solve for x: p(x)=x^3+6x^2+3x-10=0

Therefore, the maximum revenue is $2,925 for a group of 65 people.

An equation is a mathematical statement that shows the equality of two expressions, usually consisting of variables and/or constants. It contains an equals sign (=) that separates the expressions on either side of the sign. Equations are used to solve problems, model real-world situations, and represent mathematical relationships. They can be solved by performing operations on both sides of the equals sign until a solution is obtained.

Here,

Let x be the number of people in the group above 35. If the fair is $60 for a group of exactly 35 people, the revenue for this group would be:

R(35) = $60 x 35 = $2,100

For a group of x people, the fair would be:

$60 - $1x

So, the revenue for this group would be:

R(x) = ($60 - $1x) x

Expanding the expression:

R(x) = $60x - $1x²

To find the number of people that maximize revenue, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:

x = -b/2a

where a = -1 and b = 60

x = -60/(2*(-1))

= 30

So, the size of the group for which the revenue is the greatest is 35 + 30 = 65 people.

To find the maximum revenue, we substitute x = 30 in the equation for R(x):

R(65) = ($60 - $1*30) * 65

= $2,925

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We can see that the roots are:

α = 1 + 1.5i

β = 1 - 1.5i

Then the expression is:

1/(2α + β) + 1/(α + 2β) =  0.53

Here we first need to find the roots of the quadratic equation:

2x²-4x+5=0

Using the quadratic formula we will get:

[tex]x = \frac{4 \pm \sqrt{(-4)^2 - 4*2*5} }{2*2} \\\\x = \frac{4 \pm \sqrt{-24} }{4} \\\\x = 1 \pm 1.5i[/tex]

So the two solutions are:

α = 1 + 1.5i

β = 1 - 1.5i

Then the expression becomes:

1/(2α + β) + 1/(α + 2β)

1/(2 + 3i + 1 - 1.5i) + 1/(1 + 1.5i + 2 - 3i)

1/(3 + 1.5i) + 1/(3 - 1.5i)

To remove the complex part for the denominators we need to multiply and divide by the complements in each fraction, so we will get:

(3 - 1.5i)/(​3 + 1.5i)*(3 - 1.5i) + (3 + 1.5i)/(3 - 1.5i)*(3 + 1.5i)

[(3 - 1.5i) + (3 + 1.5i)]/(3² + 1.5²)

6/11.25 = 0.53

That is the solution.

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The probability that an adult resident has 3 or more vehicles 0.54.

The probability of an adult resident having 3 or more vehicles is the sum of the probabilities associated with owning 3, 4, or 5 or more vehicles:

P(3 or more vehicles) = P(3) + P(4) + P(5 or more)

P(3 or more vehicles) = 0.38 + 0.13 + 0.03

P(3 or more vehicles) = 0.54

Therefore, the probability that an adult resident has 3 or more vehicles is 0.54.

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Answer:

the answer is (25,75,125,175)

Therefore, the new coordinates after dilation are:

Z' = (0, 1) and (8, 5).

A coordinate is a set of numbers or values that represent the position or location of a point or object in space. Coordinates are often used in mathematics, geometry, and science to describe the location of objects in a two-dimensional or three-dimensional space.

In a two-dimensional coordinate system, such as the Cartesian coordinate system, a point is represented by two values, usually denoted as (x, y), where x represents the horizontal distance from a fixed point called the origin, and y represents the vertical distance from the origin.

In a three-dimensional coordinate system, a point is represented by three values, usually denoted as (x, y, z), where x, y, and z represent the horizontal, vertical, and depth distances from the origin.

by the question.

To dilate an image by a scale factor of 2 with the center of dilation at the blue dot, we need to double the distance between each point and the blue dot.

First, we calculate the distance between each point and the center of dilation:

[tex]|X' - blue dot| = |-1 - (-2), -3 - (-2)| = (1, 1)|y' - blue dot| = |3 - (-2), 1 - (-2)| = (5, 3)[/tex]

To double the distance, we simply multiply each distance by 2:

[tex]|X' - blue dot| * 2 = (2, 2)|y' - blue dot| * 2 = (10, 6)[/tex]

Finally, we add the doubled distances to the blue dot to get the new coordinates:

[tex]Z' = blue dot + |X' - blue dot| * 2 = (-2, -1) + (2, 2) = (0, 1)Z' = blue dot + |y' - blue dot| * 2 = (-2, -1) + (10, 6) = (8, 5)[/tex]

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Answer:

134.16 meters and length of shadow is 268.33 meters

Step-by-step explanation:

Applying Pythagoras. Let the the distance from the end of the shadow to building top be the hypotenuse side 300 meter, building height be X and the adjacent be the shadow length which is twice the height of the building 2XTherefore from Pythagoras theorem:Squared of hypotenuse side= to sum of squares of the other sidesC^2= a^2+b^2300*2= X^2+2X^290000= 5X^2X^2= 90000/5X^2=18000X= 134.16 meters2X = 268.33 metersTherefore the height of building is 134.16 meters and length of shadow is 268.33 meters

We can claim that the mean study time of the entire population of high school students is not significantly different from 1.5 hours, at a significance level of 0.05.

We need to perform a hypothesis test using the given information to determine whether the mean study time of the entire population of high school students is different from 1.5 hours.

Null hypothesis: The population mean study time is equal to 1.5 hours.

Alternative hypothesis: The population mean study time is different from 1.5 hours.

On Calculating p value using test statistics, we get p=1.

The p-value for a two-tailed test with 49 degrees of freedom is 1, meaning that there is no evidence to reject the null hypothesis. Therefore, we can claim that the mean study time of the entire population of high school students is not significantly different from 1.5 hours, at a significance level of 0.05.

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The quartic function that is the best fit for the given data is:

y = 0.538x^4 + 0.042x^3 - 2.186x^2 + 0.108x

A quartic function is described as a fourth-degree polynomial: a function which has, as its highest order term, a variable raised to the fourth power.

We will  use a regression analysis in order to find the quartic function that is the best fit for the given data,

Using a regression tool, we obtain the following quartic function that models the data with three significant digits:

y = 0.538x^4 + 0.042x^3 - 2.186x^2 + 0.108x

Therefore, the quartic function that is the best fit for the given data is:

y = 0.538x^4 + 0.042x^3 - 2.186x^2 + 0.108x

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Since ∠CGB is a right-angle triangle, ∠CGE is measured at 17°.

The opposing angles created by the intersection of two lines are known as vertical angles or vertically opposite angles, and they are always equal in size.

An angle with a measure of exactly 90 degrees (or [tex]\pi[/tex]/2) is referred to as a right angle.

In light of the posed query,

m∠FGA = 73°

Since ∠FGA and ∠BGE are vertical angles,

⇒ ∠mFGA=∠BGE=73°

Now, ∠CGB is a right-angle triangle, therefore,

⇒m∠CGE + m∠EGB = 90°

⇒ x° + 73° = 90°

⇒x° = 90° - 73°

⇒x° = 17°

Hence, the ∠CGE's measure is 17°.

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Answer:

B. 6 1/4

Step-by-step explanation:

[tex]15\cdot \cfrac{5}{12}\implies \cfrac{15\cdot 5}{12}\implies \cfrac{3\cdot 5\cdot 5}{3\cdot 4}\implies \cfrac{5\cdot 5}{4}\implies \cfrac{25}{4}\implies 6\frac{1}{4}[/tex]

Answer:

1 hot dog = $1.45

1 juice drink = $1.05

Step-by-step explanation:

let x rep hot dog

y rep juice drink

Baxter= 6x+4y=12.9

Farley=3x+4y=8.55

6x+4y=12.9

-3x+4y=8.55

3x+0=4.35

x=4.35/3=1.45

y=1.05

After answering the provided question, we can conclude that The y-intercept is denoted by b. (the point where the line crosses the y-axis)

In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the line's gradient and b is the más, which is the point on the line where it intersects the y-axis. Because it allows you to speedily see the line and ascertain its slope and y-intercept, the slope-intercept form is a useful way to represent a line's equation. The slope of the line indicates its steepness, while the esta indicates in which the line intersects the y-axis.

The slope-intercept equation for a line is:

y = mx + b

where:

The dependent variable is y. (usually the vertical axis)

x is the independent variable (usually the horizontal axis)

The slope of the line is given by m.

