The region bounded by y = x2 + x - 2 and y = 0 is rotated about the z-axis. Find the volume of the resulting solid by any method. Volume =

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

A number's  root is that factor of the number that, when multiplied by itself, yields the original number. Specifically, squares and square roots are exponents. Think of the number nine. This can be expressed as  or as 3 x 3.

Here,

If an equation have 2 roots , it means it is a quadratic function

If D=0, a quadratic function has two roots that are equal.

D (discriminant) = 0

=>b24ac=0 is required for a polynomial function to have equal roots.

Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

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The line represented by the table is:

y = 2x + 40

A general linear relationship is written as:

y = ax + b

Where a is the slope and b is the y-intercept.

If the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

a = (y₂ - y₁)/(x₂ - x₁)

We can use the first two pairs:

(6, 52) and (9, 58)

Then we will get:

a = (58 - 52)/(9 - 6)

a = 6/3 = 2

y = 2x + b

To find the value of b, we replace the values of one of the points, if we use the first one (6, 52), then we will get:

52 = 2*6 + b

52 = 12 + b

52 - 12 = b

40 = b

The line is:

y = 2x + 40

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Answer:

15

Step-by-step explanation:

Sum of 'n' terms formula is given by:-    

s=n/2(2a+(n-1)d)  

s=13/2[2xa+(13-1)5]    

s=13/2(2xa+12x5)    

s=13/2(2a+60)    

585=13/2(2a+60)    

585 x (2/13) = 2a + 60

90 = 2a + 60  

90-60 = 2a

30 = 2a

a = 15

If the loan is repaid in 15 months, the interest on the loan is approximately $332.14.

To calculate the interest on a loan, we can use the formula:

Interest = Principal × Rate × Time

In this case, the principal (amount borrowed) is $2,750, the interest rate is 9.7% per annum (which needs to be converted to a monthly rate), and the time is 15 months.

First, we need to convert the annual interest rate to a monthly rate. Since there are 12 months in a year, the monthly interest rate is 9.7% / 12 = 0.00808 (rounded to five decimal places).

Now we can calculate the interest using the formula:

Interest = $2,750 × 0.00808 × 15

Calculating this, we find:

Interest = $2,750 × 0.00808 × 15 = $332.14 (rounded to two decimal places)

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Answer:

54

Step-by-step explanation:

x=6

3*3=9*6=54

Answer:

5832

Step-by-step explanation:

Note:

(x^a)^b = X^(ab)

Cube both sides of the equation to obtain the answer.

\(3^{x} = 18\\(3^{x} )^{3} =18^{3} \\3^{3x} =5832\)

To create a clean and minimalist look for a line graph, it is generally recommended to remove the gridlines, tick marks, and possibly the axis titles. These elements can clutter the graph and distract from the main focus, which is the data itself.

The primary objective of a line graph is to visually represent the data in a clear and concise manner. To achieve a clean look, it is often beneficial to remove unnecessary elements that do not contribute directly to the understanding of the data.

Gridlines, while they can assist in reading values, can create visual noise and make the graph appear cluttered. Removing gridlines allows the data points to stand out more prominently. Similarly, tick marks along the axes can be reduced or eliminated to minimize distractions and focus attention on the plotted data.

Axis titles, though important for providing context, may sometimes be redundant or self-explanatory based on the nature of the graph or if the data is accompanied by clear labels. If the graph is already labeled adequately, removing the axis titles can help create a cleaner and less cluttered appearance.

It's important to consider the specific context and intended audience of the graph. Adjustments should be made in a way that maintains clarity and readability while achieving a clean and visually appealing design.

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If the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

As we know that,

Statustical significance refers to claim that a result from data generated by testing or experimentation is likely to be attributable to specific cause.

Sample size is the total number of individuals or items that comprise a sample.

And, the variance is a descriptive statistic, which falls under the category of a measure of spread.

The circumstance in which a very small treatment effect can be found to be significant is best described by option A: If the sample size big and the sample variance is small.

A large sample size will increase the probability that the results of a statistical test will yield significant results. This is why most statistical tests are accompanied by a measure of effect size. A statistically significant result associated with a very large sample size, will likely have a small effect size, an undesirable result for a researcher, as it implies one of the only reasons significant results were obtained was due to the large sample, not necessary the magnitude of the experimental effect.

Likewise, if variance is small, this will also increase the probability that the results of a statistical test will yield significant results. Variance is simply another word in statistics for the error. A decrease in error will lead to an increased probability of obtaining significant results, hence the idea that a small amount of variance will lead to an increased probability of significant results.

Hence, if the sample size is small and the sample variance is large then

small treatment effect still be statistically significant.

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The equation f¹(f(x)) = ƒfƒ˜ ¹(x)) = is known as the conjugation formula. It is used in many areas of mathematics, including complex analysis and algebra. In this formula, f(x) is a function, and f¹(x) is its inverse function. The ƒfƒ˜ ¹(x) is the conjugate function of f(x).

To understand the conjugation formula, let's first consider the function f(z) = z². This function maps a complex number z to its square. For example, if z = 2 + 3i, then f(z) = (2 + 3i)² = -5 + 12i.

Now, let's find the inverse function f¹(z) of f(z). Since f(z) = z², we can write z = f¹(f(z)) = f¹(z²). Solving for f¹(z), we get f¹(z) = ±√z.

The conjugate function of f(z) is ƒfƒ˜ ¹(z) = z*², where z* is the complex conjugate of z. For example, if z = 2 + 3i, then z* = 2 - 3i, and ƒfƒ˜ ¹(z) = (2 - 3i)² = -5 - 12i.

Now, let's apply the conjugation formula to the function f(z) = z². We have f¹(f(z)) = f¹(z²) = ±√z² = ±z. Also, we have ƒfƒ˜ ¹(z) = z*². Therefore, the conjugation formula gives us f¹(f(z)) = ƒfƒ˜ ¹(z). In other words, ±z = z*².

In conclusion, the conjugation formula is a useful tool in mathematics that relates a function to its inverse and conjugate functions.

It can be used to simplify expressions and solve equations in various areas of mathematics, such as complex analysis and algebra.

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If a storage tank holds 50,000 gallons of water then its volume is 189.25 cubic meters.

The volume of the storage tank in cubic meters can be calculated by first converting the volume from gallons to liters and then converting from liters to cubic meters.

Step 1: Convert the volume from gallons to liters:
50,000 gallons * 3.785 liters/gallon = 189,250 liters

Step 2: Convert the volume from liters to cubic meters:
189,250 liters * (1 cubic meter/1000 liters) = 189.25 cubic meters

Therefore, the volume of the storage tank is 189.25 cubic meters.

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Answer:

x = - \(\frac{4}{5}\)

Step-by-step explanation:

Given

5x - 2 = 25x + 14 ( subtract 25x from both sides )

- 20x - 2 = 14 ( add 2 to both sides )

- 20x = 16 ( divide both sides by - 20 )

x = \(\frac{16}{-20}\) = - \(\frac{4}{5}\)

Answer:

D. One.

Step-by-step explanation:

Answer:

Step-by-step explanation:

According to the diagram we observe:

As we know the exterior angle is same as the some of the remote interior angles.

It can be shown as:

Substitute the values and solve for x:

Find the measure of m∠ABC:

The matching answer choice is D.

Answer:

\(m=4\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (-2, 1)

Point (-3, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Whave established that the series l~=l an - z converges uniformly for Re(z) ≤ c

What is uniformly?

The keyword "uniformly" refers to the concept of uniform convergence. In the context of the given question, it is stated that the series l~=l an - z converges uniformly for Re(z) ≤ c. Uniform convergence means that the convergence of the series is independent of the value of z within a certain range (Re(z) ≤ c in this case).

To show that the series l~=l an - z converges uniformly for Re(z) ≤ c, where an is a bounded sequence of complex numbers and we choose the principal branch of n - z, we need to demonstrate that for any ε > 0, there exists an N such that for all n > N and for all z with Re(z) ≤ c, the inequality |l~=l an - z| < ε holds.

Given that an is a bounded sequence, there exists an M > 0 such that |an| ≤ M for all n.

Let's consider the series l~=l an - z. We can write it as:

l~=l an - l z.

Now, since |an| ≤ M for all n, we have:

|an - z| ≤ |an| + |z| ≤ M + c.

By choosing N such that M + c < ε, we can ensure that for all n > N and for all z with Re(z) ≤ c, the inequality |an - z| < ε holds.

Now, using the triangle inequality, we have:

|l~=l an - z| ≤ |an - z|.

Since we have shown that |an - z| < ε for n > N and Re(z) ≤ c, it follows that |l~=l an - z| < ε for n > N and Re(z) ≤ c.

Therefore, we have established that the series l~=l an - z converges uniformly for Re(z) ≤ c.

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Answer:

17,960

Step-by-step explanation:

Given the following data, book cost (in dollars) = 200, 130, 400, 500, 345.

First of all, we will find the mean of the given data.

\(Mean = \frac{200+ 130+ 400+500+ 345}{5}\\Mean =\frac{1575} {5 }\\Mean = 315\)

Or

Mean = (200+130+400+500+345)/5

Mean = 1575/5 = 315.

Second step is to subtract the mean from each book cost;

(200-315) + (130-315) + (400-315) + (500-315) + (345-315)

(-115)+(-185)+85+185+30

Next you square the above deviation;

\((-115)^2+(-185)^2+85^2+185^2+30^2\\13225+34225+7225+34225+900\\= 89800\)

Then, divide the above by the average which is 5 in this case.

\(Variance = \frac{89800}{5}\\\\Variance = 17960\)

Hence, the value of the variance is 17,960.

Answer:

c and e

Step-by-step explanation:

If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

To determine if two triangles are similar, you need to check if their corresponding angles are congruent and their corresponding sides are proportional.

To state if the triangles in each pair are similar, follow these steps:

1. Identify the corresponding angles: Compare the angles of one triangle to the angles of the other triangle. If all the corresponding angles are congruent, then the triangles are similar.

2. Check for proportional sides: Compare the lengths of the corresponding sides of the two triangles. If the ratios of the corresponding sides are equal, then the triangles are similar.

3. If both the corresponding angles and sides are congruent and proportional, respectively, you can state that the triangles are similar.

For example, consider two triangles with angles A, B, and C, and sides a, b, and c. If you find that angle A of one triangle is congruent to angle A of the other triangle, angle B is congruent to angle B, and angle C is congruent to angle C, and the ratios a/b, b/c, and a/c are all equal, then you can conclude that the two triangles are similar.

Remember, similarity is not the same as congruence. Similar triangles have the same shape but can differ in size.

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Sorry but your screenshot is very blur. please give clear photo so that we can read question and answer it.

Therefore, the amount of error occurred by applying the model is 1.79 (rounded to 2 decimal places)

Given data: t Sales 16 2 13 3 25 4 32 5 21

Error, in applied mathematics, the difference between a true value and an estimate, or approximation, of that value. In statistics, a common example is the difference between the mean of an entire population and the mean of a sample drawn from that population.

The relative error is the numerical difference divided by the true value; the percentage error is this ratio expressed as a percent. The term random error is sometimes used to distinguish the effects of inherent imprecision from so-called systematic error, which may originate in faulty assumptions or procedures. The methods of mathematical statistics are particularly suited to the estimation and management of random errors.

The model for forecasting sales can be expressed as follows:

E (Yi) = β0 + β1Xi Here, Yi = t, Sales Xi = i. The given values of t Sales and Xi are:

t Sales : Xi 16 2 13 3 25 4 32 5 21 We need to find out the amount of error occurred by applying the model.

Hence, SE = Sqrt ((Σ (Yi - E (Yi))^2) / (n - 2)), where n = Number of observations.

SE = Sqrt ((Σ (Yi - E (Yi))^2) / (n - 2))SE = Sqrt ((12.97) / (6))SE = 1.79

Therefore, the amount of error occurred by applying the model is 1.79 (rounded to 2 decimal places).Hence, the required answer is 1.79.

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Answer:

x = -1/2

Step-by-step explanation:

Answer: 5x(x + 4)

hope i helped

Answer:

5x . (x+4)

Step-by-step explanation:

Make sure not to use too many points next time if anything only use ten unless your asking someone to write an essay or you need your answer quick

The simplified expression that is equivalent to \(7a \cdot 5b \div 6c \cdot 2d$ is $70abd$.\)

What is expression?

In mathematics, an expression is a combination of numbers, variables, and operators (such as addition, subtraction, multiplication, and division) that can be evaluated to produce a value.

To simplify the expression \($7a \cdot 5b \div 6c \cdot 2d$\), we can combine the multiplication and division operations using the order of operations (also known as PEMDAS) which tells us to perform multiplication and division before addition and subtraction.

First, we can simplify the multiplication of \($7a$\) and \($5b$\) to get \($35ab$\).

Next, we can simplify the division of \($6c$\) by multiplying by its reciprocal, \($\frac{1}{6c}$\), to get 1.

Finally, we can simplify the multiplication of \($35ab$\) and \($2d$\\\) to get \(70abd$.\)

Therefore, the simplified expression that is equivalent to \(7a \cdot 5b \div 6c \cdot 2d$ is $70abd$.\)

So,

\($7a \cdot 5b \div 6c \cdot 2d = \frac{35ab}{6c} \cdot 2d$\)

\($= \frac{35ab \cdot 2d}{6c}$\)

\($= \frac{35 \cdot 2 \cdot abd}{6c}$\)

\($= \frac{70abd}{6c}$\)

\($= \frac{35abd}{3c}$\)

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The length of a side of the picture is 3.39 centimeters. The area of a frame is calculated by multiplying the width of the frame by the perimeter of the picture.

Let x be the length of a side of the picture. The area of the picture is x². The area of the frame is 2x. The total area is x² + 2x.

We are given that the area of the picture is 2/3 of the total area. This means that x² = 2/3(x² + 2x).

Solving for x, we get x = 3.39 centimeters.

Here are some additional explanations:

The area of a square is calculated by multiplying the length of one side by itself.

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Answer:

It's friday for me so here u go

Step-by-step explanation:

Answer:

if the teacher buys 4 packa of markers and 3 packs of pens she would have the same amount

A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.

If the null hypothesis is correct, the F statistic will be low because the between-treatment variation (numerator) won't be greater than the residual or error variation (denominator). The F statistic will be high if the null hypothesis is untrue.

The residual variance, also known as the error variance, is the denominator of the F-ratio in a repeated-measures ANOVA and quantifies the amount of variance that would be predicted if neither a systematic treatment effect nor a personal characteristic were to influence the variability of the scores.

Hence we get the required answer.

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Answer:

tenth is 14.7 whole number is 15 hundredth is 14.76