how to solve that and what is the answer

The solution to the system of equations in this problem is given as follows:

X = [28571

      14286].

The system is defined by the following equation:

X = DX + E.

The matrices D and E are known, while X = [A; B] is the output matrix. Applying the multiplication of matrices, the system of equations is defined as follows:

Inserting this system into a calculator, the solution is given as follows:

Hence the matrix X is given as follows:

X = [28571

      14286].

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The probability that the maximum of the two dice is greater than or equal to six is 0.722.

What is probability?

Probability is a way of calculating how likely something is to happen. Probability can range from 0 to 1, with 0 indicating an impossibility and 1 indicating a certainty.

We are given that two six-sided dice numbered from one through six are rolled.

The sample space of the event is

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Probability that the maximum of the two dice is greater than or equal to six is

26 out of 36 i.e. 26/36

This is equal to 0.722.

Hence, the probability that the maximum of the two dice is greater than or equal to six is 0.722.

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The probability of selecting two different coloured chips is the fraction 14/49.

Probability is the fraction of the required outcome event divided by the number of possible outcomes of events.

total possible outcome = 7

blue chips = 4

red chips = 2

white chips = 1

probability of selecting blue chips = 4/7

probability of selecting red chips = 2/7

probability of selecting white chips = 1/7

probability of selecting two coloured chips at random = 4/7 × 2/7 + 4/7 × 1/7 + 2/7 × 1/7

probability of selecting two coloured chips at random = 8/49 + 4/49 + 2/49

probability of selecting two coloured chips at random = 14/49

Therefore, the probability of selecting two different coloured chips is the fraction 14/49

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If the matrix xt x is not invertible, then its determinant is equal to 0. A determinant of 0 implies that the matrix is singular, meaning that its columns are linearly dependent.

This means that one of the columns of x can be expressed as a linear combination of the other columns, which implies that there is only one way in which the invertibility problem may arise: when the columns of the matrix x are linearly dependent.

If the determinant of xt x is equal to 0, then at least one column of x can be expressed as a linear combination of the others. For example, if column c can be expressed as a linear combination of columns a and b, then we can write:

c = k1a + k2b

where k1 and k2 are constants. This means that the information in column c is already represented in columns a and b, and so it is redundant.

This is the only way in which the invertibility problem of xt x may arise. If the columns of the matrix are linearly independent, then the determinant of xt x will be non-zero, and the matrix will be invertible.

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Your question is incomplete, but most probably, the full question was:

Proof that [tex]X^{T} X[/tex] is not invertiblethen at least one column of x is a linear combination of the others. This implies that there is only one way in which a problem with the invertibility of xt x may arise

From the graph, the compound inequality represented is x < -2 and x > 5

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequalities shows the non equal comparison of two or more numbers and variables. Compound inequality is an inequality that is composed of more than one inequality.

From the graph, the inequality is not a solid circle, so it is either > or < sign.

From the graph, the inequality shown is x < -2 and x > 5

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Answer:

Step-by-step explanation:

4x+3x=6+2

7x/7=8/7

=1.143

Answer: X=22

According to equation given :-

4x-2=3x+6 ----------------------(1)

4x - 2 +3x+6=180 -------------(2)

hence put equation (1) in (2) which that

4x - 2 +4x-2=180

2* ( 4x-2 ) = 180

4x-2 =90

4x = 88

x= 22 (answer)

The answer is B. diverges.

Theorem 9.11 states that if the sequence of positive terms (an) satisfies the condition 1/an^p converges, then the p-series ∑an converges if p > 1 and diverges if p ≤ 1. In this case, the positive terms of the sequence are given by [1/(n^(3/2))]. So, [1/an^p] = [1/(n^(3/2))^p] = [1/n^(3p/2)].

For the series to converge, we need [1/an^p] to converge, or [1/n^(3p/2)] to converge.

If 3p/2 > 1, then [1/n^(3p/2)] converges and the series converges.

If 3p/2 ≤ 1, then [1/n^(3p/2)] diverges and the series diverges.

So, to determine the value of p, we need to find the value of p such that 3p/2 = 1. Solving for p, we find that p = 2/3.

Since 2/3 ≤ 1, the series diverges. Therefore, the answer is B. diverges.

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Answer: PQ is 9 units.

Step-by-step explanation:

The length of PQ can be found using the proportion of OQ and OP.

(PQ / OQ) = (OP / OQ)

PQ = (OP / OQ) * OQ

Substituting in the given values:

PQ = (9 / 11) * 11

PQ = 9

Therefore, the length of PQ is 9 units.

Part a: Amy's net amount in a year from her day job is found as $40411.

Part b: Amy under spend this year by amount $8331.

Part a:

The calculation is done bi- weekly.

Total days = 2*7 = 14.

Net amount = $1550.

Net amount for the year = (1550/ 14)*365

Net amount for the year = $40411

Thus, Amy's net in a year from her day job is found as $40411.

Part b:

Total amount spend : Sum of all expenditures.

Total amount spend : $32,080

Difference =  $40,411 - $32,080

Difference =  $8331

Thus, based on her net income as well as annual expenditures summary,

Amy under spend this year by amount $8331.

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The height of the tower is 600 feet

What is angle of elevation and the angle of depression?

Angle of elevation: The angle of elevation is the angle produced by the line of sight with the horizontal when the item is above the horizontal level.

Angle of depression: The angle of depression is the angle produced by the line of sight with the horizontal when the item is below the horizontal level.

Let's call the height of the tower "h".

Using trigonometry, we can set up equations based on the angles of elevation and depression:

tan 38° = h / 300

tan 29° = (h - 300) / 300

Solving for h,

h = 300 * tan 38°

h = 300 * 0.8192

h = 245.76

Now,

300 * tan 29° = (h - 300) / 300

300 * 0.5672 = (h - 300) / 300

h - 300 = 300 * 0.5672 / 0.5672

h - 300 = 300

h = 600

So, The height of the tower is 600 feet, rounded to 2 decimal places.

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The function representing number of fish each 't' year

n ( t ) = (600t + 500) / ( 0.5t + 1) best defines option A. The number of fish get larger every year , but does not exceed the number 1200.

Let 'n' represents the number of fish.

't' represents the year.

The function representing the number of fish in 't' years is :

n ( t ) = (600t + 500) / ( 0.5t + 1)

Number of cans poured in the lake by farmer is equal to 5

Number of fish in each can = 100

Let t = 1

n(1) = 600(1) + 500 / 1.5

     = 733.33

t= 2

n(2) =  600(2) + 500 / 2

       =850

n(3) = 600(3) + 500 / 2.5

      = 920

Therefore, the function n ( t ) = (600t + 500) / ( 0.5t + 1) best describes the option A. The number of fish get larger every year , but the number does not exceed  1200.

The above question is incomplete, the complete question is:

The wildlife game commission poured 5 cans of fish (each can contained approximately 100 fish) into a farmer's lake. the function n defined by

n ( t ) = (600t + 500) / ( 0.5t + 1) represents the approximate number of fish in the lake as a function of time (in years).Which one of the following best describes how the number of fish in the lake changes over time?

A. The number of fish gets larger each year, but does not exceed 1200.

B. The number of fish gets smaller every year but does not get smaller then 1200.

C. The number of fish gets larger each year, but does not exceed 600.

D. The number of fish gets larger each year, but does not exceed 500.

E. The number of fish gets smaller every year, but does not get smaller than 500.

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Answer:

below

Step-by-step explanation:

20750 is to 172.2 as   x is to 103.9

20750 /172.2 = x / 103.9

x = $ 12519.89

The value of h can be any value other than 2.

The augmented matrix of a consistent linear system must have a unique solution, which means the determinant of the coefficient matrix must be non-zero.

       [1 h

        3 6]

The determinant of this matrix is (1 * 6) - (3 * h) = 6 - 3h.

For the determinant to be non-zero and the system to be consistent, 6 - 3h must not be equal to zero, so h cannot be equal to 2.

Therefore, the value of h can be any value other than 2.

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Answer:

YXZ=AXZ

because if you see the letters they form triangle

if Monique wanted to run 7/8 mile and she went to the school track which was one quarter of a mile long. The number of lap Monique will complete is

One complete lap around a track or across a pool, from one end to the other: The track has 400 meters or approximately 25 mile per lap.

