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On solving the provided question, we can say that from the graphs The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations οr charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue tοgether the nodes, οften referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of expοnential growth. a logarithmic graph in the shape οf a triangle

The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technοlogical advancement.

Priοr to technological advancement, the opportunity cost of treating HIV/AIDS rises as the wοrld deviates from its PPF. The pοtential cost of treating more HIV/AIDS cases falls as a result of technοlogical advancements since less other commοdities and services must be sacrificed in οrder to treat more HIV/AIDS patients. Alternatively, the world might treat mοre HIV/AIDS patients right now by forgoing the same number of other commοdities and services.

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Answer:

3,641 cups drank

Step-by-step explanation:

A quart is 4 cups

At the start of the party, there were 912 quarts, multiply that by 4 to get 3,648 cups

At the end of the party, only 7 cups remained

3648 - 7 = 3,641 cups drank

(a) W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.

(b) W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.

(c) We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5

What is the quadratic equation?

The quadratic equation is a formula used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable.

(a) To find the locally linear approximation of W at t=3, we first need to find W(3) and W'(3).

We know that at time t=3, the volume of water in the tub is 2.5 cubic feet. Therefore, W(3) = 2.5.

To find W'(3), we need to use the fact that the rate of change of the volume of water in the tub is equal to the rate of water flowing in minus the rate of water leaking out.

So, W'(t) = F(t) - L(t).

At time t=3, we have F(3) = arctan(π/2 - 3/10) ≈ 1.383 cubic feet per minute, and L(3) = 0.03(20*3 - 3² - 75) = 0.9 cubic feet per minute. Therefore, W'(3) = 1.383 - 0.9 = 0.483 cubic feet per minute.

The locally linear approximation of W at t=3 is given by:

W(t) ≈ W(3) + W'(3)(t-3)

W(t) ≈ 2.5 + 0.483(t-3)

To approximate the volume of water in the tub at time t=3.5, we plug in t=3.5 into the above equation:

W(3.5) ≈ 2.5 + 0.483(0.5) ≈ 2.7625 cubic feet.

(b) To find W''(8), we first need to find an expression for W'(t). We know that:

W'(t) = F(t) - L(t)

Taking the derivative with respect to t:

W''(t) = F'(t) - L'(t)

We know that F(t) = arctan(π/2 - t/10), so F'(t) = -1/(10π/4 - t²/100 + t/5²) * (1/5), where we used the chain rule and the derivative of arctan(x) = 1/(1+x²). Evaluating this expression at t=8, we get F'(8) ≈ -0.0397 cubic feet per minute.

We also know that L(t) = 0.03(20t - t²- 75), so L'(t) = 0.03(20 - 2t). Evaluating this expression at t=8, we get L'(8) = -0.6 cubic feet per minute.

Therefore, W''(8) ≈ -0.0397 - (-0.6) ≈ 0.5603 cubic feet per minute per minute.

Interpreting the meaning of W''(8), we see that it represents the rate of change of the rate of change of the volume of water in the tub at time t=8. Specifically, W''(8) tells us how quickly the volume of water in the tub is changing with respect to time at time t=8 is changing.

(c) Yes, there is a time t for which the volume of water in the tub is neither increasing nor decreasing. This occurs when the rate of water flowing into the tub is equal to the rate of water leaking out. That is, we need to find a value of t such that F(t) = L(t).

We can solve for t numerically using a graphing calculator or other numerical method. One possible solution is t ≈ 5

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The triangles ΔPQM and ΔPRM are congruent. Then angle Q is identical to angle R.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The line segment PM is the median of the isosceles triangle ΔPQR.

Point M is the midpoint of QR by the definition of the median.

In triangles ΔPQM and ΔPRM, then we have

PQ = PR                   {Given}

QM = RM                 {Mid point}

MP = MP                  {Reflexive property}

The triangles ΔPQM and ΔPRM are congruent to each other by SSS postulates.

∠Q = ∠R

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The complete question is given below.

The line segment PM is the median of the isosceles triangle ΔPQR. Drag and drop a statement or reason to each box to complete the proof.

Given: PQ ≅ PR

Prove: ∠Q ≅ ∠R

The time it takes the bicycle to travel along the road is 20 seconds.

The rate of change of position of an object in any direction is called as Speed.

The formula for speed is Distance divided by Time.

So Time = distance / speed

we need to know the distance the bicycle travels to use this formula.

If we have this distance, we can divide it by the speed of 5 m/s to find the time.

Let the distance is 100 meters, then the time taken is:

time = distance / speed = 100 / 5 = 20 seconds

Hence, the time it takes the bicycle to travel along the road is 20 seconds.

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The complete question is given below:

A bicycle travels along with the road at an average speed of 5 m/s work out the time it takes the bicycle to travel along the road of distance 100 meters.

Give your answer in seconds

In the division example at the right A and B represent different digits. The sum of A and B if the remainder is zero is 8.

This is one of the four basic mathematical operations and it is the process of splitting a number or an amount into equal parts.

The table shows all possible answers for A÷B with no remainder when digits from 1-9 for A and B are considered.

Since A is not equal to B such as  A=6, B=2, divides it with no remainder. Therefore the sum of A and B is 8, so the cell (6,2) contains 8.

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The same shape and similar are relationship between ΔXYZ and ΔUVW options (A) and (D) are correct.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We have given two triangles with dimensions.

Take the ratio of the corresponding sides:

12/24 = 5/10 = 13/26 = 1/2

The ratios of the corresponding sides are same which means the triangle are similar and having same shape.

Hence, the same shape and similar are relationship between ΔXYZ and ΔUVW option (A) and (D) are correct.

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The complete question is in the attached image.

The slope of the line on the graph is equal to: A. -1/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Based on the information provided, we can logically deduce the following data points on the line:

Points on x-axis = (-2, 4).

Points on y-axis = (2, 0).

Substituting the given data points into the slope formula, we have the following;

Slope, m = (0 - 2)/(4 + 2)

Slope, m = -2/6

Slope, m = -1/3.

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Answer:

The total possible outcomes that exist are:

                            2400

Step-by-step explanation:

We are given four dices:

first is a standard 6-faced die.

The second die has 4 faces.

Third dice has 10 faces.

Fourth dice has 10 faces.

Now when all the dice are thrown together then the total number of possible outcomes are:

( Since there are 4 numbers possible for the first die, 6 for second and 10 each for third and fourth)

                   The answer is:

                          2400

piecewise function defines the function graphed between y=2x+3 and y=-1/3x+3.

How to compare linear equations?

The comparison method, a procedure for solving systems of independent equations, starts by rewriting each equation with the same variable as the subject. Any of the variables may be chosen as the first variable to isolate. Each equation is now an isolated-subject equation, and equation where one variable is isolated.

Given:

y = 2x+3

y = -1/3x+3

The left portion of the blue curve is y = 2x+3 but it is only graphed when x < 0 (we could argue that  but I'll set that aside for the other portion).

The right portion is the line y = -1/3x + 3 and it's only graphed when

Both lines have y-intercept 3.

The slopes are 2 and -1/3.

The equations are

y = 2x + 3; y = -1/3 x + 3e could have this piecewise function

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The decimal number is -5.690134489..... irrational number. Therefore, option C is the correct answer.

Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.

Here,

-9.121212121212......

This decimal number is non terminating, but repeating

So, the decimal number is rational number

-1.5000000000.....

This decimal number is non terminating, but only zeros are repeating

So, the decimal number is rational number

-5.690134489.....

This decimal number is non terminating and non repeating

So, the decimal number is irrational number

-9.121212121212....

This decimal number is non terminating, but repeating

So, the decimal number is rational number

Therefore, option C is the correct answer.

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Given the set of statements according to the questions are:

1) 28 ∈ A -  true.

2) 8 ∈ B -  true.
3) 31 ∉ A -  false.
4) 1 ∈ B  - false

What is a set?

In mathematics, a set is a collection of distinct objects or elements that are grouped together as a single entity. The objects in a set can be anything: numbers, people, animals, colors, or even other sets. The elements of a set are usually enclosed in braces, {}.

