Find the rate of change over the interval 2 < x < 5; f(x)= 2x^2+5 (use this function).

Answer:

[tex]\boxed{x=0}[/tex]

Step-by-step explanation:

We need solve for x

[tex]3=x+3-5x[/tex]

substract 3 to both sides of the equation:

[tex]3-3=x+3-5x-3\\0=-4x[/tex]

divide both sides of the equation by -4

[tex]\frac{0}{-4}=\frac{-4x}{-4}\\0=x\\\equiv x=0[/tex]

The value of "x" that satisfies the equation is x=0,

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

For the given system of linear inequalities (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.

An equation with a linear expression and a relational operator is referred to as a linear inequality. Regions in a coordinate plane or space that fulfil a linear inequality are defined by the inequality. A linear inequality in two dimensions defines a half-plane, which, depending on the inequality, is either above or below a line. A linear inequality in three dimensions defines a half-space that, depending on the inequality, is either above or below a plane. In optimization situations, when the objective is to determine the greatest or lowest value of a linear function under a set of constraints represented by linear inequalities, linear inequalities are frequently utilised.

The given system of inequalities is:

5x + 15y ≤ 325

20x + 35y ≤ 1200

Here, x is the number of batches of soap and y is the number of batches of lotion.

Thus, (53, 4) represents 53 batches of soap and 4 batches of lotion were produced.

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Answer:51

Step-by-step explanation:

The specificity of the test based on the given screening results is 0.967 (rounded to three decimal places).

To calculate the specificity, divide the number of true negatives (TN) by the total number of negative results (TN+FP). In this case, that would be 687/(687+22), which is equal to 0.967 (rounded to three decimal places).

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The cumulative distributive function (CDF) Fx(3) is 0.61.

The cumulative distributive function (CDF) of a random variable X is the probability that X takes a value less than or equal to x. In this case, we are asked to find Fx(3).

Since the random variable X is given with a probability mass function, we can calculate the CDF by summing the probabilities of X being less than or equal to 3. This can be expressed as: [tex]Fx(3) = P(X<=3).[/tex]
For X = 0, P(X<=3) = 0.23.
For X = 1, P(X<=3) = 0.23 + 0.13 = 0.36.
For X = 2, P(X<=3) = 0.23 + 0.13 + 0.10 = 0.46.
For X = 3, P(X<=3) = 0.23 + 0.13 + 0.10 + 0.15 = 0.61.

Therefore, the cumulative distributive function (CDF) Fx(3) is 0.61.

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Step-by-step explanation:

The formula to solve for the area of a circle is given by,

A

=

1

4

π

d

2

where

d

is the diameter.

Substituting the given, we have

A

=

1

4

×

3.14

×

(

3

ft

)

2

=

1

4

×

3.14

×

9

ft

2

A

=

7.065

ft

2

Next, solve for the circumference.

The formula for the circumference of a circle is written as,

C

=

π

d

where

d

is the diameter.

Substituting the given, we have

C

=

3.14

×

3

ft

C

=

9.42

ft

Hence, the

Area

=

7.065

ft

2

and the

Circumference

=

9.42

ft

.

Answer:

A = 19.625 ft²

C = 15.7 ft

Step-by-step explanation:

The equation for the area of a circle is πr², where r is the radius.

The radius is half of the diameter, so the radius here is 2.5.

Plug the radius into the equation and substitute 3.14 for π:

A  = 3.14 x 2.5²

2.5² = 2.5 x 2.5 = 6.25

A = 3.14 x 6.25 = 19.625

Area = 19.625 ft²

The equation for the circumference of a circle is 2πr.

Plug the radius into the equation and substitute 3.14 for π:

C = 2 x 3.14 x 2.5

C = 15.7

Circumference = 15.7 feet.

The fraction of the guests are 10 or 11 years old is 5/6

A fraction represents a part of a whole, where the whole is divided into equal parts.

To find the fraction of guests who are 10 or 11 years old, we need to add the fractions of guests who are 10 years old and 11 years old.

3/12 of the guests are 10 years old, which can be simplified to 1/4.

7/12 of the guests are 11 years old.

Therefore, the fraction of guests who are 10 or 11 years old is

1/4 + 7/12 = 3/12 + 7/12

Add the fractions

= 10/12

Simplify the fraction

= 5/6

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The surface area of the rectangular prism is 170 square yards.

Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.

To calculate the surface area of the rectangular prism, add the areas of each of its faces.

The front and back faces are 5 yards by 6 yards in size, so each has an area of:

5 yards x 6 yards equals 30 square yards

The top and bottom faces are 5 yards by 5 yards, so each has an area of:

5 yards x 5 yards equals 25 square yards

The two side faces have dimensions of 6 yards by 5 yards, for a total area of:

30 square yards = 6 yards x 5 yards

As a result, the surface area of the rectangular prism is as follows:

Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area

= 30+30+25+25+30+30

= 170 square yards

As a result, the rectangular prism has a surface area of 170 square yards.

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False. A probability distribution for a discrete variable is not exclusive, collectively exhaustive list of numerical outcomes for that variable and the probability of occurrence associated with each outcome.

A probability distribution for a discrete variable is a list of all possible values that the variable can take on, along with the probability of each value occurring. The values must be collectively exhaustive (meaning they include all possible outcomes) and mutually exclusive (meaning that each outcome cannot occur at the same time as any other outcome). However, the numerical outcomes do not have to be exclusive, as they can have the same probability of occurring. For example, a coin toss has two possible outcomes (heads and tails) with equal probability, and a dice roll has six possible outcomes with equal probability. These probabilities can be represented using a probability distribution.

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Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.

The study of arbitrary events or experiments falls under the purview of probability, a subfield of mathematics. A value between 0 (impossible) and 1 is used to estimate the possibility or chance of an event occurring (certain). Several disciplines, including science, engineering, economics, finance, and more, utilise the idea of probability. It is frequently determined by dividing the number of positive events by the total number of outcomes that could occur.

given

(a) To find P, we can utilize the complement rule (T&D). The addition to T&D is the possibility that the chosen player is a pitcher or a Dominican. We thus have:

The equation P(T&D) = 1 - P(T'UD') = 1 - P(T') - P(D') + P(T'D')

P(T), P(D), and P(TD) are all provided as 0.42, 0.105, and 0.056 respectively. As a result, we may determine the complements' probabilities:

P(T') = 1 - P(T) = 1 - 0.42 = 0.58 P(D') = 1 - P(D) = 1 - 0.105 = 0.895 P(T'D') = P(TD)' = 1 - (P(T) + P(D) - P(TD)) = 1 - (0.471 + 0.42 + 0.105 - 0.056)

By replacing these values, we obtain:

P(T&D) = 1 - 0.58 - 0.895 + 0.471 = 0.046

As a result, there is a 0.046 percent chance that the chosen player is a non-pitcher from outside the Dominican Republic.

(b) In order to determine the likelihood that the chosen player is a pitcher given that he is from the Dominican Republic, we must first determine P(P|D). Bayes' Theorem may be applied:

P(P|D) equals P(D|P)P(P)/P (D)

P(D) = 0.105 and P(TD) = 0.056 are the values provided. Therefore,

P(P) is defined as P(TD') / P(D') = 0.056 / 0.895 0.0626.

P(D|P) is equal to P(T|D) / P(P) = 0.056 / 0.0626 0.895.

By replacing these values, we obtain:

P(P|D) = (0.895)(0.0626) / 0.105 ≈ 0.053

Given that he is from the Dominican Republic, the likelihood that the chosen player is a pitcher is roughly 0.053.

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The complete question is :-   Of all major league baseball players on 2008 Opening Day rosters:

42% are pitchers (call this event T)

10.5% are from the Dominican Republic (call this event D)

5.6% are pitchers from the Dominican Republic

A player is selected at random.

(a) Find P(T&D), the probability that that the selected player is a non-pitcher who is not from the Dominican.

(b) Given the information that the selected player is from the Dominican Republic, what is the probability that he is a pitcher?

(c) Given the information that the selected player is a non-pitcher, what is the probability that he is not Dominican?

Sure! I can help you with that.

First, we should calculate the profit made by the shopkeeper. To calculate the profit, we will multiply the selling price of the table with 20%, which is 20% of 5400, or 1080.

Next, we should subtract the profit from the selling price to find the cost price of the table.

The cost price of the table = 5400 - 1080

The cost price of the table = 4320

Therefore, the cost price of the table is ₹ 4320.

17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.

1) Option a. Depreciation expenses of $6,710 will be recorded each year. is correct.

2) Option c. 175,000 × 7.99% is correct

3) Option b. $105,000 is correct.

1) The annual payments of $10,000 and the recorded cost of the asset of $67,100 are used to calculate the annual depreciation expense using the straight-line method.

Depreciation expense = (Recorded cost of the asset - Residual value) / Useful life

= ($67,100 - $0) / 10 years

= $6,710 per year.

2) The effective interest method calculates interest expense by multiplying the carrying value of the bond (i.e., the amount at which it was issued minus any discount or plus any premium) by the effective interest rate (i.e., the rate that discounts the bond's future cash flows to the carrying value).

Therefore, the interest expense for the first year on the bonds would be $175,000 × 7.99% = $13,965.

3) The dividends declared during the year can be calculated as follows:

Dividends declared = Net income - Increase in retained earnings - Decrease in dividends payable

= $150,000 - ($345,000 - $300,000) - ($29,000 - $19,000)

= $105,000.

