what is the mean absolute deviation of 12 4 6 12 10 8 4 4

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

Step-by-step explanation:

\(x^{2}\) + 18x +c = 25+c

\(x^{2}\) + 18x +\(9^{2}\) =25+\(9^{2}\)    (the c just cancels out and add \(9^{2}\))

\((x+9)^{2}\) -106 = 0

Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.

What is polynomial?

A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.

Here,

When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.

This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.

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The series to 10 term is

1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512

An equation that represents a sequence based on a rule is called a recurrence relation.

Finding the following term, which is dependent upon the prior phrase, is made easier (previous term). We can readily predict the following term in a series if we know the preceding term.

The term is predicted by multiplying the preceding term by 2

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To sketch the region enclosed by the given curves, we can start by plotting the two curves:

Curve 1: x = 20 - 5y^2

Curve 2: x = 5y^2 - 20

Let's first analyze the curves and determine the orientation of the region. From the equations, we can see that both curves are symmetrical about the y-axis. The curve 1 is a downward-opening parabola, and curve 2 is an upward-opening parabola.

To find the area of the region, we need to determine the limits of integration. Since the curves are symmetrical, we can integrate with respect to y over the interval where y varies from the bottom curve to the top curve.

To find the intersection points of the curves, we can set the two equations equal to each other:

20 - 5y^2 = 5y^2 - 20

Rearranging the equation, we get:

10y^2 = 40

y^2 = 4

y = ±2

So the intersection points are (2, 2) and (-2, -2).

Now, let's sketch the region:

-2 |_______

| /

| /

| /

|/__________

|___________| 2

The region is bounded by the curves and the y-axis.

To find the area of the region, we can integrate with respect to y:

A = ∫[from -2 to 2] [(curve 1) - (curve 2)] dy

A = ∫[-2 to 2] [(20 - 5y^2) - (5y^2 - 20)] dy

Simplifying the expression:

A = ∫[-2 to 2] (40 - 10y^2) dy

Now, we can integrate:

A = [40y - (10/3)y^3] |[-2 to 2]

Evaluating the expression:

A = [(40(2) - (10/3)(2)^3) - (40(-2) - (10/3)(-2)^3)]

A = [(80 - (80/3)) - (-80 - (80/3))]

A = (80 - 80/3) - (-80 - 80/3)

A = (240/3 - 80/3) + (240/3 + 80/3)

A = (160/3) + (320/3)

A = 480/3

A = 160

Therefore, the area of the region enclosed by the given curves is 160 square units.

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Step-by-step explanation:

6 significant figures......

Answer:

The correct answer is six

Answer:

47

Step-by-step explanation:

20*47= 940

940*5=4,700

47*100=4,700

Answer:

I believe is 3 4/6

Step-by-step explanation:

22/5  : 6/5

22/5 * 5/6

22/6

11/3

3 4/6

Answer:

11/3 or 3and2/3

Step-by-step explanation:

To change a mixed number into a fraction, you multiply the whole number by the denominator and add it to the numerator.

4 and 2/5 = 22/5

1 and 1/5 = 6/5

To divide fractions, flip one upside down and then multiply top by top, bottom by bottom

(22/5) / (6/5) = (22/5) x (5/6) = (22x5)/(5x6) = 110/20 = 11/3 or 3and2/3

The effective interest method is used to amortize the bond premium. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond. The journal entry for bond issuance is as follows: Dr. Cash 205,000, Dr. Premium on Bonds Payable 5,000, Cr. Bonds Payable 210,000

The effective interest method is a method of amortizing bond premium or discount that takes into account the time value of money. The effective interest is the interest that would be earned if the bond were purchased at its market value and held to maturity. The carrying value of the bond increases by the effective interest each period, and the premium is amortized over the life of the bond.

The journal entry for bond issuance records the proceeds from the sale of the bonds, the premium on bonds payable, and the bonds payable. The proceeds from the sale of the bonds are equal to the face value of the bonds plus the premium.

The premium on bonds payable is a liability that represents the excess of the issue price of the bonds over their face value. The bonds payable account is a long-term liability that represents the amount that the company owes to the bondholders.

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Answer:

Add 4x to both sides

Step-by-step explanation:

on Edge

Answer:

\(\textsf{(a)} \quad -4 < x\leq 1\)

\(\textsf{(b)} \quad [3, 19)\)

Step-by-step explanation:

Given compound inequality:

\(\dfrac{9+x}{5} < 5+x\leq 6\)

\(\textsf{If\: $a < u\leq b$ \:then\: $a < u$ \:and\: $u\leq b$}.\)

\(\textsf{Therefore \:$\dfrac{9+x}{5} < 5+x$ \:and\: $5+x\leq 6$}\)

Solve the inequalities separately:

Inequality 1

\(\begin{aligned}\dfrac{9+x}{5} & < 5+x\\9+x & < 5(5+x)\\9+x & < 25+5x\\9+x -5x& < 25+5x-5x\\9-4x & < 25\\ 9-4x-9 & < 25-9\\-4x & < 16\\-x & < 4\\x & > -4\\ \end{aligned}\)

Inequality 2

\(\begin{aligned} 5+x & \leq 6\\ 5+x-5 & \leq 6-5\\x & \leq 1 \end{aligned}\)

Combine the intervals:

\(-4 < x\leq 1\)

Given equation:

\(y=x^2+3\)

As the domain is restricted to  -4 < x ≤ 1, the range is also restricted.

The vertex (minimum point) of  \(y = x^2 + 3\)  is when x = 0.

As x = 0 lies within the restricted domain, y = 3 is the lowest value of the range.

\(x=-4 \implies y=(-4)^2+3=19\)

Therefore, the range is:

Answer:

60

Step-by-step explanation:

3.92 = (6.56/100) * _

To solve for _, we can multiply both sides by 100:

100 * 3.92 = (6.56/100) * _

100 * 3.92 = 6.56 * _

_ = (100 * 3.92) / 6.56

Therefore, _ = 60.

Answer: 60

Step-by-step explanation:

Answer:

bearing of A from C is - 65.24°

the distance |BC| is 187.84 m

Step-by-step explanation:

given data

girl walks AB = 285 m (side c)

bearing angle B = 78°

girl walks AC = 307 m (side a)

solution

we use here the Cosine Law for getting side b that is

ac² = ab² + bc² - 2 × ab × cos(B)     ...............1

307² = 285² + x²  - 2 × 285 cos(78)

x = 187.84 m

and

now we get here angle θ , the bearing from A to C get by law of sines

sin (θ) =

sin (θ) =  0.5985  

θ = 36.76°

and as we get here angle BAC that is

angle BCA = 180 - ( 36.76° + 78° )

angle BCA = 65.24°

and here  negative bearing of A from C so - 65.24°

Step-by-step explanation:

Answer:

WELL 17

Step-by-step explanation:

60 DIVED BY 5 IS 12

SO 12 DIVIDED BY 204 IS 17 SOOOOOO 17 IS THE ANS

By mathematical induction, the statement, n^(n) * (2n - 1) = n^2 - 4 is true for all positive integers n ≥ 3.

Base case: For n = 3, we have:

3^(3) * (2(3) - 1) = 27 * 5 = 135

3^(2) - 4 = 9 - 4 = 5

So the statement is true for n = 3.

Inductive step: Assume that the statement is true for some arbitrary positive integer k ≥ 3. That is,

k^(k) * (2k - 1) = k^2 - 4

Now we want to show that the statement is true for k+1. That is,

(k+1)^(k+1) * (2(k+1) - 1) = (k+1)^2 - 4

First, let's simplify the left-hand side:

(k+1)^(k+1) * (2(k+1) - 1) = (k+1) * k^k * (2k+1) * 2

= 2(k+1) * k^k * (2k+1)

= 2k^k * (2k+1) * (k+1) * 2

= 2k^k * (2k+1) * (2k+2)

= 2k^k * (4k^2 + 6k + 2)

= 8k^(k+2) + 12k^(k+1) + 4k^k

Now let's simplify the right-hand side:

(k+1)^2 - 4 = k^2 + 2k + 1 - 4

= k^2 + 2k - 3

Now we want to show that the left-hand side is equal to the right-hand side. So we need to show that:

8k^(k+2) + 12k^(k+1) + 4k^k = k^2 + 2k - 3

Let's first isolate the k^2 and 2k terms on the right-hand side:

k^2 + 2k - 3 = (k^2 - 4) + (2k + 1)

= k^k * (2k - 1) + (2k + 1)

Now we can substitute in our inductive hypothesis:

k^k * (2k - 1) + (2k + 1) = k^k * (k^2 - 4) + (2k + 1)

= k^(k+2) - 4k^k + 2k + 1

= k^(k+2) + 2k^(k+1) - 4k^k + 2k - 2k^(k+1) + 1

= 8k^(k+2) + 12k^(k+1) + 4k^k - 6k^(k+1) + 2k - 2

So we have shown that:

8k^(k+2) + 12k^(k+1) + 4k^k = k^2 + 2k - 3

Therefore, by mathematical induction, the statement is true for all positive integers n ≥ 3.

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The sum of the squared deviations of each individual sample observation from the mean of all observations is referred to as the within-group sum of squares or the error sum of squares in one-way ANOVA.

In one-way ANOVA (analysis of variance), the sum of the squared deviations of each individual sample observation from the mean of all observations is referred to as the "within-group sum of squares" or the "error sum of squares."

ANOVA is a statistical method used to compare the means of two or more groups to determine if there are significant differences among them. In one-way ANOVA, we have a single independent variable (or factor) that divides the data into different groups or levels.

The goal is to assess whether the variation within the groups is significantly smaller than the variation between the groups.

To calculate the within-group sum of squares, we first compute the mean of each group and then calculate the squared deviation of each observation within its respective group mean.

These squared deviations are then summed across all groups to obtain the total within-group sum of squares.

The within-group sum of squares represents the variability of the data within each group or sample.

It quantifies how far the individual observations deviate from their respective group means.

Smaller values indicate less variability within each group, suggesting that the observations are more homogeneous within the groups.

Conversely, the between-group sum of squares measures the variability between the group means.

It reflects the differences among the sample means and indicates whether the groups have distinct characteristics or if the differences are due to random chance.

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Step-by-step explanation:

Angles DEC and DFC are both 90°, therefore DC is the diameter of the circle.

That makes angle DBC = 90° as well, so x = 90.

Answer:

D

Step-by-step explanation:

you find the radius by using the diameter

hence radius = diameter divide by 2 which is 1÷2 which is 0.5

next step the volume of the cylinder is πr^ 2h

22÷7 × 0.5×0.5×8 gives you 6.2857 to 5 significant number

The volume of the​ cylinder will be 6.28 square yards.

A cylinder is a closed solid that has two parallel circular bases connected by a curved surface.

The diameter of a cylinder is 1 yd.

The height is 8 yd.

Then the volume of the​ cylinder will be

Volume = (π / 4)d² h

Volume = (π / 4) x 1² x 8

Volume = (π / 4) x 8

Volume = 2π

Volume = 6.28 square yards

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Answer: 5

Step-by-step explanation:

We are looking for the number of years below the 25th percentile, which is given by the first quartile.

Since the first quartile is 5, we know that about 25% of Carlson High School teachers have fewer than 5 years of experience.

3.25 • 5 + 2.50 • 3 + 2 • 3 = x

16.25 + 7.50 + 6 = x

29.75 = how much they spent all-together

The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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We are given the following ratios:

We are asked to determine if the ratios are equivalent. To determine that, we will divide each element of the first ratio by 2, we get:

We get the ratio 2:9, since two ratios are equivalent if both elements of one ratio is a multiple of a corresponding element of the second ratio, and we got by dividing the first ratio by 2 the following:

This means that the given ratios are not equivalent.

Answer:

Step-by-step explanation:

The probability of occurring event A is 23% or 0.23.

To find the probability of event A:

Divide the number of events in A to the total number of events.

Number of events in A = 12

Total number of events = 12+20+20

=52

P(A)=Number of events in A/Total number of events

\(=\frac{12}{52}\)

Divide both sides by 12:

\(=\frac{3}{13}\)

\(=0.23\)

\(=23\) %

Hence, the probability of occurring event A is 23% or 0.23.

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A beverage company has decided to manufacture a new juice with mixed flavors, which is prepared from orange and pineapple. The vitamin contents are 5% of vitamin A and 2% of vitamin C in the orange flavor, while pineapple flavor contains 8% of vitamin C.

The company's policies are to add at least 20 L of orange flavor to the new juice and limit the vitamin C content to no more than 5%. The cost of orange flavor is $1000 per liter, while the cost of pineapple flavor is $400 per liter.To satisfy a minimum demand of 100 L of juice, we must determine the optimal amount of each flavor to use.A) A linear programming model is needed for the company to solve this problem (Minimize production cost of the new juice)B) Use a graphic solution for this problem.The objective function of the optimization problem can be given as:min C = 1000x + 400yThe constraints that the company has are,20x + 0y ≥ 100x + y ≤ 5x ≥ 0 and y ≥ 0The feasible region can be identified by graphing the inequality constraints on a graph paper. Using a graphical method, we can find the feasible region, and by finding the intersection points, we can determine the optimal solution.The graph is shown below; The optimal solution is achieved by 20L of orange flavor and 80L of pineapple flavor, as indicated by the intersection point of the lines. The optimal cost of producing 100 L of juice would be; C = 1000(20) + 400(80) = $36,000.C) If the company decides that the juice should have a vitamin C content of no more than 7%, it would alter the problem's constraints. The new constraint would be:x + y ≤ 7Dividing the equation by 100, we obtain;x/100 + y/100 ≤ 0.07The objective function and the additional constraint are combined to create a new linear programming model, which is solved graphically as follows: The feasible region changes as a result of the addition of the new constraint, and the optimal solution is now achieved by 20L of orange flavor and 60L of pineapple flavor. The optimal cost of producing 100 L of juice is $28,000.

In conclusion, the optimal amount of each flavor that should be used to satisfy a minimum demand of 100 L of juice is 20L of orange flavor and 80L of pineapple flavor with a cost of $36,000. If the company decides that the juice should have a vitamin C content of no more than 7%, the optimal amount of each flavor is 20L of orange flavor and 60L of pineapple flavor, with a cost of $28,000.

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Answer:

12n-5

Step-by-step explanation:

Since each box has 12 cupcakes, we can multiply n by 12 as there is 12 cupcakes for every box.

12n

Now she eats 5 cupcakes, so we subtract 5 from the equation

Hope this helps!

Answer:

40 dollars.

Step-by-step explanation:

28=(.7)x

40=x

Thus, the original price was 40 dollars.

Answer:

1/x^12

Step-by-step explanation:

x^-12

We know that a^ -b = 1 / a^b

x^-12

1/x^12