Veronika’s five test scores are 59, 80, 95, 88, and 93. If the outlier of 59 is removed, what is the mean absolute deviation of the remaining four test scores

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Using a system of equations, it will take 5 weeks for Shop B to repair as many cars as Shop A.

A system of equations is called simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

                                                              Shop A  Shop B

The number of cars already repaired      55         30

The number of cars repaired per week   5           10

Let the number of cars repaired by Shop A in w weeks = 5w + 55

Let the number of cars repaired by Shop B in w weeks = 10w + 30

For the number of cars repaired by each shop to equate, 5w + 55 = 10w + 30

5w - 10w = 30 - 55

-5w = -25

w = 5

Thus, using simultaneous equations, we can conclude that it will take Shop B 5 weeks to repair as many cars as Shop A.

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Answer:  56.24545388

Step-by-step explanation:

A common question is How many pound in 124 kilogram? And the answer is 273.373205109 lbs in 124 kg. Likewise the question how many kilogram in 124 pound has the answer of 56.24545388 kg in 124 lbs.

By  converting 124 pound to kilogram has the answer of 56.24545388 kg in 124 lbs.

To convert 124 lbs to kg multiply the mass in pounds by 0.45359237. The 124 lbs in kg formula is [kg] = 124 * 0.45359237. Thus, for 124 pounds in kilogram we get 56.24545388 kg.

The fundamental mass unit in the metric system is the kilogramme (kg). The mass of 1,000 cubic centimetres of water is very close to (and was originally intended to be exactly) one kilogramme. The actual weight of a pound is 0.45359237 kg.

In its initial form, a solid platinum cylinder served as the kilogram's symbol in the late 18th century. However, it turned out to be difficult and cumbersome to measure the mass of a volume of water, thus the platinum artefact itself ended up being the standard. It was replaced in 1889 by a standard kilogramme, which was constructed of the same platinum-iridium alloy as the bar being used at the time to define the metre and was also a solid cylinder with a height equal to its diameter.

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Answer:

1000a+100b+10c+d

Step-by-step explanation:

place value of a =1000×a

place value of b=100×b

place value of c=10c

place value of d=1×d

Spatial join, selecting by location, and intersect function are all used in GIS to combine or extract spatial information from multiple layers. The primary characteristics that distinguish a spatial join from selecting by location and intersect function are:

In summary, the primary characteristic that distinguishes a spatial join from selecting by location and intersect function is that a spatial join combines layers based on their spatial relationship, while selecting by location and intersect function extract features based on their spatial relationship.

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Answer: directrix.

hoped this helped lmk if it did

We need to find the derivative which is the rate of change

So, when x is infinite, the function g(x) has the greatest rate of change

Answer:

n = 11/3

Step-by-step explanation:

n = certain number

6n - 1 = 21

6n = 22

n = 22/6 or 11/3

Answer:

SAS

is the correct answer of this question

Answer:

SAS

Step-by-step explanation:

SAS is an abbreviation for side angle side, which is what your triangle shows.

Answer:

666

Step-by-step explanation:

Answer:

5x³ + 4x² - 3x - 1

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

(2x³ + 4x² + 3) + (3x³ - 3x - 4)

Step 2: Simplify

Answer:

\(3.8*10^1\)

Step-by-step explanation:

So we'll be using PEMDAS, which is an acronym used to explain order of operations. It stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

P- Parentheses:

(2x3+4x2+3)+(3x3−(3x−4))

M- Multiplication (within Parentheses):

(6+8+3)+(9−(-12))

A- Addition (within Parentheses):

(6+8+3)+(9−(-12))

17 + 21

A- Addition:

38

Now, we'll take that number and put it in standard form, which is the number with only one number outside of the decimal times ten to the however many times it can be divided by ten.

So,

38/10 = 3.8

So,

3.8 * 10^1 is your answer.

Suppose we're asked to solve the first order linear differnetial equation,

\(\longrightarrow\rm{\dfrac{dy}{dx}+y\cdot P(x)=Q(x)}\)

To solve this equation we have to find out a term called 'Integrating Factor' given by,

\(\rm{I_f=e^{\int P(x)\ dx}}\)

such that the solution of the equation is,

\(\displaystyle\longrightarrow\rm{y\cdot I_f=\int Q(x)\cdot I_f\ dx}\)

Here the given differential equation is,

\(\longrightarrow\rm{\dfrac{dy}{dx}-\dfrac{y}{x}=3x}\)

\(\longrightarrow\rm{\dfrac{dy}{dx}+y\left(-\dfrac{1}{x}\right)=(3x)}\)

Here,

\(\longrightarrow\rm{P(x)=-\dfrac{1}{x}}\)

Integrating wrt x,

\(\displaystyle\longrightarrow\rm{\int P(x)\ dx=-\int\dfrac{1}{x}\ dx}\)

\(\displaystyle\longrightarrow\rm{\int P(x)\ dx=-\ln|x|}\)

[We will consider constant of integration as zero.]

