Ethan uses the function f(x) = 2x2 + 2x + 4 to track the temperature of a substance over 8 hours. You know that
f(3) = 28 meaning that the temperature of the substance is 28°C when you plug in a 3 for x. What is the domain
of Ethan's function?

As per the question we have ─

m = 32

n = 150

We need to evaluate each expression given below ─

25) 2n - 200

Putting the value of n = 150

= 2(150) - 200

= 300 - 200

26) m (-12)

putting the value for m = 32

= 32(-12)

Answer:

25) 100

26) -384

Step-by-step explanation:

25) 2 * 150 -200 = 100

26) 32 (-12) = -384

For the given fraction x^2-8x+16/x^2-16 if x≠4 and x≠-4 the simplified fraction is (x-4)/(x+4).

Simplified fraction refers to the fractions in their lowest form which has been reduced and simplified. The numerator and denominator in the fraction are reduced in simplified fraction to the extent that the only common factor between them is 1.

In order to simplify the fraction (x^2-8x+16)/(x^2-16), first, we must factor the numerator and denominator of the fraction:

Numerator: x^2-8x+16 = (x-4)(x-4) = (x-4)^2

Denominator: x^2-16 = (x-4)(x+4)

So the fraction becomes:

(x-4)^2/(x-4)(x+4)

Next, we can simplify the fraction by canceling out the (x-4) term in the numerator and denominator:

(x-4)/(x+4)

Therefore, the simplified fraction is (x-4)/(x+4) if x≠4 and x≠-4.

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Exercise caution when making predictions beyond the observed range of data, and consider factors such as data quality, model assumptions, and potential limitations.

To perform quadratic extrapolation of a time series, you can use a quadratic model to estimate or predict the value of z at a future time t+1. Here's how you can do it:

Collect your time series data up to time t and note down the corresponding values of z.

Fit a quadratic model to the available data points. The quadratic model has the form: z = at^2 + bt + c, where a, b, and c are coefficients that need to be determined.

Use regression techniques such as least squares regression to estimate the coefficients a, b, and c of the quadratic model using the available data.

Once you have the estimated coefficients, substitute the value t+1 into the quadratic model equation to predict the value of z at time t+1.

For example, if your quadratic model is z = 2t^2 + 3t + 1, and you want to predict the value of z at time t+1, you would substitute the value (t+1) into the equation:

z(t+1) = 2*(t+1)^2 + 3*(t+1) + 1

After evaluating this equation, you will obtain the predicted value of z at time t+1 based on the quadratic extrapolation of the time series.

It's worth noting that extrapolation carries some inherent uncertainty and assumes that the underlying patterns in the time series will continue in the future. Therefore, exercise caution when making predictions beyond the observed range of data, and consider factors such as data quality, model assumptions, and potential limitations.

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Answer:

4v^2 + 6v + 3

Step-by-step explanation:

Answer: 5 yards will be left over.

Step-by-step explanation:

8 * 7 = 56

so then you would minus 56 from 61 which equals 5.  Sorry if that's a weird way to get it but...

Answer:

the answer is Any Real Number

because  4(x + 1) = 4x + 4 for all value of x

Step-by-step explanation:

Answer: 12(3x + 2)

Step-by-step explanation:

=12 x 3x + 12 x 2

= 12(3x + 2

The probability of spinning a 4 on the spinner is 1/12.

Given, a spinner having two numbers 4 & 9

the sector having number 9 has an angle of 30°.

We have to find the probability of spinning a 4 on the spinner

So, the probability of spinning a 4 is,

Probability = (Area of sector having number 4)/(Area of the circle)

Probability = (30°/360°×π×r²)/(π×r²)

Probability = 1/12

Hence, the probability of spinning a 4 on the spinner is 1/12.

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The standard deviation is relatively small when the data are all concentrated close to the mean, exhibiting little variation or spread.

The standard deviation could be a degree of the changeability or spread of a set of information. It is calculated by finding the square root of the normal of the squared contrasts between each information point and the cruel(mean).

In other words, it tells us how much the information values are scattered around the mean.

When the information is all concentrated near the cruel(mean), it implies that the contrasts between each information point and the cruel are moderately little.