The y-intercept is denoted by b. (the point where the line crosses the y-axis)

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In physics, work is energy transferred to or from an object by applying a force along a displacement and the work done in the given situation is 120J.

In physics, work is energy transferred to or from an object by applying a force along a displacement.

In its simplest form, work done with a constant force in the direction of motion is equal to the product of the force and the distance traveled.

Expressing this concept mathematically, the work W is equal to the force f multiplied by the distance d, or W = fd.

If the force is applied at an angle θ to the displacement, the work done is W = fd cos θ.

So, the work done is calculated as follows:

W = 40lb*3ft

W = 120 J

Therefore, the work done in the given situation is 120 J.

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The standard error of the mean for the given sample of 375 homes is 0.186. This means that the mean of 4.2, as estimated from the sample, is likely to be within 0.186 of the true population mean.

Standard deviation is a measure of the variability or spread of a dataset. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. Standard deviation gives a measure of how spread out the values in a dataset are from the mean value. Higher standard deviation indicates greater spread or variability of the values.

The random variable X is the number of people in a household for a given sample size of 375 homes. This random variable is important in estimating the population mean of the number of people in a household.

To calculate the standard error of the mean (SE), we first need to calculate the sample size:

n = 375

Then, we can calculate the standard error of the mean as follows:

SE = (2.1)/(√375)

SE = 0.186

Therefore, the standard error of the mean for the given sample of 375 homes is 0.186. This means that the mean of 4.2, as estimated from the sample, is likely to be within 0.186 of the true population mean.

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Complete questions as follows-
In a certain year; according to a national Census Bureau, the number of people in a household had a mean of 4.39 and a standard deviation of 2.23. This is based on census information for the population. Suppose the Census Bureau instead had estimated this mean using a random sample of 375 homes. Suppose the sample had a sample mean of 4.2 and standard deviation of 2.1 .Identify the random variable X. Indicate whether it is quantitative or categorical What is the random variable X? O A The mean number of people in a household B. The number of people in a household OC. The number of households in the country OD.

Monte Carlo simulation can done by generating a large number of random points within the quarter circle and the square, we can obtain an accurate estimate of pi using the formula pi/4 = area Q/area S.

Monte Carlo simulation is a statistical method that involves generating random numbers to simulate real-life scenarios. In this case, we will use the method to approximate the value of pi by generating random points inside the quarter circle Q and the square S.

The algorithm for this simulation is as follows:

1. Set the number of random points (n) to be generated.

2. Initialize two counters: count_Q and count_S to zero.

3. Generate n random points within the square S. Each point is represented by a pair of random numbers (x,y) such that 0 <= x <= 1 and 0 <= y <= 1.

4. For each point generated, determine if it falls within the quarter circle Q by checking if x^2 + y^2 <= 1. If it does, increment the count_Q by 1.

5. Increment the count_S by 1 for every point generated.

6. Calculate the ratio of count_Q to count_S, which represents the ratio of the area of Q to the area of S.

7. Multiply the ratio obtained in step 6 by 4 to get an approximation of pi.

The logic behind this algorithm is that the ratio of the areas of the quarter circle Q to the square S is pi/4. Thus, by generating random points within the square S and determining the number of points that fall inside the quarter circle Q, we can estimate the value of pi.

To implement this algorithm in Excel, we can use the RAND() function to generate random numbers for the x and y coordinates of each point. We can then use an IF statement to determine if each point falls within the quarter circle. We can use a loop to generate a large number of random points, such as 10,000 or 100,000, to obtain a more accurate estimate of pi.

In summary, Monte Carlo simulation is a powerful tool for approximating the value of pi using random numbers and the properties of geometric shapes. By generating a large number of random points within the quarter circle and the square, we can obtain an accurate estimate of pi using the formula pi/4 = area Q/area S.

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Answer:

100 times

Step-by-step explanation:

60/0.6 = 100

[tex]\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=8\\ r=12 \end{cases}\implies V=\cfrac{\pi (12)^2 (8)}{3} \\\\\\ V=384\pi \implies \stackrel{using~\pi =3.14 }{V=1206}~cm^3[/tex]

now, we're making an assumption that's a rectangular prism pool, so the volume is simple the product of length and widh and height, which we have, let's convert them all to improper fractions.

