Which of the following equivalent forms of the function f(x)=4x2+4x−24 is the most suitable to indicate the x-coordinates of the x‑intercepts of the graph of y=f(x) in the xy‑plane?


f(x)=4(x2+x−6)


f(x)=4(x−2)(x+3)


f(x)=2(x−2)(2x+6)


f(x)=(2x−4)(2x+6)

Answer:

the second

Step-by-step explanation:

refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice

Converting information from surveys or other data sources so it can be used in statistical analysis is referred to as data conversion.

To ensure that the data is comparable and can be utilized to draw accurate conclusions, the information must be standardized and converted into a common format.

Data conversion is a time-consuming and challenging task that requires the use of specialized software or tools. However, once the data is converted into a consistent format, it can be easily analyzed and used to make informed decisions.

In statistical analysis, the data conversion procedure is critical because the data is often collected from various sources, and each source may use a different format or structure.

There are many different types of data conversion methods used in statistical analysis are data cleaning, data normalization, data integration and data transformation.

The method chosen depends on the type of data being collected and the analysis that will be performed.

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Question:

Converting information from surveys or other data sources so it can be used in statistical analysis is referred to as ___________.

The probability that at least 25% of 300 randomly sampled candies will be orange, using a normal approximation, is approximately 0.008 or 0.8%.

To find the approximate probability that the random sample of 300 candies will contain 25% or more orange candies, we can use the normal approximation to the binomial distribution. The mean of the binomial distribution is np = 300 x 0.21 = 63, and the standard deviation is the square root of npq, where q = 1 - p = 0.79. So, the standard deviation is sqrt(300 x 0.21 x 0.79) = 5.08.
To use the normal approximation, we need to standardize the sample proportion of orange candies, which is p-hat = 0.25, using the formula z = (p-hat - p) / sqrt(pq/n). The standardized value is z = (0.25 - 0.21) / sqrt(0.21 x 0.79 / 300) = 2.39.
Now, we can use the standard normal distribution table or calculator to find the probability that a standard normal random variable is greater than 2.39. The probability is approximately 0.008. Therefore, the approximate probability that the random sample of 300 candies will contain 25% or more orange candies is 0.008 or 0.8%.
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Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

x = 0.8

Step-by-step explanation:

4x + 8 = 7.2 + 5x ( subtract 4x from both sides )

8 = 7.2 + x ( subtract 7.2 from both sides )

0.8 = x

Answer:

x^2 - 2x - 4 = 0.

Step-by-step explanation:

Written in factor form we have:

(x - ( 1 + √5)( x - (1 - √5)) = 0

(x - 1 -√5)( x - 1 +√5)) = 0        Expanding:

x^2 - x +√5x  - x + 1 - √5 - √5x + √5 - 5 = 0

x^2 - 2x - 4 = 0.

Answer: D!!!!!!!

Step-by-step explanation:

Answer:

79507

Step-by-step explanation:

because 64000(1+15/200)^3= 79507

Answer:

The answer in decimal form is 33.6.

The answer in fraction form is \(33\frac{3}{5}\).

Step-by-step explanation:

To find 40% of 84, multiply 84 and 0.4.

84 × 0.4 = 33.6

The answer in decimal form is 33.6.

The answer in fraction form is \(33\frac{3}{5}\).

Hope this helps!

Answer:

1,2,4and 8

Step-by-step explanation:

Answer: No

Answer and Explanation: The numbers 2, 2, and 2 are the prime factors of 8 because 8 divided by 2 equals 4. Thus, 2 and 4 are factors of eight.

Answer:

16

Step-by-step explanation:

This is a piecewise function, so for h(6) use 3x-2 because 6≠0 and 6≠7.

h(6) = 3(6) - 2 = 16

Answer:

x = 1

Step-by-step explanation:

x3 + 4 = 7

3x + 4 = 7

3x = 7 - 4

3x = 3

x = 1

^^

Answer:X3= 3 or X=1

Step-by-step explanation:

X3+4=7

X3= 7-4

X3= 3

or

3x+4=7

3x=7-4

3x=3

x=3/3

x= 1

The largest country in Europe by population is Russia. With a population of over 144 million people, Russia holds almost twice as many inhabitants as the second-largest country in Europe, Germany.

The reason why Russia has the largest population in Europe is mainly due to its vast geographical area, which includes diverse ethnic groups and natural resources, thus supporting a larger population. Additionally, historical factors such as migration, urbanization, and economic growth have also contributed to Russia's high population numbers.

One of the main reasons for Russia's large population is its size. As the largest country in the world, Russia covers almost 1/8th of the world's landmass, providing ample room for its citizens to reside. Additionally, Russia's population growth has been influenced by various factors throughout history, including immigration, wars, and government policies. Despite declining birth rates in recent years, Russia's population remains the largest in Europe.

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Answer:

35

Step-by-step explanation:

Since we know the amounts of each vitamin per serving all we have to do is find the difference.

We do this by subtracting 90 from 125.

125 - 90 = 35

Solution:

Given the function below

Applying the general cosine function formula

The amplitude is

The period is

Hence, the period is 6 and amplitude is 2

The graph of the function is shown below

The numerical answer for the given integral is 4084101 / 1024, which is different from the analytic answer 6155.

To solve the given integral, we can use the properties of integration and the fact that integration is a linear operation.

Let's begin by integrating with respect to x10 first:
∫₀¹ dx10 (x1 + x2 + ... + x10)²

By applying the power rule for integration, we get:
= 1/3 (x1 + x2 + ... + x10)³ + C

Next, we integrate with respect to x9:
∫₀¹ dx9 [1/3 (x1 + x2 + ... + x10)³ + C]

Again, using the power rule, we get:
= 1/12 (x1 + x2 + ... + x10)⁴ + C

We repeat this process for x8, x7, ..., x1, until we reach x1:
∫₀¹ dx8 [1/12 (x1 + x2 + ... + x10)⁴ + C]
= 1/60 (x1 + x2 + ... + x10)⁵ + C

∫₀¹ dx7 [1/60 (x1 + x2 + ... + x10)⁵ + C]
= 1/360 (x1 + x2 + ... + x10)⁶ + C

∫₀¹ dx6 [1/360 (x1 + x2 + ... + x10)⁶ + C]
= 1/2520 (x1 + x2 + ... + x10)⁷ + C

∫₀¹ dx5 [1/2520 (x1 + x2 + ... + x10)⁷ + C]
= 1/20160 (x1 + x2 + ... + x10)⁸ + C

∫₀¹ dx4 [1/20160 (x1 + x2 + ... + x10)⁸ + C]
= 1/181440 (x1 + x2 + ... + x10)⁹ + C

∫₀¹ dx3 [1/181440 (x1 + x2 + ... + x10)⁹ + C]
= 1/1814400 (x1 + x2 + ... + x10)¹⁰ + C

∫₀¹ dx2 [1/1814400 (x1 + x2 + ... + x10)¹⁰ + C]
= 1/21772800 (x1 + x2 + ... + x10)¹¹ + C

Finally, we integrate with respect to x1:
∫₀¹ dx1 [1/21772800 (x1 + x2 + ... + x10)¹¹ + C]
= 1/244823040 (x1 + x2 + ... + x10)¹² + C

Now, let's substitute the limits of integration (0 and 1):
[1/244823040 (1 + 1 + ... + 1)¹² + C] - [1/244823040 (0 + 0 + ... + 0)¹² + C]

Since there are 10 terms in the parentheses, we have:
= 1/244823040 (10)¹²
= 1/244823040 (10^12)
= 10^12 / 244823040
= 4084101 / 1024

Therefore, the numerical answer for the given integral is 4084101 / 1024, which is different from the analytic answer 6155.

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The equation of the line with a slope of 1/4 that passes through the point (16,-2) is y = (1/4)x - 6.

We can use the point-slope form of a linear equation to write the equation of the line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Substituting the given values, we get:

y - (-2) = (1/4)(x - 16)

Simplifying this equation, we get:

y + 2 = (1/4)x - 4

Subtracting 2 from both sides, we get:

y = (1/4)x - 6

Therefore, the equation of the line with a slope of 1/4 that passes through the point (16,-2) is y = (1/4)x - 6.

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Answer:

Sorry about the person above. The answer would be:

C. \(3x + 2y = 22\) and \(5x + 2y = 39\)

Explanation:

I just did the test.

Answer:

C

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

x + 2x + 69 = 90

3x + 69 = 90

3x = 21

x = 7

The measure of angle S and T is equal to 103° from the given figure.

From the given figure, ∠P=93°, ∠Q=156° and ∠R=85°.

In the figure, it is given that ∠S and ∠T are equal.

Here, ∠P+∠Q+∠R+∠S+∠T=540°

93°+156°+85°+x+x=540°

334+2x=540

2x=540-334

2x=206

x=206/2

x=103°

m∠S=m∠T=103°

Therefore, the measure of angle S and T is equal to 103° from the given figure.

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The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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Answer:

The speed in the first part is 16 mph.

Step by step explanation:

The total distance is 48 miles. The total time is 4 hours.

In the second part of the trip, he was traveling at speed s for distance d for 2 hours.

In the first part of the trip he was traveling

at twice the speed, or 2s, for distance 48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part of trip:

48 - d = 2s * 2

d + 4s = 48 Equation 1

Second part of the trip:

d = s * 2

d = 2s =

Equation 2

Equations 1 and 2 form a system of equations in two unknowns, d and s.

d + 4s = 48

d = 2s

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48 =

s=8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) =

16.

The speed in the first part is 16 mph.

Check:

d = 2s = 2(8) = 16

48 - d = 48 - 16 = 32

The second part is 16 miles. The first part is 32 miles.

16 miles at 8 mph takes 2 hours.

32 miles at 16 mph takes 2 hours.

2 hours + 2 hours = 4 hours.

Our answer is correct.

Answer: The speed in the first part is 16 mph.

Answer:

\(V=2080m^3\)

Step-by-step explanation:

The volume formula for triangular prism is  \(V=\frac{1}{2}bhl\)

\(V=\frac{1}{2}(26)(20)(8)\)

\(V=\frac{1}{2}(4160)\)

\(V=2080\)

Hope this helps

Answer:

The answer is 2080m^3

Step-by-step explanation:

The formula for volume of a prism is 1/2 x length x width x height

Hope it helps :)

Answer: 26.4 ft.

Step-by-step explanation: To find the numerical value of 8 meters in feet you need to use unit multipliers. In this case, you need to multiply 8 meters by 3.3 ft / 1 meter. This would cancel out the meters, making the unit feet. 8*3.3 = 26.4, so the answer is 26.4 ft.

The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

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In all together, Clara ate 20 nuts.

Given is that Clara snacked on a mix of almonds and pecans. She ate 3 almonds for every 1 pecan. Clara ate 10 more almonds than pecans.

We can write the system of equations as -

y = 3x

y = x + 10

Equating the value of {y}, we get -

3x = x + 10

2x = 10

x = 5          ...(1)

y = x + 10 = 15

y = 15         ...(2)

x + y = 15 + 5 = 20

Therefore, in all together, Clara ate 20 nuts.

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Answer:

the sq root of m6 is m3

Step-by-step explanation:

The square root of m6 = √ (m6) = (m6)1/2

= m[6 × (1/2)] → multiplying exponents

= m3

Answer:

m^(3)

Step-by-step explanation:

To find the square root of \(m^{6}\), you can use the rule that the square root of \(x^{n}\) is equal to \(x^{n/2}\).

In this case, x = m and n = 6, so the square root of \(m^{6}\) is equal to \(m^{6/2}\) = \(m^{3}\). This means that the square root of \(m^{x}\) is \(m^{3}\).

Therefore, in about 15 years and 2 months, the senior class will have about 100 students.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).

Then, we can write the following equation to represent the situation:

P\((1-r)^{n}\) = 100

We know that the current population of the senior class is 320, so we can substitute these values into the equation:

320\((1-0.07)^{n}\) = 100

Simplifying the equation, we get:

\(0.93^{n}\) = 0.3125

Taking the natural logarithm of both sides, we get:

n ln (0.93) = ln (0.3125)

Dividing both sides by ln (0.93), we get:

n = ln (0.3125) / ln (0.93)

Using a calculator, we find that n is approximately equal to 15.21 years.

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