A firm faces the revenue function: R(x)=4x-x^2 , where x is the
quantity produced. If sales increase from x_1=2 to x_2=4 the
average rate of change of its revenue is
A decline of $2 for every extra unit sold.
An increase of $4 for every extra unit sold.
A change of $0 (no change in revenue) for every extra unit sold.

Answer:

x=-1

Step-by-step explanation:

Answer:

X = -1

Step-by-step explanation:

Step-by-step explanation:

First we have to turn this from standard form to slope-intercept form.

We'll subtract 3x on both sides to get:

\(y > - 3x + 9\)

Now in order to graph this inequality, you must know that:

(The line will be graphed above for your convenience⤴⤴⤴)

Hope this helps :)

The domain of ggg is option D: -7 ≤ x ≤ 4.

To determine the domain of a function, we need to identify the set of all possible values for the independent variable, in this case, x, for which the function is defined.

In option D, the domain is specified as -7 ≤ x ≤ 4. This means that x can take any value within the closed interval from -7 to 4, inclusive.

In other words, the domain of ggg includes all real numbers between -7 and 4, including -7 and 4 themselves. This interval represents the range of values for x that satisfy the given conditions for the function ggg.

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The true mean number of times college students text per day falls within this interval.

To find the 98% confidence interval for the mean number of times per day that college students text, we can use the following formula:

Where:

Z = Z-score corresponding to the desired confidence level

n = sample size

n = 144 students

Confidence Level = 98% (which corresponds to a Z-score of 2.326)

Substituting the given values into the formula, we can calculate the confidence interval:

Confidence Interval = 25.4 ± 2.326 * (16.6 / √144)

Calculating the values inside the parentheses:

16.6 / √144 = 16.6 / 12 = 1.383

Calculating the product of Z * (σ / √n):

2.326 * 1.383 = 3.219

Finally, calculating the confidence interval:

Confidence Interval = 25.4 ± 3.219

Lower Limit = 25.4 - 3.219 = 22.181

Upper Limit = 25.4 + 3.219 = 28.619

Rounded to 3 decimal places, the 98% confidence interval for the mean number of times per day that college students text is approximately (22.181, 28.619).

This means that we are 98% confident that the true mean number of times college students text per day falls within this interval.

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The arrow reaches a maximum height of 245 meters and stays in flight for 14 seconds.

To find the maximum height and flight time for the arrow, we'll use the given height equation and concepts of projectile motion.
Maximum height:
1. First, we need to find the time (t) at which the arrow reaches its maximum height. This occurs when the vertical velocity is zero. The velocity equation is the derivative of the height equation: v = dh/dt = -10t + 70.
2. Set the velocity equation to zero and solve for t: 0 = -10t + 70. Solve for t: t = 7 seconds.
3. Now that we have the time, plug it into the height equation to find the maximum height: h = -5(7^2) + 70(7) = -245 + 490 = 245 meters.
Flight time:
1. The arrow's flight time is the time it takes to reach the ground (h = 0) after reaching its maximum height.
2. Set the height equation to zero and solve for t: 0 = -5t^2 + 70t. Factor out a common term: 0 = 5t(-t + 14). This gives two possible solutions for t: t = 0 seconds (initial time) and t = 14 seconds.
3. The arrow stays in flight for 14 seconds, as the 0 seconds correspond to the initial time.
In summary, the arrow reaches a maximum height of 245 meters and stays in flight for 14 seconds.

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Answer: C

Step-by-step explanation:

(15*23) + (15*6)

345 + 90

435

Answer:

b = 2a + c

Step-by-step explanation:

Given

a = \(\frac{1}{2}\) (b - c)

Multiply both sides by 2 to clear the fraction

2a = b - c ( add c to both sides )

2a + c = b

After the rearrangement, the equation as b the subject b = 2a + c.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given that the equation;

a = 1/2 ( b - c)

Rearranging the equation;

a =  1/2 ( b - c)

Multiplying 1/2 to the the terms of brackets,

a = (b/2) - (c/2)

b/2 = a + (c/2)

Divide by 2 on both sides of the equation;

b = 2a + c

Therefore, the equation as b the subject b = 2a + c.

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The rigid motion that verifies the congruence of two triangles using the Side-Angle-Side (SAS) criterion is the combination of a translation and a rotation.

To establish congruence between two triangles using the SAS criterion, we need to show that the triangles have two corresponding sides and the included angle equal in measure. This can be achieved through a specific rigid motion, which preserves the shape and size of the triangles.

The first step in the rigid motion is a translation. Translation involves moving the entire triangle along a straight line without altering its shape or size. By sliding one triangle along the plane, we can place the corresponding sides of the two triangles in the same position.

The second step is a rotation. A rotation is a transformation that turns the triangle around a fixed point, called the center of rotation. By rotating one triangle around its center, we can align the corresponding angles of the two triangles. By combining the translation and rotation, we ensure that the sides and the included angle of the two triangles match, verifying their congruence using the SAS criterion.

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Answer:

\(\huge\boxed{\boxed{ \sf 0. {4x}^{2} - 3.2x + 5.7}}\)

Step-by-step explanation:

and

we are done

Answer:

34

Step-by-step explanation:

Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.


Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.

Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.

These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.

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No; multiplication of polynomials is not necessarily commutative.

So, the correct answer is D.

The expressions given are not equal when simplified. To see why, we can use the distributive property of multiplication over addition to expand each expression.

For the first expression, we have:

(x³ − 5x²)(2x + 3) + (² − 4x) = 2x⁴ - 10x³ + 3x³ - 15x²+ x²- 4x = 2x⁴ - 7x³ - 14x² - 4x

For the second expression, we have:

(x² − 4x) + (2x + 3)(x³ − 5x²) = x² - 4x + 2x⁴ - 10x³ + 3x² - 15x = 2x⁴ - 10x³ + 4x² - 19x

As we can see, the two expressions are not the same.

To answer the question about whether the expressions would be equal if simplified, the correct answer is D.

This is because multiplication of polynomials is not necessarily commutative, meaning that the order in which we multiply the terms can affect the result.

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Answer:

Step-by-step explanation:

Use the given proportion

Solve this for a, divide both sides by 6:

It means

Answer:

98/15

Step-by-step explanation:

21/5+7/3

63/15+35/15

=98/15

Thanks Hope It Help

To find the standard deviation of the data summarized in the given frequency distribution, we can perform the following calculations. The table provides the necessary calculations for the standard deviation of the data summarized in the given frequency distribution:

Waiting time (minutes) Number of customer Midpoint (x) of Class Boundary of Class

f(x) 0-39 (0+3)/2=1.5 -0.5, 3.5+1.5 (9) (1.5) (9) = 13.5

4-7 16(4+7)/2=5.5 -3.5, 7.5+3.5 (16) (5.5) (16) = 88.0

8-11 15(8+11)/2=9.5 -7.5, 11.5+7.5 (15) (9.5) (15) = 213.75

12-15 8(12+15)/2=13.5 -11.5, 15.5+11.5 (8) (13.5) (8) = 91.875

16-20 2(16+20)/2=18 -16, 20+16 (2) (18) (2) = 92

Sum 60 (363.2)

Mean = Sum of (f(x)) / Sum of (f) = 363.2 / 60 = 6.0533

The variance, σ², can be calculated using the formula [Sum of (f(x²)) - {Sum of (f(x))² / Sum of (f)}] / (Sum of (f) - 1). Plugging in the values, we get:

σ² = [1103.2 - {363.2² / 60}] / (60 - 1) = 104.36

The standard deviation, σ, can be calculated using the formula √σ². Hence, the standard deviation of the data summarized in the given frequency distribution is approximately 10.2 minutes.

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The given options represent four different algebraic expressions in terms of x and y. We will determine which of these options represent a linear equation. The option that represents a linear equation is D.

y = x + 4. Linear equation in one variable is of the form,

ax + b = 0, where a and b are constants, and a ≠ 0.

The correct option is D.

It represents a straight line when plotted on a graph. The degree of the equation is 1. The slope of the line is given by -a/b and the y-intercept is given by -b/a. The solution of the equation is given by x = -b/a. Linear equation is also called first degree equation. The option D represents a linear equation of the form,

y = x + 4, where a = 1 and

b = 4.The degree of the equation is 1.

ax + b = 0.

where a and b are constants, and a ≠ 0. It represents a straight line when plotted on a graph. The degree of the equation is 1. The slope of the line is given by -a/b and the y-intercept is given by -b/a. The solution of the equation is given by x = -b/a. Linear equation is also called first degree equation. The option D represents a linear equation of the form,

y = x + 4, The solution of the equation is given by

x = -b/a. Linear equation is also called first degree equation. The option D represents a linear equation of the form,

y = x + 4, where

a = 1 and

b = 4. The degree of the equation is 1.

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The probability of having at least one employee not have a college degree is 0.595

Here it is given that the 74% of employees have a college degree.

Hence, the probability of one employee having a college degree is

74/100

= 0.74

The probability that an employee does not have a college degree is

1 - 0.74

= 0.26

Hence

The above problem is clearly a Binomial distribution. with n = 120 and p = 0.26

"success" is when one employee does not have a college degree.

Therefore the probability that at least 1 employee does not have a college degree is

P(X≥1)

= 1 - P(X = 0)

A binomial distribution with sample n and probability p has a PMF

ⁿCₓ  X  pˣ X  (1 - p)ⁿ⁻ˣ

where x is a random variable

Here

n = 3

p = 0.28

x = 0

Hence we get

³C₀  X  0.26⁰ X  (0.74)³

0.405

Therefore,

P(X≥1)

= 1 - 0.405

= 0.595

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Answer:its 3,5,7,9,11

Step-by-step explanation:i m pretty sure it's this one because I got it from briainly

Answer:

b

Step-by-step explanation:

i took the test and this was right

5star answer don't u think????

Answer:

 \(Y=2\)

Step-by-step explanation:

From the question we are told that

Number of Flower to be planted n=38

Flower per Fiats f=5

Since Number of Flower to be planted \(n=38\)

Therefore Fiats bought must tally or be greater than \(n=38\)

Generally The Multiply of 5 greater than and closest to 38 is 8

 \(X=5*8\)

 \(X=40\)

Generally the Total amount of Fiats Bought is given by

 \(X=40\)

Therefore The Number of flowers Y left is

 \(Y=X-n\)

 \(Y=40-38\)

 \(Y=2\)

Answer:

A single number that estimates the value of an unknown parameter is called a point estimate.

Step-by-step explanation:

Don't see the point (haha) of elaborating

The perpendicular line has an equation of y + 7 = -1/7(x - 3)

The equation is given as

y = 7x + 14

Also, from the question

The point is given as

Point = (3, -7)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 7

This means that the slope of y = 7x + 14 is 7

Perpendicular lines have their slopes to be opposite reciprocals

This means that the other line has a slope of -1/7

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/7

(x₁, y₁) = (3, -7)

So, we have

y = -1/7(x - 3) - 7

Evaluate

y = -1/7(x - 3) - 7

Add 7 to both sides

y + 7 = -1/7(x - 3)

Hence, the equation of the perpendicular line is y + 7 = -1/7(x - 3)

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To solve the equation \(2^{x-1} - 7 = 9\), we add 7 to both sides make the bases the same, and equate the exponents.

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential expression

\(2^{x-1} - 7 = 9\).

\(2^{x -1} = 9 + 7.\)

\(2^{x-1} = 16.\)

\(2^{x-1} = 2^4\).

x - 1 = 4.

x = 5.

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The conclusion about p using an absolute value inequality would be that |p - 72| ≤ 4. This means that the difference between the true proportion p and the estimated proportion 72% is no more than 4%.

In other words, p is most likely to fall within the range of 68% to 76%, as determined by the margin of error in the statistical polling calculation. This emphasizes the importance of recognizing and accounting for the potential for error and uncertainty in estimating percentages and proportions in various fields, including politics and marketing.
To describe the conclusion about the percentage (p) in statistical polling using an absolute value inequality, you can use the margin of error (4% in this example) as a way to create the inequality.
In this case, we have a poll result of 72% and a margin of error of 4%. So, the absolute value inequality would be:
|p - 72%| ≤ 4%
This inequality shows that the difference between the true percentage (p) and the poll result (72%) should be less than or equal to the margin of error (4%). In other words, the true percentage (p) is most likely to be between 68% and 76% (72% minus 4% to 72% plus 4%).

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Answer:

There are $\boxed{3}$ paths from $A$ to $B.$

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The correlation Illustrates that B. The graph shows a positive correlation, and it is a non-linear model.

In this scenario, the width would be plotted on the x-axis of the scatter plot while the length in centimeters would be plotted on the y-axis of the scatter plot.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select the format trend line, and then tick the box to display an equation for the line of best fit on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the width and length, a linear equation for the line of best fit is given by y = 1.31x + 0.02.

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Answer: The graph shows no correlation, and it is neither linear nor exponential.

Step-by-step explanation:

try doing a line of fit you're ALWAYS. gonna be ignoring other dots/points/coorids.

Why it's not a correlation is because nothing is together. You could consider a lot of dots on the edge.

If that doesn't make sense to you lets go through each answer

The graph shows a negative correlation, and it is a linear model.

The coordinates don't form any specific line

None of the coordinates are together

there's no slope since there's no line of fit.

it's THE SAME FOR THE OTHER ANSWER CHOICES BESIDES:

'The graph shows no correlation, and it is neither linear nor exponential.'