.......???????????????​

Answer: Yes, the Mean Value Theorem can be applied to f(x) = 9x^3 on the closed interval [1, 2].

To find all values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a), we first find the derivative of f(x):

f'(x) = 27x^2

Then, we can use the Mean Value Theorem to find a value c in the open interval (1, 2) such that:

f'(c) = (f(2) - f(1))/(2 - 1)

27c^2 = 9(2^3 - 1^3)

27c^2 = 45

c^2 = 5/3

c = +/- sqrt(5/3)

Therefore, the values of c in the open interval (1, 2) such that f'(c) = (f(b) - f(a))/(b - a) are:

c = sqrt(5/3), -sqrt(5/3)

Note that these values are not in the closed interval [1, 2], as they are not between 1 and 2, but they are in the open interval (1, 2).

Step-by-step explanation:

The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.

The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.

We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.

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A patient weighing 220 pounds needs 293 milligrams of medicine.

We have given that,

patient weighing 162

pounds requires 216 milligrams of medicine

We have to calculate the amount of medicine required by a patient weighing 220 pounds

Consider the value of amount of medicine is x.

Set up a proportion.

pounds / milligrams of medicine

What is the proportion we get?

[tex]162/216=220/x[/tex]

So,

[tex]162/216=220/x[/tex]

[tex]162x=216\times220[/tex]

[tex]162x=47,520[/tex]

[tex]x=47,520/162[/tex]

[tex]x=293[/tex]

A patient weighing 220 pounds needs 293 milligrams of medicine.

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The equation of the line that passes through the points (1,3) and (2,2) is y = -x + 4.

To find the equation of the line, we can use the slope-intercept form of a linear equation, y = mx + c, where m is the slope and c is the y-intercept.

First, we need to find the slope of the line. The slope is given by:

where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get:

Next, we can use one of the given points and the slope to find the y-intercept. Using the point (1,3), we get:

Simplifying this equation gives us:

c = 4

Therefore, the equation of the line in slope-intercept form is:

y = -x + 4.

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Answer:

3

Step-by-step explanation:

Interval 3 ≤ x ≤ 5 means all f(x) values from x= 3 inclusive  to x = 5 inclusive

At x = 3 f(x) = 2

At x = 5, f(x) = 8

Change in f(x) = Δf(x) = 8 - 2 = 6

Change in x = Δx = 5 - 3 = 2

Average rate of change
= Δf(x)/Δx

= 6/2

= 3

The simplified form of the given expression as required to be determined in the task content is; 2x⁴√5.

It follows from the task content that the Simon form of the given expression √20x⁸ is required to be determined from the task content.

On this note, since the given expression is; √20x⁸.

We have that; = √ (4 × 5 × x⁸)

Therefore, since 4 and x⁸ are perfect squares; it follows that we have;

= 2x⁴ √5.

Ultimately, the simplified form of the given expression as required to be determined is; 2x⁴ √5.

Complete question; The correct expression is; √20x⁸.

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The perimeter of the figure is 16p + 10.

The whole length of a two-dimensional or three-dimensional shape's sides or edges is known as its perimeter. It is frequently referred to as the shape's perimeter or circumference. It is possible to determine the perimeter of many geometric forms with accuracy. The perimeter is a key idea in geometry and has several practical uses, such as determining the radius of a circular racetrack or determining the length of fencing required for a certain property.

The perimeter of a figure is the sum of the lengths of all its sides.

Thus,

Perimeter = (p - 9) + (7p + 5) + (p - 9) + (7p + 5)

Perimeter = 2p + 2(7p) + 2(5)

Perimeter = 16p + 10

Hence, the perimeter of the figure is 16p + 10.

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The probability of randomly drawing a penny is 6/24 or 1/4, since there are 6 pennies out of a total of 24 coins.

How to solve and What is Probability?

The probability of randomly drawing a quarter is 10/24 or 5/12, since there are 10 quarters out of a total of 24 coins. The probability of randomly drawing a coin that is not a penny is 18/24 or 3/4, since there are 18 coins that are not pennies out of a total of 24 coins.

Probability is the branch of mathematics that deals with measuring the likelihood or chance of an event or outcome occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Probability theory is used to make predictions and informed decisions based on available data in various fields, including statistics, finance, engineering, and science.

It involves understanding and analyzing random events, and determining the likelihood of specific outcomes. Probability is an essential tool for decision-making in various applications, such as risk analysis, game theory, and quality control.

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Answer:

See Below.

Step-by-step explanation:

To find the perimeter of a trapezoid, you simply add up the lengths of all four sides.

In this case, the trapezoid has sides of 8 cm, 10 cm, 16 cm, and 10 cm.

Perimeter = 8 cm + 10 cm + 16 cm + 10 cm

Perimeter = 44 cm

Therefore, the perimeter of the trapezoid is 44 cm.

Ryan makes a profit of £240.  the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

Ryan spends £190 to buy 80 jumpers. He sells 50% of the jumpers, i.e. 40 jumpers, at £12 each. This brings the total sales to £480. Then, he puts the remaining 40 jumpers on a Buy one get one half price offer. He sells 20 of the remaining jumpers using this offer. Therefore, the total sales now amount to £600. By subtracting the cost of the jumpers, i.e. £190, from the total sales, we calculate that Ryan makes a profit of £240.

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None of the available options match the parabola's equation.

To determine the equation of a parabola, we can utilize the vertex form. Assuming we can read the coordinates (h,k) from the graph, the aim is to utilize the coordinates of its vertex (maximum point, or minimum point), to formulate its equation in the form y=a(xh)2+k, and then to determine the value of the coefficient a.

A parabola's vertex form is given by:

[tex]y = a(x-h)^2 + k[/tex]

where (h,k) is the parabola's vertex.

[tex]y = a(x-5)^2 - 3[/tex]

These values are substituted into the equation to produce:

[tex]-15 = a(2-5)^2 - 3[/tex]

[tex]-15 = 9a - 3[/tex]

[tex]-12 = 9a[/tex]

[tex]a = -4/3[/tex]

[tex]y = (-4/3)(x-5)^2 - 3[/tex]

This equation is expanded and simplified to produce:

[tex]y = (-4/3)x^2 + (32/3)x - 53[/tex]

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Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

Answer:

the numbers are

[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]

Step-by-step explanation:

then there difference is

square root of 10 + 5 -(- square root of 10 +5)

=

[tex]2 \sqrt{10} [/tex]

and the cube of there sum is 15^3 = 15* 15* 15

= 3375

The correct answer is: (4, 3) is a member. Its cardinality is 4.

Matching the sets on the left with a true statement about the Cartesian product of those sets on the right:{1, 2} × {3, 4} = {(1, 3), (1, 4), (2, 3), (2, 4)}{1, 2, 3, 4} × {3, 4, 5, 6} = {(1, 3), (1, 4), (1, 5), (1, 6), (2, 3), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 3), (4, 4), (4, 5), (4, 6)}{4, 5, 6, 7} × {4, 5, 6, 7} = {(4, 4), (4, 5), (4, 6), (4, 7), (5, 4), (5, 5), (5, 6), (5, 7), (6, 4), (6, 5), (6, 6), (6, 7), (7, 4), (7, 5), (7, 6), (7, 7)}{a, e, i, o, u} × {b, g, t, d} = {(a, b), (a, g), (a, t), (a, d), (e, b), (e, g), (e, t), (e, d), (i, b), (i, g), (i, t), (i, d), (o, b), (o, g), (o, t), (o, d), (u, b), (u, g), (u, t), (u, d)}{1, 2, 3} × {1, 2, 4} = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 2), (2, 4), (3, 1), (3, 2), (3, 4)}The following are true statements about the Cartesian product of these sets:its cardinality is 4. (4, 3) is a member.

Therefore, the correct answer is: (4, 3) is a member. Its cardinality is 4.

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Answer:

[tex]5x {}^{3} - x + 5x + 2[/tex]

Step-by-step explanation:

Greetings!!!

So to find the sum of (f+g)(x) just simply add these two functions

Add like terms together

If you have any questions tag it on comments

Hope it helps!!!

To conclude, the probability of the Acme Drug Company seeing a percent difference of -.13 or less if the true difference is 0 is quite low and is equal to 0.0934.

The probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is quite low. This is because a difference of -.13 is a very small percentage in comparison to a true difference of 0.

Mathematically, the probability of this happening would be equal to the area under the standard normal distribution curve for values between -0.13 and 0. In other words, the probability that the Acme Drug Company would see a percent difference of -.13 or less if the true difference is 0 is equal to the area from the left tail of the standard normal distribution curve up to the mean (0) of the curve.

