Help please, I was not in class when the lesson was happening and now I’m very confused.

Thank you :)

The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

To find the pseudoinverse of a matrix A, the first step is to take the singular value decomposition (SVD) of A, which can be written as A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix with nonnegative singular values. The pseudoinverse of A is given by A^+ = VΣ^+U^T, where Σ^+ is the same as Σ except that the nonzero elements of Σ are replaced by their inverses.

Next, the projection matrices are given by AtA and AA+, which are used to project a vector onto the column space and the row space of A, respectively.

The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

Whether a solution is exact or unique depends on the rank of A and the number of linearly independent columns and rows. If the rank of A is equal to the number of columns, then the solution is unique, otherwise, the solution may not be unique.

Therefore, The "best" solution z+ = A^+b is the one that minimizes the 2-norm of the residual vector r = b - Az. In general, not all right-hand sides b will have a unique solution z+, and even if there is a solution, it may not be exact (i.e., Az ≠ b).

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The linear system of equations in the question are resolved as follows;

Question 4

The true statements are;

Question 6

A linear system consists of two or more linear equations that operate simultaneously.

Question 4;

The system of equations is presented as follows;

Equation 1: 10·x - 2·y = 15

Equation 2: 4·x + y = 6

Plugging in the values of x = 1.5, y = 0, we get;

10 × 1.5 - 2 × 0 = 15

4 × 1.5 + 0 = 6

The point (1.5, 0), satisfies both equations in the system of equations, therefore, the point (1.5, 0) is a solution of the system of equations.

The true statements are therefore;

Question 6;

The linear system of equation is presented as follows;

-4·x - 8·y = 5

x = 4·y + 7

The substitution method can be used by plugging in the value of x = 4·y + 7, in equation (1) as follows;

-4·x - 8·y = 5

-4·(4·y + 7) - 8·y = -24·y - 28 = 5

Adding 28 to both sides, we get;

-24·y - 28 + 28 = 5 + 28

-24·y + 0 = 5 + 28 = 33

-24·y = 33

y = 33/(-24) = -11/8

y = -11/8 = -1.375

x = 4 × (-11/8) + 7

x = -11/2 + 7 = (-11 + 14)/2 = 3/2

x = 3/2 = 1.5

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Answer:

Step-by-step explanation:

How to solve a quadratic equation using the Quadratic Formula.

Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, c.

Write the Quadratic Formula. Then substitute in the values of a, b, c.

Simplify.

Check the solutions.

The four methods for solving a quadratic issue are the quadratic formula, using square roots, factoring, and completing the square.

A quadratic equation in algebra is any equation that can be written in standard form as where x stands for an unknown value, a, b, and c stand for known numbers, and where a ≠ 0.

Problems involving squares and quadrangles and quadratic equations are closely related. In actuality, the word quadratic comes from the Latin word quadratus, which means square.

The quadratic formula, using square roots, factoring, and completing the square are the four ways to solve a quadratic problem. An overview of all the many approaches to solving a quadratic equation is what I'd want to discuss right now.

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Answer:

the number of children on the trip=31

The number of adult=9

Step-by-step explanation:

Let's call the number of adults on the trip "a" and the number of children on the trip "c".

We know that:

a + c = 40 (the total number of people on the trip)

And:

3a + 2c = 89 (the total number of sandwiches given out)

We can use the first equation to solve for one variable in terms of the other:

a = 40 - c

And substitute this into the second equation:

3(40 - c) + 2c = 89

Expanding and simplifying:

120 - 3c + 2c = 89

120 - c = 89

Subtracting 120 from both sides:

-c = -31

So c = 31, the number of children on the trip.

And the number of adults on the trip, a = 40 - c = 40 - 31 = 9.

The rule for the translation is (-3, -4).

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.

JKL is the original figure.

J'K'L' is the transformed figure after applying cetain rule.

We obtain J'K'L' by translating the original image left 3 units and down by 4 units.

The rule should be (-3, -4)

Hence,  the rule for the translation is (-3, -4).

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Answer: Guaranteed

Step-by-step explanation:

Answer: Certain to happen

Hope this helps :)

Step-by-step explanation:

It's important to remember that when regarding probabilities with decimals, 0 is considered least likely, and 1 is most likely.

The lowest necessary yield strength for the axle material is 113.88 M/mm^2.

Torsional moment of Mv = 2×10^7 Nmm.

Bending moment of Mb = 1×10^7 Nmm

Axial force = 10^3 kN

Axial Stress = Axial Force/(πd^2/4)

Axial Stress = 10^3 × 10^3/(π(100)^2/4)

Axial Stress = 4 × 10^6/3.14 × 10^4

Simplifying

Axial Stress = 1.274 × 10^2

Axial Stress = 127.4

The combined tension of a torsional moment and a bending moment is known as shear stress.

τ = 16/πd^3√(Mv^2 + M^2)

τ = 16/π(100)^3√[(2×10^7)^2 + (1×10^7)^2]

τ = 16/π(10)^6√[4×10^14 + 10^14]

τ = 16/π(10)^6√[5×10^14]

After solving, we get

τ = 113.88 M/mm^2

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The complete question is:

The figure shows a circular axial made of steel that is loaded by a torsional moment of Mv=2×10^7 Nmm, a bending moment of Mb = 1×10^7 Nmm and an axial force of 10^3 kN. If a safety factor against yielding of 1,5 is required, what is the lowest necessary yield strength for the axle material?

The probability of winning the game, given t tails, is equal to [tex]0.5^t[/tex] .It's important to note that the outcome of each flip is independent.

The probability of winning the game in which you have flipped t tails and need to flip t consecutive heads can be calculated as follows:

Each flip of the coin has a probability of 0.5 of landing heads and 0.5 of landing tails. So, for the first flip, the probability of flipping a head is 0.5. For the second flip, the probability of flipping two heads in a row is

[tex]0.5 * 0.5 = 0.25[/tex]

For the third flip, the probability of flipping three heads in a row is

[tex]0.5 * 0.5 * 0.5 = 0.125[/tex]  , and so on.

Therefore, the probability of winning the game, given t tails, is equal to 0.5^t. For example, if you have flipped 2 tails, the probability of winning the game by flipping 2 consecutive heads is

[tex]0.5 * 0.5 = 0.25.[/tex]

It's important to note that the outcome of each flip is independent, so the probability of winning the game given t tails is constant regardless of the number of tails flipped prior to the current flip.

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We can use (A) V = 16lw as a volume function.

Because the volume of a rectangular box is given by the product of its length, width, and height. In this case, the height is fixed at 8 cm, so the volume would be calculated as V = 16 x l x w, where l = 2w.

A three-dimensional space's volume is measured. t is frequently expressed numerically using units derived from SI (such the cubic Meter and litre) or by different imperial or US customary units (such as the gallon, quart, cubic inch). Volume and length (cubed) are related concepts.

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The sequence is neither arithmetic nor geometric.

Informally, a sequence in mathematics is a list of items that are in some order (or events). It possesses members, much like a set (also called elements, or terms). The length of the series is the number of ordered elements in the sequence, which could be unlimited.

Also, Arithmetic sequences, geometric sequences, quadratic sequences, and special sequences are the four primary categories of distinct sequences you need to be familiar with.

Squares, rectangles, circles, cones, cubes, and other shapes that can be created using geometry are known as geometric forms. In structural, civil, and architectural engineering, geometric forms are frequently used.

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The sequence from response to question 1 is neither arithmetic nor geometric.

The sequence in mathematics is the order of value of items or events. Usually, it contains a number or a series of numbers with a length of series that can be unlimited.

If the sequence has common differences from one value to another it can be considered as an arithmetic sequence, for example, 2,4,6,8. If the sequence has common ratios from one value to another it can be considered as a geometric sequence, for example, 2,4,8,16.

Since the response in question 1 doesn't have either common differences or common ratios, so it is neither arithmetic nor geometric.

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The selling price of the house that Laurie sold was $562,000.

The selling price is the amount paid by the customer to purchase the goods. The actual selling price is the amount paid by the customer for a product or service. This is the price that is more than the cost of products and includes a proportion of profit.

The cost price of an item is the amount spent to buy it or the price at which it is manufactured.

Let's call the selling price of the house "P".

The commission fee of 2.5% on the selling price of the house is equal to 0.025 * P.

Since Laurie made a commission of $14,050, we can set up the following equation:

0.025 * P = 14050

Dividing both sides by 0.025:

P = 14050 / 0.025 = 562000

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0.453592 kilograms are in a pound.

How many kilograms are in a pound?

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Answer: k = 24, y = 24x

Step-by-step explanation:

y = kx (the variables x and y varies directly)
when x = 3, y = 72
k = y/x = 72/3 = 24
y = 24x

When dealing with complicated expressions that involve the addition and subtraction of positive and negative numbers, it is important to remember the following rules.

Nobody's a mathematical object used to count level and measure it is in the fundamental concept in mathematics and you used in many different way number can be used to represent anything from quantity of object to ideas in the concept additionally number are used to describe relationship between different object or concept.

First, when adding or subtracting two numbers with the same sign, the sum or difference will have the same sign as the numbers. For example, adding 5 + 3 gives 8 and subtracting 5 – 3 gives 2, both of which are positive numbers.

Second, when adding or subtracting two numbers with different signs, the sum or difference will have the sign of the number with the largest absolute value. For example, adding 5 + (-3) gives 2 and subtracting 5 – (-3) gives 8, both of which are positive numbers.

Third, when multiplying and dividing positive and negative numbers, the product or quotient will have the sign of the number with the largest absolute value. For example, multiplying 5 x (-3) gives -15 and dividing 5 / (-3) gives -1.67, both of which are negative numbers.

Finally, when dealing with expressions with multiple operations, it is important to use the correct order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This allows for the correct evaluation of an expression.

By remembering these rules, it is possible to add and subtract positive and negative numbers in complicated expressions.

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68.26% percent of months have maintenance costs in the range of $200 to $300

The monthly maintenance cost per square foot is calculated by dividing the total cost by the property's total area. It is multiplied by the unit area of each home to determine the individual maintenance contributions.

Your home's square footage can also be used to estimate your yearly maintenance expenses. If you follow this guideline, you should begin by figuring annual maintenance expenditures at $1 per square foot. Your estimated annual maintenance cost for a 2,000 square foot home is $2,000.

Costs incurred during normal measures to maintain an asset's original state are referred to as maintenance costs. Simple electrical repairs, bulb replacement, paint touch-ups, pool cleaning, etc. are a few examples of maintenance charges.

Remember that, [tex]P(X < A) = P(Z < (A - \mu )/\sigma)[/tex]

and given that \mu = [tex]$250\ and \ \sigma = \$50[/tex]

So, P(maintenance cost is in the range $200 to $300) = P(200 < X < 300)

= P(X < 300) - P(X < 200)

= P(Z < (300 - 250)/50) - P(Z < (200 - 250)/50)

= P(Z < 1) - P(Z < -1)

= 0.8413 - 0.1587

= 0.6826

= 68.26%

Thus, 68.26% percent of months have maintenance costs in the range of $200 to $300

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If Jackson invested $320 in an account paying an interest rate of 3. 2% compounded continuously, assuming no deposits or withdrawals are made, it would take: 3.37 years

for the value of the account to reach $410

To solve this problem, we can use the formula for continuously compounded interest:

where A is the final amount, P is the initial amount (320), r is the interest rate (3.2%), and t is the time in years.

Solving for t, we get:

Plugging in the values, we get:

Approximating this, we get:

So it would take about 3.4 years for the value of the account to reach $410.

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As a result, the radius of convergence, R, is equal to one. As a result, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 +...) = x + 16x^2 + 64x^3 +... This is the function f's power series representation (x).

A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example.

Here,

The power series representation for f(x) = x(1 + 8x)^2 can be found by expanding the function (1 + 8x)^2 as a Taylor series centered at x = 0:

(1 + 8x)^2 = 1 + 16x + 64x^2 + ...

So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ...

This is the power series representation for the function f(x).

To determine the radius of convergence, R, we use the formula:

R = 1 / limsup |a_n|^(1/n)

where a_n is the nth coefficient in the power series and limsup refers to the limit superior of the sequence {|a_n|^(1/n)}.

In this case, a_n = 16n x^n, so |a_n|^(1/n) = |16n|^(1/n) * |x|^(1/n). Since |16n|^(1/n) is a constant, the limit superior is just equal to |x|^(1/n). Therefore,

R = 1 / limsup |a_n|^(1/n) = 1 / |x|^(1/n) = 1

So, the radius of convergence, R, is equal to 1. So, f(x) = x(1 + 8x)^2 = x(1 + 16x + 64x^2 + ...) = x + 16x^2 + 64x^3 + ... This is the power series representation for the function f(x).

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A rhombus has reflectional symmetry over either of its diagonals.

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Answer:

25/3

Step-by-step explanation:

Let's call the number of students who picked sport "s" and the number of students who picked painting "p". We know:

p + s = 5 (the number of students who picked painting and sport)

42 - p - s = 8 (the number of students who did not pick either)

s = 2p (twice as many picked sport as painting)

From the first equation, we can solve for p:

[tex]\sf:\implies{p + 2p = 5}[/tex]

[tex]\sf:\implies{3p = 5}[/tex]

[tex]\sf:\implies{p = 5/3}[/tex]

So, 5 students picked painting and 10 students picked sport. And the number of students who picked sport but not painting is:

s - p = 10 - 5/3 = 10 - 5/3 = 25/3.

Answer: 75.2 °F

Step-by-step explanation: (24°C × 9/5) + 32 = 75.2°F

The calculation would be (24 x 9/5) + 32 = 75.2°F.

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The probability that the selected ride will be closed is given as follows:

E. 0.77.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For this problem, the percentages are given, hence we must just identify the correct percentages.

The probability of the park being closed is defined as follows:

Hence the probability that the park is closed is obtained as follows:

p = 0.75 + 0.08 x 0.25

p = 0.75 + 0.02

p = 0.77.

Meaning that option E is the correct option.

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The probability of the selected ride being closed is 0.77

Let R be the event that a ride is closed due to icy weather, and

M be the event that a ride is closed due to mechanical problems.

So, we have

Using the Law of Total Probability, we have:

P(M) = P(R) + P(M | R') * P(R')

So, we have

P(M) = 0.75 + 0.08 * (1 - 0.75)

Evaluate

P(M) = 0.77

Hence, the probability is 0.77

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The interest on the loan is: $375.44

The maturity value is: $4,775.44.

Maturity value and interest on a loan can be calculated as follows:

Maturity value: it is the amount of the loan plus the interest charged on it. It can be calculated using the formula:

MV = P + I

where MV is the maturity value, P is the principal (original loan amount), and I is the interest charged on the loan.

Interest: it is the amount charged by the lender for the use of their money. It can be calculated using the formula:

I = P * r * t

where I is the interest, P is the principal, r is the interest rate, and t is the term of the loan (in years or days).

Therefore:

Exact interest: 4,400 * 6% * 172/365 = $375.44

Maturity value: 4,400 + 375.44 = $4,775.44

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If there is a pattern 1 tree then 2 bead.  If there are a total of 42 tree and bead, then 84 bead is needed to complete the pattern as 42 tree and 84 bead.

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All parts of the probelm given regarding probability have been solved and provided below.

We have been told that a personnel director interviewed 11 senior engineers for four job openings and had scheduled six interviews for the first day and five for the second day of interviewing. Now let us assume that the candidates are interviewed in a random order.

(a) The probability that any quantity, lets say x, of the top four candidates are interviewed on the first day can be calculated using -

= h(x; 6,4,11) = (4;x) (7;6-x) / (11;6)

(b) The expected number of candidates, if top four candidates to be interviewed on the first day can be found out using -

= E[X]=nM/N

=  6*4 / 11

= 2.1812

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The x-axis should contain the independent variable (also known as the "explanatory variable"), and the y-axis should contain the dependent variable (also known as the "response variable").

Definition of X and Y Graph?

The x-axis and the y-axis, which together make up a graph's coordinate plane, can be used to define an x and y graph.

The y-axis and the x-axis each stand in for one of the two axes: the horizontal or horizontally oriented. The origin, or point of reference for the plane, is the intersection of the x- and y-axes.

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The x-axis (horizontal line) of the graph should have the independent variable, and the y-axis should have the dependent variable (vertical line). At the origin, the location of the coordinates, the x and y axes intersect (0,0).

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The truth about the end behavior of the graph is

The end behavior of function typically says the characteristics of the function at the ends

Examining the given graph it can be deduced that end behavior is  described as

x ⇒ -∞ f(x) ⇒ ∞

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Answer:

Step-by-step explanation:

The truth about the end behavior of the graph is

D. As the x-values go to negative infinity, the function's values go to positive infinity.

Answer:

$81.15

Step-by-step explanation:

So to find the total amount of money, you take the original price and add the sales tax.

We need to find the sales tax first, which is telling us to multiply the original price by 0.065.. so lets do that

(79.95)(0.065) = 5.19675

Since we got that answer there, we add that to the original price

$79.95 + $5.19675 = $81.14675

Which rounds to $81.15

Answer:

Step-by-step explanation:

A sequence can be generated by using an=an−1+17, where a1=15 and n is a whole number greater than 1. The first 5 terms in the sequence are:

a2 = a1 + 17 = 15 + 17 = 32

a3 = a2 + 17 = 32 + 17 = 49

a4 = a3 + 17 = 49 + 17 = 66

a5 = a4 + 17 = 66 + 17 = 83

So the first 5 terms in the sequence are:

15, 32, 49, 66, 83