If f(x) = x + 15, find f(3)

Step-by-step explanation:

(b + 3)(b + 7) = ...

= b² + (3 + 7)b + (3•7)

= b² + 10b + 21

Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

To determine the time Edna should leave, we need to subtract the travel time from the desired arrival time.

If Edna needs to be at Jake's party at 2:30 PM and it takes her 23 minutes to drive there, she should leave 23 minutes before 2:30 PM.

To calculate the departure time, we subtract 23 minutes from 2:30 PM:

2:30 PM - 23 minutes = 2:07 PM

Therefore, Edna should leave at 2:07 PM in order to arrive at Jake's party by 2:30 PM

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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The value of the rate of growth in Japan is - 0.55.

From the question above, :Birth rate = 7.7 per thousand

Death rate = 9.8 per thousand

Net migration = 0.55 per thousand

The rate of growth can be calculated using the following formula:

r = (birth rate - death rate) + net migration

Where,r = rate of growth

birth rate = number of live births per thousand in a population in a given year

death rate = number of deaths per thousand in a population in a given year

net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year

Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.

Therefore, the rate of growth in Japan is - 0.55.

Your question is incomplete but most probably your full question was:

thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total

population • 100 but im not sure how to do it with net migration.

Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan

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Answer:

x > 8/15

Step-by-step explanation:

x -1/2x + 1/3 > 3/5​

Combine like terms

2/2x - 1/2x +1/3 > 3/5

1/2x   + 1/3 > 3/5

Subtract 1/3 from each side

1/2x + 1/3 -1/3 > 3/5 -1/3

1/2x  > 3/5 -1/3

Get a common denominator

1/2x > 9/15 - 5/15

1/2x > 4/15

Multiply each side by 2

2 * 1/2x > 4/15 * 2

x > 8/15

Answer:

Step-by-step explanation:

The minute hand of a clock overtakes the hour hand at intervalsof M minutes of correct time. The clock gains or loses in a day by=(720/11−M)(60×24/M) minutes.

Here M = 64. The clock gains or losses in a day by

=(720/11−M)(60×24/M)=(720/11−64)(60×24/64)

=16/11(60×3/8)=2/11(60×3)=360/11=32(8/11) minutes.

The average water level in Boston Harbor over the 24-hour period is 7.2 feet.

To find the average water level in Boston Harbor over the 24-hour period, we need to calculate the average value of the function H(t) over the interval [0, 24]. The Mean Value Theorem for Integrals states that if f(x) is continuous on the interval [a, b], then there exists a number c in the interval (a, b) such that the average value of f(x) over [a, b] is equal to f(c).

In our case, the function H(t) = 4.8 sin[(π/6)(t - 10)] + 7.6 is continuous over the interval [0, 24]. To find the average value, we integrate H(t) over the interval [0, 24] and divide by the length of the interval.

Let's calculate the integral first:

∫[0,24] H(t) dt = ∫[0,24] (4.8 sin[(π/6)(t - 10)] + 7.6) dt

Using the antiderivative of the sine function and evaluating the integral over the interval [0, 24], we get:

= [-9.6 cos[(π/6)(t - 10)] + 7.6t] evaluated from 0 to 24

= (-9.6 cos[4π] + 7.6 * 24) - (-9.6 cos[0] + 7.6 * 0)

= (-9.6 + 182.4) - (-9.6)

= 172.8

The length of the interval [0, 24] is 24 - 0 = 24.

Therefore, the average water level over the 24-hour period is:

Average = (1/(24 - 0)) * ∫[0,24] H(t) dt

= (1/24) * 172.8

= 7.2

To determine the times of the day when the water level equals the average, we need to find the values of t that satisfy H(t) = 7.2. We can solve this equation:

4.8 sin[(π/6)(t - 10)] + 7.6 = 7.2

Simplifying the equation, we have:

4.8 sin[(π/6)(t - 10)] = 7.2 - 7.6

4.8 sin[(π/6)(t - 10)] = -0.4

Dividing by 4.8, we get:

sin[(π/6)(t - 10)] = -0.4/4.8

sin[(π/6)(t - 10)] = -1/12

To find the values of t, we can take the arcsine (inverse sine) of both sides:

(π/6)(t - 10) = arcsin(-1/12)

Solving for (t - 10), we have:

(t - 10) = (6/π) * arcsin(-1/12)

Finally, solving for t:

t = (6/π) * arcsin(-1/12) + 10

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The line in the scatterplot is not a good representation of the data.

Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.

A scatterplot is used to visualize the relationship between two variables and the line doesn't provide any insight into that relationship. The points in the scatterplot are scattered and there is no discernible pattern to the points that would suggest the line is a good representation of the data. Additionally, the line is not continuous and varies in slope, suggesting that it is not a good fit for the data. Therefore, the line does not provide a good representation of the data and should be removed.

