finally, the distance from the digital camera's lens to the image that it forms is \(10.125 m\).

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1)13/4: Rational (a fraction)

2)√17: Irrational (square root of a non-perfect square)

3)3π: Irrational (product of a rational number and an irrational number)

4)0.1 (1 bar): Rational (repeating decimal)

5)-√2: Irrational (negative square root of a non-perfect square)

6)√24: Irrational (square root of a non-perfect square)

7) -√49: Rational (negative square root of a perfect square)

1)13/4: Rational - This number is a fraction, and any number that can be expressed as a fraction is considered rational. In this case, 13/4 can be simplified to 3.25, which is a rational number.

2)√17: Irrational - The square root of 17 cannot be expressed as a simple fraction or terminating decimal. It is an irrational number, meaning it cannot be expressed as a ratio of two integers.

3)3π: Irrational - π (pi) is an irrational number, and when multiplied by a rational number like 3, the result is still an irrational number. Therefore, 3π is an irrational number.

4)0.1 (1 bar): Rational - This number is a repeating decimal, indicated by the bar over the 1. Although it does not have a finite representation, it can be expressed as the fraction 1/9, which makes it rational.

5)-√2: Irrational - Similar to √17, the square root of 2 is also an irrational number. Multiplying it by -1 does not change its nature, so -√2 remains an irrational number.

6)√24: Irrational - The square root of 24 is an irrational number because it cannot be expressed as a simple fraction or terminating decimal. It can be simplified to √(4 × 6), which further simplifies to 2√6, where √6 is an irrational number.

7)-√49: Rational - The square root of 49 is 7, which is a rational number. Multiplying it by -1 does not change its nature, so -√49 remains a rational number.

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The complete question is :

Select whether the following numbers are rational or irrational.

1. 13/4

2. \sqrt{17}

3. 3 π

4. 0.1 (1 bar)

5. - \sqrt{2}

6. \sqrt{24}

7. - \sqrt{49

Answer:

The lines are parallel

Step-by-step explanation:

Answer:

Step-by-step explanation:

Put the equations into slope-intercept form.

x-5y = 30 ⇒ y = ⅕x - 6

10y = 2x + 90 ⇒ y = ⅕x + 9

Both lines have slope = ⅕, so the lines are parallel.

Answer:

y = -(5/6)x + 0.917

Step-by-step explanation:

We can calculate a slope with the two given points:

(-2.5,3) and (3.5,-2)

Rise (change in y) = -2 - (3) = -5

Run (change in x) = 3.5 - (-2.5) = 6.0

Slope = Rise/Run = -5/6

The line has the following form:

y = -(5/6)x + b

We can find b, the y-intercept, by using one of the two points in the equation and then solve for b.  I'll choose (-2.5,3):

y = -(5/6)x + b

3 = -(5/6)*(-2.5) + b

3 = 2.083 + b

b = 0.917

y = -(5/6)x + 0.917

Answer:

Can you post a picture of the figure?

Their hourly wage in 9 more years is $23.60 per hour.

To find the hourly wage in 9 more years, we can use the formula for exponential growth:

A = \(P * (1 + r)^t\)

Where:

To find the annual growth rate, we can use the formula:

r = \((A/P)^(^1^/^t^)\) - 1

Substituting the given values, we get:

r = \((\$16.09 / \$6.90)^(^1^/^1^1^)\) - 1

r = 0.0883 or 8.83%

Now we can use this growth rate to find the hourly wage in 9 more years:

A = $6.90 * \((1 + 0.0883)^9\)

A = $23.60 (rounded to the nearest cent)

Therefore, the hourly wage of the automobile plant workers in 9 more years, if their wages continue to grow exponentially at the same rate, would be $23.60 per hour.

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Step-by-step explanation:

13x-3= 3x+2 +55 (exterior angle is equal to the sum of 2 opposite interior angles)

or, 13x-3x=57+3

or,10x=60

x=60/10

x=6

FAB =13x-3

=13*6-3

=75

Answer:

see explanation

Step-by-step explanation:

(9m + 4)² - (9m - 4)² ← expand both factors using FOIL

= 81m² + 72m + 16 - (81m² - 72m + 16) ← distribute parenthesis by - 1

= 81m² + 72m + 16 - 81m² + 72m - 16 ← collect like terms

= 144m

= 72(2m)

which is divisible by 72 for all m

The curve represented by this polar equation is a vertical line with angle  = /6 passing through the point (r, /6). To sketch this curve, simply draw a vertical line at an angle of /6 on the polar plane.

In conclusion, the curve with the given polar equation  = /6 is a vertical line passing through the point (r, /6).
To sketch the curve with the given polar equation  = -/6, follow these steps:
To sketch the curve with the given polar equation  = /6, we first need to understand what this equation represents. In polar coordinates, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis ().
1. Understand the polar equation: The equation  = -/6 tells us that the angle  is constant and equal to -/6 radians, or -30 degrees.

2. Convert to degrees (optional): By converting -/6 radians to degrees, we get -30 degrees.
In this equation,  is constant at /6, which means that all points on the curve have the same angle of /6. This creates a vertical line passing through the point (r, /6) on the polar plane.

3. Sketch the curve: Since  is constant at -30 degrees, the curve is a straight line (or ray) that extends from the origin (the pole) and makes an angle of -30 degrees with the positive x-axis.

4. Label the curve: label the curve with the given polar equation θ = -π/6.

In summary, the curve described by the polar equation  = -/6 is a straight line (or ray) extending from the origin and making an angle of -30 degrees with the positive x-axis.

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