Give a real world example of an object/scenario in which a limit would exists Approximate the limit.

The values of p and q are 3 and 2.

Given:

The equation of the graph is y = pq^x where p and q are positive constants.

From the graph:

curve linear course points are:

(0,3) and (1,6)

substitute points in y = pq^x

3 = pq^0

3 = p*1

p = 3

y = pq^x

6 = pq^1

6 = p*q

6 = 3*q

divide by 3 on both sides

6/3 = 1

q = 2

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The process is capable of producing outputs within the specification limits is true.

There are a number of potential reasons for why the process is not meeting the target value. One possibility is that the target value is too ambitious and is not realistic given the current process capability. Another possibility is that there is some inherent variability in the process that is not being accounted for. It is also possible that there are some external factors that are affecting the process, such as changes in the raw materials or the environment.

The design engineers have established an upper specification limit of 22 and a lower specification limit of 18. This means that they are confident that the process is capable of producing outputs within these limits. However, the fact that the process is consistently averaging 19.8 with a standard deviation of 0.5 suggests that there is some room for improvement.

One potential way to improve the process is to focus on reducing the inherent variability. This can be done by identifying and addressing the sources of variability in the process. Another potential way to improve the process is to reduce the target value. This may be necessary if the current target value is not realistic given the process capability.

It is also important to monitor the process over time to ensure that it is remaining within the specification limits. This will help to identify any potential issues that may arise and allow for corrective action to be taken if necessary.

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A.The process is in statistical control.

B.The process is capable of producing outputs within the specification limits.

C.The process is capable of producing outputs within the tolerance limits.

D.The process is capable of producing outputs within the control limits.

E.The process is capable of producing outputs that are normally distributed. The process is capable of producing outputs within the specification limits

which statement concerning this process is true?

The solution of the inequality: 4 - 2x > 12

is -4 > x

Here we have the following inequality:

4 - 2x > 12

To solve the inequality, we need to isolate the variable x in one of the sides of the inequality.

First, if we add 2x in both sides we will get:

4 > 12 + 2x

Now we can subtract 12 in both sides, then we will get:

4 - 12 > 2x

-8 > 2x

Now we can divide both sides by 2, so we get:

-8/2 > x

-4 > x

That is the solution.

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To find the measure of angle BCD, we need to determine the measure of angle BCA first.

In a regular 20-gon, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a 20-gon, the sum of the interior angles is (20-2) * 180 = 3240 degrees.

Since the 20-gon is regular, each interior angle has the same measure. Therefore, each interior angle of the 20-gon measures 3240 degrees / 20 = 162 degrees.

Angle BCA is one of the interior angles of the 20-gon, so it measures 162 degrees.

Now, in the heptagon BACD, the sum of the interior angles is given by the formula: (n-2) * 180 degrees, where n is the number of sides of the polygon. So, in a heptagon, the sum of the interior angles is (7-2) * 180 = 900 degrees.

Since the heptagon is regular, each interior angle has the same measure. Therefore, each interior angle of the heptagon measures 900 degrees / 7 = 128.571 degrees (rounded to three decimal places).

Angle BCA is one of the interior angles of the heptagon, so it measures 128.571 degrees.

Finally, angle BCD is the difference between angles BCA and BCD: angle BCD = angle BCA - angle BCD = 162 degrees - 128.571 degrees = 33.429 degrees (rounded to three decimal places).

Therefore, angle BCD measures approximately 33.429 degrees.

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Let B, A, and D be three consecutive vertices of a regular 18-gon. A regular heptagon is constructed on \(ABbar\), with a vertex C next to A. Find\(\leqBCD\) ∠\(BCD\) , in degrees.

To determine the degrees of angle BCD in this problem, we must first discover the degree of each interior angle of the 20-gon and the heptagon. Calculating these values, and subtracting them from 180, we find the measure of angle BCD equals to 69.43 degrees.

In this problem, we need to find the measure of angle BCD of a heptagon formed on a side of a regular 20-gon. We have that consecutive vertices B, A, D of 20-gon and vertex C of a heptagon formed on line segment AB is our interest point.