A lap is end to end of a track and in the problem a lap is 1/4 mile and Monique wants to complete 7/8 miles'. the comparison is as follows

assuming the number of laps is L

1 lap = 1/4 mile

L laps = 7/8 miles

cross multiplying

1 * 7/8 = L * 1/4

multiplying by 4 for each side

1 * 7/8 * 4 = L * 1/4 * 4

1 * 7/8 * 4 = L * 1

7/8 * 4 = L

hence option C is correct

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The mean and standard deviation of the sampling distribution of the sample mean (average) of the SAT math scores are:

(b) Mean = 515, SD = 114/√100

The mean of the sampling distribution of the sample mean is equal to the population mean (515), because the expected value of the sample mean is equal to the population mean. The standard deviation of the sampling distribution of the sample mean is called the standard error, and it is equal to the population standard deviation divided by the square root of the sample size (114/√100).

The result (b) is determined based on the central limit theorem, which states that as the sample size increases, the distribution of the sample mean approaches a normal distribution with mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is 515 and the population standard deviation is 114, so the standard deviation of the sampling distribution of the sample mean is equal to 114/√100. This result can be mathematically proven using the formula for the standard deviation of the sample mean:

SD of sample mean = σ/√n, where σ is the population standard deviation and n is the sample size.

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Three different formulas or rules for the terms of a sequence {an} if the first three terms of this sequence are 1,2,4 are as follows:

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The length of the GH is 4, when H is the midpoint of GI.

An area of a line that connects two distinct locations is referred to as a line segment. It is the least path between two places that can be determined to have a length.

A line segment's midpoint is the point on the segment when it is divided into two similar segments. The point on a line segment that is equally spaced from the two terminating points is known as the midpoint of the segment.

Given that H is the midpoint of GI.

Then we can say that,

GI / 2 = GH

Substitute the equations of the length of GH and GI as given:

(9x - 19) / 2 = 3x - 5

9x - 19 = 2(3x - 5)

9x - 19 = 6x - 10

9x - 6x = -10 + 19

3x = 9

x = 3

Substitute the value of x in the equation of the length of the segment GH thus:

GH = 3x - 5

GH = (3)(3) - 5

GH = 4

Hence, the length of the GH is 4, when H is the midpoint of GI.

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Answer: false

Step-by-step explanation: 1st we collect the Like Terms which would make the new equation 3y + 8 = 3y + 5 then we can cancel the 3y's bc they're equal and leaves us with 8 = 5 which we could see is false, so this equation is false

The scale factor of the dilation, expressed in function notation, (x, y) → (k·x, k·y), is (x, y) → (0.5·x, 0.5·y)

A dilation transformation is a transformation in which the dimensions of the image are obtained by multiplying the dimensions of the pre-image by a value, known as a scale factor of the dilation.

The possible table, based on the similarities of the coordinate points can be presented as follows;

Pre-Image [tex]{}[/tex]    Image

(2, 4) [tex]{}[/tex]             (1, 2)

(1, 0)  [tex]{}[/tex]            (0.5, 0)

(-4, -1) [tex]{}[/tex]           (-2, -0.5

The specified formula for the image, following the dilation of the point (x, y) by a scale factor of k is; (x, y) → (k·x, k·y)

Therefore, we get;

k = k·x/x = k·y/y

The comparison of the points in the table with the points (x, y), and (k·x, k·y), indicates that we get;

When (x, y) = (2, 4) and (k·x, k·y) = (1, 2)

Therefore;

k = k·x/x = k·y/y = 1/2 = 2/4  = 0.5

The scale factor of the dilation , k = 0.5, therefore;

(x, y) → (0.5·x, 0.5·y)

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The measure of the central angle associated to the circular arc is equal to 4 / 3 rad.

