How do u do this????

The least-squares error in the least-squares solution of ax = b is given by the equation:

[tex]||b - ax||^2 = (b - ax)^T(b - ax) = b^Tb - 2a^Tbx + a^Tax[/tex]

The least-squares solution is the value of x that minimizes this error. This occurs when the derivative of the error with respect to x is equal to zero, and the second derivative is positive.

To find the least-squares solution, we take the derivative with respect to x and set it to zero:

[tex]-2a^T(b - ax) = 0\\a^Tb = a^Tax[/tex]

This gives us the normal equation, which is the equation that x must satisfy in order to minimize the error. The solution of this equation is:

[tex]x = (a^Ta)^-1a^Tb[/tex]

This is the least-squares solution of the equation ax = b, and it is the value of x that minimizes the least-squares error. The least-squares error is given by the equation:

[tex]||b - ax||^2 = b^Tb - 2a^Tbx + a^Tax = b^Tb - a^T(a(a^Ta)^-1a^Tb) = b^Tb - a^T(a^Tb)[/tex]

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The slope intercept form of the line is y=mx+c where m is the slope of the line and c is the y-intercept is +3

What is meant by slope?

Change the equation x−y=3 in slope intercept form:

x + y = 3

⇒y = x - 3

⇒y= + x−3

Hence, the slope of the line x + y= -3 is m= - 1 and the y+intercept is +3.

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The sum of the interior angle measures of the given polygon , given that it is a convex polygon is 540 °

The polygon given is a convex polygon , and has 5 sides . This means that it is a Pentagon .

Each interior angle in a regular convex pentagon, measures 108 ° . This means that the sum of the interior angle measures is therefore :
= Measure of interior angles x Number of angles in Pentagon

= 108 x 5

= 540 °

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Answer:

Geometric -64, 128,-256

Step-by-step explanation:

It follows the same pattern of alternating + and - and has the quadratic increase as the others

Answer: B

Step-by-step explanation:

Alex's expression about the sequence is incorrect and Sara's thought is correct

From the question, we have the following parameters that can be used in our computation:

Event: Three-jump, two-step cycle

Represent the number of jumps with x

So, we have the following representation

Event: Three- x, two-step cycle

When represented as an equation, we have

Event = 3x + 2

The number of times is 5

So, the sequence is represented as

Sequence = Event * 5

Substitute the known values in the above equation, so, we have the following representation

Sequence = (3x + 2) * 5

Evaluate the product

Sequence = 15x + 10

This means that the sequence is 15x + 10

Hence, Alex is incorrect and Sara is right

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You can solve exponential decay questions using the decay rate and the exponential decay formula.

Exponential decay is a common mathematical concept that can be difficult to master. Fortunately, there are some key strategies that can help you solve exponential decay questions.

To begin, it’s important to understand the concept of exponential decay, which is the decrease in the value of a quantity over time.

From there, you’ll need to identify the decay rate, or the speed at which the quantity is decreasing.

Next, you’ll want to use the exponential decay formula to calculate the final value of the quantity.

The formula is

dN/dT = -λN

where

N = quantity

λ= exponential decay constant

T= time

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Answer: B is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

96=(32+x)x2=?

The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) is 2.527.

The exact length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated using the formula for arc length.

This formula states that the length of a parametric curve from t=a to t=b is equal to the integral of the square root of the sum of the squares of the respective derivatives of x and y, evaluated from a to b.

Using this formula, the length of the curve y=sqrt(x-x^2)+sin^-1(sqrt(x)) can be calculated by integrating the square root of (1-2x)^2 + (1/sqrt(x))^2 from 0 to 1. This yields a length of approximately 2.527.

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At least 4 days means 4 or more; in this example, 4, 5, or 6

a 17/190  ≈ 0.089

b 24/190  ≈ 0.126

Step 1:

At least 4 days means 4 or more; in this example, 4, 5, or 6. So

Estimated Probability (Car Refill Gaps)

in general ,estimated probability observe =The frequency of a particular

                                                                            outcome/The no: of times an

                                                                                               experiment is

                                                                                                    repeated

This particular task observes=The no: of time a 4 day refill gap occurs/

                                                                 The total frequency  of refill gap

                                                                                                        days

Case a total of 190 refill gap days occurred. Of those 17 were 4 days gap

Estimated probability in these case 17/190 or 0.089

This particular task observe= The no : of times 4 day or more refill gap

                                                   occurs/The total frequency of refill gap

                                                                    day

Case a total of 190 refill gap day occurred of these 24 were 4+ day gap

Estimated probability in these case 24/190 or 0.126

Step 2:

a 17/190 ≈ 0.089

b 24/190  ≈  0.126

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The scale factor of the dilation is 1.5.

