Use the method of completing the square to transform the equation 3x^2−12x+8=0. Which equation shows the transformed equation?
Is my answer correct?

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

Yes, the large-sample confidence interval will be valid.

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

A sample is considered large when n ≥ 30.

By 'valid', it means that the confidence interval procedure has a 95% chance of producing an interval that contains the population parameter.

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Answer:

24 cars are green

Step-by-step explanation:

We know

Amir notices that 3 out of every 50 cars that pass by his window are green.

So, the ratio is 3:47

To get from 50 to 400, we time 8.

If he observes 400 cars, what is the best estimate of how many will be green?

We take

3 x 8 = 24 cars are green

So, there will be 24 cars that are green.

Answer:

201.06

Step-by-step explanation:

The volume of a cylinder is the area of the base (\(\pi 2^2\)) times the height (16).

Answer:

V = 201 ft^3

Step-by-step explanation:

\(v = \pi {r}^{2} \times h \\ v = 3.14 \times {2}^{2} \times 16 \\ v = 200.96 \\ v = 201 \: \: {ft}^{3} \)

I hope that is useful for you :)

Answer:

Let p be the probability assigned to faces with 1 to 5 spots (since their probabilities are unaffected) and let x be the probability assigned to the face with 6 spots. Then, we have the equation:

0.21 = x + p

Since the probabilities of all six faces must add up to 1, we also have the equation:

1 = 5p + x

Solving these equations simultaneously, we get:

p = 0.146

x = 0.064

Therefore, the probability assigned to the faces with 1 to 6 spots (in order) are:

0.146, 0.146, 0.146, 0.146, 0.146, and 0.064.

Step-by-step explanation:

The value of f left parenthesis 3 right parenthesis is 45.

According to the statement

We have given that the F(x) = 5(x)^2

and we have to find the value when Sophia have a 3 right parenthesis.

So, Parenthesis are used in mathematical expressions to denote modifications to normal order of operations.

And now we have to find the value for 3 right parenthesis

And for this purpose we have to put the value X= 3 in the f(x) then

F(x) = 5(x)^2

F(3) = 5(3)^2

F(3) = 5*9

F(3) = 45.

here the value of 3 right parenthesis is 45.

So, The value of f left parenthesis 3 right parenthesis is 45.

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Answer:

lets solve it.

Taking LHS:

81^3/2=(81*81*81)/2

531,441/2

265,720.5

Now comparing RHS and LHS

265,720.5 & 9

and they are not equal, thus false.

Answer b

Because -2-5 adds -5 to it equals -7

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The Root Cause Analysis technique used to identify the underlying causes of a problem is the Ishikawa diagram. It is a graphical tool also known as the Fishbone diagram or Cause and Effect diagram. The other techniques mentioned, such as the Rule of 72, Marginal Analysis, and Bayesian Thinking, are not specifically associated with Root Cause Analysis.

Root Cause Analysis is a systematic approach used to identify the fundamental reasons or factors that contribute to a problem or an undesirable outcome. It aims to go beyond addressing symptoms and focuses on understanding and resolving the root causes. The Ishikawa diagram is a commonly used technique in Root Cause Analysis. It visually displays the potential causes of a problem by organizing them into different categories, such as people, process, equipment, materials, and environment. This diagram helps to identify possible causes and facilitates the investigation of relationships between different factors. On the other hand, the Rule of 72 is a mathematical formula used to estimate the doubling time or the time it takes for an investment or value to double based on compound interest. Marginal Analysis is an economic concept that involves examining the additional costs and benefits associated with producing or consuming one more unit of a good or service. Bayesian Thinking is a statistical approach that combines prior knowledge or beliefs with observed data to update and refine probability estimates. In the context of Root Cause Analysis, the Ishikawa diagram is the technique commonly used to visually analyze and identify the root causes of a problem.

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Answer:

17.6 laps

Step-by-step explanation:

Total distance to be covered = 2 miles

distance coved in each lap = 400 yards

We know that 1 mile = 1760 yards

therefore, 4 miles will make = 4×1760

= 7040 yards.

Number of laps to be taken

= Total distance to be covered ÷ distance coved in each lap

= 7040/400 = 17.6 laps

Therefore, it would take 17.6 laps to cover a distance of 4 miles if lap were 400 yards.

Option d) {(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)} is the correct answer.

A function is a mathematical relation that maps each element in a set to a unique element in another set.

To determine which relation is a function between the given options, we need to check whether each input has a unique output.

In option a), the input -1 has two outputs, 3 and 2, which violates the definition of a function.

In, Option b) has two outputs for the input 0, violating the same definition.

In, Option c) has two outputs for the input 0, but it also has two outputs for the input -2, which violates the definition of a function as well.

In, Option d) is the only relation that satisfies the definition of a function, as each input has a unique output. Therefore, Option d) is the correct answer.

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There are total 35 students in the class.

Given that,

Vikas ranks 9th in the class,

Assume that there are 'n' number of students in the class  

Therefore,

There are 8 students who have scored better than him.