Herein we find the information of the radius of a circle and the length of its circular arc, whose relationship is shown by the following formula:

s = θ · r

Where:

If we know that r = 6 yd and s = 8 yd, then the measure of the central angle is:

θ = s / r

θ = (8 yd) / (6 yd)

θ = 4 / 3 rad

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Answer:

11.390625 in^3

Step-by-step explanation:

2.25^3 = 11.390625 in^3

Answer: 0.08 dollars

Step-by-step explanation:

8.64 divided by 9 = 0.96

0.96 divided by 12 = 0.08

Answer: n=110, m=110

Step-by-step explanation: I think m=110 because of vertical angles. m might also equal 70.

Out of the following statements A)It will be called every time the event listener is triggered, C. It must be passed to the event listener as the second argument and   D.It can be either an anonymous or a named function that is true of the event listener's callback function.

An event listener's callback function is a function that is triggered when an event is fired and the callback function is responsible for handling the event. A callback function must be passed to the event listener as the second argument, and it can be either an anonymous or a named function.

The callback function will be called every time the event listener is triggered, and it must always define a parameter for the event object. This allows the callback function to access the event object's properties and methods to handle the event accordingly. The event object contains information about the event, such as the type of event, the target element, and more. By accessing this information, the callback function can determine how to handle the event.

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The amount of rainfall in Nashville than in Miami would be 0.67.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the rainfall in Albany is 0.33. The amount of rainfall in Miami is calculated as:-

Rainfall = 1 - 0.33

Rainfall = 0.67

Hence, the amount of rainfall in Nashville than in Miami would be 0.67.

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The total trip took a total of 1.87 hours.

Speed is the rate at which an object's position changes, measured in meters per second. For example, if an object starts at the origin, and then moves three meters in three seconds, its speed is one meter per second. The equation for speed is simple: distance divided by time

Given here: Total distance=120 km and 59 km at 90 km/hr and the remaining distance at 50 km/hr

Remaining distance= 120-59

                                 =61 km

Thus for the first 59 km the time it took was

Time= Distance/ Speed

       = 59/90

       =0.65 hr

Similarly time taken for the second part of the journey is = 61/50

                                                                                               =1.22

Hence, total time taken for the trip is 1.22+0.65=1.87 hr.

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To calculate the total cost of the fence, we need to know the length of the fence.

In a right-angled triangle, the length of the fence can be calculated using the Pythagorean theorem, which states that the length of the hypotenuse (the fence) is equal to the square root of the sum of the squares of the other two sides (the base and the height of the triangle).

So, the length of the fence (C) = square root of (A^2 + B^2), where A is the base and B is the height of the triangle.

If the base of the triangle is x and the height of the triangle is y, then the cost of the fence can be calculated using the formula:

Cost = (length of fence) x (cost per meter)

Cost = (square root of (x^2 + y^2)) x 1.26

In order to calculate the cost, the farmer needs to know the values of x and y.

The total cost of the triangular shaped fence is A = £ 530

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of side AB = 145 m

Now , the measure of ∠BAC = 59°

From the trigonometric relations

tan θ = opposite / adjacent

tan 59° = BC / 145

Multiply by BC on both sides , we get

BC = 241.320524941 m

Now , the hypotenuse of the triangle is

H = √ ( 145 )² + ( 241.320524941 )²

H = √ ( 21,025 + 58,235.595757

H = √79,260.595757

H = 281.53258 m

Now , the total perimeter of triangle is P = 281.53258 + 241.320524941 + 145

P = 667.85310877 m

Now , fence costs £1.26 per meter

A = 667.85310877 m / £1.26

So , the total cost is A = £ 530

Hence , the total cost is A = £ 530

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The approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

Total of 22 is more than 4500 is equivalent to average of 22 is more than [tex]$\frac{4500}{22}[/tex]=204.545

[tex]$$\begin{aligned}P(\bar{x} > 204.545) & =1-P(\bar{x} < 204.545) \\& =1-P\left(\frac{\bar{x}-\mu}{\sigma / \sqrt{u}} < \frac{204.545-195}{35 / \sqrt{22}}\right) \\& =1-P(z < 1.2792) \\\end{aligned}$$[/tex]

                        = 1 - 0.8997

                        = 0.1003

                        = 10.03%

Therefore, the approximate probability P that the total weight of the passengers exceeds 4500 pounds is 10.03%.

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