Which of the following is true regarding functions
Check all that apply

{} the vertical line test may be used to determine whether a function is one- to- one.

{} the horizontal line test may be used to determine whether a function is one- to- one.

{} a function is a relation in which each value of the input variable is paired with exactly one value of the output variable.

{} a sequence is a function whose domain is the set of real numbers

Solution.

Initial population = 205

After 1 year, population = 205 - 7 = 198

After 2 years , population = 198 - 7 = 191

After 3 years , population = 191 - 7 = 184

We can generate a table of value for the changes

One point on the line = (0, 205)

The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park

Answer:

Step-by-step explanation:

bbbbbbbbbbb

Answer:

upwards or to the right

Step-by-step explanation:

If the a value is positive, then the parabola opens upward or to the right, and if the a value's negative, it opens down or to the left. Hope this helps!

No, lecture notes collected during a bachelor degree study are not a type of date. Lecture notes are a collection of the notes taken by a student during the lectures in the course of their bachelor degree study.

They are not the same as dates, which are the specified days on which something happens or is planned to happen. Lecture notes are usually written in the form of summaries of a lecture, which are usually made up of the important points that the student has noted down during the lecture.

They may also include diagrams, equations, and other visual aids that the student has used to illustrate the material covered. Lecture notes are not the same as dates, as they are not related to any specified days. They are simply summaries of the lecture topics discussed by the professor in the course of the student’s bachelor degree study.

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Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11,.The length of fd is 2.28.

we can use the property that corresponding sides of similar triangles are proportional to find the length of side fd. let's set up the proportion:

ab/de = bc/ef = ac/df

plugging in the given values, we get:

11/3.3 = 7.9/ef = 7.6/fd

simplifying, we get:

fd = (7.6 x 3.3) / 11fd = 2.28 answer choice c. 2.28 is the correct answer.

Triangle ABC ~ triangle DEF. triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled

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The equation for the hyperbola with foci (0,±5) and asymptotes y=± 3/4 x is:

y^2 / 25 - x^2 / a^2 = 1

where a is the distance from the center to a vertex and is related to the slope of the asymptotes by a = 5 / (3/4) = 20/3.

Thus, the equation for the hyperbola is:

y^2 / 25 - x^2 / (400/9) = 1

or

9y^2 - 400x^2 = 900

The center of the hyperbola is at the origin, since the foci have y-coordinates of ±5 and the asymptotes have y-intercepts of 0.

To graph the hyperbola, we can plot the foci at (0,±5) and draw the asymptotes y=± 3/4 x. Then, we can sketch the branches of the hyperbola by drawing a rectangle with sides of length 2a and centered at the origin. The vertices of the hyperbola will lie on the corners of this rectangle. Finally, we can sketch the hyperbola by drawing the two branches that pass through the vertices and are tangent to the asymptotes.

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Answer:

Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Step-by-step explanation:

Given that:

A standard deck of 52 playing cards with 4 suits.

A be the event of drawing a card with 6 from the deck.

B be the event of drawing a black card from the deck.

So, event A will have 4 possibilities i.e. {6 of club, 6 of spade, 6 of diamond, 6 of heart}

And event B will have 26 possibilities {Any card (including 6) from club or spade}

Intersection of two sets is defined as the common elements in the two sets.

As per the explanation of the sets and elements in the sets given above:

If we take intersection it will be:

{6 of club or 6 of spade}

Hence, Correct answer is option D) drawing the 6 of clubs or the 6 of spades

Answer:

drawing the 6 of clubs or the 6 of spades is the right answer

Step-by-step explanation:

Answer:

ƒ(−1) = −3

Explanation:

From the graph, we have the point (-1, -3).

This means that:

• When x=-1

• The value of f(x)=-3.

Therefore, the value of f(-1) is -3.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be $605.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Here, Mae Ling earns a weekly salary of $365 plus a 5.0% commission on sales at a gift shop.

The amount that she make in a workweek if she sold $4,800 worth of merchandise will be:

= $365 + (5% × $4800)

= $605

The amount is $605.

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The slope-intercept form will be easier to write the equation of the line.

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

The equation of the line for the slope and intercept form is y = mx + c. Where m is the slope of the line and c is the y-intercept of the line.

Therefore, the slope-intercept form will be easier to write the equation of the line.

