The endpoints of segment MP areM(-2,-4) and P(8,11) . If K portions MP in a ratios of MK:KP= 1:4, what are the coordinates of K?

The complement of set A, denoted by ​ A`, is the collection of all elements that belong to the universal set but are not part of set A. It's not necessary to mention the universe (also known as U) if it's understood which set of elements is being referred to.

The complement of a set A is the collection of all elements that belong to the universal set but not to set A. It is denoted as ​ A` and does not include any elements that are already in set A. The universal set, also known as U, contains all possible elements and is assumed to be known. Therefore, when referring to the complement of a set, it is not necessary to mention the universal set explicitly. The complement of a set is useful in determining the set of elements that are not part of a particular set, and it can be used in various mathematical operations.

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Answer:

c= 1

Step-by-step explanation:

To get rid of (c) on the right side, simply divide 2^n both side. But first collect like terms on the left side so you will get 2^n + 1 which you will then simplify the like term(2^n) and you will left with c= 1.

Answer:correct

Step-by-step explanation:

I had the same question

Answer:

4 units

Step-by-step explanation:

Length would be 6 units and width would be 4 units

6*4 = 24 proving my claim to be true

Answer:

Width = 4 units

Step-by-step explanation:

Let us pose the width as w, and the length as l. If the length is 2 units greater than the width, consider the following;

\(l = 2 + w,\\\\w = width,\\l = length\)

The area of this rectangle can be determined through length * width / l * w, and is given to be 24 square units. We can say l = 2 + w instead, solving for the width ( w );

\(( 2 + w ) * w = 24,\\2w+w^2=24,\\\left(w-4\right)\left(w+6\right)=0,\\w = 4, w = - 6\\\\Solution - width = 4 units\)

As the width couldn't be a negative value, we had to take the positive of 4 and - 6, which was 4 units.

Answer:

step 1: distribute -1

step 2: combine like terms

step 3: subtract 4 on both sides

step 4: divided both sides by -8, so u can isolate M alone

M=-2

Step-by-step explanation:

To find the value of h such that the system has infinitely many solutions, the two equations must be equivalent, meaning they represent the same line. Let's analyze the given equations:

Equation 1: -9x - 21y = -12
Equation 2: 27x + hy = 36

First, we can simplify Equation 1 by dividing by -3:
3x + 7y = 4

Now, let's compare the coefficients of the x and y terms in both equations. We can notice that the coefficient of x in Equation 2 is 9 times the coefficient of x in the simplified Equation 1. To make the two equations equivalent, the coefficient of y in Equation 2 should also be 9 times the coefficient of y in the simplified Equation 1:

9 * 7y = hy
9 * 7 = h
h = 63

So, when h = 63, the two equations represent the same line, and the system has infinitely many solutions.

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Sounds at 85 dBA can cause hearing loss if listened to for more than 8 hours. Sounds above 85 dBA can damage your hearing more quickly. For every 3-dB increase in noise levels above 85 dBA, the safe listening time is cut in half. You can, for example, listen to sounds at 85 dBA for up to 8 hours.

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Answer:

fitting a simple linear regression first select the cell in data set second on the analyse it ribbon tap in statistical analysis group click fit model and then click the simple degradation model 3rd the wild drop down list select the response variable 4th in the X drop down let's select the predicated

answer = 5

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting two points, and is usually denoted by m. Generally, a line's steepness is measured by the absolute value of its slope, m. The larger the value is, the steeper the line. Given m, it is possible to determine the direction of the line that m describes based on its sign and value:

A line is increasing, and goes upwards from left to right when m > 0

A line is decreasing, and goes downwards from left to right when m < 0

A line has a constant slope, and is horizontal when m = 0

A vertical line has an undefined slope, since it would result in a fraction with 0 as the denominator. Refer to the equation provided below.

Slope is essentially change in height over change in horizontal distance, and is often referred to as "rise over run." It has applications in gradients in geography as well as civil engineering, such as the building of roads. In the case of a road the "rise" is the change in altitude, while the "run" is the difference in distance between two fixed points, as long as the distance for the measurement is not large enough that the earth's curvature should be considered as a factor. The slope is represented mathematically as:

m =

y2 - y1

x2 - x1

the solutions on the interval [0, 2π) are approximately:

x ≈ 0, 0.3927, 1.1781, 1.9635, 2.7489, π/2, π

To solve the equation 3 sin(4x) = -6 sin(2x) on the interval [0, 2π), we can use double angle and power reducing formulas to simplify the equation and find the values of x.

Let's start by applying the double angle formula for sine:

sin(2θ) = 2sin(θ)cos(θ)

Using this formula, we can rewrite the equation as:

3sin(4x) = -6(2sin(2x)cos(2x))

Next, we can use the power reducing formula for cosine:

cos(2θ) = 1 - 2sin²(θ)

Applying this formula to the equation, we have:

3sin(4x) = -6(2sin(2x)(1 - 2sin²(2x)))

Simplifying further:

3sin(4x) = -6(2sin(2x) - 4sin³(2x))

Distributing the -6:

3sin(4x) = -12sin(2x) + 24sin³(2x)

Now, we can combine like terms:

24sin³(2x) + 12sin(2x) - 3sin(4x) = 0

Factoring out sin(2x):

3sin(2x)(8sin²(2x) + 4sin(2x) - 1) = 0

Setting each factor equal to zero:

sin(2x) = 0

This gives us the solutions:

2x = 0, π, 2π

Simplifying:

x = 0, π/2, π

Now let's solve the quadratic factor:

8sin²(2x) + 4sin(2x) - 1 = 0

We can use the quadratic formula to find the values of sin(2x):

sin(2x) = (-4 ± √(4² - 4(8)(-1))) / (2(8))

sin(2x) = (-4 ± √(16 + 32)) / 16

sin(2x) = (-4 ± √(48)) / 16

sin(2x) = (-4 ± 4√3) / 16

sin(2x) = (-1 ± √3) / 4

Now, let's solve for 2x:

2x = sin⁻¹((-1 + √3) / 4)

2x = sin⁻¹((-1 - √3) / 4)

Using the inverse sine function, we can find the values of x:

x = (1/2)sin⁻¹((-1 + √3) / 4) ≈ 0.3927, 1.9635

x = (1/2)sin⁻¹((-1 - √3) / 4) ≈ 1.1781, 2.7489

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The volume of the preservative inside the box is 487.83 cm³.

The total volume of the box is calculated by using the following formula as shown below.

V = L x B x W

where;

V = 16 cm  x  8 cm  x  8 cm

V = 1,024 cm³

The total volume of the metal spheres inside the box is calculated as follows;

V = 16 x ( ⁴/₃πr³ )

where;

V = 16 x ( ⁴/₃π(2 cm)³ )

V = 536.17 cm³

The volume of the preservative inside the box = 1,024 cm³ -  536.17 cm³

= 487.83 cm³

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Answer:

it is linear because there is no answers on the input side that are the same and there is no numbers on the output that are the same  if it was nonlinear there would have 2 be some numbers that are the same but the answer is linear because there are no numbers that are the same

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

The result of the piecewise functions at the given values of the independent variable are

a) g(0) = 5

b) g(-7) = -2

c) g(2) = 7

a) To evaluate g(0), we need to use the first condition in the definition of g(x), since 0 is greater than or equal to -5. Therefore, we have:

g(0) = 0 + 5 = 5

So g(0) = 5.

b) To evaluate g(-7), we need to use the second condition in the definition of g(x), since -7 is less than -5. Therefore, we have:

g(-7) = (-7 + 5) = -2

So g(-7) = -2.

c) To evaluate g(2), we need to use the first condition in the definition of g(x), since 2 is greater than or equal to -5. Therefore, we have:

g(2) = 2 + 5 = 7

So g(2) = 7

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Answer: 46

Step-by-step explanation:

Answer:

72m²

Step-by-step explanation:

yeh that's pretty easy actually

Step-by-step explanation:

(m-3)w²-8w+8=0........colllecting like terms

m+w²-8w=3-8

m-7w=-5

mw=-5+-7

mw=-12

mw/mw=-12/mw.....mw will be cancled out by mw so the answer is -12/mw

The correct answer is b) 1.397. The value of t, the critical value of the t distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than t, can be found using a t-distribution table or statistical software.

By referring to a t-distribution table or using statistical software, we can determine that the critical value with 8 degrees of freedom and a probability of 0.10 of being larger than t is approximately 1.397.

Thus, the correct answer is b) 1.397. This value is important because it allows us to make inferences about the population based on sample data, particularly when the population's standard deviation is unknown. The t distribution becomes increasingly similar to the standard normal distribution as the degrees of freedom increase. In this specific case, the critical value of 1.397 can be used to conduct hypothesis tests or construct confidence intervals when working with a sample size of 9 (8 degrees of freedom = sample size - 1) and a significance level of 0.10.

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The correct answer is b) 1.397. The value of t, the critical value of the t distribution with 8 degrees of freedom, which satisfies the condition that the probability is 0.10 of being larger than t, can be found using a t-distribution table or statistical software.

By referring to a t-distribution table or using statistical software, we can determine that the critical value with 8 degrees of freedom and a probability of 0.10 of being larger than t is approximately 1.397.

Thus, the correct answer is b) 1.397. This value is important because it allows us to make inferences about the population based on sample data, particularly when the population's standard deviation is unknown. The t distribution becomes increasingly similar to the standard normal distribution as the degrees of freedom increase. In this specific case, the critical value of 1.397 can be used to conduct hypothesis tests or construct confidence intervals when working with a sample size of 9 (8 degrees of freedom = sample size - 1) and a significance level of 0.10.

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Hence, the greatest possible difference between AC and AB is -2 units.

Let's denote the lengths of the three sides of the triangle as AB, BC, and AC.

Given that AC is the longest side and AB is the shortest side, we can express the perimeter of the triangle as:

Perimeter = AB + BC + AC = 384 units

To find the greatest possible difference between AC and AB, we want to maximize the value of (AC - AB). Since AC is the longest side and AB is the shortest side, maximizing their difference is equivalent to maximizing the value of AC.

To find the maximum value of AC, we need to consider the remaining side, BC. Since the perimeter is fixed at 384 units, the sum of the lengths of the two shorter sides (AB and BC) must be greater than the length of the longest side (AC) for a valid triangle.

Let's assume that AB = x and BC = y, where x is the shortest side and y is the remaining side.

We have the following conditions:

AB + BC + AC = 384 (perimeter equation)

AC > AB + BC (triangle inequality)

Substituting the values:

x + y + AC = 384

AC > x + y

From these conditions, we can infer that AC must be less than half of the perimeter (384/2 = 192 units). If AC were equal to or greater than 192 units, the sum of AB and BC would be less than AC, violating the triangle inequality.

Therefore, to maximize AC, we can set AC = 191 units, which is less than half the perimeter. In this case, AB + BC = 384 - AC = 193 units.

The greatest possible difference between AC and AB is (AC - AB) = (191 - 193) = -2 units.

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Answer:

A = 20

Step-by-step explanation:

12/3 = A/5

60 = 3A

A = 60÷3 = 20

hope that helps and plss tell me if you have any questions :))

Answer:

\(\boxed{-3x + 1}\)

Step-by-step explanation:

\(-7x + 2 + 4x - 1\)

\(= -7x + 2 +4x + -1\)

Combine Like Terms:

\(= -7x + 2 + 4x + -1\)

\(= (-7x + 4x) + (2 + -1)\)

\(= -3x + 1\)

Hope this helped you!

The Taylor polynomial T₅(x) is 0.99500416 and by use the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

What is Taylor Series?

The Taylor series or Taylor expansion of a function in mathematics is the infinite sum of terms represented in terms of the function's derivatives at one particular point. The function and the sum of its Taylor series are roughly equivalent for the majority of typical functions at this point.

Taylor series or Taylor expansion:

Infinity ∑ (n = 0) fⁿ(a)/n! (x - a)ⁿ

Where,

n! = factorial of n

a = real or complex number

fⁿ(a) = nth derivative of function f evaluated at the point a.

As given function is,

f(x) = cosx, a = 0, x = 0.1

Taylor polynomial of degree 'n' for f(x) center a,

Tₙ(x) = f(a) + f'(a)(x - a) + f''(a)/2 (x - a)² + f'''(a)/3 (x - a)³ + ......+ fⁿ⁻¹(a)/(n - 1)! (x - a)ⁿ⁻¹ + fⁿ(a)/n! (x - a)ⁿ

Evaluate values as follows:

f(x) = cosx ⇒ f(0) = 1

f'(x) = -sinx ⇒ f'(0) = 0

f''(x) = -cosx ⇒ f''(0) = -1

f'''(x) = sinx ⇒ f'''(0) = 0

f⁴(x) = cosx ⇒ f⁴(0) = 1

f⁵(x) = -sinx ⇒ f⁵(0) = 0

Substitute obtained values in Taylor series,

T₅(x) = 1 + (0) (x - 0) + (-1)/2 (x - 0)² + 0 + 1/24(x - 0)⁴ + 0

T₅(x) = 1 -1/2x² + 1/24x⁴

At x = 0.1

T₅(0.1) = 1 -1/2(0.1)² + 1/24(0.1)⁴

T₅(0.1) = 1 - 0.005 + 4.16 × 10⁻⁶

T₅(0.1) = 0.99500416

Hence, the Taylor polynomial T₅(x) is 0.99500416.

Evaluate the maximum possible size of the error:

cos(0.1) = 0.99999847

T₅(0.1) = 0.99500416

Icos(0.1) - T₅(0.1)I = 0.99999847 - 0.99500416

Icos(0.1) - T₅(0.1)I = 0.00499431

Icos(0.1) - T₅(0.1)I = 49943.1 × 10⁻⁷.

Hence, the Error Bound the maximum possible size of the error is 49943.1 × 10⁻⁷.

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To find the approximate direction angle of vector v = ⟨8, -1⟩, we can use trigonometry and the inverse tangent function (arctan). Therefore, the approximate direction angle of vector v is approximately -0.1244 radians or -7.12 degrees.

The direction angle (θ) of a vector can be calculated using the formula:

θ = arctan(y/x)

where (x, y) are the components of the vector.

For the given vector v = ⟨8, -1⟩, we have x = 8 and y = -1.

θ = arctan((-1)/8)

Using a calculator or a mathematical software, we can evaluate this expression to find the approximate direction angle:

θ ≈ -0.1244 radians or approximately -7.12 degrees.

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The particular solution is:

y = -1 - e^(3x)

We have the differential equation:

y' - 3y = 3

To find the integrating factor, we multiply both sides by e^(-3x):

e^(-3x)y' - 3e^(-3x)y = 3e^(-3x)

Notice that the left-hand side is the product rule of (e^(-3x)y), so we can write:

d/dx (e^(-3x)y) = 3e^(-3x)

Integrating both sides with respect to x, we get:

e^(-3x)y = ∫ 3e^(-3x) dx + C

e^(-3x)y = -e^(-3x) + C

y = -1 + Ce^(3x)

Using the initial condition y(0) = -1, we can find the value of C:

-1 = -1 + Ce^(3*0)

C = -1

So the particular solution is:

y = -1 - e^(3x)

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The coordinate vector of p(t) = 1 + 4t + 7t2 relative to the basis B = {1 + t2, t + t2, 1 + 2t + t2} is (3, 1, 2).

To find the coordinate vector of p(t) relative to B, we need to express p(t) as a linear combination of the basis vectors. Let p(t) = a(1 + t2) + b(t + t2) + c(1 + 2t + t2), where a, b, and c are scalars. We can solve for a, b, and c by equating the coefficients of the corresponding powers of t on both sides of the equation. This gives us the system of equations:

a + c = 1

b + 2c = 4

a + b + 2c = 7

Solving this system of equations gives us a = 3, b = 1, and c = 2. Therefore, the coordinate vector of p(t) relative to B is (3, 1, 2). This means that p(t) can be expressed as 3(1 + t2) + 1(t + t2) + 2(1 + 2t + t2) in terms of the basis B.

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Answer:

y = 3/4x-3

Step-by-step explanation:

The equation of a line in slope intercept form is

y = mx+b where m is the slope and b is the y intercept

The y intercept is -3 ( where it crosses the y axis)

The slope is  change in y over change in x

We go up 3 and over to the right 4

The slope is 3/4

y = 3/4x-3

Answer:

y=3x-18

Step-by-step explanation:

using point slope form, the equation would b y+3 = 3(x-5)

slope intercept equation is y=mx+b, so try to get the equation before in that form

distruibute the 3: y+3 = 3x-15

subtract the 3: y = 3x-18

Answer:

Step-by-step explanation:

"The capture-recapture of individually distinctive signature whistles has not been attempted before," says the paper's senior author Dr Tess Gridley, Co-Director of Sea Search and the Namibian Dolphin Project and a postdoctoral fellow in the Department of Botany and Zoology at SU. "The dolphins use these sounds throughout life and each has its own unique whistle. Therefore, by recording signature whistles over time and in different places we can calculate where animals are moving to and how many animals there are in a population."

Working with Dr Simon Elwen of Stellenbosch University, the Namibian Dolphin Project has been researching Namibia's resident bottlenose dolphins for the past 12 years, and built up a catalogue of more than 55 signature whistles dating back to 2009.

This particular study was led by Emma Longden, who began the project during her BSc (Hons) Marine Biology degree at the University of Plymouth. As an undergraduate, Emma completed an internship with the Namibia Dolphin Project for a month in 2016, and returned again in 2018 to complete work on the mark-recapture project.

She analysed more than 4000 hours of acoustic data from four hydrophones positioned along the coast south and north of Walvis Bay, Namibia, during the first six months of 2016.

All in all, they identified 204 acoustic encounters, 50 of which contained signature whistle types. From these encounters, 53 signature whistle types were identified; 40 were in an existing catalogue developed in 2014 for the Walvis Bay bottlenose dolphin population, and 13 were newly identified. Of the 53 signature whistle types identified, 43% were captured only once, whereas the majority (57%) were recaptured twice or more.

"One of the great things about bioacoustics is that you can leave a hydrophone in the water for weeks at a time and collect so much data without interfering with the lives of the animals you are studying," says Emma, whose work on the project was also supervised by Dr Clare Embling, Associate Professor of Marine Ecology at the University of Plymouth.

Dr Embling added: "This work is incredibly important as it allows us to track and count the number of dolphins in small vulnerable populations. It builds on our previous research looking at the impacts of noise on marine organisms and monitoring vulnerable marine mammal populations. It also showcases the fantastic level of research that our marine biology students are able to achieve, and the opportunities available to them through our partnerships with conservation organisations such as the Namibia Dolphin Project and the Ocean Giants Trust."

Future research includes the work undertaken by PhD student Sasha Dines from Stellenbosch University to further refine the technique to better understand the population of endangered humpback dolphins in South Africa. Another PhD student, Jack Fearey from the University of Cape Town, is continuing to conduct research along the Namibian Coast.

X is a connected set but not a path-connected set. X={x,0xe[0,1}U{1/nyneN,ye{0,1]}U{0,1}.

To prove that X is connected, let us assume that X can be divided into two disjoint non-empty open sets A and B. Since X is the union of different points, any point in X will be in either A or B. Let us take an arbitrary point p in A. Since A is open, there is an open ball centered at p that is contained in A. Because B is disjoint from A, it follows that every point in this ball is also in A. By a similar argument, any point in B must have a ball centered at that point that is entirely contained in B. Thus, X must be either in A or B and hence, cannot be divided into two disjoint non-empty open sets. However, X is not path-connected since there is no path between points in [0,1] x {0} and {1} x {1}. Thus, it is connected but not path-connected.

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Answer:

I can't see it.

Step-by-step explanation: