Benoît has a home business selling antique watches. If he sells x watches, in thousands, his profit, P, in thousands of dollars, is given by

P=−50x^2 + 550x − 900

Determine Benoît’s break-even points

Determine his maximum profit and how many antique watches he must sell to achieve this profit.

2 1/8 pints

2.125 pints

Answer:

a cube...............................

Step-by-step explanation:

To solve the given system of differential equations using elimination, we can eliminate variables one by one to obtain a simplified system of equations. We start by differentiating the first equation and substituting the resulting expression into the second equation to eliminate x2'.

The given system of differential equations is:

x1'(t) = x2

\(x2'(t) = 2x3 - 2x4 + 3e^-t + 2x3'\)

\(x3'(t) = - (1/2)x2 + (1/4)x4 - (1/4)x4'\)

\(x4'(t) = x5\)

\(x5'(t) = -x2 + 2x3 - x5\)

To eliminate x2', we differentiate the first equation with respect to t:

x1''(t) = x2'

Substituting this into the second equation gives:

\(x2'(t) = 2x3 - 2x4 + 3e^-t + 2x1''(t)\)

Next, we differentiate the third equation to eliminate x3':

x3''(t) = -(1/2)x2' + (1/4)x4' - (1/4)x4''

Substituting this into the fourth equation gives:

x4'(t) = x5 + x3''(t)

Lastly, we differentiate the fifth equation to eliminate x5':

x5''(t) = -x2' + 2x3' - x5'

Substituting this into the fourth equation gives:

x4'(t) = x5 - x5''(t)

We now have a system of equations without any derivatives, which we can solve simultaneously to find the values of x1, x2, x3, x4, and x5 as functions of t. The specific method of solving the system will depend on the specific values and initial conditions given in the problem.

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The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.

The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.

The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.

By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.

Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.

Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.

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Question

The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.

putting all the values in the formula, we havecosθ = (v*w) / (||v|| ||w||)cosθ = 102 / (√105 * √161)cosθ = 102 / 403.60cosθ = 0.2525So, cosine of the angle between v and w is 0.2525.

Given v = (1,2,10) and w = (4,9,8) and cos = 67To find: Cosine of the angle between v and w.

To find the cosine of the angle between v and w, we will use the dot product formula cosθ = (v * w) / (||v|| ||w||) where θ is the angle between v and w, ||v|| and ||w|| are magnitudes of vectors v and w respectively.

Step-by-step solution:

Let's calculate the magnitudes of vector v and w.||v|| = √(1² + 2² + 10²) = √105||w|| = √(4² + 9² + 8²) = √161The dot product of v and w is: v*w = (1 * 4) + (2 * 9) + (10 * 8) = 4 + 18 + 80 = 102

Now, putting all the values in the formula, we havecosθ = (v*w) / (||v|| ||w||)cosθ = 102 / (√105 * √161)cosθ = 102 / 403.60cosθ = 0.2525So, cosine of the angle between v and w is 0.2525.

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Answer: Review the picture. This is the formula.

Step-by-step explanation: Just multiply the terms and you’ll get the volume. Remember to not measure the diameter but half of that which is the radius! I hope this helps but please comment down below if you need more help!

Answer: V = (1/3)πr2h.

Step-by-step explanation:

To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

Given:

Eliminating negative exponents:

Example:

1)  \(x^{-5}\)

on reciprocal:

= 1/x^5

eliminated negative

2) \(x^{-7}y^{-4}\)

= x^-7*1/y^4

= 1/x^7y^4

Therefore To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

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The quality control sample statistic that indicates a quality characteristic that is an attribute is the proportion.

In quality control, a quality characteristic is classified as either a variable or an attribute.

Variable: A quality characteristic that can be measured on a continuous scale, such as length, weight, or temperature. Statistical measures such as mean, range, variance, and standard deviation are used to describe the variability and central tendency of variable data.