Then the integrating factor is,

\(\longrightarrow\rm{I_f=e^{\int P(x)\ dx}}\)

\(\longrightarrow\rm{I_f=e^{-\ln|x|}}\)

Since \(\rm{e^{b\,\ln(a)}=a^b,}\)

\(\longrightarrow\rm{I_f=x^{-1}}\)

\(\longrightarrow\rm{\underline{\underline{I_f=\dfrac{1}{x}}}}\)

Hence the integrating factor for the given differential equation is 1/x.

The probability that a person will wait for more than 66 minutes is 0.1587

Given;

The time spent waiting in line is approximately normally distributed with the mean will be ' X '.

The mean given is μ = 44 minutes

The standard deviation is δ = 22 minutes

The probability that a person will wait for more than 66 minutes is;

P ( X > 66 ) = P [ X - μ/δ > 66 - μ/δ]

                  = P [Z > 66 - 44 / 22]

                  = P [Z > 1]

                  = 1 - P(Z ≤ 1)

                  = 1 - 0.8413

                  = 0.1587

The probability that a person will wait for more than 66 minutes is 0.1587.

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Answer:

3 12

- = -

5 20

Step-by-step explanation:

5×4=20

3×4= 12

Based on data, it is better to describe the centers of distribution in terms of median because the data distribution is not symmetric. The Option B is correct.

To determine a better measure of center, we must examine the symmetry of the data distribution. We can do it by constructing box plots or dot plots but because we have small data set, we will examine the data visually.

By looking at the data, we see that those distributions are not perfectly symmetric with some values have more spread out than the others. So, it is better to describe the centers of distribution in median rather than in mean.

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Answer:

1^sqrt(2) = 1 is always true

Step-by-step explanation:

Step-by-step explanation:

it is always 1 because the teacher said.....lol

Answer:

None

Step-by-step explanation:

They have the same slope so they are parallel and will never intersect.

Answer:

No solutions

Step-by-step explanation:

I just did it on Khan Academy.

Answer:

ok so I'm English not a hundred percent sure on your break down of money......so if I'm right in thinking that a nickel = 5 cents, dime = 10cents and a quarter =25cents

you add the amounts together

so 25 + 30 +20 = 75 cents.

there are 100 cents in a dollar so 100/100 X 75=75%

I have no idea how you got to 44%

Answer:

The answer is 15

Step-by-step explanation:

adding 3 to y for each time 1 is added to y. since you start with a base of 9, we can conclude this answer by taking 3 times 15, which is 45, then adding 9, which makes 54. Like this:

0 | 9

1 | 12

2 | 15

...

13 | 48

14 | 51

15 | 54

To solve the differential equation using the exact method, we need to verify that it is exact. A first-order differential equation of the form M(x,y)dx + N(x,y)dy = 0 is exact if and only if ∂M/∂y = ∂N/∂x.

In this case, we have:

M(x,y) = e^{y+x} + ye^y

N(x,y) = xe^y - 1

∂M/∂y = e^{y+x} + e^y + ye^y

∂N/∂x = e^y

Since ∂M/∂y is not equal to ∂N/∂x, the equation is not exact. However, we can make it exact by multiplying both sides of the equation by a suitable integrating factor. An integrating factor is a function that when multiplied by both sides of a differential equation, makes it exact.

To find the integrating factor, we need to find a function μ(x,y) such that:

μ(x,y)∂M/∂y - ∂μ/∂y M(x,y) = μ(x,y)∂N/∂x - ∂μ/∂x N(x,y)

By comparing the coefficients of dx and dy, we get:

∂μ/∂y = xe^y - 1

∂μ/∂x = e^{y+x} + ye^y

Integrating the first equation with respect to y and the second equation with respect to x, we get:

μ(x,y) = e^{xy} - y

μ(x,y) = e^{y+x} + ye^y + f(x)

Equating the two expressions for μ(x,y), we get:

e^{xy} - y = e^{y+x} + ye^y + f(x)

Taking the derivative of both sides with respect to x, we get:

ye^{xy} = e^{y+x} + ye^y f'(x)

Solving for f'(x), we get:

f'(x) = \frac{ye^{xy}-e^{y+x}}{ye^y}

Integrating both sides with respect to x, we get:

The solution of the first order differential equation using Exact method is -e⁻¹

We must determine whether the differential equation meets the criteria for being exact in order to solve it using the exact method, which is given by:

∂M/∂y = ∂N/∂x

where M and N, respectively, are the dx and dy coefficients.

