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The equation of a plane in 3-space with equation c1x + c2y + c3z + c4 = 0 can be determined by passing through three non-collinear points (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). This is given by the determinant equation:

Copy code

| x  y  z  1 |

| x1 y1 z1 1 | = 0.

| x2 y2 z2 1 |

| x3 y3 z3 1 |

However, if the three distinct points are collinear, meaning they lie on the same line, then the determinant equation becomes undefined as the determinant of a 3x3 or smaller matrix with linearly dependent rows or columns is equal to zero. This means that there is no plane that passes through three collinear points as a plane requires at least three non-collinear points to be defined.

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Answer:

The type of number -5.41 is a rational number.

Step-by-step explanation:

What type of number is -5.41?

A rational number is a number that can be expressed as a fraction of two integers. 5.41 can be expressed as -5.41 / 1000.

An integer and whole number is a number that does not have any fraction or decimal. -5.41 is a decimal number, thus it is not an integer and a whole number.

The function's multiplicative rate of change will be 0.5. Then, C is the right answer.

Suppose we're trying to determine the multiplication.

To determine the multiplicative power of an item, we just need to divide it by the item immediately preceding it.

Suppose one act is modified

Assume that b is the base, x is the exponent function's power, and an is the leading coefficient.

Exponent is provided as

y = a(b)ˣ

Examples :

Y = 0.125 when x = 2

0.125 = ab² ...1

Y = 0.0625 when x = 3

0.0625 = ab³ ...2

Equation 2 divided by equation 1 yields

b = 0.0625 / 0.125

b = 0.5.

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The complete question is: What is the multiplicative rate of change of the given functions?

a. 1/3

b. 2/3

c. 2

d. 9

The point that is [tex]\sqrt{2}[/tex] units away from the point (-1, 5) is (-1 + [tex]\sqrt{2}[/tex], 5 + [tex]\sqrt{2}[/tex]).

The Pythagorean theorem is a fundamental mathematical principle that relates the lengths of the sides of a right triangle. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean theorem states that a^2 + b^2 = c^2.

This theorem has many practical applications in mathematics and science, including the calculation of distances, heights, and angles in a variety of geometric and engineering problems. It is also widely used in trigonometry, where the relationship between the sides and angles of a right triangle is studied.

The Pythagorean theorem was named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. However, the theorem was known and used by the Babylonians and Indians well before Pythagoras was born. In fact, the theorem is so important that it is sometimes called the "Pythagorean theorem" despite the fact that it predates Pythagoras by several centuries.

This can be found by using the Pythagorean theorem to find the distance between the two points and then adding or subtracting that distance from the x and y coordinates of the original point.

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Subtract 1 from each value in the confusion matrix to change it from 1 to 10 to 0 to 9.

To change a confusion matrix from 1 to 10 to 0 to 9, you need to subtract 1 from each value in the matrix. For example, if your original confusion matrix looks like this:

1     2      3

4    5     6

7    8     9

10   11   12

To convert it to a 0 to 9 range, you need to subtract 1 from each value:

0 1 2

3 4 5

6 7 8

9 10 11

This can be easily done using a loop or by using the -1 operator on the entire matrix. The specific method would depend on the programming language and data structure used to represent the matrix.

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Answer:

m<4 = 100

Step-by-step explanation:

Because 1 is opposite to 4 they equal the same degree

Answer:

Step-by-step explanation:

(1) Yes, the table is proportional

4.5/25  = 5.4/30 = 6.3/35 = 7.2/40  

= 0.18

For a $50 bill the donation will be

50 X 0.18 = $9

Hence, 0.18 times of the dinner bill is donated to charity

(2) Yes, this is also proportional

a1 = 0.47

a2 = 0.68

a3 = 0.89

a4 = 1.10

d = a2 -a1 = a3 -a2 = a4 - a3

= 0.21

For a 6 ounce letter the A.P will be a6 so

a6 = a + 5d

= 0.47 + 5(0.21)

= 0.47 + 1.05

= 1.52

Hence , For every ounce of weight the cost gets increased by 0.21 the weight

Answer: 630 rabbits

Step-by-step explanation: it shows that the population of rabbits grows by 70 each 4 years so we will have to add 70 to 560 which is 630 rabbits.

The population of rabbits in the year 2014 will be growing exponentially.

So, we can write a function

P = A · [tex]\alpha ^{x}[/tex]

where,

A is the original rabbits

[tex]\alpha[/tex] is the ratio of the increase

[tex]x[/tex] is the time (the unit is year)

In 2004, the population of the rabbits was 490

∴ P = 490 · [tex]\alpha ^{x}[/tex]

In 2008, the population increases to 560

∴ 560 = 490 · [tex]\alpha ^{2008-2004}[/tex]

   560 = 490 · [tex]\alpha ^{4}[/tex]

  [tex]\alpha ^{4\\[/tex] = [tex]\frac{560}{490}[/tex] = [tex]\frac{8}{7}[/tex]

  [tex]\alpha[/tex]   = [tex]\sqrt{\frac{2\sqrt{14} }{7} }[/tex]

In 2014, x = 2014- 2004 = 10

P = 490 · [tex]\sqrt{\frac{2\sqrt{14}}{7} } ^{10}[/tex]

  ≅ 684

Hence, the population of rabbits in the year 2014 will be approximately 684.

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Answer:

Why not and what??

Step-by-step explanation:

wait why is that and also that not even a question

The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ... where a = pi/4

The taylor polynomial with 4 nonzero terms of The function f(x)=sin(4x)f(x)=sin⁡(4x) has a series. find the first 4 nonzero terms in the series is f(x) = 4x - (4x)³ + (4x)⁵ - (4x)⁷ + ...

                                       3!        5!      7!

The taylor polynomial can be calculate as follows:

f(x) = sin(4x)

f' = 4cos(4x)

f'' = -16 sin(4x)

f''' = -64 cos(4x)

f⁽⁴⁾ = 256 sin(4x)

f⁽⁵⁾ = 1024 cos(4x)

The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ...

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The resultant image of point A(-12,3) , after a scale factor 1/3 and a rotation of 270 degrees is (1, 4).

In Geometry, dilation simply refers to a type of transformation which typically changes the size of a geometric object with respect to a specific scale factor, but not its shape.

Next, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/3 centered at the origin as follows:

Ordered pair A (-12, 3) → Ordered pair A' (-12 × 1/3, 3 × 1/3) = Ordered pair A' (-4, 1).

By applying a rotation of 270° about the origin to the given figure, the location of A" is given by:

(x, y)                                   →         (y, -x)

Ordered pair A' (-12, 3) → Ordered pair A'' = (1, -(-4) = (1, 4).

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The partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.

The value of the land located at the point (x,y) is calculated by the equation V(x,y) = (150+5x)e^(-0.04x-0.04y). Here, x is measured in miles east of city center and y is measured in miles north of city center. To calculate the value of the land at the point (3,-2), we substitute in the equation x = 3 and y = -2. This gives us V(3,-2) = (150+5*3)e^(-0.04*3-0.04*(-2)) = 181.95. Therefore, the value of the land located at the point (3,-2) is 181.95 thousand dollars per square mile. To calculate the partial derivative of this equation with respect to x, we take the derivative of the equation with respect to x while keeping y constant. This gives us Vx(3,-2) = 5e^(-0.04*3-0.04*(-2)) = 5.07. Therefore, the partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.

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The area of the semicircle is 3.14 square feet.

The formula for  area of a semicircle is A = ([tex]\pi[/tex]* r^2) / 2

Here A = Area

         r = Radius

Given:

Given that the radius of the semicircle is 2 feet.

We need to Find out the area of the semicircle.

The value of [tex]\pi[/tex] is 3.14

A = ([tex]\pi[/tex] * 2^2) / 2

Substituting π = 3.14 and r = 2, we get;

A = (3.14 * 4) / 2

A = 6.28 / 2

A = 3.14 square feet

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The number of solutions of the system y = 3x + 5 is one because it is a linear equation.

An equation in which is  the highest power of to the  variables 1 is knowns as the  linear equation. Mathematically: it is an  algebraic equations that can be also  written in the form of  ax + b = 0 or ax + by + c = 0, where a, b and c are definitely real numbers and x and y are variables with the highest power one.

Linear equations are equations in which the variables are raised to the power of 1, and the graph of the equation is a straight line. As a result, there is only one solution to the equation, which is when the line intersects the x-axis. This means that the equation has only one set of x- and y-coordinates, where x is the independent variable and y is the dependent variable, that satisfy the equation. The x-coordinate of the solution is the same as the value of x that makes the equation true and the y-coordinate is the value of y for this same x-value.

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If Mirka is 5 years old, her parents start to give her pocket money of 50p per week , then the amount of pocket money does Mirka get in the first year is £26 .

the amount that Mirka gets per week is = 50p ;

Age of Mirka is = 5 years ;

When Mirka is 5 years old, she starts to receive 50p per week in pocket money. On her birthday, her parents increase her pocket money by 50p.

that means ;

So, for the first year, the pocket money will be 50p per week for 52 weeks (1 year),

Pocket money in the first year = 50p × 52 weeks = £26 .

Therefore , Mirka will get £26 in the first year of her birthday .

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Answer:

24 = 31.4n + (–8.4)

Step-by-step explanation:

The two people who have same birthday is 1.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Assuming no leap year

P (two people in a room and they are sharing a birthday) = 1-(364/365)

P (3 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex]×[tex]\frac{363}{365} )[/tex]

P (4 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex] ×[tex]\frac{363}{365}[/tex] ×[tex]\frac{362}{365} )[/tex]

and so on, let n people in a room.

P (n people in a room and at least two of them are sharing birthday = 1-[tex]\frac{365!}{365^n(365-n)!}[/tex] )

we find out the nearly after n = 60 this becomes equals to 1.

Therefore, the two people who have same birthday is 1.

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The tight asymptotic bound for the function f(n) = 4f(n/2) + c is T(n) = O(n²).

A recursion tree is a graphical representation of a recursive function that shows the repeated calls of the function. The tree is constructed by expanding each call of the function into a separate node.

For the given function f(n) = 4f(n/2) + c, the recursion tree is attaced below:

f(n/4) f(n/4) f(n/4) f(n/4)

The height of the tree is log2(n), and at each level, there are 4 calls of the function. Hence, the total number of nodes in the tree would be [tex]4^{log2(n)} = n^2[/tex].

The tight asymptotic bound for the function can be found using the Master Theorem, which states that for a recurrence relation of the form T(n) = aT(n/b) + f(n), if f(n) = O([tex]n^c[/tex]) for some constant c, then T(n) = O([tex]n^d[/tex]), where d = max(c, log b(a)).

For this function, a = 4, b = 2, and c = 1. Hence, d = max(1, log2(4)) = max(1, 2) = 2. Thus, the tight asymptotic bound for the function is T(n) = O([tex]n^2[/tex]).

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llllllllylylylltyllylltlylltl ok bye

The polygons are similar. The  correct similarity statement is JKML ~ PQRS.

Similar polygons are two polygons with the same shape, but different sizes.  If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor.

Therefore, the corresponding sides have the same proportion. The corresponding angles of similar polygons are also the same.

Therefore, let's check if the polygons are similar as follows:

Hence,

2.5 / 1.5 = 8  /4.8

Hence, the polygon are similar as follows:

JKML ~ PQRS

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Answer:

he can buy total snack with $20

four hot dogs and four peanuts

four hot dogs = $12

four peanuts= $6

6 + 12 = 20

Step-by-step explanation:

Answer:

The answer would be 70.4

The angle between the ladder and the ground is 78.78

Ladder is a structure for climbing up or down that consists essentially of two long sidepieces joined at intervals by crosspieces on which one may step.

It is given that the length of the ladder is 36 foot and the distance between the base and the ladder is 7 feet.

Here we can see that the hypotenuse is 36 foot and the base is 7 feet.

To find the angle between the ladder and the ground we take the cos inverse of 7÷36

Let the angle between the ladder and the ground is ‘x’.

We know, cosx  = base

                           hypotenuse

⇒ cosx 7

            36

⇒x = cos (-1) 7

                 36

⇒ x = 78.78

Therefore, The angle between the ladder and the ground is 78.78

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[tex]3(4-x)=18[/tex]

Distribute everything outside of parentheses:

[tex](3)(4)+(3)(-x)=18[/tex]

[tex]-3x+12=18[/tex]

Subtract 12 from both sides:

[tex]-3x+12-12=18-12[/tex]

[tex]-3x=6[/tex]

Divide both sides by -3:

[tex]\dfrac{-3x}{-3} =\dfrac{6}{-3}[/tex]

[tex]\fbox{x = -2}[/tex]

Answer:

[tex] \sf \: x = - 2[/tex]

Step-by-step explanation:

Given equation,

→ 3(4 - x) = 18

Now the value of x will be,

→ 3(4 - x) = 18

→ 12 - 3x = 18

→ -3x = 18 - 12

→ -3x = 6

→ x = 6 ÷ (-3)

→ [ x = -2 ]

Hence, the value of x is -2.

Answer:

Below

Step-by-step explanation:

Since you are working with a number line with decimals. You'll have to convert all of these to decimals.

✓14 and ✓15 would be calculator problems with the following solutions:

✓14 = 3.74

✓15 = 3.87

24/7 is pretty much 24 divided by 7

24/7 = 3.43

Now that you have the 3 in decimal form

✓14 can go between 3.7 and 3.8

✓15 can go between 3.8 and 3.9

24/7 can go between 3.4 and 3.5

Answer:

At 4:58.

Step-by-step explanation:

The time for the 700th hiccup is 5 * 7000

= 3500 seconds.

= 3500/60

= 58.33 minutes,

The contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

Proof by contrapositive: Suppose that x is not irrational, meaning that x can be written as a fraction of two integers, x = a/b, where a and b are integers and b ≠ 0.

If x can be written as a fraction of two integers, then 1/x can be written as a fraction as well: 1/x = b/a.

Since 1/x can be written as a fraction of two integers, it follows that 1/x is rational.

Therefore, if x is not irrational (i.e. it is rational), then 1/x is also rational.

Thus, the contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

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Answer:

Either 63.5 + 76.5 + 2x = 180 or some variation of it.

Step-by-step explanation:

The sum of all the angles in a triangle equals 180 so any answer would have to add up the three angles given and set them equal to 180.

If none of the answers on your end match anything I've wrote, try to write the answer choices in the comments or add a picture so I can further help you.

The nine and seven hundredths can be written as 9.07. The solution has been obtained by using decimals.

What are decimals?

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.

We are required to write the decimal number of the given words by considering the integral part and the decimal part

So, here the integral part is nine i.e. 9 and the decimal part is seven hundredths i.e. 7/100 = 0.07

Now, after adding both the parts, we get

9 + 0.07 = 9.07

Hence, the nine and seven hundredths can be written as 9.07.

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