Since A, B, D are consecutive vertices of a regular 20-gon, we first calculate the value of each interior angle using the formula (n-2)×180/n, where n is the number of sides. So the measure of each interior angle of the 20-gon is (20-2)×180/20 = 162 degrees.

The heptagon shares one of its vertices with the 20-gon (i.e., point A). Point C is a neighboring vertex of A in this heptagon. The angles of a regular heptagon are calculated in the same way, using the formula (7-2)×180/7, which gives approximately 128.57 degrees.

Therefore, to calculate the measure of angle BCD, let's note that it equals to (180 - angle BAC) + (180 - angle CAD). Since angles BAC and CAD are parts of the 20-gon and the heptagon respectively, it will be (180 - 162) + (180 - 128.57) = 18 + 51.43 = 69.43 degrees.

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Answer:

1/6 of the bread

Step-by-step explanation:

Given data

Let the amount of the loaf of bread be 1

But they are expected to share half

hence the amount to be shared is= 1/2 bread

The number of children is 3

Hence

=1/2/3

=1/2*1/3

=1/6 bread

Hence each child will get 1/6 of the bread

Answer:

If you mean multiply I think

5y

Step-by-step explanation:

Answer:

-(-45) and -|45|

Step-by-step explanation:

Opposite of a number can also me termed the conjugate of such number. For example, the conjugate (opposite) of a is -a.

Also any value in the modulus sign can either be a negative or positive value. For example |a| can be +a or -a.

According to the question, we are to find the numbers that are equivalent to opposite of -45 i.e which of them are conjugate of -45.

To do this, we are to select the values in the options that will return +45.

Let's look at each option.

For -(-45):

Since the product of two negative sign will give a positive(+), then -(-45) = +45 and hence the value is opposite of -45

For -45:

-45 is a negative value and can never be positive since 45 is not inside a modulus sign. Hence, -45 is not equal to opposite of -45.

For −|−45|, |-45| can only return a positive value since -45 is already in a modulus sign. What the modulus sign will do is convert it to positive value i.e |-45| = 45. Hence -|-45| ≈ -(45) which is not also equivalent to the opposite of-45.

For -|45|:

The value inside modules will return both +45 and -45, hence it can be written as -|45| = -(-45) = +45. This shows that -|45| is also equivalent to the opposite of -45.

Answer:

-(-45) and -|45|

Step-by-step explanation:

Answer:

  5.25 m

Step-by-step explanation:

A diagram can help you understand the question, and can give you a clue as to how to find the answer. A diagram is attached. The problem can be described as finding the sum of two vectors whose magnitude and direction are known.

__

In navigation problems, direction angles are specified a couple of different ways. A bearing is usually an angle in the range [0°, 360°), measured clockwise from north. In land surveying and some other applications, a bearing may be specified as an angle east or west of a north-south line. In this problem we are given the bearing of the second leg of the walk as ...

  N 35° E . . . . . . . 35° east of north

Occasionally, a non-standard bearing will be given in terms of an angle north or south of an east-west line. The same bearing could be specified as E 55° N, for example.

A vector is a mathematical object that has both magnitude and direction. It is sometimes expressed as an ordered pair: (magnitude; direction angle). It can also be expressed using some other notations;

In the latter case, "cis" is an abbreviation for the sum cos(θ)+i·sin(θ), where θ is the direction angle.

Sometimes a semicolon is used in the polar coordinate ordered pair to distinguish the coordinates from (x, y) rectangular coordinates.

__

The first leg of the walk is 3 meters due north. The angle from north is 0°, and the magnitude of the distance is 3 meters. We can express this vector in any of the ways described above. One convenient way is 3∠0°.

The second leg of the walk is 2.5 meters on a bearing 35° clockwise from north. This leg can be described by the vector 2.5∠35°.

The final position is the sum of these two changes in position:

  3∠0° +2.5∠35°

Some calculators can compute this sum directly. The result from one such calculator is shown in the second attachment:

  = 5.24760∠15.8582°

This tells you the magnitude of the distance from the original position is about 5.25 meters. (This value is also shown in the first attachment.)