Using a standard normal distribution calculator, we can see that the probability of the Acme Drug Company seeing a percent difference of -.13 or less is 0.0934. This probability is extremely low and it is not likely that the Acme Drug Company would experience such a small percent difference.

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The points determined by the real numbers 3.2, 9.5, 50, and 263 are all located on the unit circle at their respective distances from the origin.

The unit circle is a circle of radius 1 centered at the origin of a coordinate system, usually the Cartesian coordinate system. In this system, a point (x,y) is determined by its real number x, where x is the horizontal distance from the origin and y is the vertical distance from the origin. For example, the point determined by the real number 3.2 is located at (3.2, 0), since 3.2 is the horizontal distance from the origin. Similarly, the point determined by the real number 9.5 is located at (9.5, 0).

The point determined by the real number 50 is located at (50, 0). Finally, the point determined by the real number 263 is located at (263, 0). The unit circle is often used in trigonometry to describe the position of points on the circle with an angle in standard position (in radians). For example, if the point determined by the real number 3.2 has an angle in standard position of 3.2 radians, then the point located at (3.2, 0) on the unit circle is the same point. Similarly, if the point determined by the real number 9.5 has an angle in standard position of 9.5 radians, then the point located at (9.5, 0) on the unit circle is the same point. The same is true for the points determined by the real numbers 50 and 263, respectively.

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Proved that the sum of measure of three angles of triangle is 180 using the Polygon Angle Sum Theorem

To prove that the sum of the measures of three angles of a triangle is 180 degrees, we can use the Polygon Angle Sum Theorem, which states that the sum of the measures of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

A triangle is a polygon with three sides, so we can apply the Polygon Angle Sum Theorem to a triangle to find the sum of its interior angles. Using n=3, we have:

Sum of measures of interior angles of triangle = (n-2) × 180 degrees

= (3-2) × 180 degrees [since we are dealing with a triangle]

= 1 × 180 degrees

= 180 degrees

Therefore, the sum of the measures of the interior angles of a triangle is 180 degrees. This means that the sum of the measures of the three angles in a triangle is always 180 degrees, regardless of the size or shape of the triangle.

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Answer:

the cross is the blue color

Answer: 4.5

Step-by-step explanation:

A^2 +B^2 =C^2

A^2 + 6^2 =7.5^2

A^2 + 36= 56.25

A^2= 20.25

A= square root of 20.25

A= 4.5

As a result, the percentage of adults who selected math is different from the percentage of kids who did.

As a number out of 100, a percentage is a method to express a proportion or a fraction. It is symbolized by the number %. If there are 25 boys in a class of 100 pupils, for instance, then there are 25% of boys in the class. It is a helpful method to compare quantities and to express changes in values over time.

given

120 80

Total    200

Women Overall Party A Party B

70 60

Overall    130

Therefore, there are 130 ladies in the group.

b) The chart indicates that 70 women plan to support Party A.

Thus, the percentage of adults who selected English was 40% of 48, which is equal to 0.4 times 48 and 19.2 when rounded to the closest whole number.

b) Reeshma is not accurate. The percentage of adults who selected math is 35%, while for children it is 40%, according to the pie chart.

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The complete question is:-   complete the two-way table, which shows the voting intentions of a group of men and women. a How many women are in the group?

Men

Party A Party B 120

Total    200

Women   130

Total       380

b How many women intend to vote for Party A?

2 A group of 48 adults are asked what their favourite subject was at school. They can choose from

maths, English and science.

A group of 32 school children are asked the

same question.

The mean distance Jaison jogged over 9 days is 7 meters per day. This was calculated by adding up all the distances he jogged and dividing by 9.

To calculate the average distance that Jaison jogged over the 9 days, we used the formula for mean, which involves summing up all the distances he jogged and dividing by the total number of days. After adding up the distances, we found that the total distance Jaison jogged was 63 meters. Dividing this by the 9 days gives us an average distance of 7 meters per day. Therefore, Jaison jogged an average of 7 meters each day over the 9-day period.

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The range of the quadratic function above is (-∞, 7].

In mathematics, a quadratic prοblem is οne that invοlves multiplying a variable by itself, alsο knοwn as squaring. In this language, the area οf a square is equal tο the length οf its side multiplied by itself. The term "quadratic" cοmes frοm the Latin wοrd fοr square, quadratum.

Tο determine the quadratic functiοn's range, we must first determine the functiοn's minimum and maximum pοints. The given functiοn is in vertex fοrm, with the vertex at the pοint (h, k), where h is the vertex's x-cοοrdinate and k is the vertex's y-cοοrdinate.

We can see frοm the given equatiοn that the vertex is at the pοint (1, 7). Because the cοefficient οf the x² term is pοsitive, the parabοla οpens upwards and the vertex is the functiοn's minimum pοint.

Thus, The range of the quadratic function above is (-∞, 7].

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Answer:

25%

Step-by-step explanation:

The experimental probability of drawing a white marble can be found by dividing the number of times a white marble was chosen by the total number of trials:

Experimental probability of drawing a white marble = number of times a white marble was chosen / total number of trials

In this case, the number of times a white marble was chosen is 18, and the total number of trials is 80, so:

Experimental probability of drawing a white marble = 18/80 = 0.225 or 22.5%

To compare the experimental probability with the theoretical probability, we need to know the total number of marbles in the bag and the number of white marbles in the bag. Let's assume that there are 4 colors of marbles in the bag (red, white, black, and green), and that each color has an equal number of marbles. This means that there are a total of 4 x 18 = 72 marbles in the bag, and 18 of them are white.

The theoretical probability of drawing a white marble can be found by dividing the number of white marbles by the total number of marbles:

Theoretical probability of drawing a white marble = number of white marbles / total number of marbles

In this case, the number of white marbles is 18, and the total number of marbles is 72, so:

Theoretical probability of drawing a white marble = 18/72 = 0.25 or 25%

Comparing the two probabilities, we can see that the experimental probability (22.5%) is slightly lower than the theoretical probability (25%). This could be due to chance or sampling error in the experiment, or it could indicate that the actual probability of drawing a white marble is slightly lower than the theoretical probability.

The condition that must be true in order for a confidence interval based on de Moivre's equation to be valid is:

d. The underlying distribution of the data must be normally distributed.

A confidence interval is an interval estimate of a population parameter that specifies a range of values within which the parameter is likely to lie with a certain level of confidence. In other words, it represents the degree of uncertainty associated with the estimate.

De Moivre's equation is a formula for approximating the probability of a specific number of successes in a series of independent Bernoulli trials. This formula is only relevant if the sample size is large enough such that the normal approximation to the binomial distribution is valid. Thus, this formula can be used to calculate confidence intervals for binomial proportions when the sample size is large enough to apply the normal approximation.

Answers to other options:

a. We must be forming a confidence interval for a coefficient in a multiple regression model - This statement is incorrect. De Moivre's equation is not related to multiple regression models.

b. All of these answers are correct - This statement is incorrect because not all of the options are correct. Only one option is correct.

c. We must be forming a confidence interval for a population mean based on a sample mean - This statement is incorrect. De Moivre's equation is not relevant for calculating confidence intervals for population means. The Central Limit Theorem is used instead.

Hence, option "d" only is true.

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Therefore, you would be more likely to win the game by choosing option (2) - winning if the spinners do not match.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of mathematics, science, engineering, finance, and other fields to model and analyze uncertain situations. It helps to make predictions, to assess risks and opportunities, and to make informed decisions based on available information. Probability theory provides a foundation for statistical inference, which is used to draw conclusions from data and to test hypotheses about the underlying population.

Here,

In the "Two Spinner Game", there are two possible outcomes for each spin - a match or a non-match. The probability of the spinners matching is the probability of both spinners landing on the same color. Let's say that there are 3 red sections, 3 blue sections, and 2 green sections on each spinner.

The probability of the first spinner landing on red is 3/8, and the probability of the second spinner landing on red is also 3/8. Therefore, the probability of both spinners landing on red (a match) is (3/8) x (3/8) = 9/64.

Similarly, the probability of both spinners landing on blue (another match) is (3/8) x (3/8) = 9/64, and the probability of both spinners landing on green (a match) is (2/8) x (2/8) = 4/64.

The probability of the spinners not matching is the probability of them landing on different colors. There are 3 different pairs of colors that are not a match: red-blue, red-green, and blue-green. The probability of each of these pairs is (3/8) x (3/8) = 9/64.

So, there are 6 possible outcomes, and the probability of winning by a match is 9/64 + 9/64 + 4/64 = 22/64, or about 34.4%. The probability of winning by a non-match is 3 x 9/64 = 27/64, or about 42.2%.

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