Given av av 25202 +S= _V, ат as² as find a change of variable of S to x(S) so that this equation has constant coefficients. =

Answer:

15

Step-by-step explanation:

The two true statements regarding the circle equation are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9"

"The center of the circle lies on the x-axis."

Remember that the equation for a circle of center (a, b) and radius R is:

(x - a)^2 + (y - b)^2 = R^2

Here we have the equation:

x^2 + y^2 - 2x - 8  =0

First we need to complete squares on x, remember the perfect square trinomial:

(a - b)^2 = a^2 - 2ab + b^2

So we can rewrite:

x^2 + y^2 - 2x - 8  =0

(x^2 - 2x) + y^2 = 8

Now we can add and subtract 1:

(x^2 - 2x) + y^2 + 1 - 1 = 8

(x^2 - 2x + 1) + y^2 - 1 = 8

(x - 1)^2 + y^2 = 8 + 1

(x - 1)^2 + y^2 = 3^2

So, the center is (1, 0) and the radius is 3.

Then the true statements are:

"The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9" it is also 3.

"The center of the circle lies on the x-axis." because the center is at (1, 0).

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Answer:

The median is 33.5

Step-by-step explanation:

In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.

The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.

The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.

To find the median of the given numbers, we first need to arrange them in ascending order:

12 17 28 31 36 54 55 71

Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.

To find the average, we add the two numbers and divide by 2:

(31 + 36) / 2 = 67 / 2 = 33.5

Therefore, the median of the given numbers is 33.5.

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The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Answer:

i cant see it?

Step-by-step explanation:

Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

The number that would have to be added to "complete the square" is 49

From the question, we have the following parameters that can be used in our computation:

x² + 14x - 14 = 0

From the above number, we have

Coefficient of x = 14

Divide this number by 2

So, we have

Coefficient of x/2 = 7

Take the square of the result

So, we have

(Coefficient of x/2)² = 49

This means that the number that would "complete the square" is 49

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Answer:

Step-by-step explanation:

Use Pythagorean to find the missing side:

Find perimeter:

Find area:

both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.

China is using the comparative advantage perspective in regards to not trading silk with Germany in exchange for automobiles. According to the theory of comparative advantage, a country should specialize in producing and exporting the goods or services that they can produce more efficiently or at a lower opportunity cost compared to other goods and services.

In this case, China has a comparative advantage in producing silk and a comparative disadvantage in producing automobiles compared to Germany, which has a comparative advantage in producing automobiles and a comparative disadvantage in producing silk.

Hence, both countries can benefit from trade by specializing in the goods and services that they are relatively more efficient at producing and exchanging them with each other.

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4,7,10,13,16

Step-by-step explanation:

if you find what is difference between them like there is 3 different in this example. and there's is your answer

Answer:

4, 7, 10, 13, 16---arithmetic sequence since the common difference is 3.

Answer: 12,620,256

Step-by-step explanation:

Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.

Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is \(^{n+r-1}C_r=\ ^{31+8-1}C_{31}\)

\(=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256\)

Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256

Answer:

It's 13<26

Step-by-step explanation:

Answer:

6. b. j+ 8

7. b. n - 2

8. a. Addition

9. d. y ÷ -5

10. c. 18 - 19

11. a. 10 + 6

12. b. Divided by

13. a. three added to 5

14. b. 9

15. b. 75

Answer: C

Step-by-step explanation:

The volume of a sphere is defined to be:

\(Volume=\frac{4}{3} \pi r^3\)

Plug in the values to get:

\(Volume=\frac{4}{3} (3.14)(3.5)^3=179.5in^3\)

Answer:

question 1: answer is 4

question 2: answer is 1

Step-by-step explanation:

We can answer the questions based on the given triangles in this way:

a) sin(BAC) depends only on AB, BC, and BCA, and are the same in both drawings, we have sin(BAC) = 3/5.

b) ∠BAC in the drawing where it is acute is ≈ 36.9°.

c) The ∠BAC in the drawing where it is obtuse is ≈ 143.1°.

The angles of a triangle when added together is always 180°.

To calculate the angles of a triangle, we use the formulas like the Law of Cosines, the Law of Sines, or trigonometric functions like sine, cosine, and tangent.

a) To find sin(BAC), we shall use the Law of Cosines to first find the length of AC:

(AC)² = (AB)² + (BC)² - 2(AB*BC)cos(BCA)

AC² = 15² + 18² - 2(15*18)cos(30°)

AC² = 729

AC = 27

Next, we use the Law of Sines to find sin(BAC):

sin(BAC) / AB = sin(BCA) / AC

sin(BAC) / 15 = 1/2 / 27

sin(BAC) = 3/5

Since sin(BAC) only depends on AB, BC, and BCA, which are the same in both drawings, we have sin(BAC) = 3/5 in both drawings.

b) In the acute triangle, we have:

sin(BAC) / AB = sin(BCA) / AC

sin(BAC) / 15 = 1/2 / 27

sin(BAC) = 3/5

BAC = arc sin(3/5)

BAC ≈ 36.9°

c) In the obtuse triangle, we have:

sin(BAC) / AB = sin(BCA) / AC

sin(BAC) / 15 = 1/2 / 27

sin(BAC) = 3/5

Since sin(BAC) is positive and ≤ 1, we know that BAC is an acute angle or a reflex angle.

But we are told that BAC is obtuse angle, meaning:

BAC = 180° - arc sin(3/5)

BAC ≈ 143.1°

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Observed from our graph,

At 2 afternoon

At 8 afternoon

From 100% to 40% between 2PM and 4 PM:

(100 - 40)/(4 - 2) = 60/2 = 30% per hour

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. For example, 1 percent of 1,000 chickens equals 1/100 of 1,000, or 10 chickens; 20 percent of the quantity is 20/100 1,000, or 200.

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Answer:

ok this was a good one so here

Step-by-step explanation:

time (seconds)

distance (meters)

speed (meters per second)

4 120 30

25 750 30

9 270 30

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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The sample standard deviation is (B) $3.16.

Therefore, the sample standard deviation is (B) $3.16.

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The complete question is given below:
If the sample variance for a frequency distribution consisting of hourly wages was computed to be 10, what is the sample standard deviation?

A. $4.67

B. $3.16

C. $1.96

D. $10.00

Answer:

The volleyball team won 15 games.

Answer:

That would be 15

Step-by-step explanation:

Good Luck!

Answer:

(0-2)

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

A horizontal line has a slope of zero

Using the formula

m = (y2-y1)/(x2-x1)

    = (1-1)/(2 - -2)

    = 0/(2+2)

    = 0/4

The probability of getting a z-score greater than 0.15 is approximately 0.5693.

The probability of getting more than 2100 nails in a bag is approximately 0.5693.

The number of nails in a bag is a discrete random variable, so it's not appropriate to use a normal distribution to model it.

Also, the mean of 8.9 and standard deviation of 5.56 are for a single nail, not for a bag of 225 nails.

To answer the question, we need more information on the distribution of the number of nails in a bag.

Assuming that the distribution is approximately normal, the mean of the number of nails in a bag would be 225 * 8.9 = 2009 and the standard deviation would be the square root of 225 * (5.56)^2 = 59.11.

With these values, we can use a standard normal distribution to find the probability of getting more than 2100 nails in a bag:

z = (2100 - 2009) / 59.11 = 0.15

Note: This calculation assumes that the distribution is approximately normal, and that the mean and standard deviation of a single nail are accurate. These assumptions might not hold in practice, so the answer should be taken with caution.

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A parallel conversion is a method of implementing a new system in which the old and new systems run simultaneously for a period of time. While this approach can have its benefits, there are also potential problems that may arise.

One of the problems with a parallel conversion is that there is a higher risk, as there are two systems running at the same time, which can be costly and require additional resources. Another problem is that the old hardware might fail, which can cause data loss or delays in the conversion process. On the other hand, a lower risk may not be applicable in a parallel conversion because the risk factor is already high. Also, the users have to enter data into both systems, which can be time-consuming and prone to errors. Finally, an abrupt conversion is not applicable in a parallel conversion because both systems are running together. Overall, the parallel conversion method requires careful planning and execution to minimize the potential problems and ensure a smooth transition.

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Answer:

14 is B, 15 is C

Step-by-step explanation:

Therefore, the graph with 11 vertices and 17 edges is the graph with the maximal number of vertices that satisfies the given conditions.

Let's denote the number of vertices in the graph as V. Since each vertex has a degree of at least 3, the sum of the degrees of all vertices must be at least 3V. But since each edge contributes to the degree of two vertices, the sum of the degrees of all vertices is also equal to 2E (where E is the number of edges in the graph). Therefore, we have:

3V ≤ 2E

3V ≤ 2(17)

3V ≤ 34

V ≤ 11.33

Since V is an integer, the largest possible value of V is 11. Therefore, the graph with 11 vertices and 17 edges is an example of a graph that satisfies the given conditions.

To show that there is no graph with a larger number of vertices that satisfies the given conditions, we can use the Handshaking Lemma, which states that the sum of the degrees of all vertices in a graph is equal to twice the number of edges. If we assume that there is a graph with more than 11 vertices and 17 edges, then at least one vertex must have a degree greater than 3 (since the sum of the degrees is equal to 2E). But if a vertex has a degree greater than 3, then there must be at least one vertex with degree less than 3 (since the sum of the degrees is equal to 2E). This contradicts the given condition that each vertex has a degree of at least 3. Therefore, there is no graph with a larger number of vertices that satisfies the given conditions.

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A) H0: μ = 8mg, Ha: μ ≠ 8mg.

B) \(t = (x̄ - μ) / (s / sqrt(n)) = (10.3 - 8) / (2 / sqrt(25)) = 5.5\).

C) Degrees of freedom = n - 1 = 24, two-tailed t-test, α = 0.01, critical values are  ±2.492. p-value < 0.01.

D) We reject the null hypothesis and conclude that there is strong evidence that the mean amount of active ingredient in all dosages produced is different from 8 mg. The sample mean is significantly higher than 8 mg, indicating that the production process needs improvement.

(A) The null hypothesis is that the population mean of the active ingredient is equal to 8 mg, while the alternative hypothesis is that it is different from 8 mg. In symbols, H0: μ = 8 vs. Ha: μ ≠ 8.

(B) We apply the t-test formula to determine the value for the test statistic:

\(t = (xbar - μ) / (s / sqrt(n))\)

where Î14 is the estimated population mean, n is the number of samples size, x bar represents the sample mean, and s is the standard deviation of the sample. Plugging in the values from the problem, we get:

\(t = (10.3 - 8) / (2 / sqrt(25)) = 3.25\)

(C) To determine the critical value or the p-value, we look up the t-distribution with 24 degrees of freedom ( df = n - 1) and a two-tailed significance level of 0.01. The critical values are  ±2.492, while the p-value is less than 0.01.

(D) Based on the results, we reject the null hypothesis and conclude that the mean amount of active ingredient in all dosages produced is different from 8 mg at the 1% significance level. In practical terms, this means that the drug production process needs to be investigated and improved to ensure that the correct amount of active ingredient is consistently delivered in each dosage.

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Answer:

The height of the rectangle can be determined by dividing the area of the rectangle (59.5 square inches) by the base of the rectangle (7 inches). This equals 8.5 inches, which is the height of the rectangle.