__

You may have noticed that adding two vectors often results in a triangle. The magnitude of the vector sum can also be found using the Law of Cosines to solve the triangle. For the triangle shown in the first attachment, the Law of Cosines formula can be written as ...

  a² = b² +o² -2bo·cos(A) . . . . where A is the internal angle at A, 145°

Using the values we know, this becomes ...

  a² = 3² +2.5² -2(3)(2.5)cos(145°) ≈ 27.5373

  a = √27.5373 = 5.24760 . . . . meters

The distance from the original position is about 5.25 meters.

_____

Additional comment

The vector sum can also be calculated in terms of rectangular coordinates. Position A has rectangular coordinates (0, 3). The change in coordinates from A to B can be represented as 2.5(sin(35°), cos(35°)) ≈ (1.434, 2.048). Then the coordinates of B are ...

  (0, 3) +(1.434, 2.048) = (1.434, 5.048)

The distance can be found using the Pythagorean theorem:

  OB = √(1.434² +5.048²) ≈ 5.248

Answer:

x=d

Step-by-step explanation:

Answer:

g(1) = 1.8696

g(2) = 1.8662

Step-by-step explanation:

Simply plug in the x values into the equation in a calc and you should get your answer.

Answer:

Step-by-step explanation:

I think it's B or C because if you look closely u see that the line goes up then straight on 4. Go for an educational guess.

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

1.5 per minute

Step-by-step explanation:

unit rate is how many in 1 minute so 45 divided by 30 is 1.5 and if you want to check your answer do 1.5 x 30 which is 45

Answer:

Area of the circle=π×(radius)²

→3.14×(0.3)²=3.14×0.09=0.28yd²

0.28yd² is the right answer.

The population of the town in 5 years will be approximately 28,982.

A data pattern known as exponential growth exhibits faster expansion over time. Compounding generates exponential profits in finance. Exponential growth is possible in savings accounts with a compounding interest rate. Compound returns in finance lead to exponential development. One of the most potent forces in finance is the power of compounding. With the help of this idea, investors may generate sizable sums with little start-up money. Compound interest savings accounts are typical instances of exponential development.

Given that, population of a town increases by 3% each year.

The population after 5 years is calculated by:

Population in 5 years = Initial population x (1 + rate) raised to time.

That is,

Population in 5 years = 25,000 x (1 + 0.03)⁵

Population in 5 years = 25,000 x 1.159274

Population in 5 years = 28,981.85

Hence, the population of the town in 5 years will be approximately 28,982.

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The percent that the new frame is bigger than the original frame if the width of the frame remains the same is 9.1%.

From the information, the painting, square in shape, is placed in a wooden frame with width of 10% of the length of the side of the paining. The painting was enlarged by 10%.

Let the length be Illustrated as 10cm.

Width = 10% × 10cm

= 1cm

New Length = 10cm + (10% × 10cm)

= 11cm

The old perimeter will be:

= 2(1 + 10)

= 22cm

New perimeter will be:

= 2(1 + 11)

= 24cm

The percentage increase will be:

= (24 - 22) / 22 × 100

= 2/22 × 100

= 9.1%

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Answer:

add up the prices of everything they're buying, divide it by 75 and then multiple the whole answer by 100.

Step-by-step explanation:

The function f(x) = 10x - x² is a quadratic function.

A quadratic function is a polynomial function of degree 2, which means the highest power of the variable is 2. In the given function, the variable x is raised to the power of 1 in the term 10x, and it is raised to the power of 2 in the term -x². This indicates that the function is a quadratic function.

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants. In the given function, a = -1, b = 10, and c = 0 (since there is no constant term). So, the function f(x) = 10x - x² fits the form of a quadratic function.

Quadratic functions are known for having a graph in the shape of a parabola. In this case, the parabola opens downward because the coefficient of the x² term is negative (-1). The graph of the function will have a vertex at the maximum point, which in this case is (5, 25).

Therefore, the function f(x) = 10x - x² is indeed a quadratic function.

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Answer:

86.5

We add them together, which is 173, and since there are two terms, divide by 2

173/2=86.5

Answer:

86.5

127 + 46 / 2 = 86.5

I could be wrong but I believe this is correct.

The area of this triangle was 18 square units.

Let's use the given information to set up some equations. We are told that the sum of the lengths of the three sides of the triangle is 18. Let's call the lengths of the two shorter sides a and b, and the length of the hypotenuse c. Then, we have a + b + c = 18.

We are also told that the sum of the squares of the lengths of the three sides is 128. Using the Pythagorean theorem, we know that a² + b² = c². So, we can rewrite this equation as a² + b² + c² = 128.

Now we have two equations with three variables. We need to find a way to eliminate one of the variables. We can do this by using the first equation to solve for one of the variables in terms of the other two. Let's solve for c:

c = 18 - a - b

Now we can substitute this expression for c into the second equation:

a² + b² + (18 - a - b)² = 128

Expanding and simplifying, we get:

2a² + 2b² - 36a - 36b + 144 = 0

Dividing by 2, we get:

a² + b² - 18a - 18b + 72 = 0

We can rewrite this equation as:

(a² - 18a + 81) + (b² - 18b + 81) = 38

Completing the square, we get:

(a - 9)² + (b - 9)² = 5

So we have:

(a - 9)² = 1

(b - 9)² = 1

This gives us four possible solutions:

a = 8, b = 10, c = 18 - a - b = 0 (not possible)

a = 10, b = 8, c = 18 - a - b = 0 (not possible)

a = 9, b = 9, c = 0 (not possible)

a = b = c = 6√2

The only valid solution is the last one, where all three sides have the same length of 6√2. To find the area of the triangle, we can use the formula:

Area = (base x height)/2

Since this is a right triangle, one of the sides is the base and the other is the height. So we can choose any two sides to use as the base and height. Let's choose a and b:

Area = (a x b)/2

Substituting the values a = 6√2 and b = 6√2, we get:

Area = (6√2 x 6√2)/2

Area = 36/2

Area = 18

Therefore, the area of the right triangle with sides of length 6√2 is 18 square units.

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Answer:

the backpack will be on the ground in 3 seconds but it will first make contact with the ground in 2.5 seconds

Step-by-step explanation:

the equation would be:  y = -16t² + 100

if you solve for 't' then you will find the amount of time until it lands

0 = -16t² + 100

-100 = -16t²

100/16 = t²

t = √100/16

t = 10/4 = 2.5

Answer:

D. 3 and 6

A linear model would be best for Scatterplots 3 and 6.

the answer is "None of the above".

The given  is 2x−3/x+32=213

Multiplying each term by (x+3) gives:

2x - 3 = 2(13) (x + 3)2x - 3 = 26x + 78

Subtract 26x and 78 from both sides: 2x - 26x = 78 + 3 - 24x = 81 x

                                                                              = -81/-24 x = 9/8

So, the solution of 2x−3/x+32=213 is none of the above.

Option E is the correct answer as the solution is 9/8 which is not listed as one of the answer choices.

Therefore, the answer is "None of the above".

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The incenter Theorem states that the angle bisectors of a triangle intersect at a point equidistant from the sides.

using the Angle Bisector Theorem and the congruence of triangles.

Incenter theorem can use the properties of angle bisectors and the concept of congruent triangles.

Triangle ABC

The angle bisectors of triangle ABC intersect at a point equidistant from the sides.

Draw the triangle ABC.

Let the angle bisectors of angles A, B, and C meet the opposite sides at points D, E, and F, respectively.

Prove that the distances from the incenter denoted as I to the sides of the triangle are equal.

Consider angle A.

Since AD is the angle bisector of angle A, it divides angle A into two congruent angles.

Let's denote them as ∠DAB and ∠DAC.

By the Angle Bisector Theorem, we have,

(AB/BD) = (AC/CD) ___(1)

Similarly, considering angle B and angle C,

(CB/CE) = (BA/AE) ___(2)

(CA/FA) = (CB/BF) ____(3)

Rearranging equations (1), (2), and (3), we get,

AB/BD = AC/CD

CB/CE = BA/AE

CA/FA = CB/BF

Rearranging equation (1), we get,

AB/BD = AC/CD

AB × CD = AC × BD

Similarly, rearranging equations (2) and (3), we get,

CB × AE = BA × CE

CA × BF = CB × FA

Now, consider triangles ABD and ACD.

According to the Side-Angle-Side (SAS) congruence ,

AB × CD = AC× BD

Angle DAB = Angle DAC (common angle)

Therefore, triangles ABD and ACD are congruent.