So, The total number of students with a rank better or equal to Vikas,

= 8 + 1 (Vikas himself)

= 9.

Now, his friend got the 35th rank which is the last rank

This means that there are a total of 35 students in the class.

Also, also given that,

Vikas's rank from the last is 27th,

This means that there are 26 students who have scored lower than Vikas.

So, the total number of students with a rank worse or equal to Vikas,

= 26 + 1 (Vikas himself)

 = 27.

Therefore, The total number of students in the class = 35.

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Functions are special relaionships that connect an element of one set of numbers, with one element in another set of numbers.

The most comon way to represent functions is connecting elements of a set of Real numbers called the "Domain", to another number in a set called the Range (and whose elements are identified with the letter "y")

Using math operations one can relate x values with y values via an equation of the type:

y = 2 x - 5

where you have a mathematical form of that relationship, that allows you to know given the value of one member (x) of the Domain what number is associated with it in the Range.

For example, try the number x = 0

and see which y number connects with it:

y = 2 (0) - 5 = 0 - 5 = -5

Then you say that the number 0 in the Domain connects with the number -5 in the Range.

This relationship can also be given with coordinate pairs of the form:

(x, y) mentioning in the first position (where the x is), the number in the Domain that connects to the "y" number of the Range). The y goes in the second place. so for example in the relationship we found above, x = 0 connects with y=-5, you would have a shortcut way to write it as the pair: (0, -5) that tells you which x connects with which y.

The functions can also be given in graph form by plotting the relationship between members of the Domain and the Range on the plane. Graphing a point in the plane location that corresponds to the connected x and y values (like you do in the game "battlefield" when you locate ships on the board.

I know this is very general, but hopefully you got the idea ofa function as a special relationship between numbers, and that they can be expressed in different fashions.

The probability that the mixture will test positive is approximately 0.4744 or 47.44%

In this blood testing procedure, the mixture will test positive if at least one of the individual samples tests positive. To determine the probability of the mixture testing positive, we can first find the probability that all individual samples test negative and then subtract that from 1.

The probability that an individual sample tests negative is 1 - 0.12 = 0.88, since there is a 0.12 chance that it tests positive. As there are 5 samples, and we assume they are independent, we can multiply the probabilities together to find the probability that all samples test negative: 0.88^5 ≈ 0.5256.

Now, to find the probability that the mixture tests positive (meaning at least one individual sample is positive), we can subtract the probability of all samples being negative from 1: 1 - 0.5256 ≈ 0.4744.

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Answer:

The way I was taught to do it is to change value into a total fraction, then multiple the numerators together, multiply the denominators together, and finally reduce as far as possible.

7/9 x 5 2/5 = 7/9 x 27/5 = 189/45 = 4 9/45 = 4 1/5

1 3/4 x 4 1/6 = 7/4 x 25/6 = 175/24 = 7 7/24

Answer:

(4, 5)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

3x + 3y = 27

x - 3y = -11

Step 2: Solve for x

Step 3: Solve for y

Answer:

0.0000000045, 0.0000097 and 0.000167 isthe acending order

Using the concepts of discrete and continuous variables, it is found that the correct option is:

The six minute half mile time is continuous data the number of people trying out for team is discrete data

In this problem, the number of people can be 0, 1, 2, ..., so it is discrete.

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1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:

2) Based on that, we can do the following to find the next two terms:

Thus, the next terms are -5 and 2

The inequality that represents the numbers of rides and games you can afford is 0.50x + 2y ≤ 2.50.

Yes. (1, 1) is a solution of the inequality.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Let x be the number of rides and let y be the number of games.

The inequality will be:

0.50(x) + 2(y) ≤ 2.50

0.50x + 2y ≤ 2.50

When x and y are 1, this will be:

0.5 + 2 ≤ 2.50

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Oliver has 5 pieces of string each of length 4 2 12 feet and Destiny has 4 pieces of string each of length 5 14 16 feet.

Now, let's use an estimation strategy to determine who has the most string by rounding the length of each string to the nearest whole number.The nearest whole number to 4 2 12 is 4The nearest whole number to 5 14 16 is 6Now, we can determine who has the most string by multiplying the rounded lengths of each string by the number of strings they have:Oliver has 5 strings, so he has about 5 × 4 = 20 feet of stringDestiny has 4 strings, so she has about 4 × 6 = 24 feet of string

Therefore, Destiny is estimated to have about 24 − 20 = 4 more feet of string than Oliver. Thus, Destiny is estimated to have 4 more feet of string than Oliver.

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There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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The procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 2 cm, 3 cm, 4 cm, and 5 cm is option C.

Knowing that 3^2 +4^2 = 5^2, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

The Pythagorean Theorem is a relationship that exists between the sides of a right triangle, which is a triangle with one interior angle of 90 degrees. According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Converse of the Pythagorean Theorem is an inverse statement that implies that if a triangle's sides satisfy the relationship described in the Pythagorean Theorem, then the triangle is a right triangle.