This comes about in a little while of squared contrasts, which in turn leads to a little standard deviation. On the other hand, when the information is more spread out, it implies that the contrasts between each information point and the cruel are bigger.

This comes about in a bigger entirety of squared contrasts, which in turn leads to a bigger standard deviation.

For case, let's consider two sets of information:

Set A and Set B.

Set A:

2, 3, 4, 5, 6

Set B:

1, 3, 5, 7, 9

Both sets have the same cruel(mean) (4.0), but Set A encompasses a littler standard deviation (1.4) than Set B (2.8).

This is because the information values in Set A are all moderately near to the cruel(mean), while the information values in Set B are more spread out.

Subsequently, we will say that the standard deviation is generally small when the information is all concentrated near the mean, showing a small variety or spread.

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When using statistics in a speech, you should usually cite exact numbers rather than rounding off. The correct option among the following statement is: b. cite exact numbers rather than rounding off. When citing the statistics, you should cite exact numbers rather than rounding off.

Statistics is the practice or science of gathering, analyzing, interpreting, and presenting data. It is a mathematical science that examines, identifies, and explains quantitative data. In many areas of science, business, and government, statistics play a significant role. The information collected from statistics is used to make better choices based on data that may be trustworthy, precise, and valid.The Role of Statistics in a Speech Statistics is an important tool for speakers to use in a presentation. They can be used to make the speaker's point clear and to convey his or her message. To be effective, statistics should be used correctly and ethically.

The following guidelines should be followed when using statistics in a speech: State your sources. It is important to let the audience know where the statistics came from. You should cite your sources and explain why you used them. If you gathered the data yourself, explain how you did it.Make sure your statistics are accurate. Check the numbers to ensure that they are accurate. If possible, use data from a reliable source. When using numbers, be specific. Don't round them off or use approximations.Don't use too many statistics. Too many statistics can be difficult to understand. Use statistics that are relevant to your topic. Use examples to help your audience better understand the statistics.

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Proper usage of statistics in a speech should include citing exact numbers, not overloading with too many stats, making clear the source, keeping a steady speaking rate, and not manipulating data to suit the argument. Providing anecdotal examples can also help audience better understand the statistical facts.

When using statistics in a speech, the best practices include citing exact numbers rather than rounding off, ensuring not to overload the speech with too many statistics, and being transparent about the source of the statistics. It's not ethical or professional to manipulate statistics to make your point. Instead, present them honestly to build trust with your audience. It's also important to keep the pacing of your speech consistent and not rush when presenting statistics.

In explaining a complex idea like a statistical result, providing an anecdotal example can be effective. This brings the statistic to life and makes it more relatable for the audience. However, when a source is cited, or a direct quotation is being employed, it's best to adhere to a recognized citation style like APA to maintain a professional standard.

Remember, the key to using statistics effectively in your speech is to portray them honestly, ensure they support your argument, and presented in a way that your audience can easily understand.

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In the given parallelogram vwxy: x = 3; m∠Y = 65° and ∠YVX = 61° by (alternate interior angle).

A quadrilateral with the opposing sides parallel is called a parallelogram (and thus opposite angles equal).

In the given parallelogram vwxy:

Parallel sides are equal.

So, 2x = 6

x = 6/2 = 3

Opposite pair of angles are also equal.

So,

∠W = ∠Y = 65°

Now,

∠YVX = 61° (alternate interior angle).

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Answer:

£42.04 is the correct answer.

Step-by-step explanation:

Cost of pack of 15 bread rolls = £1.91

Cost of pack of 20 cheese slices = £2.23

She has to buy exactly twice as many cheese slices as bread rolls.

She has to make more than 100 cheese sandwiches.

Number of bread rolls required for 100 bread rolls.

Minimum 15\(\times\)7 = 105 bread rolls are to be bought.

105 bread rolls mean 210 cheese slices but it is a pack of 20 cheese slices.

So, at least 220 cheese slices can be bought.

But, 220/2 = 110 bread rolls are not possible to be bought.

So, at least 120 (15 \(\times\) 8 i.e. 8 packs) bread rolls have to be bought and 120 \(\times\) 2 = 240 (20 \(\times\) 12 i.e. 12 packs) of sandwiches have to be bought.

So, minimum amount to be spent for at least 100 cheese sandwiches

= 1.91 \(\times\) 8 + 2.23 \(\times\) 12 = £42.04

Answer:

£42.04

Step-by-step explanation:

We can conclude that the special tutoring session seems to have had a positive impact on the students' performance, as their mean score increased from below 60% to 70%.

We can conclude that the special tutoring session has been effective since the students' mean score increased from 60 percent to 70 percent on the second test.

The students who scored less than 60 percent on the first test were given a special tutoring session, which resulted in their mean score increasing to 70 percent on the second test.

Therefore, we can conclude that the special tutoring session has been effective in improving the students' performance on the second test.

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A schematic diagram is used to describe the wiring details of a specific piece of equipment.

A schematic diagram is a graphical representation that depicts the electrical connections, components, and circuitry of a system or device.

It provides a simplified and standardized visual representation of the wiring and electrical connections, allowing engineers, technicians, or users to understand the internal workings of the equipment.

In a schematic diagram, different symbols and lines are used to represent various electrical components such as resistors, capacitors, switches, transformers, and wires.

The connections between these components are illustrated using lines that indicate the flow of electrical current.

Schematic diagrams are widely used in various fields, including electronics, electrical engineering, telecommunications, and industrial automation.

They are essential for designing, troubleshooting, and repairing equipment as they provide a clear and concise representation of the electrical connections and functionalities.

Overall, schematic diagrams serve as a vital tool for understanding the wiring details of a specific piece of equipment, enabling efficient analysis, troubleshooting, and communication of electrical systems.

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Answer:

21

Step-by-step explanation:

Area of a rectangle is base x height so 7 x 3 so 21

Question:

Find the area of the following figure below (btw the number on the left is 3)

Answer:

21

Step-by-step explanation:

Formal:

L x W = Area

^ ^ ^        ^

3 x 7 = 21

Answer:

0.3048 or  1/3.281

Step-by-step explanation:

To create a conversion factor the first thing is to find the equivalence between these two units meters and feet.

We have that 1 ft is equivalent to 0.3048 meters, therefore and as long as you want to go from meters to feet, the following operation must be performed:

x feet * 0.3048 meters / 1 foot = x * 0.3048 meters.

It could also be x / 3.281 meters

That is, let x be any value of length in feet, it must already be multiplied by 0.3048 or divided by 3.281.

Answer:

numerator: 0.3048 meters

denominator: 1 foot

Step-by-step explanation:

The three definitions of positive semidefiniteness (PSD) for a symmetric matrix A are equivalent.

Proof:

(a) implies (b):

Let λ be an eigenvalue of A and v be the corresponding eigenvector. We have Av = λv.

If x = v, then xAx = vAv = λv⋅v = λ||v||² ≥ 0.

Since this holds for all eigenvectors v, all eigenvalues of A must be nonnegative.

(b) implies (c):

If all eigenvalues of A are nonnegative, A can be diagonalized as A = QΛQ^T, where Q is an orthogonal matrix and Λ is a diagonal matrix with the eigenvalues on the diagonal. Since A is symmetric, Q is an orthonormal matrix.

Let U = QΛ^(1/2)Q^T, where Λ^(1/2) is a diagonal matrix with the square roots of the eigenvalues on the diagonal.

Then U is a square root of Λ, and we have A = QΛQ^T = QΛ^(1/2)Λ^(1/2)Q^T = UU^T.

(c) implies (a):

If A = UU^T, then for any nonzero vector x, we can write x = U^Ty for some vector y.

Now, xAx = (U^Ty)(UU^T)(U^Ty) = y^T(UU^T)U^Ty = y^TAA^Ty = (A^Ty)^T(A^Ty) = ||A^Ty||² ≥ 0.

Since xAx ≥ 0 for all nonzero x, A is positive semidefinite.

In conclusion, the three definitions are equivalent, and any one of them can be used to determine positive semidefiniteness of a symmetric matrix A.

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The number of respondents needed in a poll to adequately represent a larger population depends on several factors, such as the size of the population, the level of confidence desired, and the margin of error tolerated.

The general rule of thumb is that a sample size of at least 400 respondents is needed to provide a representative sample for a population of 100,000 or less. However, for larger populations, a sample size of at least 1,000 respondents may be required.

It is also important to note that a larger sample size does not always guarantee more accurate results. Other factors such as the sampling method, the wording of the questions, and the response rate can also impact the accuracy of poll results. Therefore, it is essential to carefully design and conduct polls to ensure their results are adequately representative of the larger population.

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Step-by-step explanation:

a thing or situation that is annoying because it is complicated or involves a lot of effort

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Answer:

110°

Step-by-step explanation:

Since angle B is 30° and the ratio of a to b is 2:1, multiply 30 by 2 to get the measure of angle a = 60°.

Since angles a is 60° And the ratio of a to c is 3:1, divide 60 by 3 to get the measure of angle c = 20°.

add them up:

60 + 30 + 20 = 110°

Manasseh led the people of Judah into almost as much evil as the people who formerly lived in Canaan.

The correct answer to the given question is: True.

Manasseh was the king of Judah, and he is widely regarded as one of the most evil and notorious kings in the history of Judah. Manasseh led the people of Judah into almost as much evil as the people who formerly lived in Canaan. Manasseh was a king who had no respect for God's laws and His ways.

He had the power to influence his subjects in his religious decisions, and he led the people of Judah into the worship of false gods and idols. Manasseh also shed much innocent blood, and he persecuted those who were righteous and faithful to God.

Manasseh was eventually captured by the Assyrian armies, and he was imprisoned and humiliated.

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Answer:

-288

Step-by-step explanation:

To find,

The first and 18th terms as per the formula

Answer is -288

Answer:

408ft²

Step-by-step explanation:

13 x 8 x 2 = 208

10 x 8 = 80

10 x 12 = 120

120 + 80 + 208 = 408

Answer:

Step-by-step explanation:

To estimate the required sample size for estimating the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36, we need to use the formula:

n = (Z^2 * p * (1 - p)) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (for 95% confidence level, Z ≈ 1.96)

p = estimated proportion (since we have no prior information, we can use p = 0.5, which gives the maximum sample size required)

E = margin of error

Substituting the values into the formula:

n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.36^2

n = (3.8416 * 0.25) / 0.1296

n ≈ 9.6042 / 0.1296

n ≈ 74.0842

Rounding up to the nearest whole number, the required sample size is approximately 75. Therefore, you would need to survey at least 75 randomly selected Americans to estimate the true proportion of Americans who support gun control in 2018 with a 95% confidence level and a margin of error of 0.36.

Answer:

Step-by-step explanation:

Let x be the measure of the smaller angle, and y be the measure of the larger angle. Then we know that:

   x + y + 100 = 180, since the sum of the angles in a triangle is 180 degrees.

   y/x = 11/5, since the other two angles are in a ratio of 5:11.

We can use the second equation to solve for y in terms of x:

y/x = 11/5

y = 11x/5

Substituting this into the first equation, we get:

x + (11x/5) + 100 = 180

Multiplying both sides by 5, we get:

5x + 11x + 500 = 900

16x = 400

x = 25

Therefore, the smaller angle measures 25 degrees, and the larger angle measures:

y = 11x/5 = 11(25)/5 = 55

So the two angles are 25 degrees and 55 degrees.

To check this make sure the sum of all the angles is 180.

55+25+100=180

Answer:

Finding the volume of a rectangular prism is a straightforward task - all you need to do is to multiply the length, width, and height together: Rectangular prism volume = length * width * height. Where can you use this formula in real life? Let's imagine three possible scenarios: You bought a fish tank for your golden fish . It's in a regular box shape, nothing fancy, like a corner bow-front aquarium. If …

Step-by-step explanation:

Using alternating and corresponding angle theorems, the values of x are 11, 4, -4 and 10 respectively

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

1)

9x + 8 = 107 (alternating angles are equal)

9x + 8 = 107

9x = 107 - 8

9x = 99

x = 11

2)

20x = 80 (alternating angles are equal)

20x = 80

x = 4

3)

x + 84 = 80 (corresponding angles are equal)

x = 80 - 84

x = -4

4) 120 + 6x = 180

This is gotten from applying alternating angle theorem and angle on a straight line theorem

120 + 6x = 180

6x = 180 - 120

6x = 60

x = 10

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B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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