By congruence, corresponding parts are congruent.

AD = AD (common side)

Angle DAB = Angle DAC (corresponding congruent angles)

Similarly, prove that triangles ECB and ACB are congruent,

BC ×AE = BA × CE

Angle CBE = Angle CBA

Therefore, triangles BCE and ACB are congruent.

By congruence, corresponding parts are congruent.

BE = BE (common side)

Angle EBC = Angle EBA (corresponding congruent angles)

prove that triangles CAF and BAC are congruent:

CA × BF = CB ×FA

Angle ACF = Angle ACB

Therefore, triangles CAF and BAC are congruent.

By congruence, corresponding parts are congruent.

FA = FA (common side)

Angle FCA = Angle FCB (corresponding congruent angles)

Points D, E, and F are equidistant from the sides of triangle ABC.

The angle bisectors of triangle ABC intersect at a point I, called the incenter, which is equidistant from the sides.

Hence, the incenter theorem is proven.

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Answer:

\(x=\frac{2}{3}\pm\frac{\sqrt{26}}{3}i\)

Step-by-step explanation:

\(3x^2+10=4x\\\\3x^2-4x+10=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(10)}}{2(3)}\\ \\x=\frac{4\pm\sqrt{16-120}}{6}\\ \\x=\frac{4\pm\sqrt{-104}}{6}\\ \\x=\frac{4\pm2\sqrt{26}i}{6}\\ \\x=\frac{4}{6}\pm\frac{2\sqrt{26}}{6}i\\\\x=\frac{2}{3}\pm\frac{\sqrt{26}}{3}i\)

Answer:

y = 2x + 6

Step-by-step explanation:

To find the equation of a line that passes through two points, you can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.

First, let's find the slope (m) using the given points (0,6) and (2,10):

m = (\(y_{2\) - \(y_{1\)) / (\(x_{2\) - \(x_{1\))

m = (10 - 6) / (2 - 0)

m = 4 / 2

m = 2

Now that we have the slope (m = 2), we can substitute one of the points and the slope into the slope-intercept form to find the y-intercept (b). Let's use the point (0,6):

y = mx + b

6 = 2(0) + b

6 = 0 + b

b = 6

So, the y-intercept (b) is 6.

Therefore, the equation of the line that passes through the points (0,6) and (2,10) is:

y = 2x + 6

Libby takes 7/20 of the cash prize.

To determine the fraction that Libby takes, we need to find the remaining fraction after Cindy and Carmen have received their portions.

Cindy received 1/4 of the cash prize.

Carmen received 2/5 of the cash prize.

To find Libby's portion, we subtract the portions received by Cindy and Carmen from the total prize. The total prize is equivalent to 1, which represents the whole amount.

Total prize = 1

Cindy's portion = 1/4

Carmen's portion = 2/5

Now, we can calculate Libby's portion:

Libby's portion = Total prize - (Cindy's portion + Carmen's portion)

Libby's portion = 1 - (1/4 + 2/5)

To simplify the expression, we find a common denominator for the fractions:

Libby's portion = 1 - (5/20 + 8/20)

Libby's portion = 1 - (13/20)

Now, subtract the fractions:

Libby's portion = 20/20 - 13/20

Libby's portion = 7/20

Therefore, Libby takes 7/20 of the cash prize.

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The experimental probability of rolling a 1 or a 2 is 0.2.

Hence, Option A is correct.

We know that,

The experimental probability of an event is defined as the number of times the event occurred divided by the total number of trials.

In this case,

The event is rolling a 1 or a 3,

Which occurred ⇒  3 + 1

                           = 4 times.

Given that there are total number of trials = 20.

Therefore,

The experimental probability of rolling a 1 or a 3 = 4/20,

                                                                                = 1/5

                                                                                 = 0.2

Hence, the required probability is 0.2.

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The complete question is:

Sarah is playing a game in which she rolls a number cube 20 times. The results are recorded in the chart below. What is the experimental probability of rolling a 1 or a 3?

Number on cube:1,2,3,4,5,6

Number of times event occurs:3,6,1,5,3,2

A.0.2

B.0.3

C.0.6

D.0.83