Attribute: A quality characteristic that can be classified into distinct categories or attributes, such as pass/fail, presence/absence, or good/bad. Proportion is used to describe the frequency or proportion of items in a sample that exhibit a particular attribute.

To calculate the proportion, you need to determine the number of items in the sample that possess the desired attribute divided by the total number of items in the sample.

Proportion = Number of items with desired attribute / Total number of items in the sample

Based on the given options, the proportion is the appropriate quality control sample statistic for an attribute. It provides information about the relative frequency or proportion of items in the sample that possess a specific attribute, which is crucial for attribute-based quality characteristics.

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Given:

A set of all points in a plane that are a given distance from a point.

Required:

To choose the correct option for the given definition.

Explanation:

A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle.

Final Answer:

A set of all points in a plane that are a given distance from a point is called circle.

Answer:

Step-by-step explanation:

to solve this question, we need to use the graph on the left to find the proportions of students who prefer each pasta dish, and then multiply those proportions by 400 to get the estimated number of students in the whole school who prefer each pasta dish. Then we need to plot those numbers on a bar graph with the pasta dishes on the horizontal axis and the number of students on the vertical axis. The graph below shows one possible way to create the bar graph:

We can see that the vertical axis is numbered from 0 to 120 in increments of 20. The bars show the estimated number of students who prefer each pasta dish, based on the sample of 16 students. For example, since 4 out of 16 students prefer spaghetti, we can estimate that 4/16 x 400 = 100 students in the whole school prefer spaghetti. Similarly, since 3 out of 16 students prefer lasagna, we can estimate that 3/16 x 400 = 75 students in the whole school prefer lasagna. We can repeat this process for the other pasta dishes and plot them on the graph.

✧☆*: .｡. Hope this helps, happy learning! (*✧×✧*) .｡.:*☆

Answer:

19°

Step-by-step explanation:

In this problem, we have complementary angles, which add up to 90° as indicated by the right angle symbol. So, getting x° is as simple as 90°-71°=19°.

The probability that she will have no spelling mistakes on at least one of them = 0.9919.

Let, X be the random variable denoting the no. of pages among those 444 pages which Julia writes where she makes no spelling mistake.

clearly we know that,

X Binomial (444, 0.7)

So,      P(X = x) = \(4c_{x} * (0.7)^{x} * (0.3)^{(4-x)}\)

                           [when  x = 0, 1, 2, 3, 4 ..... so on until 444]

                        = 0 otherwise

According to the question, we have to find out  P(X ≥ 1) .

Now, P(X ≥ 1)

    = 1 - P(X = 0)

    = \(1 - (444c_{x} * (0.7)^{0} * (0.3)^{(4)})\)

    = 1 - 0.0081

    = 0.9919

So, the required probability is  given by, 0.9919

Hence the answer is the probability that she will have no spelling mistakes on at least one of them = 0.9919.

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Answer:

slope: 4

y-intercept: 2

Step-by-step explanation:

We are given an equation, y = 4x + 2, and we are asked to find the slope and y-intercept of the line. Looking carefully, we can see that the equation is given to us in slope-intercept form.

Slope-intercept form is:

y = mx + b

where m is the slope and b is the by-intercept.

Knowing this, we can find that 4 is the slope of the line and 2 is the y-intercept.

I hope you find my answer and explanation to be helpful. Happy studying.

Answer:

1.

Proportional:Yes

Equation:y=27*x

Number of tickets:x

Total cost:y

2.

Proportional:yes

Equation:y=4.35x

Weight:x

Total cost:y

Step-by-step explanation:

Sorry for answering late!

Answer:

7 apples

Step-by-step explanation:

You can divide the apples by 2, but you will have a decimal. The closest you can get it without having a decimal is 7 in one pile, and 6 in the other. The pile with 7 apples is bigger.

The big pile has 7 apples because 13÷2 will leave you with a remainder so if you split 13 apples, 1 apple would be left, so then you add it to one of the piles to get 7 in one pile and 6 in the other.

The advantages of the 'Monthly Reporting Form' are given below:a) Reduced administrative hassle compared to single shot: Monthly reporting forms reduce the workload of administrative work that may have been required if it was a single-shot.

For instance, when it comes to accounting and finance, monthly reporting can help to reduce the administrative burden that comes with running a business. This is because monthly reporting makes it easier to keep track of financial data, ensuring that records are updated on a more frequent basis.

There is a lower rate associated with monthly reporting forms as they can offer a reduction in cost compared to single-shot options. This is because they can save time and money in the long run, reducing the amount of work and administration required to keep track of things.

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Answer:

45% male teachers

55% female teachers

Step-by-step explanation:

multiply the number of teachers with 100 and divide it by the total number of teachers

Answer:

18>f>-9

Step-by-step explanation:

it's hard to explanation

Answer:

x = 15

Step-by-step explanation:

10x - 30 and 3x + 15 are same- side interior angles and sum to 180° , so

10x - 30 + 3x + 15 = 180 , that is

13x - 15 = 180 ( add 15 to both sides )

13x = 195 ( divide both sides by 13 )

x = 15

Step-by-step explanation:

Thus, the function g(x) is the absolute value of the quantity (x + 3), which means that it takes any input value of x, adds 3 to it, and then takes the absolute value of the resulting quantity.

If any created vertical line may cross a graph just once, it is said to be a function. If there are any points on the graph where a vertical line can pass through more than once, it is not a function.

To find the function g(x) that is a translation 3 units left of f(x) = |x|, we can start with the function f(x) = |x| and make the following transformation:

Move 3 units to the left: This means we need to subtract 3 from the input of f(x), so we get f(x + 3).

Therefore, the function g(x) can be defined as:

g(x) = f(x + 3) = |x + 3|

Thus, the function g(x) is the absolute value of the quantity (x + 3), which means that it takes any input value of x, adds 3 to it, and then takes the absolute value of the resulting quantity.

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The function g(x), where g(x) is the translation 3 units left of f(x)=|x| is:

   g(x) = |x+3|.

What is meant by a function?

The characteristic that every input is associated with exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. In mathematics, a function is indicated by a mapping or transformation. Often, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given that the function g(x) is the translation of 3 units left of f(x) = |x|.

To the left means that the translation is horizontal translation.

For any horizontal translation of a graph by a value of x units, the new function can be written as:

                         g(x)  = f(x ± k)

Now for a translation to the left side,

         g(x) = f(x + k)

This is because more units are added to x values.

So for the given question, we can write that

             g(x) = f(x+3) = |x+3|.

Therefore the function g(x), where g(x) is the translation 3 units left of f(x)=|x| is:

   g(x) = |x+3|.

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The statement by Allison that size of the sample space of this compound event is 9 is incorrect because the size of sample space is 18.

The size of sample space for compound event of drawing one marble from bag and rolling number cube is actually 18, not 9.

There are 3 possible outcomes for drawing a marble = (red, blue, or green) and 6 possible outcomes for rolling number cube = (1, 2, 3, 4, 5, or 6),

So, the total number of possible outcomes for compound event is product of number of outcomes for each individual event = (3 × 6 = 18).

The sample space for compound event can be represented as an organized list, with each outcome listed as an ordered pair of form :

{(red, 1), (red, 2), (red, 3), (red, 4), (red, 5), (red, 6), (blue, 1), (blue, 2), (blue, 3), (blue, 4), (blue, 5), (blue, 6), (green, 1), (green, 2), (green, 3), (green, 4), (green, 5), (green, 6)}.

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For Felipe and Helena's final grades, the solution is option C, [74 71].

Using the given values for Q, T, and P weights and Felipe and Helena's grades, calculate their final grades as follows:

Felipe's final grade:

0.40 x 80 + 0.50 x 60 + 0.10 x 90 = 32 + 30 + 9 = 71

Helena's final grade:

0.40 x 70 + 0.50 x 80 + 0.10 x 60 = 28 + 40 + 6 = 74

To represent the final grades for Felipe and Helena in a matrix F, given formula F = WG, where W = matrix of weights and G = matrix of grades:

[0.40 0.50 0.10]   [80 70]

F = WG = [0.40 0.50 0.10] x [60 80]

[0.40 0.50 0.10] [90 60]

Performing matrix multiplication:

[32 + 30 + 9  28 + 40 + 6]

F = WG = [32 + 40 + 6 28 + 40 + 3]

[36 + 25 + 6 36 + 20 + 3]

Simplifying:

[71 74]

F = WG = [78 71]

[67 59]

Therefore, [74 71] for Felipe and Helena's final grades, respectively.

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The correct option is D. The number of accidents is being used as the operational definition of automobile accidents in this study. The independent variable would be gender (male or female), which is used to compare the differences in driving ability between men and women.

Many factors can contribute to the number of automobile accidents a person is involved in, such as driving experience, road conditions, vehicle maintenance, and even weather. Additionally, the number of accidents can be influenced by various personal and social factors, such as age, income, and education level, as well as factors related to the vehicle itself, such as make and model. These factors can all impact driving behavior and the likelihood of being involved in an accident, regardless of gender.

Therefore, using the number of accidents as a measure of driving ability is likely to yield biased results and not representative of the true ability of men or women as drivers. To draw more meaningful conclusions about driving ability, it would be necessary to use a more comprehensive and reliable method for measuring driving skills, such as a standardized driving test or assessment of specific driving skills and behaviors.

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Dr. Marlow wants to learn whether men or women are better drivers. to determine this, she will measure driving ability by examining the number of automobile accidents people have been involved in as a driver. thus, she is using the number of accidents as the number of accidents is the basis of

a. her control group in this study.

b. a theory of good driving.

c. the independent variable in this study.

d. the operational definition of driving ability.

e. a case study examination of driving ability.

Answer:

p²-100q²

Step-by-step explanation:

p(p+10q)-10q(p+10q)

p·p+p(10q)-10q(p+10q)

p·p+p(10q)-10qp-10q(10q)

p·p+10pq-10pq-10q(10q)

p·p+0-10q(10q)

p·p-10q(10q)

p²-100q²

To determine how long it will take for a principal of $1 to become $10 with an annual interest rate of 8.5% compounded continuously, we can use the continuous compound interest formula. Additionally, we will calculate the time it takes for a deposit of $1,000 to grow in an account with monthly interest.

For continuous compound interest, the formula to calculate the final amount (A) is given by\(\(A = Pe^{rt}\)\), where P is the principal, r is the interest rate (in decimal form), and t is the time in years.

For the first scenario, we have P = $1, A = $10, and r = 8.5% = 0.085. Plugging these values into the formula, we get:

\(\(10 = 1e^{0.085t}\)\)

To solve for t, we need to take the natural logarithm (ln) of both sides and isolate t:

\(\(ln(10) = 0.085t\)\\\(t = \frac{ln(10)}{0.085}\)\)

Using a calculator, we find that t is approximately 8.14 years. Therefore, it will take approximately 8.14 years for a principal of $1 to become $10 with continuous compounding at an annual interest rate of 8.5%.

For the second scenario with a deposit of $1,000 and monthly interest, we would need additional information such as the monthly interest rate or the number of months involved to calculate the time required for the deposit to grow.

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Answer:

j.35 times

Step-by-step explanation:

Monica's age is 20 years and her father's age is 52

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Represent Monica's age by x and her father's age by y

y -x = 32 equation 1

y-16= 9(x-16)

= y-16 = 9x -144

y-9x = -144+16

y - 9x = -128 equation 2

subtract equation 2 from 1

-x-( -9x )= 32-(-128)

8x = 160

x = 160/8

x = 20

substitute 20 for x in equation 1

y = 32+x

y = 32+20

y = 52

Therefore Monica's age is 20 and her father's age is 52

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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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