Scale factor is a numerical value used to describe the relationship between two different measurements. It is used to compare two measurements of the same type, such as length, area, or volume. The scale factors are used in many mathematical equations and can be used to enlarge or reduce an image or object. For example, a scale factor of two would cause a two-dimensional object to double in size while a scale factor of one-half would cause the object to halve in size.

This can be determined by dividing the length of the sides of the original triangle by the length of the sides of the image triangle. For example, the length of the side of the original triangle connecting (0,0) and (3,0) is 3, and the length of the side of the image triangle connecting (0,0) and (4.5,0) is 4.5. Dividing 4.5 by 3 gives 1.5, which is the scale factor.

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The probability of at least two people bringing the same item is 0.19.

The probability of two people bringing the same item can be calculated using the formula P(A∩B) = P(A) × P(B). In this case, P(A) and P(B) are both 1/10, since each person has the same chance of choosing any one of the 10 items on the list. Therefore, the probability of two people bringing the same item is 1/100. To calculate the probability of at least two people bringing the same item, we can use the formula P(A∪B) = P(A) + P(B) - P(A∩B). In this case, P(A∪B) = 1/10 + 1/10 - 1/100 = 0.19. Therefore, the probability of at least two people bringing the same item is 0.19.

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Answer:

y = 2x + 7

Step-by-step explanation:

Answer: To find the price of the sweater before the discount, you need to determine how much the discount saved Rahul and divide that amount by the discount rate.

The discount saved Rahul 20 / 0.25 = 80 rupees.

So, the price of the sweater before the discount was 80 + 20 = 100 rupees.

Step-by-step explanation:

Answer:

slope = 2

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 3) and (x₂, y₂ ) = (4, 7) ← 2 points on the line

m = [tex]\frac{7-3}{4-2}[/tex] = [tex]\frac{4}{2}[/tex] = 2

Answer:

1+1=2

Step-by-step explanation:

2=1+1

There are 3 medium pizzas and 6 large pizza.

Let medium pizza = x

Let large pizza = y

Since she she places the order from Tony's pizza across the street, she learns that each medium pizza has 6 slices, and each large pizza has 8 slices and Ms. Johnson orders 9 total pizzas with a total of 66 slices

This will be:

x + y = 9 ..... i

6x + 8y = 66 ..... ii

From i, x = 9 - y

Put this into equation ii

6x + 8y = 66

6(9 - y) + 8y = 66.

54 - 6y + 8y = 66.

2y = 12

Divide

y = 12/2

y = 6.

Therefore there are 6 large pizzas

Medium pizza = 9 - 6 = 3

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Answer: 10

Step-by-step explanation:

Using the Pythagorean theorem we know a^2 + b^2 = c^2.

We can plug in 8 and [tex]2\sqrt{41[/tex] for b and c.

a^2 + 8^2 = [tex]2\sqrt{41}[/tex]^2

a^2 + 64 = 164

a^2 = 100

a = 10

Answer:

10 : 24 : 26

15 : 36 : 39

Step-by-step explanation:

You can multiply all numbers in the ratio to find equivalent ratios that would function as different sets of sides because it's just a larger version of the 5: 12 : 13 triangle

By using the unit conversion method, 2 million seconds converted to days are equal to 23 days.

A unit conversion expresses the same aspect as another unit of measurement. For example, time can be expressed in minutes rather than hours, and distance can be represented from miles to kilometers, feet, or any other unit of measurement.

In this situation, you need to convert between seconds and days:

A day consists of 24 hours. Therefore, the fraction 24 hours/day is equal to 1. There is no value change when multiplying a number by 1. The same holds true for the conversion factors 1 hour/60 minutes and 1 minute/60 seconds.

If you multiply 2,000,000 seconds (2 million seconds) by these conversion factors, you will change the seconds to days:

2,000,000 sec. x (1 min/60 sec.) x (1 hour/60 min) x (1 day / 24 hours)

Therefore, all that is required is to divide 2,000,000 by the product of 60, 60, and 24.

(2,000,000) / (60*60*24) = 2,000,000 / 86,400 = 23.148 days ≈ 23 days

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The two places she can put lens and give object and image distances are 15cm and 75cm.

The Lens equation gives us:

1/f = 1/u + 1/v

From the problem we know that,

v=90-u

By solving

u² - 90u + 1125 = 0.

An optical system's focal length, which is the inverse of the system's optical power, indicates how strongly the system converges or diverges light. A system with a positive focal length is said to converge light, and one with a negative focal length is said to diverge light.

A negative focal length, on the other hand, indicates how far in front of the lens a point source must be located to form a collimated beam, for the special case of a thin lens in air, where a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus. For more generic optical systems, the focal length is merely the inverse of optical power and lacks any intuitive significance.

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The vertices of ABC shown as A(-4, 4), B(-2, 4), and C(-3, 2). when reflected across the y-axis to produce the image A'B'C', the coordinate of the vertex A is

Reflection is one of the movements in transformation that involve creation of mirror image

Transformation rule for reflection over x-axis at origin (0, 0)) is

(x, y) → (x, -y)

Transformation rule for reflection over line y-axis at origin (0, 0)) is

(x, y) → (-x, y)

The problem involves reflection over y axis hence we use the rule

(x, y) → (-x, y)

Vertex A has the coordinate of the preimage as A(-4, 4) then after reflection the coordinate of the image will be A' (4, 4)

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Answer:

lose 12y yards AKA( 3rd option)

Step-by-step explanation:

Answer: 77x+21y

Step-by-step explanation:

To find triangle pairs congruent by the HL (Hypotenuse-Leg) condition, first identify the hypotenuse (the longest side) and the leg (the side adjacent to it).

To find triangle pairs congruent by the HL condition, first identify the hypotenuse and the leg in each triangle. The hypotenuse is the longest side, while the leg is the side adjacent to it. Once the hypotenuse and leg have been identified in both triangles, measure them to ensure they are the same length. If they are the same length, then the triangles are congruent by the HL condition. If the hypotenuse and leg of both triangles match in length, then the two triangles are congruent to each other. This means all three sides of the two triangles will be the same length, making them congruent by the HL condition.

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The implicit differentiation of the given function is dy/dx = ((-4x-8y))/((8x +12y+ 13)).

In implicit differentiation, each side of an equation with two variables (usually x and y) are differentiated by treating one of the variables as a function of the other. The technique of implicit differentiation enables the determine the derivative of y with respect to x without having to solve the given equation for y. The chain rule must be used whenever the function y is being differentiated because of the assumption that y may be expressed as a function of x.

In order to find the differentiate implicitly,

d/dx  (2x^2+8xy+6y^2+13y-2)=0

4x + 8y + 8xdy/dx + 12ydy/dx + 13dy/dx = 0

dy/dx (8x + 12y + 13) = -4x -8y

dy/dx = ((-4x-8y))/((8x +12y+ 13))  

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The value of the derivative of D at t = 8 is equal to -0.5 is At 8 a.m. the water level decreased at a rate of 0.5 meters per hour.

A function that has a derivative at each point in its domain is referred to as a differentiable function of one real variable in mathematics.

In other words, a graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function has no break, angle, or cusp and is smooth (it is locally well approximated as a linear function at each interior point).

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The markup price is $464 and the expression to find the markup price is 320×1.45

Markup shows how much more a company's selling price is than the amount the item costs the company.

Given that, the price of a $320 tablet after a 45% markup.

This mean that, the tablet price is being hiked by 45%,

Therefore,

Total price will be = 45% of 320 + 320

= 45 / 100 x 320 + 320

= 144 + 320

= 464

Hence, the markup price is $464 and the expression to find the markup price is 320×1.45

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Answer:

Step-by-step explanation: go to the x axis that goes left to right and go to the #4 and then go down 3

Answer:

x = 14

Step-by-step explanation:

given Δ MNO and Δ QRS are similar then the ratios of corresponding sides are in proportion , that is

[tex]\frac{NO}{RS}[/tex] = [tex]\frac{MN}{QR}[/tex] ( substitute values )

[tex]\frac{x}{7}[/tex] = [tex]\frac{10}{5}[/tex] = 2 ( multiply both sides by 7 to clear the fraction )

x = 7 × 2 = 14

The correct answer is option a). The parameter of interest is the mean mpg of the 10 cars.

This parameter is important because it is the average mpg of the sample that is being used to measure the fuel efficiency of the car model. This parameter is important because it provides an indication of how efficient the car model is. By measuring the mpg of a sample of 10 cars, the researchers can get an indication of how the entire population of cars of this particular model perform.

The mean mpg of all cars of this particular model is the population parameter and is the overall average mpg of all cars of this particular model. The mpg measurements of this car model is the individual measurements for each car in the sample, which are used to calculate the mean mpg of the 10 cars.

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The scalar product of two parallel unit vectors, is equals to one i.e., i.e., = 1 , = 1 and = 1 .

Scalar Product: The scalar product is also known as dot product. The scalar product of two vectors can be constructed by taking the component of one vector in the direction of the other vector and multiplying it by magnitude of other vector. That gives scalar as a result. Scalar don't have a direction associated with them. The scalar product of vector A and vector B is equal to |A| |B|Cosθ , where |A|, |B| represent magnitude of vector A and vector B and θ angle between the two vectors direction.

We have to determine the scalar product of , and Here and are the unit vectors in the direction along the x-axis. So, they are parallel to each other, that's why θ = 0° and = 1 . Therefore, = (1) (1) cos 0° = 1. Similarly, = 1 ( unit vectors in direction along the y-axis) and = 1 ( along z-axis). Hence, the dot product of the two unit vectors and is equal to one for each