Here, \(M = e^{y+x} + ye^y\)  and\(N = xe^y - 1.\)

∂M/∂y = \(e^{y+x} + e^y + ye^y\)

∂N/∂x = \(e^y\)

We must discover the integrating factor to make the equation precise because  ∂M/∂y does not equal ∂N/∂x. The formula for the integrating factor is

μ =\(e^{\int\limits(\partial N/\partial x - \partial M/\partial y)/N dx = e^{\int\limits(1 - e^{-y})/x dx} = e^y ln|x|\)

We obtain the following by multiplying the given equation by the integrating factor:

\((e^{2y+x}ln|x| + ye^yln|x|)dx + (xe^yln|x| - ln|x|)dy = 0\)

We can now check if the equation is exact:

∂M/∂y = \(e^{2y+x}ln|x| + e^y + ye^yln|x|\)

∂N/∂x = \(e^yln|x|\)

As both are equal, the equation is exact.

By integrating the coefficients of dx with respect to x and dy with respect to y, we can now get the potential function u(x,y):

u(x,y) = ∫\((e^{2y+x}ln|x| + ye^yln|x|)dx = x e^{2y+x} ln|x| - x ye^yln|x| + f(y)\)

∂u/∂y = \(xe^{2y+x} + e^yln|x| + ye^y\)

Comparing this with N, we get:

∂u/∂y = ∫Ndy = ∫\((xe^y-1)dy = xe^y - y + g(x)\)

Using u's partial derivative with regard to y, we can calculate:

\(xe^{2y+x} + e^yln|x| + ye^y = xe^y + g'(x)\)

Comparing the coefficients of \(e^y\) and ln|x|, we get:

g'(x) = \(xe^{2y+x} - ye^y\)

When we combine both sides in relation to x, we get:

g(x) = \((1/3)xe^{2y+3x} - xye^y + C\)

where C is the integration constant.

When we change the values of u and g in the formula u(x,y) = g(x) + C, we obtain:

\(x e^{2y+x} ln|x| - x ye^yln|x| + (1/3)xe^{2y+3x} - xye^y = C\)

Substituting the initial condition y(0) = -1, we get:

C = -e⁻¹

As a result, the following is the differential equation's solution:

\(x e^{2y+x} ln|x| - x ye^yln|x| + (1/3)xe^{2y+3x} - xye^y = -e^{(-1)\)

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

Answer:

B

Step-by-step explanation:

given f(x) then f(x ± a ) is a horizontal translation of f(x)

• if + a , then a shift left of a units

• if - a then a shift right of a units

here g(x) is the graph of f(x) moved 2 units right , then

g(x) = (x - 2)²

Answer:

Subtract everything from 180. The square boxes represent 90°.

1. 180-80-40 = 60°

2. 180-90-32 = 58°

3. 180-45-90 = 45°

4. 180-90-78 = 12°

5. 180-90-15 = 75°

6. 180-55-25 = 100°

7. 180-90-36 = 54°

8. 180-90-30 = 60°

9. 180-60-30 = 90°

Hope this helped :)

Answer: If the figure is rotated 90 degrees counter clockwise about the origin, ... Triangle LMN has vertices L(-1,4), M(-2,4), and N(-1,-1).

Step-by-step explanation:

90 Degrees

Answer:

50 Candy

Step-by-step explanation:

We know that 2/5 of the bag is 60 candy. By taking this information we can conclude that 1/5 of the bag is 30 candy. We know that 1/5 of the bag is 30, so 30 times 5 is 150 candy.

Now that we have found out that there is 150 candy total we can know divde 150 by 3 to find out how much candy is in 1/3 of the bag.

150/3 = 50 Candy

1/3 of the bag represent 50 candy.

The equation f(x) = x^5 - 2x^3 - 2 has a root in the interval [-2, 0] by the Intermediate Value Theorem.

To apply the Intermediate Value Theorem and show that there is a root (a point where f(x) = 0) for the equation f(x) = x^5 - 2x^3 - 2, we need to demonstrate that f(x) changes sign over a given interval.

First, we evaluate f(x) at two points, a and b, such that f(a) and f(b) have opposite signs. Let's choose a = -2 and b = 0:

f(-2) = (-2)^5 - 2(-2)^3 - 2 = -18

f(0) = (0)^5 - 2(0)^3 - 2 = -2

Since f(-2) = -18 is negative and f(0) = -2 is positive, f(x) changes sign over the interval [-2, 0]. According to the Intermediate Value Theorem, there must exist at least one value c within this interval where f(c) = 0, indicating the presence of a root.

Therefore, by satisfying the requirements of the Intermediate Value Theorem and showing a change in sign between f(-2) and f(0), we can conclude that there is a root for the equation f(x) = x^5 - 2x^3 - 2 within the interval [-2, 0].

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We can learn a lot about a population if we select a subset of it.

One kind of set is a sample space. It is a clear listing of every event that could occur in a statistical experiment. A statistical experiment's events are a subset of the sample space.

A subset is a smaller group of results that are part of the bigger group.

Subsets are events, and events are subsets. A subset is an event of a sample space, and an event is a potential result of an experiment. A random experiment's sample space is a set (S) that contains all of the experiment's potential outcomes.

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Answer:

9

Step-by-step explanation:

(5)3-6(5)+4(3)2

(15-30)+4(3)2

-15+ 24

=9

Answer:

The answer is: x < 1

Step-by-step explanation: