Find the profit function if cost and revenue are given by C(x) = 181 +2.9x and R(x) = 6x -0.05x².

The regression model for predicting points/game as a function of yards/game will use the data from the Excel file to determine the statistical parameters that describe the relationship between the two variables.

Regression analysis is a statistical tool used to determine the relationship between two or more variables. In this case, we will use regression analysis to develop a model for predicting points/game as a function of yards/game.

The intercept is the point at which the regression line intersects the y-axis. The slope is the steepness of the regression line. The correlation coefficient (r-value) is a measure of the strength of the relationship between the two variables.

A value of 1 indicates a perfect positive relationship, a value of -1 indicates a perfect negative relationship, and a value of 0 indicates no relationship.

The statistical significance of the model is determined by the p-value. The p-value is the probability that the relationship between the two variables is due to chance.

If the p-value is less than 0.05, we can say that the relationship is statistically significant, meaning that it is unlikely to be due to chance.

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Using Compound Interest, The population of bears would be 1851 after 8 years with 2% increase every next year.

Compound interest is defined.

Savings interest that is calculated on both the principal and the interest accrued over the course of prior periods is called compound interest. The monthly compound interest formula is used to get the compound interest every month. The formula for compound interest is as follows: CI = P(1 + (r/12)). 12t - P, where t is the passing of time, P is the total amount of the principal, and r is the interest rate in decimal form.

Formula: Amount = P(1+r/100)ⁿ

where, P is principle

r is rate of increase in the given time period

n is time in years

Given that,

P = 1580

r = 2%

n = 8 years

∴ Population of bear  = 1580(1 + 2/100)⁸

                                 = 1580(1+0.02)⁸

                                 = 1580(1.02)⁸

                                 = 1580(1.171)

                                 = 1851

Thus, the population of bears would be 1851 after 8 years.

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The function The output is one more than twice the input x" is f(x) = 2x + 1.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The given statement is "The output is one more than twice the input x"

Therefore, If 'x' is the input then the output is 2x + 1.

So, The function can be written as f(x) = 2x + 1.

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The roots of the quadratic equation, x²+4x+1=0, are x = -2+√3 or -2-√3

The quadratic formula is a formula that provides the solution(s) to a quadratic equation.

Quadratic formula :-

x = -b±√b²-4ac / 2a

Given that, a quadratic equation, x²+4x+1=0, we need to solve it by using quadratic formula,

Quadratic formula :-

x = -b±√b²-4ac / 2a

Here, a = 1, b = 4 and c = 1

Therefore,

x = -4±√4²-4×1×1 / 2

x = -4±√16-4 / 2

x = -4±√12 / 2

x = -4±2√3 / 2

x = -2±√3

Therefore, x = -2+√3 or -2-√3

Hence, the roots of the quadratic equation, x²+4x+1=0, are x = -2+√3 or -2-√3

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The question was incomplete, so I solved for,

Solve the following quadratic equation by using quadratic formula method: x²+4x+1=0

Answer:

15/2

Step-by-step explanation:

If y is proportional to x, then the equation is

y = kx, where k is the constant of proportionality.

Here we have

f = 15/2 g, so the constant of proportionality is 15/2.

13.2% of 200 would be 26.4

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. It is frequently represented by the percent sign, "%".

A percentage is a dimensionless number; it has no unit of measurement

13.2% of 200 would be:

13.2% is represented as:

13.2/100

Thus, 13/100 * 200 would be 26.4

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13.2% of 200 = ?

What is 13.2 percent of the number 200

Answer:

positive

Step-by-step explanation:

3/5 + 3/5 = 6/5   positive

The sum of this infinite geometric series is -25/9.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The given geometric series is -5+4-16/5+64/25-256/125

The general formula for finding the sum of an infinite geometric series is S= a/1-r, where s is the sum, a is the first term of the series, and r is the common ratio.

Here, a=-5 and r= -4/5

Now, S = -5/(1+4/5)

= -5/(9/5)

= -25/9

Therefore, the sum of the series is -25/9.

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The equation is 230-q=336 which is solved by combining like terms to result in q=-106.

What are like terms?

The term "like terms" in algebra refers to terms that have the same variable raised to the same power. Only the numerical coefficients can vary in terms that are similar to algebra. To make the algebraic formulae simpler, we can combine like terms.

The statement of an equation is given as -

336 is 230 decreased by q.

230 is decreased by q is equivalent to 230 subtracted by q and the number obtained by the above arithmetic operation of subtraction is equal to 336.

The mathematical equation is written as -

230-q=336

Simplify the equation by combining like terms -

-q=336-230

-q=106

q=-106

Therefore, on evaluating the equation the result is -106.

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Answer: -735

Step-by-step explanation:

735 feet below sea level is just 735 below 0, so -735 :)

Answer:x=4

Step-by-step explanation:

Juwan travelled distance of 36 miles from his home before his tire went flat.

Distance is inversely correlated with time.

Distance = rate*time

d = rt

into town: d = 6t

back home: d = 3(18-t)

As the distance equal to d.

6t = 3(18-t)

6t = 54 - 3t

6t + 3t = 54

9t = 54

t = 6 hours.

So, the distance;

d = 6*6 = 36 miles

Thus, Juwan travelled 36 miles from his home before his tire went flat.

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The required probability of the son with normal vision is 0.50 and for the normal  blood clotting is 0.

Parent phenotype                                         Carrier woman

Affected man (Hemophilic)                           (colorblindness)

Parents X^h Y                                                    XX^C

Gametes X^h, Y X, X^C

Progeny                      X X^h       X^C X^h        X^C Y,       XY

Total outcome = 100

Favourable outcomes for a son with normal vision is= 50

Probability of a son with normal vision = 50/100

                                                                = 0.50

probability of a son with normal blood clotting = 0 / 100

                                                                             = 0

Therefore, the probability of the son with normal vision and normal blood clotting is 0.50 and 0 respectively.

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The required unit of the measure of the mean is given as in Dollars. Option A is correct.

What does math's median mean?

When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median.

                               When working with a small data collection, you must first count the number of data points (n) and organize them in ascending order.

Due to that,

With a mean of $21,800 and a standard deviation of $400, the price distribution for a specific car model is roughly typical. Four of the model's cars will be chosen at random as the sample.

                                  It must be established which unit of measurement is appropriate for the mean of the sample distribution of the car's pricing.

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Factor when dividing the function the remainder is zero. The factorized form of the function  is 3(x^2-2x-80).

A factor of a function is a factor which when multiplied by another the result is the function itself.

here, we have,

We know that in order to factorize a function of the second-order, we need to take the common terms out from the expression,

f(x) = 3x^2 - 6x - 240

now,

Taking 3 as the common terms out of the entire function,

f(x) = 3x^2 - 6x - 240

     = 3(x^2-2x-80)

Hence, the factorized function, f(x) = 3x^2 - 6x - 240 is 3(x^2-2x-80)

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The 24% of the calories in one slice of pizza come from fat.

To find the percentage of calories from fat in one slice of pizza, we use the formula:

(Calories One gram of fat provides 9 calories, so 8 grams of fat provide 8 x 9 = 72 calories.

Therefore, the percentage of calories from fat in one slice of pizza is:

(72 / 300) x 100 = 24%

Calories are units of energy that a food or drink produce. we can normally find calorie numbers listed on food items, and wearables like the best fitness trackers allow you monitor how many calories you are burning by doing different activities.

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Gender and ethnicity are categorical variables and therefore, the standard deviation cannot be calculated for variables.

The standard deviation is a measure of the spread or dispersion of the data around the mean. In other words, it tells us how far each data point in a set is from the average of the set.

When we analyze data, it's important to understand how much variation there is in the data, and the standard deviation is one way to do this.

When it comes to the three dependent variables in the data set (gender, age, and ethnicity), it is important to understand that the standard deviation is only calculated for numerical data.

However, age is a numerical variable, and the standard deviation can be calculated for it.

To find the standard deviation of the ages, we need to first find the mean of the ages and then subtract each age value from the mean and square the result.

Next, we add up all the squared deviations and divide by the number of ages minus one. Finally, we take the square root of the result, and that gives us the standard deviation of the ages in the data set.

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The hypothesis that I propose is that the higher the GDP per capita, the higher the percentage of population that is considered to be living in democracy.

To test this hypothesis, a simple linear regression equation can be used, where Y is the percentage of population living in democracy, and X is the GDP per capita. From the graph, we can see that the linear equation is Y = 0.0006X + 51.7. This means that, for every additional $1,000 of GDP per capita, the percentage of population living in increases by 0.6%. This could be explained by the fact that higher GDP per capita often results in higher levels of socioeconomic development, which in turn leads to better access to education, and other social services. In turn, this can lead to higher levels of political participation, which is associated with higher levels of democracy.

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Answer:

x=-91

Step-by-step explanation:

So to solve, 42= -x/7+29 we first have to simplify both sides:

42= -1/7x+29

Then we have to flip the equation:

-1/7x+29=42

Okay so now we subtract 29 from both sides:

-1/7x=13

Now we Multiply both sides by 7/(-1)

And your final answer is = -91

To check input x:

42=-91/7+29

and you end up with 42

42=42

so its correct

Answer:

1. angle BAC and angle CAD are a linear pair. This means they both angle measures add up to 180 degrees.

2. 180= x + 132

3. 132+48 = 180

4. Angle BAC= 48 degrees.

Step-by-step explanation:

2. To solve for x, subtract 132 from both sides.

If the area of the circular base of a cone is 9π cm².  lateral area of the cone is 36π cm² and the  the total surface area painted black is approximately 43.2π square feet.

1. Let's call the radius of the circular base "r". The area of the circular base is 9π, so:

r² = 9

r = 3

Since the slant height is four times the radius, the slant height is 4 * 3 = 12.

The lateral area of a cone can be calculated using the formula:

A = π * r * l

Where:

r = radius

l = slant height

Plugging in the values, we get:

A = π * 3 * 12

A = 36π

2. Let's call the radius of each cone "r" and the circumference of the base of each cone is 8π, so:

2 * π * r = 8π

r = 4

The lateral surface area of a cone can be calculated using the formula:

A = π * r * l

Where:

r = radius

l =slant height

Plugging in the values, we get:

A = π * 4 * 12

A = 48π

Since 70% of the lateral surface area is painted red, 30% is painted black. So, the total surface area painted black for each cone is:

0.3 * 48π

= 14.4π

And the total surface area painted black for all three cones is:

3 * 14.4π

= 43.2π

Therefore   the approximate lateral area of the cone is 36π cm² and the total surface area painted black is approximately 43.2π square feet.

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The dimensions of the poster with the smallest area is ([tex]12\sqrt{389} +24[/tex]) units width and ([tex]\sqrt{389} /6+4[/tex]) units height.

It is a measurement of a point or line extended in one direction, according to the notion of dimension. Each shape we see has a few dimensions.

The statement indicating the powers to which the fundamental units are to be increased in order to obtain one unit of a derived quantity is known as the dimensional formula of any quantity. The formulation for any physical quantity Q's dimensional formula is given by,

Dimensional Formula: Q = [tex]M^{a}L^{b}T^{c}[/tex]

The area of printable area is wh.

wh = 778

Due to margins on both sides, the poster is w + 2*12 wide and h + 2*2 tall.

We want to reduce the poster's size =

(w+ 2 * 12)(h + 2 * 2) or (w + 24)(h + 4)

Wh = 778, thus we can replace it with h = 778/w.

Then, A = (w + 24)(778/w + 4)is the poster's size, which we aim to reduce.

(w + 24)(778/w + 4) = 778 + 4w + 18672/w + 96 =

4w + 874 + 18672/w

We minimize this by calculating

the formula dA/dw = 4 - 18672/w2 and setting it to 0

[tex]4-18672/w^{2} =0[/tex]

[tex]4w^{2} =18672[/tex]

[tex]w^{2} =18672/4[/tex]

[tex]w=\sqrt{4668}=12\sqrt{389}[/tex]

[tex]h=778/(12\sqrt{389} )=\sqrt{389} /6\\[/tex]

Keep in mind that the margins' ratio matches that of h and w.

In due to the fact that the problem requests the poster's width and height,

Width = [tex]12\sqrt{389} +24[/tex]

Height = [tex]\sqrt{389} /6+4[/tex]

Thus, the width is ([tex]12\sqrt{389} +24[/tex]) units and the height is ([tex]\sqrt{389} /6+4[/tex]) units.

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Answer:

35 million

Step-by-step explanation:

The peak of sales in this problem is the vertex of the parabola that can be graphed from the given equation.

The vertex of a parabola is defined as:

[tex]\left(-\dfrac{b}{2a}, \dfrac{b^2 - 4ac}{4a} \right)[/tex]

when a, b, and c correspond to the unfactored quadratic form: [tex]ax^2 + bx + c[/tex].

So, we can use the given equation:

[tex]S = -4x^2 + 24x - 1[/tex]

to assign the following variables:

[tex]a = -4[/tex],   [tex]b = 24[/tex],   [tex]c=-1[/tex]

Using these variables, we can find the vertex of the parabola by plugging them into the above definition.

[tex]\left(-\dfrac{b}{2a}, \dfrac{b^2 - 4ac}{4a} \right)[/tex]

[tex]\left(-\dfrac{24}{2(-4)}, \dfrac{24^2 - 4(-4)(-1)}{4(-4)} \right)[/tex]

[tex]\left(\dfrac{24}{8}, \dfrac{576 - 16}{-16)} \right)[/tex]

[tex]\left(3, 35 \right)[/tex]

So, the peak sales for the game are 35 million.

A set of outcomes from an experiment to which a probability is assigned is called "Event." Therefore, the option d is the correct answer. This term is related to probability.

Probability is a statistic that expresses the results of a specific experiment or activity. A simple experiment is to flip a coin twice. There are some terms related to probability, as below:

Examining a procedure or interviewing a chosen sample of people in order to collect data is known as a survey.

The population is the entire group of participants in research with its characteristics that will be a data source.

The sample space is the set of all possible outcomes. The sample space is indicated with letter S.

S = {H, T}.

Event is a set of outcomes from an experiment to which a probability is assigned. Any subset of the sample space (S) is called an event.

S = {H, T}.

The number of individuals or observations included in a study is referred to as the sample size. Usually, n is used to indicate this number.

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Answer:

v=424.1cm³

Step-by-step explanation:

v=πr²h

v=π×3²×15

v=424.1150082

∴v=424.1cm³

The measure of each angle is -

∠E = 63°

∠F = 43°

∠D = 74°

Scale factor tells us by how much one quantity is greater than the other. It is denoted by {K}. Mathematically -

K = a/b                        .... Eq { 1 }

Rewriting, we get -

a = Kb                             .... Eq { 2 }

If a side length [a] of any 2 - D figure is dilated by a scale factor of [k], then the length of new side will be [Ka].

Given are the two similar triangles as ΔABC and ΔDEF.

Since the triangles are similar, their corresponding angles are equal. We can write -

∠C = ∠F                                    {triangles are similar}

(5x + 8) = (6x + 1)

6x - 5x = 8 - 1

x = 7                                                   .... Eq { 1 }

∠A = ∠D                                                     {triangles are similar}

(8y + 2) = (11y - 25)

11y - 8y = 27

3y = 27

y = 9                                                                   .... Eq { 2 }

We can write -

∠D + ∠E + ∠F = 180°                                                        .... Eq { 3 }

(6x + 1) + (11y - 25) + ∠E = 180°

(6 x 7 + 1) + (11 x 9 - 25) + ∠E = 180°

43 + 74 + ∠E = 180°

∠E = 180 - 117

∠E = 63°

∠F = (6x + 1) = 43°

∠F = 43°

∠E = (11y - 25) = 74°

∠D = 74°

Therefore, the measure of each angle is -

∠E = 63°

∠F = 43°

∠D = 74°

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In conclusion, the length and structure of the human ear canal affect hearing by amplifying specific frequencies of sound and shielding the inner ear from strong sounds.

The measurement or expanse of something from end to end is defined as length. In other terms, it is the greater of the two or the highest of three geometrical forms or objects' dimensions. A rectangle, for example, has length and width dimensions.

Here,

The human ear canal is 2.5 cm long on average, and its form and length are crucial in hearing. Sound waves enter the ear canal and are directed towards the eardrum, which vibrates. These vibrations are subsequently conveyed to the middle ear bones, which enhance and transport the sound to the inner ear. The length and structure of the ear canal aid in the amplification of some frequencies of sound over others, a phenomenon called as resonance. This resonance improves the ear's capacity to detect particular sounds, such as speech, and makes them easier to hear.

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The mean fluoride concentration can be calculated by adding up all the values and dividing by the number of observations. In this case, the mean fluoride concentration is:

Mean = (0.915 + 0.885 + 0.911 + 0.889 + 0.921) / 5

Mean = 4.521 / 5

Mean = 0.9042 mg/l

The 90% confidence interval for the average fluoride concentration can be calculated using the standard error and a t-distribution. The standard error is given by the standard deviation of the sample divided by the square root of the number of observations:

Standard error = Standard deviation / √(Number of observations)

Since we do not have the standard deviation, we can use the sample standard deviation as an estimate. The sample standard deviation can be calculated using the formula:

Sample standard deviation = √((Σ(x_i - mean)^2) / (n - 1))

where x_i is the i-th observation and n is the number of observations.

In this case, the sample standard deviation is approximately 0.0132 mg/l. The standard error is:

Standard error = 0.0132 / √(5) = 0.0057 mg/l

The t-value for a 90% confidence interval and 4 degrees of freedom (n - 1) can be found using a t-distribution table. With a t-value of 1.833, the 90% confidence interval is:

Confidence interval = Mean ± t-value * Standard error

Confidence interval = 0.9042 ± 1.833 * 0.0057

Confidence interval = [0.8914, 0.9170] mg/l

So, the 90% confidence interval for the average fluoride concentration in the sample is [0.8914, 0.9170] mg/l. This means that we are 90% confident that the true average fluoride concentration in the population is between 0.8914 and 0.9170 mg/l.

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