Factor the expression completely.
18x2 - 32
O A. 2(3x + 2)(3x – 8)
B. 2(9x2 - 16)
O C. 2(3x - 4)(3x - 4)
O D. 2(3x + 4)(3x - 4)

Answer:

3.4, 1/4, 12%, -0.01, -26.1

Step-by-step explanation:

The simplest way to do these type of problems is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

12% is already a percentage

-0.01 = -1%

1/4 = 25%

3.4 = 340%

-26.1 = -2610%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

3.4, 1/4, 12%, -0.01, -26.1

FINAL ANSWER: 3.4, 1/4, 12%, -0.01, -26.1

Laplace transforms are an essential mathematical tool used to solve differential equations. These transforms transform differential equations to algebraic equations that can be solved easily.

To solve the differential equations given in the question, we will use Laplace transforms. So let's start:Solution:a) y" – y = t y(0) = 1, y'(0) = 1First, we take the Laplace transform of the given differential equation.L{y" - y} = L{ty}

Taking the Laplace transform of both sides gives:L{y"} - L{y} = L{ty}Using the formula, L{y"} = s²Y(s) - s*y(0) - y'(0), and L{y} = Y(s) then we get:s²Y(s) - s - 1 = (1/s²) + (1/s³)Rearranging the above equation, we get:Y(s) = [1/(s²*(s² + 1))] + [1/(s³*(s² + 1))]Now, we apply the inverse Laplace transform to find the solution.y(t) = (t/2)sin(t) + (cos(t)/2)

The solution of the differential equation y" – y = t, with initial conditions y(0) = 1, y'(0) = 1 is y(t) = (t/2)sin(t) + (cos(t)/2).

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Type I error refers to rejecting a true null hypothesis, while Type II error refers to failing to reject a false null hypothesis. Types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, etc.

Type I error is a false positive, and Type II error is a false negative. Examples of Type I errors include convicting an innocent person in a criminal trial and rejecting a new drug that is actually effective. Examples of Type II errors include failing to convict a guilty person in a criminal trial and accepting a new drug that is actually ineffective.

Various statistical analyses can be applied to the data collected in research studies, depending on the research question and the type of data. Some common types of statistical analyses include descriptive statistics, inferential statistics, correlation analysis, regression analysis, t-tests, analysis of variance (ANOVA), and chi-square tests. Descriptive statistics are used to summarize and describe the characteristics of the data, while inferential statistics are used to draw conclusions and make inferences about the population based on sample data. Correlation analysis examines the relationship between two or more variables, regression analysis explores the relationship between a dependent variable and one or more independent variables, t-tests compare means between two groups, ANOVA analyzes differences among three or more groups, and chi-square tests examine the association between categorical variables.

Type I error, also known as a false positive, occurs when we reject a null hypothesis that is actually true. This means we conclude that there is a significant effect or relationship when there is none in reality. For example, in a criminal trial, a Type I error would be convicting an innocent person. Another example is rejecting a new drug that is actually effective, leading to the rejection of a potentially beneficial treatment.

On the other hand, a Type II error, also known as a false negative, occurs when we fail to reject a null hypothesis that is actually false. In this case, we fail to detect a significant effect or relationship when one exists. For instance, in a criminal trial, a Type II error would be failing to convict a guilty person. In the context of medical testing, a Type II error would occur if we accept a new drug as ineffective when it is actually effective, resulting in the approval of an ineffective treatment.

Various statistical analyses can be applied to research study data depending on the research question and the type of data collected. Descriptive statistics are used to summarize and describe the characteristics of the data, such as measures of central tendency (e.g., mean, median) and variability (e.g., standard deviation, range). Inferential statistics are used to make inferences and draw conclusions about the population based on sample data, such as hypothesis testing and confidence interval estimation.

Correlation analysis examines the relationship between two or more variables and determines the strength and direction of their association. Regression analysis explores the relationship between a dependent variable and one or more independent variables, allowing us to predict the value of the dependent variable based on the independent variables.

T-tests are used to compare means between two groups, such as comparing the average test scores of students who received a specific intervention versus those who did not. Analysis of variance (ANOVA) analyzes differences among three or more groups, such as comparing the performance of students across different grade levels.

Chi-square tests examine the association between categorical variables, such as analyzing whether there is a relationship between gender and voting preference. These are just a few examples of the statistical analyses commonly applied to research study data, and the specific choice of analysis depends on the research question and the nature of the data.

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The work done by a force can be calculated by taking the dot product of the force vector with the displacement vector whether the force and displacement vectors are consecutive or anti-congruent.

The formula of the dot product is-

A ⋅ B = |A| |B| cos(θ)

Here A and B are the vectors  |A| and |B| which represent their magnitudes, and θ is the angle between them.

The angle between the force and displacement vectors is either 0 degrees (cos(0) = 1) or 180 degrees (cos(180) = -1) depending on whether they are parallel or antiparallel. The dot product becomes: in these circumstances.

A ⋅ B = |A| |B| (1) = |A| |B| (cos(0)) = |A| |B|

When the vectors are parallel or antiparallel, the angle is 0 or 180 degrees, respectively, and the cosine term is 1 or -1. This occurs since work done is defined as the dot product of the force and displacement vectors multiplied by the cosine of the angle between them.

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Answer:

the solution is c. perpendicular lines

Step-by-step explanation:

the slopes: 1/4 and -4 are perpendicular and intersecting

The required  types of dilation are the given scale factors are,
Scale factor  =    -4     [contaction]
Scale factor = 2.5       [Expansion]
Scale factor = 2/3       [contraction]
Scale factor = -3/4      [contraction]

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
The type of dilation can be stated as if the scale factor is positive and greater than 1 there must be an expansion while if the scale factor is less than 1 then there will be a contraction.

So
From the table,
Scale factor  =    -4     [contaction]
Scale factor = 2.5       [Expansion]
Scale factor = 2/3       [contraction]
Scale factor = -3/4      [contraction]

Thus, the required solution is given above,

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Answer:

c^2 + 3c - 40

Step-by-step explanation:

Here we are finding the product of (C+8) and (C-5). We use the FOIL method to expand this (multiplying in the order of First, Outer, Inner, Last).

(c + 8) ( c - 5)

c * c is c ^2 due to an unknown variable.

C * 8 is 8c

c * -5 is -5c

8 * -5 is -40

Now, we combine like-factors and end up with;

c^2 + 3c -40

Thank you for posting this question! If it fits suit, please mark Brainliest. If you have any other questions let me know :)

Step-by-step explanation:

answer is option D is the correct answer of this question

The density of lead can be calculated by dividing the mass of lead (350g) by its volume (30.7 cm³). The density of lead is approximately 11.4 g/cm³.

The density of a substance is defined as its mass per unit volume. To find the density of lead, we divide the mass of lead by its volume.

Given that the mass of lead is 350g and the volume is 30.7 cm³, we can calculate the density as follows:

Density = Mass / Volume

Density = 350g / 30.7 cm³

Using a calculator, we find:

Density ≈ 11.4 g/cm³

Therefore, the density of lead is approximately 11.4 grams per cubic centimeter (g/cm³). This means that for every cubic centimeter of lead, it has a mass of approximately 11.4 grams.

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(hope this helps) :)

The equation that can be used to prove 1 + tan2(x) = sec2(x) is StartFraction cosine squared (x) Over tangent squared (x) EndFraction + StartFraction sine squared (x) Over tangent squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction. the correct option is d.

In order to prove this, we can use the following identities:

tan(x) = sin(x) / cos(x)

sec(x) = 1 / cos(x)

tan2(x) = sin2(x) / cos2(x)

sec2(x) = 1 / cos2(x)

Substituting these identities into the given equation, we get:

StartFraction cosine squared (x) Over tangent squared (x) EndFraction + StartFraction sine squared (x) Over tangent squared (x) EndFraction = StartFraction 1 Over tangent squared (x) EndFraction

Therefore, 1 + tan2(x) = sec2(x).

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Answer:

60 cups

Step-by-step explanation:

you convert the 9 to ml (9 = 9000ml: 9000 ÷ 150 = 60) 60 cups

Answer:

NO.2- SSA is not the method to show the congruency of two triangles.

T|=|S|⟹ there is bijection F:S→T.

A bijection is a function between the elements of two sets in mathematics that is also referred to as a one-to-one correspondence, an invertible function, or a bijective function.

In this function, each element of one set is paired with exactly one element of the other set, and each element of the second set is paired with exactly one element of the first set.

No elements are left unpaired. A one-to-one (injective) and onto (surjective) mapping of a set X to a set Y is known as a bijective function, or f: X Y in mathematics.

One-to-one function (an injective function; a bijection from the set X to the set Y has an inverse function from Y to X) should not be confused with one-to-one correspondence. X and Y must be finite if.

According to our question-

The function f:ST |S||T| has an injective and not a surjective nature.

Assume an injective function exists: g:TS|T||S|. |T|=|S|

(this follow from the Cantor-Bernstein theorem).

|T|=|S|⟹ F:S:T has a bijection.

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The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

Transformation is the movement of a point around the coordinate plane. Types of transformations are rotation, translation, reflection and dilation.

Translation is a type of transformation which is either up, down, left or right in the coordinate plane.

The translation sequence that maps angle ABC to angle A'B'C' is (x, y) ⇒ (x + 3, y + 6)

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Answer: it would be 18 candies that are left

Step-by-step explanation:  

I did the math

Answer: 140%

Step-by-step explanation:

From the question, we are informed that price increases from $50 to $120. The percentage change will be:

= (New price - Old price)/Old price × 100

= (120 - 50)/50 × 100

= 70/50 × 100

= 1.4 × 100

= 140%

An exponential equation, y = (20) 3ᵗ, shows the number of infected people from an outbreak of whooping cough. The number of Infected people reach 1000 after 3.56 weeks.

We have an equation that shows the number of people infected from a whooping cough outbreak. This equation is y is equal to 20 times 3 to the power of t, i.e. y = (20) 3ᵗ -- (1)

where y--> number of infected people

t--> time in weeks

An exponential equation is an equation with exponents where either the exponent or part of the exponent is a variable. As we see 't' is variable so, eqution (1) is an exponential equation. We have to determine time in weeks when the number of infected people count reach 1,000. Substitute, y = 1000 in (1)

=> 1000 = (20)3ᵗ

Dividing by 20 both sides

=> 1000/20 = 3ᵗ

=> 50 = 3ᵗ

Taking natural logarithm both sides,

=> ln(50) = ln( 3ᵗ)

=> ln(50) = t ln(3)

=> t = ln(50)/ln(3)

=> t = 3.56

Hence, required value of t is 3.56 weeks.

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Answer:

2 is the answer to your question

If all other values remain constant, an increase in sample size will result in a broader confidence interval when constructing one.

The definition of the MoE, or margin of error, is

MoE = sigma ÷ sqrt(n)

The population standard deviation is represented by sigma. If you don't know sigma, utilize s to get a rough idea of it. The sample standard deviation is denoted by the variable s.

The MoE increases along with the sigma. The width or narrowness of the confidence interval is directly determined by the MoE. A smaller MoE indicates greater confidence with less error, whereas a larger MoE indicates greater net casting but increased error.

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Data types provide the information to the runtime about how much space is required in the memory. Datatypes helps to allocate memory. In OOPs bases programming languages it also helps to decide where memory should be allocated like heap and stack memory.

Data types allow a compiler to allocate the right memory space for a variable, and also let it perform type checking, marking sure the program uses the variables correctly per their defined type.

A data type is an attribute associated with a piece of data that tells a computer system how to interrupt its value. Understanding the data types ensures that data is collected in the preferred format and the value of each property is as expected.

Choosing the right data types for your tables, stored procedures, and variables not only improves performance by ensuring a correct execution plan, but it also improves data integrity by ensuring that the correct data is stored within a database.

Data type and length are the most fundamental integrity constraints applied to data in a database. Simply by specifying the data type for each column when a table is created, DB2 automatically ensures that only the correct type of data is stored in that column. Processes that attempt to insert or update the data to a non-conforming value will be rejected. Furthermore, a maximum length is assigned to the column to prohibit larger values from being stored in the table.

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Therefore, the line integral ∫c F.dr is equal to -15π/4. To use Stokes' Theorem to evaluate the line integral ∫c F.dr, we need to find the curl of F and then evaluate the surface integral of that curl over the region bounded by the curve C.

First, let's find the curl of F:

curl(F) = <(dQ/dy - dP/dz), (dR/dz - dP/dx), (dP/dy - dQ/dx)>

where F = <P, Q, R> = <2yz, 5xz, In z>

So,

dP/dy = 2z

dQ/dz = 0

dQ/dx = 0

dR/dz = 1/z

dR/dx = 0

dP/dx = 0

dP/dy = 0

dQ/dy = 0

Therefore,

curl(F) = <2/z, 0, -5x>

Now, let's find the boundary curve C. The intersection of x² + y² + z² = 9 and x² + y² = 5 gives us the following system of equations:

x² + y² = 5

x² + y² + z² = 9

Subtracting the first equation from the second, we get:

z² = 4

Taking the square root of both sides and noting that we are only interested in the positive value of z, we get:

z = 2

Substituting this into the equation of the cylinder, we get:

x² + y² = 5

This is the equation of a circle with radius sqrt(5) centered at the origin in the xy-plane. Since we want the portion of this curve above the xy-plane, we add z = 2 to the equation, giving us the boundary curve C: x² + y² = 5, z = 2.

Now, let's evaluate the surface integral of curl(F) over the region bounded by C. The surface is the portion of the sphere x² + y² + z² = 9 above the xy-plane and below z = 2. This surface is a hemisphere with radius 3 centered at the origin in the xy-plane.

∬S curl(F) . dS

= ∫0^2π ∫0^π/2 <2/(3sinφ), 0, -15sinφcosφ> . ρ²sinφ dθ dφ

= ∫0^2π ∫0^π/2 (-30/3)sin²φ cosφ dθ dφ

= -15π/4

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The probability of not selecting a green marble is equal to the total number of non-green marbles in the bag divided by the total number of marbles in the bag.

To calculate the probability: there are three green marbles out of a total of twenty-five marbles, so the probability of selecting a green marble is 3/25.

The likelihood of not selecting a green marble is then 1 - 3/25 = 22/25.

This is equal to 22/25 * 100 = 88% as a percentage.

As a result, P(not green) = 88%

Probability denotes the possibility of something happening. It is a mathematical branch that deals with the onset of a random event. The value ranges from zero to one. Probability has been tried to introduce in mathematics to predict the probability of events occurring. Probability is defined as the degree to which something is likely to occur. This is the fundamental probability theory, which is also used in probability distribution, in which you will learn about the possible outcomes of a random experiment.

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The statement B) (2³).(2¹)>(2²) is true.

The three statements involve the comparison of certain values involving powers of 2.

To determine which statement is true, we can evaluate the expressions and compare them.

A: (2³) - (2¹) < (2²)

This can be simplified to 8 - 2 < 4, which becomes 6 < 4. Since this is false, statement A is not true.

B: (2³).(2¹) > (2²)

This can be simplified to 8.2 > 4, which becomes 16 > 4. Since this is true, statement B is true.

C: (2³).(2¹) = (2²)

This can be simplified to 8.2 = 4, which becomes 16 = 4. Since this is false, statement C is not true.

Therefore, the only statement that is true is statement B: (2³).(2¹) > (2²).

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Answer:

5 to 3

Step-by-step explanation:

15/3=5

6/3=3

Answer:

5:2

Step-by-step explanation:

15:6 can both be divided by 3, 15/3 = 5, 6/3 = 2, making the ratio,

5:2 hope i helped you (and could i have brainliest it would help me!)

The range and domain of the given graph are respectively;

-∞ ≤ x ≤ ∞

-4 ≤ y ≤ ∞

Domain is defined as the set of all possible input values for which the function is possible.

Range is defined as the set of all possible output values for which the function is true for the input values.

From the graph, we see that the horizontal asymptote is at y = -4 and as such this will be the least value of the range.

We can also see that the curve is still continuous in the positive axis for y-values and so the y-values are greater than 6. Thus;

The domain is; -4 ≤ y ≤ ∞

The range from the graph is seen as x continues increasing both in the positive and negative axis region and as such the range is expressed as;

-∞ ≤ x ≤ ∞

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A rectangle with sodes of lengrh 84 and 45 has the same perimeter asa hexagon. If the sides of the hexagon all have the same length then what is the length of a side of the hexagon

(A) 41

(B) 46

(C) 43

(D) 45

(E)Other

A square has an area of 25. Two opposite side of the square each have their length tripled what is the perimeter of the new figure

(A) 40

(B) 25

(C) 60

(D) 35

(E)Other

A rectangle measures 6 centimeters by 25 centimeters the probability that a point randomly chosen inside the rectangle is closer to a side of length 25 than a side of length 6 is p/q are relatively prime positive whole numbers what is the sum of p and q

(A) 5

(B) 19

(C) 37

(D) 47

(E)Other

The three values of x that are solutions to X^3 + mx = 37x^2 +n are positive whole numbers that form a geometric sequence what is the sum of the possible values of the common ration of the geometric sequence

(A) 25/12

(B) 9/4

(C) 7/4

(D) 2

(E)Other

log base 3 of the quantity x to the seventh z to the fourth end quantity divided by y to the sixth end log

Sure hope this helps you :D

The simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.

The laws involved in the simplification of logarithmic expressions are:

In the question, we are asked to simplify the logarithmic expression,

6 log₃x - 7 log₃y + 4 log₃z.

The simplification of the provided logarithmic expression can be done as follows:-

6 log₃x - 7 log₃y + 4 log₃z,

= log₃x⁶ - log₃y⁷ + log₃z⁴ {Using the Power law: \(a log_x b= log _xb^a\)}

= log₃x⁶ + log₃z⁴ - log₃y⁷

= log₃x⁶z⁴ - log₃y⁷ {Using the Product law: \(log_xa + log_xb = log_xab\)}

= log₃{(x⁶z⁴)/y⁷} {Using the Quotient law: \(log_xa - log_xb = log_x\frac{a}{b}\)}.

Thus, the simplified form of the logarithmic expression, 6 log₃x - 7 log₃y + 4 log₃z, is log₃{(x⁶z⁴)/y⁷}. Hence, the third option is the right choice.

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