Given that D( x ) = 2 x , select all of the following that are true statements. D( x ) is a direct variation. D( x ) is a function. D( x ) is a rule for the set of points (5, 10), (6, 12) and (-2, -4). x is the dependent variable. D(6) = 3 1 Attempts Remain

There are 1,307,674,368 different methods to set up the 15 unique books on the bookshelf whilst 10 of the books are not placed on the bookshelf and order is important .

The problem requires us to find the range of arrangements viable when 15 unique books are positioned on a bookshelf however only 5 of them are placed at the bookshelf and the order is vital.

Considering that each book is unique, the number of methods of arranging the books is surely the quantity of permutations of the books, which is given by means of the formulation nPr = n! / (n - r)!.

15P5 = 15! / (15-5)! = 15! / 10!

= 1,307,674,368

Therefore, there are 1,307,674,368 different methods to set up the 15 unique books on the bookshelf.

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To determine whether the solution of the square root of the quantity 4x - 3 equals 5 is extraneous or not, we need to follow the following steps:

Step 1:  Square both sides of the equation: $4x - 3 = 5^2$

Step 2: Simplify the equation by adding 3 on both sides of the equation: $4x - 3 + 3 = 25 + 3$

Step 3: Simplify the equation further: $4x = 28$

Step 4: Solve for x by dividing both sides by 4: $\frac{4x}{4} = \frac{28}{4} \Right arrow x = 7$

Step 5: Substitute the value of x back into the original equation: $\sqrt{4x - 3} = \sqrt{4(7) - 3} = \sqrt{25} = 5$

Since the value of x satisfies the original equation, the solution is not extraneous.

Thus, the value of x = 7 is a valid solution to the equation. Therefore, we can say that the solution is not extraneous.

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Answer:

To found the number of contestants that were selected, we used 200 contestants to multiply with 3/5.

Step-by-step explanation:

1st way: 200 x 3 / 5 = 120 contestants

2nd way: 200 / 5 x 3 = 120 contestants

Answer : 120 contestants

The probability of event A or event B occurring, P(A or B), is 0.9 and d: 0.1125 is probability of A or B.

To find the probability of event A or event B occurring, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

Given that events A and B are mutually exclusive, it means that they cannot occur simultaneously. In this case, P(A and B) would be equal to 0 because the intersection of mutually exclusive events is empty.

Given:

P(A) = 0.75

P(B) = 0.15

Using the formula, we can calculate:

P(A or B) = P(A) + P(B) - P(A and B)

          = 0.75 + 0.15 - 0

          = 0.9

Therefore, the probability of event A or event B occurring, P(A or B), is 0.9.Among the provided answer choices, the correct answer is:

d: 0.1125

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Answer: 92º

Step-by-step explanation:

Since the sum of the angles of a triangle is always 180 degrees, we can use the following equation:

56º + 32º + xº = 180º

or

180º - (56º + 32º) = xº

Answer:

Step-by-step explanation:

Given a set of numbers, determine if they represent a geometric sequence. Divide each term by the previous term. Compare the quotients. If they are the same, a common ratio exists and the sequence is geometric.

Answer:

choose any one term in the sequence and divide it by the previous term

The probability that the number of people wanting new copies is more than two standard deviations away from the mean is very low. For Steph Curry making exactly three of his next five free throws, the probability is approximately 0.25.

The probability that the number of people wanting new copies is more than two standard deviations away from the mean is very low. This is because the standard deviation measures the amount of variability or dispersion from the mean. The probability of any given value being more than two standard deviations away from the mean is very slim.For Steph Curry making exactly three of his next five free throws, the probability is approximately 0.25. This can be calculated using a binomial probability formula, which states that the probability of a certain outcome (in this case, making three free throws out of five attempts) is equal to the number of ways the event can occur (3) divided by the total number of possible outcomes (5). Therefore, the probability of Curry making exactly three of his next five free throws is 3/5 or 0.25.

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Answer:

18

Step-by-step explanation:

Intersecting Secants Theorem:

6(x + 6) = 8(8 + 10)

6x + 36 = 8(18)

6x + 36 = 144

6x = 144 - 36

6x = 108

x = 18

Answer:

\(\large \boxed{\sf \ \ \dfrac{8}{7} \ \ }\)

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

   \(\dfrac{-b\pm\sqrt{\Delta}}{2a} \ \text{ where } \Delta=b^2-4ac\)

Here, we have a = -21, b = -11, c = 40, so it gives:

\(\Delta =b^2-4ac=11^2+4*21*40=121+3360=3481=59^2\)

So, we have two solutions:

\(x_1=\dfrac{11-59}{-42}=\dfrac{48}{42}=\dfrac{6*8}{6*7}=\dfrac{8}{7} \\\\x_2=\dfrac{11+59}{-42}=\dfrac{70}{-42}=-\dfrac{14*5}{14*3}=-\dfrac{5}{3}\)

We only want x > 0 so the solution is

   \(\dfrac{8}{7}\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

i) The multiplication of (3.1x\(10^0\)) and (1.5x10) results in 4.65x\(10^1\).

j) The division of (3.1x10) by (1.5x\(10^{-1\)) equals 2.07x\(10^1\).

i) To multiply numbers in scientific notation, we multiply the coefficients (3.1 and 1.5) and add the exponents (0 and 1) together. In this case, 3.1 multiplied by 1.5 gives us 4.65. Adding the exponents, \(10^0\) multiplied by \(10^1\) results in \(10^1\). Therefore, the final result is 4.65x\(10^1\).

j) When dividing numbers in scientific notation, we divide the coefficients (3.1 and 1.5) and subtract the exponents (1 and -1) from each other. Dividing 3.1 by 1.5 gives us approximately 2.07. Subtracting the exponents, \(10^1\)divided by \(10^{-1\) is equivalent to \(10^{(1-(-1))}\) which simplifies to 10^2. Hence, the result is 2.07x\(10^1\).

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Answer:

\(y = \frac{1}{2} x + \frac{5}{2} \)

Step-by-step explanation:

hope this helps!

The probability of being offered both jobs is 0.15, which is equal to the probability of job A multiplied by the probability of job B.

The probability of getting at least one of the jobs is the sum of the individual probabilities. In this case, the probability of getting at least one of the jobs is 0.40, which is equal to the sum of the individual probabilities of getting job A (0.25) and job B (0.20). This means that the probability of getting both jobs is equal to the probability of job A multiplied by the probability of job B, which is 0.25 x 0.20 = 0.15. This can be understood by considering the fact that the probability of getting both jobs is the same as the probability of getting job A and then getting job B, which is the product of the individual probabilities. Therefore, the probability of being offered both jobs is 0.15, which is rounded to two decimal places.

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Answer:

z = 9

See my attachment below for step-by-step explanation.

385 Sample size is necessary is the 95% confidence Interval for p .

Sample Size:

Sample size is defined as the number of observations used to determine estimates for a given population. Sample size was drawn from the population. Sampling is the process of selecting a subset of individuals from a population to estimate characteristics of the population as a whole. The number of entities within a subset of the population is selected for analysis

According to the Question:

The Necessary Sample Size is calculated as follows:

Necessary Sample Size =

(Z-score)² * Std Dev*(1-StdDev) / (margin of error)²

For example, given a 95% confidence level, 0.5 standard deviation, and a margin of error (confidence interval) of +/- 5%. Necessary Sample Size =

= (1.96)² x 0.5(0.5)) / (0.05)²

= (3.8416 x 0.25) / .0025

= 0.9604 / 0.0025

= 384.16

So in order to get 95% confidence level, with confidence interval of +/- 5%, and standard deviation of 0.5, I have to survey 385 samples.

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Measuring length and width can determine if the center section is within specification. The given statement is insufficient to be determined as true or false as the statement doesn't specify the length and width of what is being measured.

Therefore, we can not provide the required answer without knowing the complete question. Hence, we need further information on the complete statement. In technical terms, specifications are a set of specifications and requirements that a product, materials, service, or system must meet. Specifications are developed to ensure that products, systems, or services are consistent, trustworthy, and meet the needs of the end-user. Therefore, specifications play a crucial role in ensuring the quality and reliability of a particular product or service. It also helps to determine whether a product or service meets the required safety and performance standards or not.

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the average rate of change of the total cost as the shirt production increases from 10 to 20 is 90.

Given the function in the question;

f(x) = 3x² + 2

And production increases from 10 to 20.

To find the average rate of change, we use the expression;

[ f(20) - f(10) ] / [ 20 - 10 ]

Now, if f(x) = 3x² + 2

f(20) = 3( 20 )² + 2 = 1202

f(10) =  3( 10 )² + 2 = 302

Plug in the values and simplify

[ f(20) - f(10) ] / [ 20 - 10 ]

[ 1202 - 302 ] / [ 20 - 10 ]

[ 900 ] / [ 10 ]

900/10

90

Therefore, the average rate of change is 90.

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The value of x in the parallel line is 11.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, alternate exterior angles, vertically opposite angles, linear angles, same side interior angles etc.

Therefore, let's use the relationship of the angles to find the value of x in the lines.

10x - 26 = 7x + 7 (corresponding angles)

Corresponding angles are congruent.

Hence,

10x - 26 = 7x + 7

10x  - 7x = 7 + 26

3x = 33

divide both sides of the equation by 3

x = 33 / 3

Therefore,

x = 11

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Considering that each input is related to only one output, the correct option regarding whether the relation is a function is:

A. yes.

A relation represents a function when each value of the input is mapped to only one value of the output.

For this problem, we have that:

There are no repeated inputs, hence the relation is a function and option A is correct.

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Answer:

True

Explanation:

A proportion states the equality of two fractions. It is an equation that shows that two fractions are equivalent to each other.

Looking at the given statement;

10 altos for every 16 sopranos, 5 altos for every 8 sopranos.

This can be expressed as;

And we can see that the two fractions are equivalent, if we divide the numerator and denominator of the 1st fraction by 2 we'll have the 2nd fraction.

The final result of the division is:

(8x³ + 20x² + 10x + 1)/(2x + 1) = 4x² + 10x - 2x² = 2x² + 10x + 1

The long division process is the same as the classical long division process we use to divide numbers. The only difference is that when dividing polynomials, we divide the coefficients of the terms instead of the numbers themselves.

To begin, we divide the first two terms of the dividend (8x³ + 20x²) by the first term of the divisor (2x).

8x³/2x = 4x²

20x²/2x = 10x

We then take the result of this division (4x² + 10x) and multiply it by the divisor (2x + 1).

(4x² + 10x)(2x + 1) = 8x³ + 20x² + 2x² + 10x

We subtract this product from the dividend (8x³ + 20x² + 10x + 1).

8x³ + 20x² + 10x + 1 - (8x³ + 20x² + 2x² + 10x) = -2x² + 1

Since the remainder is a constant (1), this means that the term 2x² is the last term of the quotient.

Therefore, the final result of the division is:

(8x³ + 20x² + 10x + 1)/(2x + 1) = 4x² + 10x - 2x² = 2x² + 10x + 1

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Cylinder is consists of two circles at both sides .

There are two circles

Total area:-

The shape that makes up the top and bottom of a cylinder is Circle.

Where,

Since, There are two circles we will multiply the area by 2

\( \boxed{2\pi {r}^{2} }\)

\(\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}\)

Some important formulas related to circle:

\( \boxed{ \sf \: circumference = 2\pi r}\)

\( \boxed{ \sf \: area = \pi {r}^{2} }\)

\( \boxed{ \sf \:radius = \frac{1}{2} \times diameter }\)

\( \boxed{ \sf \:diameter = 2 \times radius }\)

There are a few different ways you can determine whether a function is always positive:

1. Analyze the function's formula: If the function's formula includes only positive terms or is a product of positive factors, it is likely that the function will be positive for all input values.

2. Graph the function: Plotting the function on the coordinate plane can give you a visual understanding of the function's behavior. If the graph always lies above the x-axis, the function is always positive.

3. Consider the function's domain: If the domain of the function consists only of positive numbers, the function will be positive for all input values in its domain.

4. Use the function's properties: If the function is increasing, continuous, and has no zeros in its domain, it will always be positive. Similarly, if the function is decreasing, continuous, and has no zeros in its domain, it will always be negative.

5. Test the function for specific input values: You can also test the function for specific input values to see if the output is always positive. For example, if the function is defined for all real numbers, you could test it for a few small positive and negative values to see if the output is always positive.

Thus, above mentioned are used to determine if a function is always positive.

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The values of b that makes the lines parallel are given as follows:

b = ± 3/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When two lines are parallel, they have the same slope.

Given two points, the slope is given as the change in y divided by the change in x.

This means that the slopes for each line are given as follows:

As they are parallel, the value of b is obtained as follows:

4b/3 = 3/b.

4b² = 9

b² = 9/4

\(b = \pm \sqrt{\frac{9}{4}}\)

b = ± 3/2.

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Answer:

\(\boxed{\red{500 + x \leqslant 4500}}\\ x \leqslant 4500 - 500 \\ \blue{\underline{x \leqslant 4000}}\)

Answer:

Less

Step-by-step explanation:

Because we don’t know the value of x.

Andre can make 6 small cranes. X is the number of small cranes, 3x is the minutes, 10 is the minute for large cranes and 30 is the total time.

3x + 10 is less than or equal to 30

3 is the minutes for the small cranes

X is the number of small cranes

10 is the minutes for the large crane

30 is the total time limit

first, subtract 10 from 30, ( 30-10) which gives you 20 so

3x is less than or equal to 20.

To figure this out, divide 20 by 3, which gives you 6 as a quotient with a remainder of two minutes.

Andre can make 6 small cranes.

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The Complete question is

Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centrepiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centrepiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.

​Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.

Solve Andre’s inequality and explain what the solution means.