A curve has the equation y = px² + r/x , where pand rare constants. d²y (a) Show that x² d²y/dx² = 2y
(b) Given that when x= -1, y = 3 and dy/dx = -9. Calculate the values of p and r.

the base of the triangular window is 24 feet and the height is 10 feet.

Let's denote the height of the triangular window as h feet. According to the given information, the area of the window is 120 square feet.

The formula to calculate the area of a triangle is:

Area = (1/2) × base × height

In this case, we can write the equation as:

120 = (1/2) × base × h

Now, we are also given that the base of the window is 4 feet more than twice the height. So we can express the base as:

base = 2h + 4

Substituting this expression for the base into the area equation, we have:

120 = (1/2) × (2h + 4) × h

Now we can solve this equation for the height.

Multiplying both sides of the equation by 2 to remove the fraction:

240 = (2h + 4) × h

Expanding the right-hand side:

240 = 2h² + 4h

Rearranging the equation and setting it equal to zero:

2h² + 4h - 240 = 0

Now we can solve this quadratic equation. Factoring out a 2:

2(h² + 2h - 120) = 0

Factoring the quadratic expression inside the parentheses:

2(h + 12)(h - 10) = 0

Setting each factor equal to zero:

h + 12 = 0   or   h - 10 = 0

Solving these equations, we get:

h = -12   or   h = 10

Since height cannot be negative in this context, we discard the negative value. Therefore, the height of the triangular window is h = 10 feet.

Substituting the height value back into the expression for the base:

base = 2h + 4

    = 2(10) + 4

    = 20 + 4

    = 24

Therefore, the base of the triangular window is 24 feet and the height is 10 feet.

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The difference in the size between the apple and the orange symbols distort the comparison.

Data that has been manipulated or distorted in a way that is false or misleading is represented graphically in a misleading graph. A misleading graph might be made purposely to mislead or unintentionally owing to a misunderstanding of how to show the data correctly or a lack of experience in that area.

Changing the axes' scale, using multiple scales for different areas of the graph, using incorrect labelling or units, and ignoring or exaggerating specific data points are a few examples of misleading graphs.

The difference in the size between the apple and the orange symbols distort the comparison.

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The equation of the quadratic function represented by this table is: f(x) = -3x^2 + 42x + 103.

To find the equation of the quadratic function represented by this table, we need to use the general form of a quadratic function:

f(x) = ax^2 + bx + c.

We can use the given values of x and f(x) to form a system of three equations, where the coefficients a, b, and c are unknown:

- 25a + 5b + c = -4  (when x = 5, f(x) = -4)

- 36a + 6b + c = 5   (when x = 6, f(x) = 5)

- 49a + 7b + c = 8   (when x = 7, f(x) = 8)

We can solve this system of equations by using elimination or substitution methods, or by using matrix algebra. Here, we will use the elimination method:

Subtract the first equation from the second equation: 11a + b = 9

Subtract the second equation from the third equation: 13a + b = 3

Solve this system of two equations in two unknowns:

11a + b = 9

13a + b = 3

Subtracting the first equation from the second equation, we get:

2a = -6

Therefore, a = -3.

Substituting this value of a into either of the two equations above, we get:

11(-3) + b = 9

b = 42

Finally, we can use any of the three original equations to find c:

-25(-3) + 5(42) + c = -4

c = 103

Therefore, the equation of the quadratic function based on given data is f(x) = -3x^2 + 42x + 103.

Note: The question is incomplete. The complete question probably is: What is the equation of the quadratic function represented by this table?

x 5 6 7 8 9 10

f(x) -4 5 8 5 -4 -19

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9514 1404 393

Answer:

  (a)  SSS

Step-by-step explanation:

Two of the sides are marked congruent, and the third side is shared (so is congruent to itself). The triangles are congruent by the Side-Side-Side (SSS) postulate.

Answer:

b^2 + 2b <= 168

Step-by-step explanation:

The base is b.

The height, h, is 4 in. greater than twice the base, so the height is 2b + 4.

The area of a triangle is bh/2. We replace h with the expression for height.

A = bh/2 = b(2b + 4)/2 = (2b^2 + 4b)/2 = b^2 + 2b

The area is b^2 + 2b.

The area is no more than 168 in.^2, so it is less than equal to 168 in.^2.

b^2 + 2b <= 168

("<=" means "less than or equal to")

Since you don't show the choices, choose an inequality that is equivalent to the one just above.

Systematic random sampling is sometimes used in place of simple random sampling due to its efficiency, representativeness, ease of implementation, and cost-effectiveness.

Systematic random sampling is sometimes used in place of simple random sampling for several reasons, including:
Efficiency:

Systematic random sampling can be more efficient than simple random sampling, as it involves selecting elements at regular intervals from the population.

This often reduces the time and effort needed to collect data compared to simple random sampling.
Representativeness:

Systematic random sampling may provide a more representative sample of the population.

By selecting elements at regular intervals, it ensures that different segments of the population are included, reducing the potential for sampling bias.
Ease of implementation:

Systematic random sampling is relatively easy to implement, as it involves fewer random selections compared to simple random sampling.

This makes it more practical for large populations or when a sampling frame is not readily available.
Cost-effectiveness:

Systematic random sampling can be more cost-effective than simple random sampling.

Since the process is more efficient, it may require fewer resources, such as time and personnel, to collect data.

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Answer:

RANGE: 120 - 160

Step-by-step explanation:

15*8 = 120

20*8 = 160

RANGE: 120 - 160

Answer:

6-inch board is cut into two pieces. One piece is two times the length of the other. Find the length

of the shorter pi

Answer:

Supplementary Angles: AOC and COD

Complementary Angles: COB and COD

Vertical Angles: AOE and COD

Adjacent Angles not supplementary or complementary: AOB and BOC

Step-by-step explanation:

Answer:

Step-by-step explanation:

Supplementary angles       : AOC & COD  

Complementary angles     :   COB & COD

Vertically angles                :  AOE & COD

Adjacent angles   (neither complementary nor supplementary)             :   AOB & BOC

Answer:

X=-1, y=1

Step-by-step explanation:

- x=2x+3

-3x=3

X=-1

Y=-1*-1=1

Tom Harris, who is twenty-four years old, decides to purchase $15,000 of ten-year term insurance. The insurance premium can be paid in different intervals: semi-annually, quarterly, or monthly.

The information by stating Tom's age, the amount of insurance he purchased, and the different payment options available (semi-annually, quarterly, and monthly). In the second paragraph, we can explain the calculations for each payment option.  a. Semi-annually: The premium amount is $62.25. This means that Tom will need to pay $62.25 every six months for the duration of the ten-year term. b. Quarterly: The premium amount for this option is not provided, so we cannot calculate it without further information. c. Monthly: The premium amount for this option is not provided either, so we cannot calculate it without additional details. It is important to note that the specific premium amounts for the quarterly and monthly payment options are missing from the given information. To calculate those premiums, we would need the respective rates or information on how they are calculated based on the insurance policy.

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2x2 + x −#6 _____________

x2 − 1

∙ x

__

2 + 2x + 1

x 2 − 4

Rewrite as multiplication.

(2x − 3)(x + 2) __

(x + 1)(x − 1) ∙ (x + 1)(x + 1) __ (x + 2)(x − 2) Factor the numerator and denominator.

(2x − 3)(x + 2)(x + 1)(x + 1) ___ (x + 1)(x − 1)(x + 2)(x − 2) Multiply numerators and denominators.

(2x − 3)(x + 2)(x + 1)(x + 1) ___ (x + 1)(x − 1)(x + 2)(x − 2) Cancel common factors to simplify.

(2x − 3)(x + 1) __ (x − 1)(x − 2)

Answer:             g(x) = 3(x + 1)2 + 2(x + 1) − 7

Step-by-step explanation:

Answer:

Total after tax and discount is $7.78

Step-by-step explanation:

(10.49×0.3)= 3.15

10.49 - 3.15 = 7.34

(7.34×0.06)= 0.44

7.34 + 0.44 = 7.78

The quotient of the expression \((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\) is given as 3/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the expression:

\((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\\\\Simplifying\ the\ expression:\\\\=(\frac{n+3}{2(n-3)})/ (\frac{3(n-3)}{n+3} )\\\\=\frac{3}{2}\)

The quotient of the expression \((\frac{n+3}{2n-6})/ (\frac{n+3}{3n-9} )\) is given as 3/2

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In this case, the margin of error for a 99% confidence interval is $0.814.

To calculate the margin of error for a 99% confidence interval, we need to use the formula:
Margin of error = Z × (standard deviation / sqrt(sample size))
where Z is the z-score for the desired confidence level. For a 99% confidence interval, the z-score is 2.576.
Plugging in the given values, we get:
The margin of error = 2.576 × (1.46 / √(30))
Simplifying this expression, we get:
Margin of error = 0.814
Therefore, in this case, the margin of error for a 99% confidence interval is $0.814. This means that we can be 99% confident that the true average cost of a latte in the population falls within $3.55 ± $0.814. In other words, the true average cost of a latte in the population could be as low as $2.736 or as high as $4.364, based on the sample data.

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The residential buildings' total assessed land value has the smallest standard deviation.

To determine the standard deviations for the commercial and residential buildings' total assessed land value and total assessed parcel value, we would need access to a specific dataset that includes these values. However, based on general trends and assumptions, residential buildings' total assessed land value is likely to have the smallest standard deviation.

Residential properties typically exhibit more homogeneity compared to commercial properties. Residential neighborhoods often consist of similar types of properties, with comparable land values within a specific area. As a result, the assessed land values for residential buildings are more likely to cluster around a mean value, resulting in a smaller standard deviation.

In contrast, commercial properties can vary significantly in terms of size, location, and intended use. They may be diverse in terms of their land value and parcel value. The assessed land values and parcel values for commercial buildings are more likely to have a wider range of values, leading to a larger standard deviation.  

Therefore, based on these general characteristics, the residential buildings' total assessed land value is expected to have the smallest standard deviation compared to the commercial buildings' total assessed land value and total assessed parcel value.

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The statement provided is actually the opposite of the correct definitions.

In database terminology, a field refers to a single piece of information that is stored in a database table. A field can contain a variety of data types such as text, numbers, dates, and so on. For example, in a database table of customer information, there might be fields for the customer's name, address, phone number, and email.

A record, on the other hand, is a complete set of information about an entity in a database. A record consists of a collection of fields that are all related to each other. For example, in the customer information table mentioned above, a single record might represent a specific customer, and would contain all the fields related to that customer (name, address, phone number, email, etc.).

So to summarize, a field is a single piece of information within a record, while a record is a collection of related fields that together represent a complete set of information about an entity in a database.

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The limit of the given expression as x approaches 1 is 0.

To evaluate the limit of the given expression as x approaches 1, we can use L'Hopital's rule, which states that if the limit of a quotient of functions is of the form 0/0 or ±∞/±∞, then the limit can be found by taking the derivative of the numerator and denominator and evaluating the new quotient at the same point.

Using L'Hopital's rule on the given expression, we get:

lim x→1 [5x/(x-1) - 5/x] = lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)]

Plugging in x = 1 directly to this expression, we get:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = (5 - 10 + 5)/(1 - 1) = 0/0

Since the limit is still in an indeterminate form, we can apply L'Hopital's rule once again:

lim x→1 [(5x^2 - 10x + 5)/(x^2 - x)] = lim x→1 [(10x - 10)/(2x - 1)] = 0

Therefore, the limit of the given expression as x approaches 1 is 0.

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To determine which postulate to be used to know  whether two triangles are congruent, observe the corresponding angles and sides of the two triangles and use the statements of those two postulates.

What is AAS congruence theorem ?

The Triangles Are Congruent Theorem (AAS) states that if two angles and a non-included side in one triangle are congruent to two angles and the matching non-included side in another triangle.

AAS congruence theorem full form is Angle Angle Side .

ASA rule:

According to the ASA rule, two triangles are said to be congruent if any two of the angles and sides that make up one triangle are equal to the corresponding two angles and sides that make up the other triangle.

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The expression as a number in scientific notation is 4.2 * 10^5

The expression is given as:

quantity 7 times 10 cubed end quantity times quantity 5.4 times 10 to the fourth power end quantity all divided by quantity 9 times 10 squared

Rewrite properly as:

[7 * 10^3 * 5.4 * 10^4]/[9 * 10^2]

Evaluate the product of 7 and 5.4

So, we have:

[37.8* 10^3 * 10^4]/[9 * 10^2]

Evaluate the product of 10^3 and 10^4

So, we have:

[37.8* 10^7]/[9 * 10^2]

Evaluate the quotient of 37.8 and 9

So, we have:

[4.2 * 10^7]/[10^2]

Evaluate the quotient of 10^7 and 10^2

So, we have:

4.2 * 10^5

Hence, the expression as a number in scientific notation is 4.2 * 10^5

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The commitment scheme for committing a single bit 0 or 1 is a bad commitment scheme.

Consider the following commitment scheme for committing a single bit 0 or 1: for 0, pick a random even element a (mod p) and commit a² (mod p). For 1, pick a random odd element and similarly commit its square. Let p be a big prime. To show that this is a bad commitment scheme, let's look at an example.

Suppose that p = 7 and the sender wants to send the value 1. Therefore, he chooses an odd number, say a = 3, and computes a² = 9 mod 7 = 2. Now he sends 2 to the receiver. The receiver has two possible options for guessing the number sent: 1 or 0. Let's assume that he guesses the number 0 and then he can choose any even number, say a = 2.

Now he computes a² = 4 mod 7. As 4 is the residue of an even number, it's impossible to distinguish between the values sent by the sender. Therefore, this is a bad commitment scheme.

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This is not a good commitment scheme.

A good commitment scheme should satisfy two properties: hiding and binding. Hiding means that the committed value should be computationally infeasible to determine without the commitment opening. Binding means that once the commitment is opened, it should be computationally infeasible to change the committed value.

In the given commitment scheme, the committed value is the square of a randomly chosen even or odd element modulo p. However, this scheme is not secure because it does not satisfy the hiding property.

To see why the hiding property is not satisfied, consider the case when the committed value is 0. Since we commit the square of a randomly chosen even element, any square root of the committed value modulo p will reveal the committed value. In this case, finding the square root of a modulo p, where a is even, is straightforward and does not require excessive computation. Therefore, an attacker can easily determine the committed value without knowing the opening.

This lack of hiding makes the commitment scheme insecure because an adversary can guess the committed value by calculating the square root. Thus, an attacker can break the hiding property of the commitment scheme, rendering it ineffective for secure communications.

In summary, the given commitment scheme is not a good one as it fails to satisfy the hiding property. It is important to use a commitment scheme that provides both hiding and binding properties to ensure the security and integrity of the committed values.

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Answer:

Table 4 represents a function.

Step-by-step explanation:

Functions require that each x-value has a unique y-value. In the other tables you see a value repeated in the x column, with a different value in the y column.

Answer:

Step-by-step explanation:

Below is the pic of how this would be set up in order to determine what it is you are looking for. The angle is set in QI, and since csc A is the reciprocal of sin, the ratio is hypotenuse over side opposite. Solve for the missing side using Pythagorean's Theorem:

\(37^2=12^2+b^2\) and

1369 = 144 + b² and

1225 = b² so

b = 35

The sec ratio is the reciprocal of cos, so if cos is adjacent over hypotenuse, the sec is hypotenuse over adjacent, which is 37/35

Answer:

100.00 difference

Step-by-step explanation:

450.00-350.00=100.00

The percent should be 100

Answer:

\(x^4 + 6x^3 - x^2 - 30x + 25\)

Step-by-step explanation:

Multiplica la expresión por sí misma y expande el corchete:

\((x^2+ 3x - 5 )^2\\\\= (x^2+ 3x - 5 )*(x^2+ 3x - 5 )\\\\= x^2(x^2+ 3x - 5 ) +3x(x^2+ 3x - 5 ) - 5(x^2+ 3x - 5 )\\ \\x^4 + 3x^3 - 5x^2 + 3x^3 + 9x^2 - 15x - 5x^2 -15x + 25\\\\x^4 + 3x^3 + 3x^3 -5x^2 + 9x^2 - 5x^2 - 15x - 15x + 25\\\\= x^4 + 6x^3 - x^2 - 30x + 25\)

Answer:

a = 1

b = 2

k = -2

Step-by-step explanation:

Given:

\(\displaystyle \large{y=k(x-a)^2(x-b)}\)

First, find the a-value and b-value by observing the graph. Notice that once the graph hits x = 1, it just goes up or concave up - that indicates to be the double roots of function. Therefore:

Our a-value is 1

Second, find the b-value. Another x-intercept beside double roots x = 1 is x = 2 as shown in the graph. Therefore:

Our b-value is 2

Third, find the k-value. Right now we have the equation:

\(\displaystyle \large{y=k(x-1)^2(x-2)}\)

To find the k-value, simply find a point’s value (x,y) to substitute. According to the graph, you can try substitute (0,4) in:

\(\displaystyle \large{4=k(0-1)^2(0-2)}\\\displaystyle \large{4=k(-1)^2(-2)}\\\displaystyle \large{4=k(1)(-2)}\\\displaystyle \large{4=-2k}\\\displaystyle \large{k=-2}\)

Therefore, the value of k is -2

Answer:

E

Step-by-step explanation:

so much words sis sossy

Answer:

Step-by-step explanation:

\(-3$<$ x\le 13\)

Anais, who bought a ribbon of length \(2 \dfrac 12 \) yards, and she trimming a curtain from it. From substraction, length of ribbon used in curtain is equals to 72 inches.

Word problems express in mathematical form. In subtraction, keywords that could signal the operation are lesser, less than, removed from. However, there are times when the idea of subtraction or taking away is inferred from the problem itself. In the problem, total length of ribbon Anais bought

= \(2 \dfrac 12 \) yards

The length of ribbon left after trimming some curtains = 1 feet 6 inches

We have to determine inches of ribbon Anais use to trim the curtains. Let it will be equal to x inches . We may notice in the provide values that they all have different units. We can convert the all different units into inches. Using uint conversation, 1 yard = 36 inches

=> \(2 \dfrac 12 \)

yards =\( 36 × \frac{ 5}{2} \)

= 90 inches

Similarly, 1 feet = 12 inches, then 1 feet + 6 inches = 12 + 6 = 18 inches

Thus, the left ribbon length = 18 inches

Using substraction method, the length in inches of ribbon that anais use to trim the curtains = total length - left length of ribbon = 90 - 18

= 72 inches.

Hence, required value is 72 inches.

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Complete question:

Anais bought

\(2 \dfrac 12 \)

yards of ribbon. She had 1 feet 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

Answer:

A. 5.4 in

Step-by-step explanation:

At the top of the line segment GH, you can see it ends on Circle D's circumference. Therefore, if you made a line segment from D to G, its length would be the radius. Lines DE and GH are perpendicular and make a 90 degree angle, so you can make line DG a hypotenuse, use pythagoreans theorem, and find the radius. However, since they intersect at a halfway point, you have to divide 10 and 4 by 2. 10/2 = 5  4/2 = 2   5^2 + 2^2 = r^2

5^2 = 25 and 2^2 = 4, so 29 = r^2. The square root of 29 is 5.385, or 5.4 inches.

I got a bit lazy answering this, but I hope it helps!

Answer:5.4

Step-by-step explanation: