what is the total area of the three triangle ?​

The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.

Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.

Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.

All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).

The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.

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The statements are as follows: The two-point forward difference requires two nodes to approximate the derivative. (True)

The two-point forward difference always requires two consecutive nodes to approximate the derivative. (False)

The three-point forward difference requires three consecutive nodes to approximate the derivative. (True)

The two-point forward difference method indeed requires two nodes to approximate the derivative. This method calculates the derivative using the difference between the function values at two neighboring points.

The two-point forward difference method does not always require two consecutive nodes. It can be used with any two nodes, regardless of whether they are consecutive or not. However, using consecutive nodes is a common and straightforward approach.

The three-point forward difference method requires three consecutive nodes to approximate the derivative. It calculates the derivative using the difference between the function values at three consecutive points. This method provides higher accuracy compared to the two-point forward difference method.

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Answer:

Step-by-step explanation:

The number of bank PINs in string which exactly four digits are even is (74​)⋅57.

To determine the number of PINs with exactly four even digits, we need to consider the number of ways we can choose four even digits from the set {0, 2, 4, 6, 8}, as well as one odd digit from the set {1, 3, 5, 7, 9}.

The number of ways to choose four even digits from a set of five is given by the combination formula: (5 choose 4) = 5! / (4! * 1!) = 5.

Similarly, the number of ways to choose one odd digit from a set of five is also 5.

Since these choices are independent, we can multiply the number of ways to choose even digits by the number of ways to choose an odd digit: 5 * 5 = 25.

Once we have chosen the even digits and the odd digit, we have fixed their positions within the PIN. The remaining two digits can be chosen freely from the set of all digits (0-9), giving us 10 * 10 = 100 possible choices.

Finally, we multiply the number of choices for the even and odd digits by the number of choices for the remaining two digits: 25 * 100 = 2500.

Therefore, the total number of PINs in which exactly four digits are even is (74​)⋅57 = 2500.

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Answer:

4 3/8 miles

Step-by-step explanation:

We are told that: the scale on a map is 1 inch =2 1/2 miles.the distance between two streets on the map is 1 3/4 inches

If 1 inches = 2 1/2 miles

1 3/4 inches =

Cross Multiply

1 3/4 × 2 1/2/1

= 7/4 × 5/2

= 35/8

= 4 3/8 miles

The actual distance between these streets is 4 3/8 miles

The expression that represents the perimeter of the rooftop is 16x.

The area encircling a two-dimensional figure is known as its perimeter. Whether it is a triangle, square, rectangle, or circle, it specifies the length of the shape. The two primary characteristics of a 2D shape are area and perimeter.

The perimeter of a square is equal to four times the length of one side.

So, the expression that represents the perimeter of the rooftop would be: 4x + 4x + 4x + 4x, which simplifies to 16x.

Therefore, the expression that represents the perimeter of the rooftop is 16x. (where x is the length of one side of the square rooftop)

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The description of the transformation of z on the complex plane that gives the product of and is to scale by a factor of 4, then rotate counterclockwise by /6 radians.

To understand this transformation, let's break it down into its components. Scaling by a factor of 4 means multiplying by 4. This scales the magnitude of by a factor of 4 but does not change its direction. Next, rotating counterclockwise by /6 radians means rotating around the origin by an angle of /6 in the counterclockwise direction. By performing these two transformations in succession, we first scale by a factor of 4, which stretches or compresses it depending on whether it is inside or outside the unit circle, respectively. Then, we rotate counterclockwise by /6 radians, which changes its angle in the counterclockwise direction by /6 radians.

The resulting transformation gives the product of and because scaling and rotation are commutative operations when applied to complex numbers. The order in which the transformations are performed does not affect the result. Therefore, scaling by a factor of 4, then rotating it counterclockwise by /6 radians, will yield the same result as scaling by a factor of 4, then rotating it counterclockwise by /6 radians.

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The length of CD is 6.32 units.

From the question, we have

CB / AB = DB / CB

CB / 14 = 10 / CB

CB² = 14 × 10

CB = √140

using the Pythagorean theorem,

AB² = CB² + AC²

14² = (√140)² + AC²

196 - 140 = AC²

AC = √56

Using the ratio of the similar triangle,

CD / AC = DB / CB

CD / √56 = 10 / √140

CD = (√56 × 10)/√140

CD = 6.32 units

the length of CD is 6.32 units.

Divide:

Repetitive subtraction is the process of division. It is the multiplication operation's opposite. It is described as the process of creating equitable groups. When dividing numbers, we divide a larger number down into smaller ones such that the larger number obtained will be equal to the multiplication of the smaller numbers. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping.

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If x varies directly as y2, then it means that x is directly proportional to the square of y. This can be expressed as x = ky2, where k is a constant of proportionality.

When x is doubled, it means that the new value of x is 2x. We can substitute this value in the equation above to get 2x = ky2. Solving for y, we get:

y2 = (2x)/k
y = sqrt((2x)/k)

Therefore, as x is doubled, y will increase by a factor of the square root of 2. This means that y will increase by approximately 1.41 times its original value.
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Answer:

250 hours

Step-by-step explanation:

Jeez can Marriyam get some more money per hour?

Ok, Marriyam is given 75 dollars so she only need to pay 325-75 = $250.

Since Marriyam earns 1 dollar an hour she need to work 250 hours.

Hopefully that helps.

If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.

In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

Marriyam was given $75 for a birthday present.

She's going to use that gift, plus the earnings from her summer job, to buy a skateboard that costs $325.

The amount left she has to earn is;

= 325 - 75 = $250

If her job pays I dollars per hour, how many hours does she need to work to buy the skateboard is;

\(= 1\times 250\\\\=250\)

Hence, If her job pays I dollars per hour, 250 hours does she need to work to buy the skateboard.

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2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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The percent of data within the interval from 39 to 55 which is normally distributed is 68.26%.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.

Given in the problem mean is 47 and Standard Deviation(SD) is 8

Probability of data within 39 to 55 is

P(x<55) - P(x<39)

Let Z be the standard deviation :

\(\phi(Z) = \frac{x - mean}{SD}\).

for  X = 39

\(\phi(Z) = \phi(\frac{x - mean}{SD})\) = \(\phi(\frac{39 - 47}{8}) = \phi(-1) = 1 - \phi(1) = 1-.8413 = .1587\)

for X = 55

\(\phi(Z) = \phi(\frac{x - mean}{SD})\) = \(\phi(\frac{55 - 47}{8}) = \phi(1) = .8413\)

The percent of data within the interval from 39 to 55

(.8413 - .1587) = .6826 = 68.26%

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The standard deviation of the population of 6 classes, with student counts of 35, 25, 37, 36, 24, and 29, is approximately 5.99. The standard deviation provides an indication of the variability in the number of students across these classes.

To calculate the standard deviation of the population of 6 classes, we can use the formula "=stdevP(first cell:last cell)" in Excel.

First, let's list the number of students in each class: 35, 25, 37, 36, 24, and 29.

Now, we will enter these numbers into Excel, selecting the first and last cells (A1:A6). Then, we use the "=stdevP()" formula to calculate the standard deviation.

The standard deviation measures the amount of variation or dispersion in a set of data. It tells us how spread out the data points are from the mean (average) value.

Using the given numbers, the standard deviation is calculated to be approximately 5.99 (rounded to two decimal places).

In summary, the standard deviation of the population of 6 classes, with student counts of 35, 25, 37, 36, 24, and 29, is approximately 5.99. The standard deviation provides an indication of the variability in the number of students across these classes.

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the area of triangle $AMN$ is 8 square cm.

To find the area of triangle $AMN$, we need to determine the lengths of its base and height.

In square $ABCD$ with side length 4 cm, $N$ is the midpoint of side $BC$, so $BN = NC = \frac{1}{2} \cdot 4 = 2$ cm.

Similarly, $M$ is the midpoint of side $CD$, so $CM = MD = \frac{1}{2} \cdot 4 = 2$ cm.

Now, we can see that $AM$ is the height of triangle $AMN$ and has a length of 4 cm, as it is parallel to side $AD$ of the square.

$AN$ is the base of triangle $AMN$ and has a length of $BN + CM = 2 + 2 = 4$ cm.

Therefore, the area of triangle $AMN$ is given by:

$A_{AMN} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8$ square cm.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

the answer is A and D

when you differentiate the question you find that the maximum point is (0,0)i.e

\( \frac{dy}{dx} = - 8x\)

when dy/dx is 0 values of x are 0,0

and the function shows that valies of x are real numbers.

The domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.

Given function as

f(x) = -4x²

The range is the set of values that correspond with the domain.

Range: (−∞,0], {y|y≤0}

Domain: (−∞,∞), {x|x∈R}

and the function shows that values of x are real numbers.

The maximum point is when differentiating the function, which is (0,0) i.e

dy/dx = -8x

Values of x are 0 when dy/dx is 0.

Hence, the domain of the graph is (−∞,∞), {x|x∈R} and the maximum point (0,0) which is the correct answer would be options (A) and (D)

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The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

Similar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.

(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}

angle B = 68°

Given that the triangle ∆ABC is similar to the triangle ∆PQR.

(2). PQ/7.5cm = 12cm/18cm

PQ = (12cm × 7.5cm)/18cm {cross multiplication}

PQ = 5cm

(3). 13cm/BC = 12cm/18cm

BC = (13cm × 18cm)/12cm {cross multiplication}

BC = 19.5cm

(4). area of ∆PQR = 1/2 × 12cm × 5cm

area of ∆PQR = 6cm × 5cm

area of ∆PQR = 30cm²

Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:

(1). angle B = 68°

(2). PQ = 5cm

(3). BC = 19.5cm

(4). area of ∆PQR = 30cm²

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The dependance on experience is reflected in the syntactic distinction between prior probability statements.

syntax refers to alphabet, while semantics refers to meaning. Syntax is the set of rules demanded to insure a judgment is grammatically correct; semantics is how one's wordbook, grammatical structure, tone, and other rudiments of a judgment coalesce to communicate its meaning. syntax is the arrangement or order of words, determined by both the pen's style and alphabet rules. consisting of or noting coinages that are combined in the same order as they would be if they were separate words in a corresponding construction The word blackberry, which consists of an adjective followed by a noun, is a syntactic emulsion.

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Answer:

22.2

Step-by-step explanation:

The volume of the cube will increase by 8 cubic centimeters per second.

Given,

The edge length of a cube is changing at a rate of 1/6 cm/sec.

We have to find the rate by which cube's volume changing when the edge length is 4 cm.

Here,

We have,

da/dt = 1/6 cm/sec

We know that, volume of cube is

V = a³

Differentiate with respect to t.

dV/dt = 3a² da/dt

Substituting da/dt = 1/6  and a = 4, we get;

dV/dt ₐ ₋ ₄ = 3 × 4² 1/6

dV/dt ₐ ₋ ₄ = 3 × 16 × 1/6

dV/dt ₐ ₋ ₄ = 16/2 = 8

Therefore,

The volume increased by 8 cubic centimeters per sec.

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Answer:

10.5

Step-by-step explanation:

v=158

l×w×h =158

l×5×3=158

l×15=158

L =158÷15=10.5

The total cost for the tiling the room is $1254.

The dimensions of rectangular room are 5m by 8.5 m.

Area of a rectangular room = 5×8.5

= 42.5 square meter

Vicki buys carpet tiles for this room each file is a square measuring 25 cm by 25 cm.

Area of carpet = 0.25×0.25

= 0.0625 square meter

Number of tiles required = 42.5/0.0625

= 680

Number of packs of tiles = 680/10 = 68

Cost of tiles = 68×18

= 1224

Total cost = 1224+30 =1254

Therefore, the total cost for the tiling the room is $1254.

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The estimate of the impact that a successful preventive program might have can be derived from

attributable risk.

In epidemiology, attributable risk or excess risk is a phrase equivalent with risk difference, which has also been used to express the attributable proportion among the exposed and the population.

Attributed risk assists in determining how much of an outcome is attributable to a certain risk factor (i.e., an estimate of the excess risk) in a population exposed to that factor.

The rate (percentage) of a health result (illness or death) in exposed persons that can be linked to the exposure is known as the attributable risk (AR). Attribitable risk measures how much more common a result is in absolute terms among the exposed than the non-exposed.

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To verify that the vector xp is a particular solution of the given nonhomogeneous linear system, we need to substitute xp into the system and check if it satisfies the equation.

The given nonhomogeneous linear system can be written in the form x' = Ax + f, where A is the coefficient matrix (2 1 1 -1) and f is the constant vector (-5 2). The vector xp = (1 3) is a particular solution if it satisfies the equation x' = Ax + f.

Substituting xp into the equation, we get:

x' = (2 1 1 -1) (1 3) + (-5 2)
  = (1 -1 2 -8)

Therefore, the left-hand side of the equation is:

x' = (1 -1 2 -8)

And the right-hand side is:

Ax + f = (2 1 1 -1) (1 3) + (-5 2)
       = (1 -1 2 -8)

Since the left-hand side is equal to the right-hand side, we can conclude that the vector xp = (1 3) is indeed a particular solution of the given nonhomogeneous linear system.

We have verified that the vector xp = (1 3) is a particular solution of the given nonhomogeneous linear system by substituting it into the equation and checking if it satisfies the equation.

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The z-score for Sami Aalto on the horizontal bar in 2005 is approximately -1.6678.

To calculate the z-score for Sami Aalto's score on the horizontal bar in 2005, we need to use the formula:

z = (x - μ) / σ

where:
x = Sami Aalto's score (8.087)
μ = mean score under the old scoring system (9.139)
σ = standard deviation under the old scoring system (0.629)

Plugging in the values, we have:

z = (8.087 - 9.139) / 0.629

Calculating this gives us:

z ≈ -1.6678

Rounding to 4 decimal places, the z-score for Sami Aalto on the horizontal bar in 2005 is approximately -1.6678.

The z-score for Sami Aalto on the horizontal bar in 2005 is approximately -1.6678.

The z-score is a measure of how many standard deviations a data point is from the mean. It allows us to compare a particular score to the distribution of scores. In this case, we are comparing Sami Aalto's score to the distribution of scores on the horizontal bar under the old scoring system.

The z-score is calculated by subtracting the mean score from the data point and dividing it by the standard deviation. In this case, Sami Aalto's score is 8.087, the mean score is 9.139, and the standard deviation is 0.629. Plugging these values into the formula, we find that the z-score is approximately -1.6678.

The z-score for Sami Aalto on the horizontal bar in 2005 is approximately -1.6678. This means that his score is about 1.6678 standard deviations below the mean score under the old scoring system.

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Answer: (7.5, 4.5)

Step-by-step explanation:

To find the midpoint, we can just find the average of the x values and the y values.

x=(10+5)/2=15/2=7.5

y=(5+4)/2=9/2=4.5

0.99999028444 is the probability that at most 22 heads occur.

What does the maths term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probability of different outcomes if we are unclear of how an event will turn out. Probability is a measure of how likely or likely-possible something is to happen.

                               For instance, there is only one method to receive a head and there are a total of two possible outcomes, hence the chance of flipping a coin and receiving heads is 1 in 2. (a head or tail). P(heads) = 12 is what we write.

probability of getting head,  P = 1/2 = 0.5

        q = 1 - p  = 1 - 0.5 = 0.5   and n = 25

 P(X ≤ 22)

 P(X = x ) = ⁿCₓ (q)ⁿ⁻ˣ (p)ˣ

      = 1 - P(x = 23) - P(24) - P(25)

  = 1 - ²⁵C₂₃(0.5)²⁵⁻²³ (0.5)²³ - ²⁵C₂₄ (0.5)²⁵⁻²⁴ (0.5)²⁴ - ²⁵C²⁵ (0.5)²⁵⁻²⁵ (0.5)²⁵

        = 0.99999028444

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The error message "Difference order N must be a positive integer scalar" is indicating that there is an issue with the input argument for the diff function.

The diff function is used to calculate the difference between adjacent elements in a vector.
In the code you provided, the line that is causing the error is:
f_prime0 = diff(f,x0,xinc);
To fix this error, you need to ensure that the input arguments for the diff function are correct.

To fix this problem, you need to look at the code in the Newton_Raphson_tutorial function and possibly also the Tutorial_m function. You probably get an error when computing the derivative with the 'diff' function.

However, we can offer some general advice on how to fix this kind of error. The error message suggests that the variable N used to specify the difference order should be a positive integer scalar.

Make sure the variable N is defined correctly and has a positive integer value.

Make sure it is not assigned a non-integer or non-scalar value.

Make sure the arguments to the diff function are correct.

The diff function syntax may vary depending on the programming language or toolbox you are using.

Make sure the variable to differentiate ('f' in this case) is defined and suitable for differentiation.

Make sure that x0 and xinc are both positive integer scalars, and that f is a valid vector or matrix.
Additionally, it's important to check if there are any other errors or issues in the code that could be causing this error message to appear.

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