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Sampling variations refers to the fact that some samples represent populations well and some do not.

The correct answer is an option (D)

Weknow that sample variability is nothing but the increasing or decreasing sample sizes that leads to changes in the variability of samples.

For exa., a sample size of 50 people taken from the same population of 20000 will give you a very different result than a sample size of 300 people.

Sampling variation is simply the variation in a statistic from sample to sample.

It is nothing but how much an estimate varies between samples.

The common measure of sampling variability are variance (σ²) and standard deviation (σ).

Thus sampling variation is nothing but  the fact that some samples represent populations well and some do not.

The correct answer is an option (D)

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The function will be a compund interest

2B times as many gallons does pool A hold than pool B.

What is gallons?

The gallon is a volumetric unit that is used in both imperial and American customary measurements.

The imperial gallon (imp gal), which is equal to 4.54609 liters and was once used in various Caribbean nations as well as the United Kingdom, Ireland, Canada, Australia, and Australia.

Given:

Swimming pool A has 2^15 gallons of water.

Swimming pool B has 2^13 gallons of water.

We have to find the number of times pool A hold than pool B.

It is obvious that Swimming Pool A holds more water than Swimming Pool B.

Consequently, we must determine how many times as many gallons Pool A holds as Pool B:

2^15 > 2^13.

Therefore,

A = 2^15,  B = 2^15

\(A = (\frac{2^1^5}{2^1^3}) B = 2B\\ A = 2B\)

Hence the proof.

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Answer:

29933.7984 km

Step-by-step explanation:

The central limit theorem requires a sample size of at least 30 be used to ensure that the sample means are normally distributed. Correct option is B.

The central limit theorem is a fundamental concept in statistics that describes the behavior of sample means as the sample size increases.

It states that, under certain conditions, the sampling distribution of the means of a random sample of size n will approach a normal distribution, regardless of the shape of the population distribution from which the sample is drawn.

The central limit theorem does not require the use of any specific sampling technique or resampling method, such as the bootstrap method. Rather, it applies to any random sample that is selected from a population, as long as the sample size is sufficiently large.

The commonly accepted rule of thumb is that the sample size should be at least 30 in order for the central limit theorem to apply. This is because a sample size of 30 or more is generally considered large enough to ensure that the sample means are normally distributed, regardless of the shape of the population distribution.

Therefore, the correct answer to the question is (b) a sample size of at least 30 be used to ensure that the sample means are normally distributed.

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(a) Annually compounded interest:

In this case, n = 1 (compounded once a year)

Future Value (a) = $500 × (1 + 0.12 / 1)^(1 * 20)

(b) Quarterly compounded interest:

In this case, n = 4 (compounded four times a year)

Future Value (b) = $500 × (1 + 0.12 / 4)^(4 * 20)

(c) Monthly compounded interest:

In this case, n = 12 (compounded twelve times a year)

Future Value (c) = $500 × (1 + 0.12 / 12)^(12 * 20)

Let's calculate the values:

(a) Future Value (annually) = $500 × (1 + 0.12)^20

Future Value (annually) ≈ $500 × 6.1917364224

Future Value (annually) ≈ $3,095.87

(b) Future Value (quarterly) = $500 × (1 + 0.12 / 4)^(4 * 20)

Future Value (quarterly) ≈ $500 × 1.03^80

Future Value (quarterly) ≈ $500 × 10.0626534032

Future Value (quarterly) ≈ $5,031.33

(c) Future Value (monthly) = $500 × (1 + 0.12 / 12)^(12 * 20)

Future Value (monthly) ≈ $500 × 1.01^240

Future Value (monthly) ≈ $500 × 20.1814079986

Future Value (monthly) ≈ $10,090.70

Therefore, if Iona earns 12% interest compounded annually, her investment of $500 will grow to approximately $3,095.87 in 20 years. If compounded quarterly, it will grow to approximately $5,031.33, and if compounded monthly, it will grow to approximately $10,090.70.

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Answer:

9

Step-by-step explanation:

8.547  =  9.000

========================================================

Explanation:

Y is between X and Z (not necessarily at the midpoint). This means the three points are on the same line. Going from left to right we have X, Y and Z in that exact order.

Put another way, segment XZ is cut into smaller pieces XY and YZ.

The smaller pieces XY and YZ add back up to the largest segment XZ.

--------------

XY + YZ = XZ

( XY ) + ( YZ ) = XZ

( 7a ) + ( 5a ) = 6a+24 ..... substitution

7a+5a = 6a+24

12a = 6a+24

12a-6a = 24 ....... subtracting 6a from both sides

6a = 24

a = 24/6 ....... dividing both sides by 6

a = 4  is the first answer we're after

-------------

Use this value of 'a' to find the length of each segment

XY = 7a = 7*4 = 28

YZ = 5a = 5*4 = 20 is the second answer we want

XZ = 6a+24 = 6*4+24 = 48

Note how XY+YZ = 28+20 = 48 to match with XZ = 48 we got in the previous line above.