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The populations of the listed countries are

India is 1.366 billion

China is 1.397 billion

Argentina is 45 million

the United States is 332 million

and Egypt is 102 million people.

Let's start with India. According to the World Bank, India's population is approximately 1.366 billion people, which is the second-largest population in the world after China. India's land area is approximately 1.269 million square miles.

Moving on to China, it has the largest population in the world, with approximately 1.397 billion people. China's land area is approximately 3.705 million square miles, making it the fourth-largest country in terms of land area.

Argentina, on the other hand, has a population of approximately 45 million people, with a land area of approximately 1.073 million square miles. This makes it the eighth-largest country in the world in terms of land area.

The United States has a population of approximately 332 million people, and its land area is approximately 3.796 million square miles. It is the third-largest country in terms of land area and the fourth-largest in terms of population.

Lastly, Egypt has a population of approximately 102 million people, with a land area of approximately 386 thousand square miles. It is the 30th largest country in terms of land area and the 14th most populous country in the world.

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Answer:

-

(x + is what you are looking for is the answer

Using  the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)

We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:

-4x + y = 3 (Equation 1)

5x - 2y = -9 (Equation 2)

Solving Equation 1 for y, we get:

y = 4x + 3

Now, we substitute this expression for y into Equation 2 and solve for x:

5x - 2(4x + 3) = -9

5x - 8x - 6 = -9

-3x = -3

x = 1

We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:

-4(1) + y = 3

y = 7

Therefore, the solution to the system of equations is (x, y) = (1, 7)

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Answer:

<abc

Step-by-step explanation:

Te surface area of the smaller figure based on the ratio is 1600m²

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding sides.

Let x be the scale factor between the smaller and larger figures.

Then we have:

(x³)/(4000) = 6912

x³ = 6912/4000

x³ = 1.728

Taking the cube root of both sides, we get:

x = 1.2

So the scale factor from the larger figure to the smaller figure is 1:1.2.

The surface area of a similar figure is proportional to the square of the scale factor.

So we can use the scale factor to find the ratio of the surface areas:

SA(smaller) / SA(larger) = 1/(1.2)²

We know that the surface area of the larger figure is 2304m^2, so we can solve for the surface area of the smaller figure:

SA(smaller) = 2304 * 1/(1.2)²

SA(smaller) = 1600m²

Therefore, the surface area of the smaller figure is 1600m²

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Based on the given data, The shape's whole surface area is about 252 mm².

Based on the image, the shape appears to be a set of rectangles with different lengths and widths.

To find the area of this shape, we can break it down into smaller rectangles and add up their areas.

Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:

Area1

= 6 mm × 4 mm

= 24 mm²

Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:

Area2

= 6 mm × 3 mm

= 18 mm²

The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:

Area3

= 6 mm × 5 mm

= 30 mm²

The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:

Area4

= 6 mm × 3 mm

= 18 mm²

The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:

Area5

= 6 mm × 15 mm

= 90 mm²

The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:

Area6

= 3 mm × 9 mm

= 27 mm²

Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:

Area7

= 5 mm × 9 mm

= 45 mm²

To find the total area of the shape, we can add up the areas of all seven rectangles:

Total Area

= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7

= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²

= 252 mm²

Therefore, the total area of the shape is approximately 252 mm².

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Answer:

False.

Step-by-step explanation:

A triangle's two smaller sides have to add to be bigger than the larger side.

Answer:

False, that cannot exist by the hypotenuse rule

Hope it helps!

The probability density function (PDF) of Y can be determined by the transformation of the PDF of X. Using the transformation rule, we can calculate that fy(y) = fx(x) |dx/dy|, where x is a function of y, since y = Fx(x).

We can use the Chain Rule to determine the derivative of x with respect to y. Since Fx is a monotone increasing function, dx/dy = 1/F'x(x). Substituting this into the transformation rule, fy(y) = fx(x) / F'x(x).

Therefore, to find fy(y), we need to calculate F'x(x). Fx is the cumulative distribution function, which means that its derivative F'x(x) is the probability density function of X, or fx(x). Substituting this into the transformation rule, fy(y) = fx(x) / fx(x). Since fx(x) = fx(2) and fx(2) is a constant, fy(y) = 1/fx(2).

To summarize, the probability density function of Y is given by fy(y) = 1/fx(2).

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the solution to the equation -16p + 37 = 49 - 21p is p = 12/5. The equation -16p + 37 = 49 - 21p is a simple linear equation with one variable, p.

Linear equations are equations where the highest exponent of the variable is one, and they can be solved using algebraic techniques.

To solve this equation, we need to isolate the variable, p, on one side of the equation. We can start by simplifying the equation by combining like terms. To do this, we can add 21p to both sides of the equation, which gives us:

-16p + 37 + 21p = 49

Next, we can combine the terms -16p and 21p, which gives us 5p. So, the equation becomes:

5p + 37 = 49

We can further simplify the equation by subtracting 37 from both sides, which gives us:

5p = 12

Finally, we can solve for p by dividing both sides of the equation by 5:

p = 12/5

So, the solution to the equation -16p + 37 = 49 - 21p is p = 12/5.

In summary, the given equation is a simple linear equation that can be solved using algebraic techniques. We can isolate the variable, p, on one side of the equation by combining like terms and simplifying the equation. Finally, we can solve for p by dividing both sides of the equation by the coefficient of p.

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Answer:

e. 8/00 ggg： What sum of money amounts to Rs. 8700 in 3 years at the rate of 24% per annum? [Ans: Rs. 5058.14]

Step-by-step explanation:

Answer:

2x=5 > -14

Step-by-step explanation:

6(x - 2) -3 ≥ -4 ( -3 + 9) +10​
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3    3        
2x=5 > -14

The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378

First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.

The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.

The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).

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The linear relationship of Maggie crocheting squares is y = 6 + 6x graph (b)

Let x be the number of hours Maggie spends crocheting squares, and let y be the total number of squares she has made.

Initially, Maggie has 6 squares made,

so y = 6 when x = 0.

For each hour that she spends crocheting squares, Maggie makes 6 more squares.

Therefore, the relationship between x and y is:

y = 6 + 6x

This is a linear relationship with a slope of 6, which means that Maggie is crocheting squares at a rate of 6 squares per hour.

This is represented by graph (b)

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Answer:

Give a brainliest answer

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

The equal symbol (=) is frequently used to separate the expressions in equations. The left-hand side (LHS) and right-hand side (RHS) of the equation, respectively, are the formulas on either side of the equal sign. If you replace the variable(s) in both expressions with the same value, they will have the same value, as indicated by the equal symbol, which denotes that the two sides are equivalent.

given

We'll name Leo's collection of toy soldiers "x" the amount.

Finally, we know that the remainder is 3 when x is split by 5. Thus, x Plus 2 must be a multiple of 5.

Using this knowledge, we can construct the following system of equations:

x = 4n (where n is a positive number) (where n is a positive integer)

x + 1 = 7m (where m is a positive number) (where m is a positive integer)

x + 2 = 5p (where p is a positive number) (where p is a positive integer)

Testing different values of x that meet these two requirements reveals that x = 38 is the only answer that also resolves the second problem.

Leo has 38 toy troops as there aren't enough for him to line them up four by four.

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The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

To find the rate of change of an edge of the cube, given that the volume decreases at a rate of 4 cubic meters per minute when the volume is exactly 27 cubic meters, follow the solution below:Let the length of the edge of the original cube be L.Let the volume of the original cube be V, such that V = L³.The rate of change of volume is given as -4 m³/min; the negative sign is used to indicate a decrease in volume, and this is obtained when the derivative of the volume with respect to time is multiplied by the negative sign.Let V₀ be the original volume of the cube, and V₁ be the volume after t minutes. Thus, V₁ = V₀ - 4t m³. We are told that V₁ = 27 m³, hence:V₀ - 4t = 27 ⇒ V₀ = 27 + 4t m³Substituting V₀ in terms of t into the expression V = L³, we have:L³ = 27 + 4tTaking the derivative of both sides with respect to t, we have:3L²(dL/dt) = 4 ⇒ dL/dt = 4/(3L²)Substituting L from the expression L³ = 27 + 4t, we have:L = (27 + 4t)^(1/3)Therefore, the rate of change of an edge of the cube is given by the derivative of L with respect to t:dL/dt = 4/(3L²) = 4/(3(27 + 4t)^2/3) ≈ 0.048 m/min (to 3 decimal places)Answer: The rate of change of an edge of the cube is approximately 0.048 m/min when the volume is exactly 27 cubic meters.

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Given a normal distribution is observed from the number of points per game for a certain basketball player. The mean for this distribution is 20 points and the standard deviation is 3 points.Using the empirical rule for normal distributions, the probability that in a randomly selected game the player scored less than 26 points is required .Empirical Rule: For a normal distribution with a mean µ and a standard deviation σ, the probability of an observation being within k standard deviations of the mean is approximately:•

68% of the observations fall within one standard deviation of the mean.• 95% of the observations fall within two standard deviations of the mean.• 99.7% of the observations fall within three standard deviations of the mean.Here, the mean is 20 points and the standard deviation is 3 points. We need to find the probability of getting less than 26 points.z-score = (x - µ) / σ = (26 - 20) / 3 = 2σ = 2According to the empirical rule, 95% of observations fall within 2 standard deviations of the mean.So, the probability that the player scored less than 26 points is 95%.Therefore, the final answer is 95% rounded to one decimal place. Answer: 95%.

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