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Answer:

7 bananas

Step-by-step explanation:

Step-by-step explanation:

Applying Pythagoras theorem ,

\({24}^{2} = {11}^{2} + {x}^{2} \\ 576 = {121} + {x}^{2} \\ {x}^{2} = 576 - 121 \\ {x}^{2} = 455 \\ x = \sqrt{455} \\ x = 21.33\)

Step-by-step explanation:

3x + 8y + 5

The true statements

5 is a constant

3x + 8y + 5 is written as a sum of three terms

3x and 5 are like terms

The x-value of the solution is -2.

To find the x-value of the solution to the given system of equations, we can solve the system by elimination or substitution method.

Let's solve it using the elimination method:

Multiply the second equation by -1:

-1(x + y) = -1(1)

This simplifies to:

-x - y = -1

Now, we can add the two equations together to eliminate the y term:

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

This simplifies to:

2x = -4

Divide both sides by 2:

x = -4/2

x = -2

Therefore, the x-value of the solution is -2.

The correct answer is A. -2.

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Answer:

87 million

Step-by-step explanation:

Every 2 months the money increases by 18million.

45 - 27 = 18

18 + 18 + 6 = 42

45 + 42 = 87

A system of linear inequalities represented by the graph are;

y > x - 2

y < 5x + 1

The general form of the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

The broken(dashed line) has the y-intercept as -2.

The slope is;

m = (0 - (-2))/(2 - 0)

m = 1

However, it is shaded above the line which means the equation is;

y > x - 2

The second line which is a solid line has the y-intercept as 1.

The slope is calculated as;

m = (-4 - 1)/(-1 - 0)

m = 5

The shaded part is below the line which denotes;

y < 5x + 1

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Answer:

- 7\(x^{6}\)\(y^{9}\)

Step-by-step explanation:

using the rule of exponents

\(a^{m}\) × \(a^{n}\) = \(a^{(m+n)}\)

given

- 7x³\(y^{5}\) (x³\(y^{4}\))

= - 7 × x³ ×x³ ×\(y^{5}\) × \(y^{4}\)

= - 7 × \(x^{(3+3)}\) × \(y^{(5+4)}\)

= - 7\(x^{6}\)\(y^{9}\)

To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

Using the tangent function, we can set up the following equation: tan(40°) = opposite/adjacent. tan(40°) = distance between the buildings/20 meters. To find the distance between the buildings, we rearrange the equation: distance between the buildings = 20 meters * tan(40°). Using a calculator, we can evaluate the expression: distance between the buildings ≈ 20 meters * 0.8391 ≈ 16.782 meters. Therefore, the buildings are approximately 16.782 meters apart. To determine the distance between the buildings, we can use trigonometry and the given information. Let's consider the triangle formed by Sari, building A, and building B. The side opposite the 40° angle is the distance between the buildings that we want to find.

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Answer:

they are 4 i think

Step-by-step explanation:

5 x 4 = 20

Answer:

100

Step-by-step explanation:

20 divided by 1/5 = 20 x 5/1 = 100

Answer:

D.3

Step-by-step explanation:

We are going to use the Slope Formula --> (y2-y1)/(x2-x1)

(9-3)/(3-1)=6/2=3

Answer:

I belive the answer is 96 ft.

Step-by-step explanation:

Hope that helps!

Among the mentioned options, Sandra's equation is –6x + 2y = 3/2

Based on the mentioned options, the one with negative sign with 6x will be the possible correct choices. The reason is, while shifting the value on Right Hand Side, the sign will change. So, we are left with the options -

-6x + y = 3/2 and -6x + 2y = 3/2

Now, here if we taken the option, the equation will have coefficients 6 and 3/2. However, in the second option, we will have to divide the expression by 2, which will give equal answer.

Calculation is as follows -

2y = 6x + 3/2

Dividing the equation by 2

y = 3x + 3/4, which is the same as Tomas' equation.

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The complete question is -

Tomas wrote the equation y = 3x +3/4. When Sandra wrote her equation, they discovered that her equation had all the same solutions as Tomas’s equation. Wzu ab, hich equation could be Sandra’s?

–6x + y = 3/2

6x + y = 3/2

–6x + 2y = 3/2

6x + 2y = 3/2

Based on the information given line A is x to infinity, y to infinity, while line B is x to infinity, y to negative infinity.

Let's start by analyzing the functions provided, to understand what happens with the y-coordinate as the x-coordinate moves:

Line A: y = 3x + 5

In this case, y and x are proportional, which means both will increase in the same direction and have an infinity behavior,

Line B: y= -6x +1

In this case, due to x being negative it is expected y becomes negative to infinity.

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Answer:

\(x=1\) ± \(i\sqrt{19}\)

Step-by-step explanation:

First off let's state the quadratic formula

Quadratic formula

\(\frac{-b+\sqrt{b^2-4ac} }{2a}\)

\(\frac{-b-\sqrt{b^2-4ac} }{2a}\)

For this question our quadratic equation is

\(x^2+20=2x\)

Now before we can apply the quadratic formula we first have to set the equation equal to zero. We do this my moving everything to one side and setting it equal to zero.

In this case, we simply move the 2x to the other side making it negative and setting the equation equal to zero.

\(x^2-2x+20=0\)

From here we plug in the values to the quadratic equation.

Now incase you don't know

\(a =\) Coefficient of \(x^2\) value

\(b=\) Coefficient of \(x\) value

\(c=\) The Constant

Now plug in values

\(a=1\)

\(b=-2\)

\(c=20\)

To get the values of x using the quadratic formula we have the plug in the values, we also have to both subtract and add the \(\sqrt{b^2-4ac}\) to \(-b\)

Plug in values into formula

\(\frac{2+\sqrt{(-2)^2-4(1)(20)} }{2(1)}\)

\(\frac{2+\sqrt{-76} }{2}\)

\(\frac{2+\sqrt{-1} *\sqrt{76} }{2}\)

\(\frac{2+i *\sqrt{76} }{2}\)

\(\frac{2+i *\sqrt{4(19)} }{2}\)

\(\frac{2+i *\sqrt{2^2(19)} }{2}\)

\(\frac{2+2i \sqrt{19} }{2}\)

\(x=1+i\sqrt{19}\)

Now repeat the steps except subtract from -b rather than add to it.

Final Answer

\(x=1\) ± \(i\sqrt{19}\)

BTW

± = plus and minus

The situation given in the question occurs due to the lower mortality rate which is seen in women of the age group 50-60.

Discrepancies between men and women's death rates and life expectancy. In general, women live longer than males. This means that, assuming everything else is equal, we should anticipate that women will make up somewhat more than half of the population.

Birth sex ratios are not equal. Males outnumber female births in every country. This means that, assuming everything else is equal, we should anticipate that men will make up somewhat more than half of the population.

The population's gender distribution can be impacted through migration. All other things being equal, we would anticipate that men would make up more than 50% of the population if some countries import a sizable amount of male-dominated labor.

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(A) This differential equation is not separable, but it is homogeneous since the degree of both terms in the brackets is the same and equal to \($2.$\) (B) The solution to the given differential equation is: \($$\boxed{y^2 = \frac{Cx^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})}$$\) where \($C$\) is the constant of integration. (C) The solution to the initial value problem is: \($$y^2 = \frac{(2\ln(5) + 8)x^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})$$\)

a) To determine whether the differential equation is separable or homogenous, let us check whether the equation can be written in the form of:

\($$N(y) \frac{dy}{dx} + M(x) = 0$$\) or in the form of:

\($$\frac{dy}{dx} = f(\frac{y}{x})$$\)

For the given equation:

\($$(x^2 + y^2) + 2xy \frac{dy}{dx} = 0$$\)

Upon dividing both sides by:

\($x^2$,$$\frac{1}{x^2}(x^2 + y^2) + 2 \frac{y}{x} \frac{dy}{dx} = 0$$or$$1 + (\frac{y}{x})^2 + 2 \frac{y}{x} \frac{dy}{dx} = 0$$\)

This equation is not separable, but it is homogeneous since the degree of both terms in the brackets is the same and equal to \($2.$\)

b) We can solve the given differential equation using the method of substitution.

First, let \($y = vx.$\)

Then, \($\frac{dy}{dx} = v + x \frac{dv}{dx}.$\)

Substituting these values into the equation, we get:

\($$x^2 + (vx)^2 + 2x(vx) \frac{dv}{dx} = 0$$$$x^2(1 + v^2) + 2x^2v \frac{dv}{dx} = 0$$$$\frac{dv}{dx} = -\frac{1}{2v} - \frac{x}{2(1 + v^2)}$$\)

Now, this differential equation is separable, and we can solve it using the method of separation of variables.

\($$-2v dv = \frac{x}{1 + v^2} dx$$$$-\int 2v dv = \int \frac{x}{1 + v^2} dx$$$$-v^2 = \frac{1}{2} \ln(1 + v^2) + C$$$$v^2 = \frac{C - \ln(1 + v^2)}{2}$$$$y^2 = \frac{Cx^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})$$\)

Therefore, the solution to the given differential equation is:

\($$\boxed{y^2 = \frac{Cx^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})}$$\)

where \($C$\) is the constant of integration.

c) Given the differential equation above and \($y(1) = 2,$\) we can substitute \($x = 1$ and $y = 2$\) in the solution equation obtained in part (b) to find the constant of integration \($C\).

\($$$y^2 = \frac{Cx^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})$$$$2^2 = \frac{C \cdot 1^2}{2} - \frac{1^2}{2} \ln(1 + \frac{2^2}{1^2})$$$$4 = \frac{C}{2} - \frac{1}{2} \ln(5)$$$$C = 2\ln(5) + 8$$\)

Thus, the solution to the initial value problem is: \($$y^2 = \frac{(2\ln(5) + 8)x^2}{2} - \frac{x^2}{2} \ln(1 + \frac{y^2}{x^2})$$\)

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By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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