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Based on the calculations, Lainie's total earnings is equal to $323.7975.

Based on the information provided about the number of days that Lainie worked, we have:

Total number of days = 4 1/2 days.

Total number of days = 9/2 days.

Total number of days = 4.5 days.

For the number of days that Lainie worked, we have:

Total number of hours = 5 1/3 hours.

Total number of hours = 16/3 hours.

Total number of hours = 5.33 hours.

Now, we can calculate the amount of money that was earned by Lainie for her work during this period of time:

Total earnings = Hourly rate × Total number of hours × Total number of days

Substituting the given parameters into the formula, we have;

Total earnings = $13.50 × 5.33 × 4.5

Total earnings = $323.7975.

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The x-coordinate for the center of gravity is 16.1, and the y-coordinate is 15.4 which is determined using average.

To find the center of gravity (also known as the centroid), we need to calculate the weighted average of the x and y coordinates using the given data points and their respective weights. The weights are represented by the "dc coordinates demand a" value for each data point.

Let's calculate the x-coordinate first:

x-coordinate = (1040 + 2525 + 830 + 1120 + 25*6) / (40 + 25 + 30 + 20 + 6) = 16.1

Now let's calculate the y-coordinate:

y-coordinate = (1240 + 3025 + 1530 + 2011 + 6*25) / (40 + 25 + 30 + 20 + 6) = 15.4

Therefore, the center of gravity is located at approximately (16.1, 15.4) in terms of x and y coordinates.

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Answer:

See below!

Step-by-step explanation:

1) 720cm - m

2) 983 mm - m

3) 130.5kL - L

4) 0.03 g - mg

5) 997 g - kg

6) 9.1 l - ml

7)3.75 c - ml

8) 41.8 in - cm

9) 156.25 lb - kg

10) 9.5 gal - l

11) 680.4 g - lb

12) 4.725 m - ft

Hope this helps, have a lovely day! :)

To solve the given initial value problem using Laplace transforms, we first take the Laplace transform of the given differential equations and apply the initial conditions. By manipulating the transformed equations, we can solve for the Laplace transforms of the variables x(t) and y(t). Finally, we use the inverse Laplace transform to obtain the solutions for x(t) and y(t).

The initial value problem consists of two coupled first-order linear ordinary differential equations. To solve these equations using Laplace transforms, we take the Laplace transform of both equations and apply the initial conditions.

Taking the Laplace transform of the first equation, we obtain sX(s) - x(0) + 2sY(s) = 0, where X(s) and Y(s) are the Laplace transforms of x(t) and y(t) respectively, and x(0) is the initial condition for x(t). Similarly, taking the Laplace transform of the second equation, we get sY(s) - y(0) - X(s) + Y(s) = 0, where y(0) is the initial condition for y(t).

Next, we substitute the initial conditions x(0) = 0 and y(0) = 196 into the transformed equations. This allows us to solve for X(s) and Y(s) in terms of the Laplace variable s. After obtaining the Laplace transforms of x(t) and y(t), we use partial fraction decomposition and inverse Laplace transform techniques to find the solutions x(t) and y(t) in the time domain.

The full solution process involving the manipulation of the Laplace transforms and the inverse Laplace transform would require more detailed calculations and specific equations. Without further information, it is not possible to provide a specific solution for x(t) and y(t) or a detailed step-by-step explanation.

In summary, to solve the given initial value problem using Laplace transforms, we would take the Laplace transform of the differential equations, apply the initial conditions, solve for the Laplace transforms of x(t) and y(t), and then use inverse Laplace transforms to obtain the solutions in the time domain.

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Each cutting machine cuts 105 parts every 3 minutes. There are 5 cutting machines because one cutting machine is shut down.

In order to determine how many parts the 5 cutting machines cut in 4 1/2 hours, multiply the factor 105/3 by 5 (number of cutting machines) by the factor 4 1/2 but in minutes:

4 1/2 = 4.5 hours = 4.5 (60 min) = 270 min

then,

(5)(105 parts/ 3min)(270 min) = 47,250

Hence, in 4 1/2 hours the rest of the cutting machines cut 47,250 parts

Answer:y-24

Step-by-step explanation:

Answer:

y-24

Step-by-step explanation:

(4y-2)+(-3y-22) step 1: multiply + to -

+(-2) +(-3y) +(-22)

4y-2-3y-22  step 2: subtract 3y to 4y and subtract 2 from -22

(4y-3y) + (-22-2)

1y-24

y-24

The value of x is either 3 or -5 based on the distance formula.

What is a co-ordinate system?

In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.

Main body:

according to question

Given points A(-1,4) and B(x,7)

Also AB = 5 cm

Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)

here by using points ,

5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)

taking square on both side ,'

25 = \((x+1)^{2} +3^{2}\)

25-9 = (x+1)²

16 = (x+1)²

taking square root on both sides,

x+1= ±4

x = 4-1 = 3                                  or              x = -4-1 = -5

Hence value of x is either 3 or -5.

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          Hello, my name is Snacks, and I will help you out! :-D

For the answer, refer to the "Answer" portion of this answer. For the step-by-step procedure, refer to the "Procedure" portion of this answer.

Thank you.

So, let's start.

\(\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\square\)

"Answer" portion ↓

\(\frak{14x+8}\)

"Procedure" portion ↓

Let's take a look at our problem, it says we need to find the perimeter of the rectangle; luckily, we have all the info we need!

This is the perimeter formula:

⇒\(\frak{Perimeter_{rectangle}=2(a+b)}\)

So basically, it says we need to take the rectangle's length (a), add it's width (b), and multiply their sum times two, and this is equal to the perimeter.

The problem tells us that:

⇒ Length 5x+5

⇒ Width 2x-1

As the equation says, we should add the length and the width:

⇒ 5x+5+2x-1

⇒5x+2x+5-1

⇒7x+4

· Hooray! We found the perimeter!

× Actually, we didn't find the perimeter, yet! Remember, we also need to multiply by 2.

Multiplication results in

⇒ 2(7x+4)

expanding the expression

⇒14x+8

· Now we did find the perimeter, and what's more, we've written it in simplest form.

\(\mathbb{LUSCIOUS\:SNACKS} -\:Greetings\:!\)

--

After cutting the four pieces of fencing for the dog run, there will be approximately 33.5 meters of fencing left on the roll.

The amount of fencing left on the roll, we need to determine the total length of the four pieces cut from the roll and subtract it from the initial length of the roll (50 meters).

The perimeter of the dog run can be calculated by summing the lengths of all four sides. For a rectangle with width 340 cm and length 1380 cm, the perimeter is given by 2 * (width + length), which equals 2 * (340 cm + 1380 cm) = 2 * 1720 cm = 3440 cm.

To convert the perimeter from centimeters to meters, we divide by 100: 3440 cm / 100 = 34.4 meters.

Therefore, the total length of the four pieces cut from the roll is approximately 34.4 meters. Subtracting this from the initial length of 50 meters gives us the remaining fencing on the roll: 50 meters - 34.4 meters = approximately 15.6 meters. Hence, approximately 33.5 meters of fencing will be left on the roll after cutting the four pieces.

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The solution to the separable differential equation y' = 3yx^2, in implicit form, is log |y| = x^3 + c, where c represents the constant of integration.

To solve the separable differential equation y' = 3yx^2, we start by separating the variables. We can rewrite the equation as y'/y = 3x^2. Then, we integrate both sides with respect to their respective variables.

Integrating y'/y with respect to y gives us the natural logarithm of the absolute value of y: log |y|. Integrating 3x^2 with respect to x gives us x^3.

After integrating, we introduce the constant of integration, denoted by c. This constant allows for the possibility of multiple solutions to the differential equation.

Therefore, the solution to the differential equation in implicit form is log |y| = x^3 + c, where c represents the constant of integration. This equation describes a family of curves that satisfy the original differential equation. Each choice of c corresponds to a different curve in the family.

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Answer:

Your answer is 7 so it's D

Step-by-step explanation:

The answer is 3 1/3 feet

Solution :

Total length of material : 13 1/3 feet

Number of sections needed : 4

so the length of new sections = Total length ÷ No. of section

                                                  = 13 1/3 ÷ 4

             13 1/3 = 40/3

so,         40/3 ÷ 6

that is    40/3 × 1/6

            = 40/12

            = 3.33 or  3 1/3

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The confidence interval at a 90 % confidence level is given as: 47.3 < μ < 48.7

Find the value of μ using the z-value formula.

z(α/2) = (x - μ) / (s / √n)

where, z(α/2) = z-value for the level of confidence α/2 = 1 - (Confidence level/100) x = sample means = population standard deviationn = sample sizes = 25, 48s = standard deviation = 2

For 90% confidence level,

α/2 = 1 - (Confidence level/100)

= 1 - 0.9

= 0.1

From the standard normal table,  z-value for 0.05 is 1.645.

Putting these values in the above formula,

,1.645 = (x - μ) / (2 / √25)

Therefore,x - μ = 1.645 x (2/5)

x - μ = 0.658

μ = x - 0.658

μ = 48 - 0.658

= 47.342

Hence, the confidence interval at a 90 % confidence level is given as: 47.3 < μ < 48.7 (approx)

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The probability of certainty is 100%=1

If Probability(p)=0.34

then

Probability (p) +cProbability (!p) = 1 where !p is used to denote "not "p

0.34+Probability(!p)=1

Probability(!p)=1−0.34=0.66

The probability that the event will not happen is 0.66.

The probability of an event can be defined as the chance of happening that particular event.

The probability that the event will happen is P(E) = 0.34.

Therefore, the probability that the event will not happen is

= 1 - P(E)

= 1 - 0.34

= 0.66

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The opportunity cost of cheese in the home country is 2 gallons of wine per pound of cheese, while in the foreign country, it is 0.5 pounds of cheese per gallon of wine.

The opportunity cost of a good represents the value of the next best alternative that must be given up producing or consume that good. In the home country, producing 1 pound of cheese requires giving up the opportunity to produce 2 gallons of wine. Therefore, the opportunity cost of cheese in the home country is 2 gallons of wine per pound of cheese. In the foreign country, producing 1 gallon of wine requires giving up the opportunity to produce 0.5 pounds of cheese. Hence, the opportunity cost of cheese in the foreign country is 0.5 pounds of cheese per gallon of wine.

To construct the world relative supply (RS) curve, we need to compare the relative labor requirements of cheese and wine production between the home and foreign countries. The relative labor requirement is obtained by dividing the labor requirement for one good by the labor requirement for the other good. In this case, we divide the unit labor requirements of cheese by the unit labor requirements of wine. For the home country, the relative labor requirement is 1 hour of cheese per 2 hours of wine, and for the foreign country, it is 2 hours of cheese per 1 hour of wine.

The world relative supply (RS) curve shows the combinations of cheese and wine that can be produced globally given the available labor supply in both countries. It is derived by combining the relative labor requirements of the two countries. By plotting different combinations of cheese and wine production on the RS curve, we can observe the trade-off between the two goods and the potential gains from trade.

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Answer:

2y

Step-by-step explanation:

2x-3=2y

2x-2y=3

Answer:

x = 3, y = 1.5

Step-by-step explanation:

Given the 2 equations

x + 2y = 6 → (1)

2x - 3 = 2y → (2)

In (2) subtract 2y from both sides and add 3 to both sides

2x - 2y = 3 → (3)

Adding (1) and (3) term by term will eliminate the y- term

3x = 9 ( divide both sides by 3 )

x = 3

Substitute x = 3 into either of the 2 equations and solve for y

Substituting into (1)

3 + 2y = 6 ( subtract 3 from both sides )

2y = 3 ( divide both sides by 2 )

y = 1.5

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer: 0.2 cm/yr

Step-by-step explanation:

simply divide centimeters by years

25.0 cm ÷ 125 yr

0.2 cm/yr ... answer



The rate of uplift is 0.2 cm/yr

hope that helps...

The solution to the given system of equations is x = 3 and y = 1.

To solve the system of equations, we can use the method of elimination. Multiply the first equation by 3 and the second equation by 4 to make the coefficients of x in both equations the same:

(12x - 15y = 51)

(12x + 16y = 20)

Now, subtract the second equation from the first equation:

(12x - 15y) - (12x + 16y) = 51 - 20

-15y - 16y = 31

Combine like terms:

-31y = 31

Divide both sides of the equation by -31:

y = 1

Substitute the value of y back into one of the original equations to find x:

4x - 5(1) = 17

4x - 5 = 17

4x = 22

x = 22/4

x = 11/2

x = 3

Therefore, the solution to the system of equations is x = 3 and y = 1.

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