[tex]\stackrel{mixed}{14\frac{1}{2}}\implies \cfrac{14\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{29}{2}}~\hfill \stackrel{mixed}{6\frac{1}{2}} \implies \cfrac{6\cdot 2+1}{2} \implies \stackrel{improper}{\cfrac{13}{2}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{length}{\cfrac{29}{2}}\cdot \stackrel{width}{\cfrac{13}{2}}\cdot \stackrel{depth}{\cfrac{13}{2}}\implies \cfrac{4901}{8} \\\\\\ \cfrac{4896+5}{8}\implies \cfrac{4896}{8}+\cfrac{5}{8}\implies 612+\cfrac{5}{8}\implies 612\frac{5}{8}[/tex]

Answer:

Commutative Property.

Associative Property.

Distributive Property.

Identity Property.

The equation of the straight line perpendicular to DE that passes through the mid-point of DE is y - 18 = 5/4(x - 1) which can be simplified to 5x - 4y + 42 = 0 where a=5, b=-4,c=42.

What is a midpoint?

In geometry, the midpoint is the middle point of a line segment. It is equidistant from the two endpoints and bisects the segment. It is also the centre of gravity of both the segment and the endpoints.

What is a straight line?

A straight line is a line of infinite length that has no curves. It can also be formed between two points, but both ends extend to infinity

According to the given information

The midpoint of DE is ((6-4)/2, (22+14)/2) = (1, 18).

The slope of DE is (14-22)/(-4-6) = -8/10 = -4/5.

The slope of the line perpendicular to DE is the negative reciprocal of -4/5 which is 5/4.

Therefore, the equation of the straight line perpendicular to DE that passes through the mid-point of DE is y - 18 = 5/4(x - 1) which can be simplified to 5x - 4y + 42 = 0.

Therefore a = 5, b=-4, c=42

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Answer:

The new price is $4.76

Step-by-step explanation: You multiply 3.40 x 0.4 to get 1.26, and then you add that to 3.40 to get the answer.

Have a great day!

Convert 4% into a decimal by doing 4 divided by 100 and you'll get 0.04.

Multiply 3.40 and 0.04 and you will get 0.136.

Add 0.136 to 3.40 and you'll get 3.536

That is the new price of the item after it is marked up.

Answer:

m = 4 + 0.18b

Step-by-step explanation:

So, we are looking to find the total amount of money that Ariella earns.

$4.00 is what she initially gets paid.

plus 18%, 18 / 100 = 0.18

then b is the amount of total bill

so, we multiply the amount of percentage which is 18% to the amount of total bill which is b to get what she additionally earns after the customers paid the bill.

so initial pay is $4 + 18% which is 0.18 multiply to b, b represents the total bill.

$4 + 0.18b = m

The volume of the dining room can be expressed in standard form as x³+ 18x² + 108x + 216, which is obtained by expanding the given expression (x+6)³ using the binomial expansion formula.

HOW TO EXPRESS THE VOLUME?

To express the volume of the dining room in standard form, we need to expand the given expression using the binomial expansion formula. The binomial expansion formula is given by:

(a + b)ⁿ = ⁿC₀ aⁿ + ⁿC₁ aⁿ⁻¹ b + ⁿC₂ aⁿ⁻²b²+ ... + ⁿCₙ₋ ₁a bⁿ⁻¹ + ₙCⁿ bⁿ

where nCk represents the binomial coefficient of selecting k items from a set of n items.

Using this formula, we can expand (x+6)^3 as:

(x+6)³ = ³C₀x³+  ³C₁x²+(6) +  ³C₂+ x (6)²+  ³C₃+ (6)³

= 1x³ + 18x² + 108x + 216

Therefore, the volume of the dining room can be expressed in standard form as:

x³+ 18x²+ 108x + 216

In standard form, the expression is arranged in descending powers of the variable, and the coefficients are written with the highest degree coefficient first. In this case, the expression is already in standard form, and we do not need to make any further changes.

To summarize, the volume of the dining room can be expressed in standard form as x³+ 18x² + 108x + 216, which is obtained by expanding the given expression (x+6)³ using the binomial expansion formula.

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The graph of the system is Option A.

In mathematics, an inequality is a statement that compares two values, expressing that one value is greater than, less than, or equal to the other value. An inequality is typically denoted using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to). For example, the inequality "x > 5" states that the value of x is greater than 5.

Inequalities are used in many areas of mathematics, including algebra, calculus, and geometry. They are also used in real-world applications such as economics, physics, and engineering to represent constraints on variables or parameters.

An inequality can be represented graphically as a shaded region on a coordinate plane. The region includes all the points that satisfy the inequality, and is usually bounded by a line or curve. For example, the inequality "y > -x + 3" represents the region above the line y = -x + 3 on a coordinate plane.

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The function required is g(x) = 2 + x - 4 + (3 - c + b) where a = 4-2+b-c, b = 6 - 3 + c, and c = 2-a-2+b.

Function is a relationship between two variables. It is represented by an equation that shows the values of one variable in terms of the other.

We can create a new function g(x) to transform f(x) so that it includes the point (-2, 2).

To do this, we need to find the values of a, b, and c where g(x)= a+(x-b)+c.

We know that f(2)=4, f(3)=4, and f(2)=2. We can use these points to solve for a, b, and c.

To solve for a, we can plug in x=2 and solve for a:

a+2-b+c = 4

a = 4-2+b-c

To solve for b, we can plug in x=3 and solve for b:

a+3-b+c = 4

b = 4-a-3-c

To solve for c, we can plug in x=2 and solve for c:

a+2-b+c = 2

c = 2-a-2+b

Now that we have a, b, and c, we can plug them into the equation

g(x) = a + (x-b) + c and get:

g(x) = 4 - 2 + (x - (4-a-3+c)) + (2 - a - 2 + b)

g(x) = 4 - 2 + (x - 4 + a + 3 - c) + (-a - 2 + b + 2)

g(x) = 4 - 2 + (x - 4) + (a + 3 - c - a - 2 + b + 2)

g(x) = 4 - 2 + x - 4 + (3 - c + b)

g(x) = 2 + x - 4 + (3 - c + b)

When we plug in x = -2, we get:

g(-2) = 2 - 2 - 4 + (3 - c + b)

g(-2) = -4 + (3 - c + b)

g(-2) = 2

We can now solve for c and b using the above equation:

-4 + (3 - c + b) = 2

3 - c + b = 6

b = 6 - 3 + c

Therefore, g(x) = 2 + x - 4 + (3 - c + b) where a = 4-2+b-c, b = 6 - 3 + c, and c = 2-a-2+b is the function required.

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Answer:

Step-by-step explanation:

Answer: (d)

[tex]sin34=\frac{opposite}{hypotenuse}=\frac{x}{12}[/tex]

Answer:

this better be a joke because what kind of teacher actually uses this

Step-by-step explanation:

The domain of the function is Dοmain = [0, 25218]

Range = [0, 45, 90, .....,1134810]

In mathematics, the domain of a function is the set of all possible input values (often referred to as the independent variable).

In this case, the maximum capacity of the stadium is 25218 people, so the domain of the function is [0, 25218], including 0 for the case of no attendance.

As we knοw fοr the given questiοn :

• Dοmain will be the number οf peοple whο will be frοm 0 tο 25218

• Range will be the amοunt οf mοney οr revenue which will be [45×0, 45×1, 45×2, ........45×25218]

Sο,

Dοmain = [0, 25218]

Range = [0, 45, 90, .....,1134810]

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The value for which f(x) is equal to 5 is c = ∛4 = 1.59, that proves the intermediate value theoerem.

We have the function:

f(x) = x³ + 1

Evaluating this on the end values of the interval [0, 3] we will get:

f(0) = 0³ + 1 =1

f(3) = 3³ + 1 = 27 + 1 = 28

Now, the value k = 5 is between these two:

1 < 5 < 28

The intermediate value theorem says that there is a value c in [0, 3] such that f(c) = 5, so let's find the value of c.

c³ + 1 = 5

c³ = 5 - 1

c³ = 4

c = ∛4

c = 1.59

That is the value for which f(x) is equal to 5.

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