By using the given data:

A = {28, 29, 30, 31, 32, 33, 34, 35};

B = The set of even numbers greater than or equal to 6 and less than or equal to 12

B = {6, 8, 10, 12}

Now lets find the answer

1) 28 ∈ A - 28 is present in set A hence, this statement is true.

2) 8 ∈ B - 8 is present in set B, hence this statement is true.
3) 31 ∉ A - 31 is present in set A, hence this statement is false.
4) 1 ∈ B - 1 is not present in set B, hence this statement is false.

Hence,

1) 28 ∈ A -  true.

2) 8 ∈ B -  true.
3) 31 ∉ A -  false.
4) 1 ∈ B  - false

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The critical value strategy entails deciding whether or not the observed test statistic is more extreme than would be anticipated if the null hypothesis were true in order to determine whether something is "likely" or "unlikely."

How do you determine the rejection zone and the crucial value?

The rejection zone is the area in which we have sufficient data to reject the null hypothesis if our test statistic falls within it. The rejection area, for the right-tailed test, for instance, is any value bigger than the critical value, or c 1 .

To execute any hypothesis test, the critical value technique entails four specific phases, which are as follows:

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Answer:

Step-by-step explanation:Angles 1 and 2 form a linear pair and are supplementary. So to find m∠2, subtract m∠1 from 180o. m∠2 = 180o - 135o = 45o.

...

Solution

m∠1 + 32 = 90 Substitute 32 for m∠2.

m∠1 = 58 Subtract 32 from each side.

m∠1 + m∠ 2 = 90 Definition of complementary angles.

Answer is B. 
y= 2x -3 y= -2x + 1

step by step

First I found the y intercepts at (red line) -3 and (green line) +1.

There is only one answer that shows these two y intercept values.

 To double check this answer, I checked the slope of each line. The red line has a slope of 2 and the green line has a slope of -2.

Slope was found on the graph finding rise over run and compared to the number next to x in the equations.

See attached graph.

The value of x are:

1)

81/2

2)

33/4

3)

13

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

First question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

45/20 = x/18

9/4 = x/18

x = 18 x 9 / 4

x = 9 x 9/2

x = 81/2

Second question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

22/8 = x/6

11/4 = x/6

x = 6 x 11 / 4

x = 66/4

x = 33/4

Third question:

Since QS is the angle bisector.

We can write as,

PQ/PS = RQ/RS

21/15 = (5x - 16)/(3x - 4)

7/5 = (5x - 16)/(3x - 4)

7(3x - 4) = 5(5x - 16)

21x - 28 = 25x - 80

80 - 28 = 25x - 21x

52 = 4x

x = 13

Thus,

The value of x is 81/2, 33/4, and 13.

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The width of rectangle  = 90 m

And, The length of rectangle = 110 m

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The perimeter of a rectangle is 400 meters.

And, The length is 20 meters longer than the width.

Now, Let the width of rectangle = x

Then, The length of rectangle = x + 20

We know that;

⇒ Perimeter of rectangle = 2 ( Length + width )

Substitute values ,

⇒ 400 = 2 (x + x + 20)

⇒ 400 = 2 (2x + 20)

⇒ 200 = 2x + 20

⇒ 2x = 200 - 20

⇒ 2x = 180

⇒ x = 90

Thus, The width of rectangle = x = 90 m

And, The length of rectangle = x + 20 = 90 + 20 = 110 m

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The equation of the circle is (x -2)² + (y+1)² = 16.

What is an equation of a circle?

A circle is the collection of all points on a plane at a specific radius from a specific point (called the center.) The diameter of a circle is the length of a line that connects two locations on the circle and passes through its center. Assume that a point's coordinates on the shown circle are (x,y). The radius is r, and the center is at (h,k).

Here according to the graph, the center of the circle is (2,-1), and the radius of the circle = 2+2=4 unit.

Now using the circle equation then

(x -p)² + (y-q)² = r²

Where p = 2 , q = -1 and r = 4 then

(x -2)² + (y+1)² = 4²

(x -2)² + (y+1)² = 16

Hence, the equation of the circle is (x -2)² + (y+1)² = 16.

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The required pair of the like fraction among the given fraction is given as 1/3 and 2/6.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

Here,
For pairs of fraction area given we have to determine that fair of like fraction,
So we have to simplify the fraction given in the pair,
1. 4/6 and 5/6 = 2/3 and 5/6which not like pair of fraction, Similarly pairs  [1/2 and 3/4] and [1/10and2/100] are not like fractions.

Now,
3. pair 1/3and2/6 is like fractions because 1/3 = 2/6 (=1/3)

Thus, the required pair of the like fraction among the given fraction is given as 1/3 and 2/6.

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Based on the information, it should be noted that the difference between the scores of the girls and boys aren't significant.

From the information, the average score for boys was 48.4 with standard deviation 12.96 and the girls had an average score

of 48.9 with standard deviation 11.85.

The computed upper limit = 2.1119

The computed lower limit = -3.1119

Since the interval (-3.1119, 2.1119) contains the between the value 0 thus the difference of boys and girls scores isn't significant.

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Answer:

Step-by-step explanation:

To find the number of calories and grams of fiber in a 2/3-cup serving, we can simply multiply the values for a 1/2-cup serving by the appropriate factor. A 2/3-cup serving is 1.5 times larger than a 1/2-cup serving, so we multiply the calorie and fiber content by 1.5.

210 calories * 1.5 = 315 calories

9 grams of fiber * 1.5 = 13.5 grams of fiber

So a 2/3-cup serving would contain 315 calories and 13.5 grams of fiber.

The length of the midsegment of trapezoid is 24 units.

An open, flat figure with four successive sides and one pair of parallel sides is termed to as a trapezoid or trapezium.

The parallel and non-parallel sides of a trapezium are called as the bases and the legs, respectively. A trapezium may also have parallel legs. The parallel sides can be slanted, vertical, or horizontal.

The altitude is the evaluation of the angle perpendicular to the parallel sides.

Now in the given question,

a = 15

b = 23

length of mid segment EF,

[tex]l=\frac{a+b}{2} \\\\l=\frac{15+23}{2} \\\\l=\frac{48}{2} \\\\l=24[/tex]

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The measure of angle R from the triangle PQR is 15.31°.

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

The formula for the cosine rule is c=√(a²+b²-2ab cosC)

In the given triangle PQR, PQ=9 units, PR=12 units and RQ=20 units

PQ²=PR²+RQ² -2×12×20cosR

9²=12²+20² -2×12×20cosR

81=144+400-480cosR

81=544-480cosR

81-544= -480cosR

-463= -480cosR

cosR= 463/480

cosR= 0.9645

∠R=15.31°

Therefore, the measure of angle R is 15.31°.

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Answer: 83%

Step-by-step explanation: Take 250 and divide it by 300

Answer:Steve

Step-by-step explanation:

Answer:

Step-by-step explanation:

Using the ratio of corresponding side lengths, we have:

x/42 = 9/35

y/21 = 9/35

z/35 = 9/35

Solving for x, y, and z:

x = (9/35) * 42 = 14

y = (9/35) * 21 = 7

z = 9

So the other two sides of the smaller triangle are 14 and 7 units.

No, it is impossible to construct a triangle PQR such that QR=3 cm, PQ=6 cm, PR=3 cm as the dimensions defy the triangle inequality theorem.

It follows from the triangle inequality theorem that the sum of any two side lengths of a triangle must be greater than the third side length and also, the difference of two side lengths of a triangle must be less than the third side lengths.

However, in this case, since QR + PR = PQ, it can be inferred that the two side lengths cannot possibly be used to construct a triangle.

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Answer:

Below

Step-by-step explanation:

Center (h,k)   is - 2, -2     radius is   1

Equation for a circle with center (h,k) and radius r    is  :

       (x-h)^2 + (y- k )^2 = r^2   <====you have to learn/remember this

 Plug in the values above to get

(x+2)^2  + (y+2)^2 = 1

Answer:

(x+2)^2+(y+2)^2=0.5625

Step-by-step explanation:

trust

Answer: 30 in

Step-by-step explanation:

To figure out perimeter, you have to add up all of the sides.

The sides of the triangle are 7, 10, and 13 in.

7+10+13=30

The answer is 30 inches.

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