Find the arithmetic mean a n of the given terms. a n₋₁ =-2 x, a n₊₁=2 x

Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the equations are given as follows:

(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).

For Gaussian elimination, the first step is building the matrix of the system, in which:

Hence, the matrix of the system is given as follows:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]

Then, we need to make the coefficient of x zero in the second and third rows, hence:

Then the matrix will be given by:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]

Now we need to make the coefficient of y on the third row zero, hence:

R3 -> 11R2 + 5R3.

Then:

[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]

From the third row, we have that:

40z = 120

z = 120/40

z = 3.

From the second row, we have that:

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

From the first row, we have that:

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution of the system is given by:

x = 5, y = -11, z = 3.

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Patterns of the given terms 8,9,10,11,.... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.

As given in the question,

Given pattern is 8,9,10,11,...

First term a₁ = 8

Second term a₂ = 9

Third term  a₃ = 10

Fourth term a₄ =11

d =aₙ - aₙ₋₁

  =a₂ -a₁

  =9 -8

  =1

8,9,10,11,... represents arithmetic progression

aₙ=8 + (n-1)d

a₅ =8+ 4(1)

   =2

a₆ =8 + 5(1)

   =13

a₇ =8 + 6(1)

   =14

Therefore, patterns of the given terms 8,9,10,11,... is arithmetic progression, where aₙ= 8 + (n-1)d, d=1. Next three terms are 12,13,14.

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For the parallelogram NELR, we get the value of x as 7°.

We are given a parallelogram NELR.

We know that , the adjacent angles of a parallelogram are supplementary.

So, we get that:

∠ N + ∠ E = 180°

Substituting the values, we get that:

7 x + 33 + 11 x + 21 = 180

18 x + 54 = 180

18 x = 180 - 54

18 x = 126

x = 126 / 18

x = 7°

Therefore, for the parallelogram NELR, we get the value of x as 7°.

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A circle is a curve sketched out by a point moving in a plane. The diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the center.

Given that radius of the circle is x/8 units. Therefore, the diameter and the circumference of the circle can be written as,

Diameter of circle = 2 × (Radius of the circle)

                             = 2 × (x/8) units

                             = x/4 units

Circumference of circle = 2 × π × (Radius of the circle)

                                       = 2 × π × (x/8) units

                                       = (x/4)π units

Hence, the diameter and circumference of the circle are (x/4) units and (x/4)π units, respectively.

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The transformation applied to the parent function is vertical compression by a factor of 0.25.

In mathematics, functions can be manipulated algebraically to obtain graphs of functions through certain transformations. Such transformations are reflections of the x-axis or the y-axis. To flip a function f(x) on the x-axis, multiply the whole function by a negative value to get -f(x), and to flip a function f(x) on the y axis, f(-x ), specify the x variable with a negative value.

Vertical compression helps shrink features vertically. Vertical compression occurs when you multiply the function by a rational scaling factor. The base of the function graph remains the same even when the graph is compressed vertically. Only initial values are affected.

It is vertically compressed by a factor of 0.25.

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The value of x if the sides are congruent is 3

The given parameters are

MN=6x-1 and MP=3x+8

For the sides to be congruent, then the following equation must be true

MN = MP

This gives

6x - 1 = 3x + 8

Collect the like terms

6x - 3x = 1 + 8

Evaluate the like terms

3x = 9

Divide by 3

x = 3

Hence, the value of x if the sides are congruent is 3

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Answer:

43

Step-by-step explanation:

the plane is 180 degrees

subtract 2x4

172

divide by 4

43

BOOM

The conditional probability formula for P(B | A) has been derived from two dependent events P(A and B).

When the outcome from one event influences the outcome of the other, two events are referred to as dependent.

Derivation of conditional probability from two dependent events P(A and B) is-

The probability multiplication rule is used to derive the conditional probability formula, P(A and B) = P(A)×P(B|A).

This rule is also known as P(AB). The Union symbol (∪) represents "and," as in event A occurring and event B occurring.

Step 1: Write the multiplication rule down:

           P(A and B) = P(A)*P(B|A)

Step 2: P(A) divides both sides of the equation:

           P(A and B) / P(A) = P(A)*P(B|A) / / P(A)

Step 3: On the right side of the equation, cancel P(A):

           P(A and B) / P(A) = P(B|A)

Step 4: Rewrite the equation as follows:

           P(B|A) = P(A and B) / P(A)

Therefore, P(B | A) conditional probability formula is compiled from two dependent events P (A and B).

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The value of f(-3) is 15.

The given function is f(x) = -3x+6. Now, f(-3) = x = -3

Substituting and Evaluating the value of x in the equation f(x) = -3x+6, we get

f(-3) = -3(-3)+6f(−3)=−3(−3)+6

f(-3) = 9+6f(−3)=9+6

f(-3) = 15f(−3)=15

∴ The value of f(-3) for the function f(x) = -3x+6 is equal to 15.

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The sum of the given finite series is 75

The given series is:

[tex]\sum\limits^{10}_{n=5} {(20-n)}}[/tex]

To find the sum of this series,

Expand the summation notation by using the properties of sum operator:

Σ(a+b) = Σa + Σb

Hence,

[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]

If a is a constant, then Σa = k. a, where k is the number of terms = upper limit - lower limit + 1

Using this property:

[tex]\sum\limits^{10}_{n=5} {20} = (10 - 5+1)\times20=6\times20=120[/tex]

Expand

[tex]\sum\limits^{10}_{n=5} {n}=5+6+7+8+9+10=45[/tex]

Hence,

[tex]\sum\limits^{10}_{n=5} {(20-n)}=\sum\limits^{10}_{n=5} {20}-\sum\limits^{10}_{n=5} {n}[/tex]

= 120 - 45 = 75

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The equation of line having slope of 5/2 is given as 2y -5x = 8.

As, per the given question;

The slope of the line is given as; m = 5/2

The coordinates of the passing points (-2, -1).

Thus, (x₁, y₂) = (-2, -1).

The equation of the becomes.

(y - y₁) = m (x – x₁)

Put the values;

y - (-1) = (5/2)(x - (-2))

Simplifying

y + 1 = (5/2)(x + 2)

2y + 2 = 5x + 10

2y -5x = 8

The equation of line is calculated as 2y - 5x = 8.

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Answer:

5

Step-by-step explanation:

[tex]d=\frac{|-3(5)-4(5)+10|}{\sqrt{(-3)^2+(-4)^2}}=5[/tex]

If Lee is laying out a design for the tiles of a section of his bathroom floor and he will use 1 white tile for every 6 black tiles to have a total of 28 tiles in the design then the number of white and black tiles Lee will use is equal to 4 and 24 respectively.

The number of white and black tiles Lee will use can be determined by using an algebraic expression.

As 1 white tile is used for every 6 black tiles, an algebraic expression can be represented as,

x + 6x = 28

By solving the value of x, the number of each type of tile that Lee will use can be calculated,

x + 6x = 28

7x = 28

x = 28 ÷ 7

x = 4

As there is one white tile for every six black tiles,

White tiles = 1(x) = 1(4) = 4

Black tiles = 6(x) = 6(4) = 24

Hence the number of white tiles Lee will use is equal to 4 and the number of black tiles Lee will use is equal to 24.

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The scale factor of the two similar cylindrical cans of tuna is 13/10.

Solids of the same type that have proportional corresponding linear measures are similar solids. In the case of similar cylinder:

height of A / height of B = radius of A / radius of B

Scale factor refers to the ratio of the corresponding dimensions of similar solids.

If the smaller cylindrical can of tuna has a radius of 4 centimeters and the larger and similar can of tuna has a radius of 5.2 centimeters, then the scale factor is:

scale factor = radius of larger can/ radius of smaller can

scale factor = 5.2 cm / 4 cm

scale factor = 13/10

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Answer:

the statement is true.

Step-by-step explanation:

Answer:

4°=1

g g g g g g g g g g

Step-by-step explanation:

The equation in slope-intercept form for the line that passes from the points (-7,2) and (5,8) is y = (1/2)x -3/2.

We know that, the slope intercept form is given by:-

y = mx + b

Where,

(x,y) is the ordered pair of every point on the line

m is the slope of the line

b is the y-intercept of the line

We know that, slope = (8-2)/(5-(-7)) = 6/12 = 1/2

Putting (-7,2) in (x,y) and m = 1/2 in the slope intercept form, we get,

2 = (1/2)(-7) + b

2 = -7/2 + b

b = -3/2

Hence, the slope intercept form of the line is y = (1/2)x -3/2.

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Answer:

15y+14

Step-by-step explanation

Answer: 14 + 15y

Step-by-step explanation:

E = Eileen’s age = 3y

M = Mum’s age

Total Age = 14 + 3y + 4(3y)

                =  14 + 15y

Total age in 7 years time is their current ages plus 7 years for each (14 years)

Eileen is 3y, and her mum is 4 times that, which is 12y, meaning that their total ages are 3y + 12y, or, 15y.

Total age is then 15y + 14. Since we don’t know what y equals, we cannot add these two terms, and we can just leave them like that!

So, the answer is 14 + 15y.

For the given situation, we can clearly say that the change in one quantity will cause a change in the second quantity as well.

Correlation is a relationship between the values ​​of two variables. A scatter plot is a useful tool for displaying data about two variables as a series of points in the x and y plane and determining whether there is a correlation between the variables.

Causality means that one event causes another. Causality can only be determined by well-designed experiments. In such experiments, similar groups receive different treatments, and the results of each group are examined.

From the above information, we concluded that a person's age and the number of cassette tapes he/she owns are correlated more he lives the more he buys the cassette tapes. So we can make relation from this,

Person's Age ∝ Number of Cassette

This clearly states that by increasing/changing one quantity we will increase/change the other quantity as well.

Similarly, now that they have a direct relation if we decrease the Age of the person, the number of Cassette's will also decrease. A positive correlation we can call it.

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Answer:

f(-4) = -7

g(-7) = 9

Step-by-step explanation:

f(x) = 2x + 1

f(-4) = 2(-4) + 1 = -8 + 1 = -7

g(x) = x^2 - 40

g(-7) = (-7)^2 - 40 = 49 - 40 = 9

The diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

An average is a mean or the central value obtained by dividing the sum of all data values by the number of data values.

Diver            Crabs observed     Dives     Average Crab per dive

Scuba Sam              33                     11               3

Wet Suit Willy          81                     18              4.5

Deep Diving Dan  104                    26              4

Thus, the diver who saw the most crabs per dive is Wet Suit Willy with an average crab per dive of 4.5 crabs.

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Answer:

Since Ian has $75 dollars, it would be enough to buy at least one DVD box set. However, there's not that much information in the statement.

Hope this helps with your question :)

-439 is the value which is equivalent to (s circle t) (negative 7).

Given,

s(x) = 2 - x²

t(x) = 3x

We have to find the value which is equivalent to (s circle t) (negative 7)

That is,

(s circle t) (negative 7) : This is a notation for compound function.

A function that takes another function as an argument is referred to as a compound function.

s(t(-7)) is the alternative notation for this compound function, which means that the value obtained from the function t(-7) will be used in the function s. (x).

Now, let's calculate the value of t(-7):

That is,

t(x) = 3x

t(-7) = 3 × (-7) = -21

Next, apply the value of t(-7) for s(x)

That is,

s(x) = 2 - x²

s(t(-7)) = s(-21) = 2 - (-21)^2 = 2 - 441 = -439

That is, -439 is the value which is equivalent to (s circle t) (negative 7).

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Part a

[tex]\frac{\pi}{3} > \frac{\pi}{4} \implies f(\pi/3)=\sin(\pi/3)=\boxed{\frac{\sqrt{3}}{2}}[/tex]

Part b

[tex]\frac{\pi}{6} \leq \frac{\pi}{4} \implies f(\pi/6)=2+\cos(\pi/6)=\boxed{2+\frac{\sqrt{3}}{2}}[/tex]

Part c

[tex]\frac{\pi}{4} \leq \frac{\pi}{4} \implies f(\pi/4)=2+\cos(\pi/4)=\boxed{2+\frac{1}{\sqrt{2}}}[/tex]

Answer:

93/250

3/8

0,375 has three numbers after a decimal so we will multiply and divide 0,375 by 1000

Answer:

Step-by-step explanation:

2x+5=6x-3​

subtract 6x

2x-6x+5=6x-6x-3

-4x+5=-3

subrtract-5

-4x+5-5= -3-5

-4x=-8

divide-4

-4x÷-4=-8÷-4

x=2

Answer: -8

Step-by-step explanation:

= 12 * (-2/3)

= -24/3

= -8

(−8) ⋅ (−2/3) = 1/3a = −5

mass of 1 mole of (−8) ⋅ (−2/3) = 1/3a = −5 = 0g

Answer: $39.62

Step-by-step explanation: To get the answer to the cost of Peter's three items, I took the prices of the three and added them together. This amount would be the amount he paid WITHOUT TAX.