Find the height of a building reaches by the tio of a ladder

We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

4metres

Step-by-step explanation:

Given the height of the trail modeled by the function h(x) = -0.1x^2 - 0.3x +2.8 , where x is the horizontal distance in kilometers

The horizontal distance occurs at the x intercept i.e at h(x) = 0

Substitute

0 = -0.1x^2 - 0.3x +2.8 ,

Multiply through by -10

0 = x^2 + 3x - 28

x^2 + 3x - 28 = 0

Factorize

x^2 + 7x - 4x - 28 = 0

x(x+7) - 4 (x+7) = 0

(x-4)(x+7) = 0

x-4 = 0 and x+7 = 0

x = 4 and -7

Since the danced cannot be negative, hence the horizontal distance of the trail is 4m

Answer:

\( \frac{1}{2} (48 \div6) - 2 + 5 \\ \frac{1}{2} (8) - 2 + 5 = 4 - 2 + 5 \\ = 2 + 5 \\ = 7\)

Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = \(-\frac{1}{3}\)a + b

To find b, substitute y and a with the given values

6 =  \(-\frac{1}{3}\)(-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = \(-\frac{1}{3}\)a + 4

Answer:

c

Step-by-step explanation:

Answer:

c. y = -1/2x - 4

Answer:

C

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c (m is the slope and c the y- intercept )

y = 2x + 8 ← is in slope- intercept form

with slope m = 2

given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{2}\) , then

y = - \(\frac{1}{2}\) x + c ← is the partial equation of the perpendicular line

to find c substitute (8, - 8 ) into the partial equation

- 8 = - 4 + c ⇒ c = - 8 + 4 = - 4

y = - \(\frac{1}{2}\) x - 4 ← equation of perpendicular line

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Answer:

The slope of a line that is perpendicular to the x-axis ​is undefined.

Step-by-step explanation:

We know that the x-axis is a horizontal line.

Therefore, the slope of a line that is perpendicular to the x-axis ​is undefined.

For example, the slope between (1, 2) and (1, 4) is:

Using the slope formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

                 = [4 - 2] / [1 - 1]

                  = 2 / 0

                  = ∞

Based on the provided informations and given values, the value of k for the given function and domain is calculated to be 11.

To find the value of k for the function G(x) = |5x - 4|, we need to evaluate the function at the endpoints of the given domain and find the maximum value.

The domain of the function is 0 ≤ x ≤ 3, so we need to evaluate the function at x = 0 and x = 3.

When x = 0:

G(0) = |5(0) - 4| = 4

When x = 3:

G(3) = |5(3) - 4| = 11

So, the maximum value of the function occurs at x = 3, and the value is 11.

Since the function is continuous over the given domain, we know that the maximum value occurs either at one of the endpoints or at a critical point in between.

The critical point is where the expression inside the absolute value bars, 5x - 4, equals zero:

5x - 4 = 0

x = 4/5

However, 4/5 is not in the given domain, so the maximum value occurs at x = 3, and the value is 11.

We know that the maximum value of the function is k, so:

k = G(3) = 11

Therefore, the value of k for the given function and domain is 11.

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Answer:

3 weeks 21 days, 5 weeks 35, 7 weeks 49, 9 weeks 63 days

Step-by-step explanation:

Each week is 7 days

Answer:

You will get $3 back

mark me as brainliest pls

Step-by-step explanation:

$25 times 8%= 2

25+2=27

30-27=3

Answer:

$3

Step-by-step explanation:

25*.08=2

25+2=27

30-27=3

A phlebotomist conducted a study involving 25,525 individuals aged between 35,535 and 44,444 years old to measure their cholesterol levels.

Summary statistics for the sample were obtained to analyze the data and draw conclusions about cholesterol levels in this specific age group. Based on the information given, we know that a phlebotomist measured the cholesterol levels of a sample of 252525 people between the ages of 353535 and 444444 years old. Here are the summary statistics for the samples:

- Sample size: 252525
- Age range: 353535 to 444444 years old
- Cholesterol levels: No information was provided about the mean, median, mode, or range of cholesterol levels in the sample.

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Answer:

-5

Step-by-step explanation:

As, x = - 1

So 2(-1)-3 = - 2 - 3 = - 5

So y = - 5

The perimeter of the given triangle when x = 1.5 is calculated as; 12 inches

The perimeter of a triangle would be the sum pf the side lengths of that triangle. We are given the side lengths as;

4x - 3 inches

4x - 2 inches

4x - 1 inches

Thus;

Perimeter = 4x - 3 + 4x - 2 + 4x - 1

Perimeter = 12x - 6

Now, when x = 1.5, we have;

Perimeter = 12(1.5) - 6

Perimeter = 12 inches

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Answer:

x       y

0     -2

1       -1

2       -0.56

Step-by-step explanation:

Answer:

Step-by-step explanation:

➡️ Pertanyaan:

7 × 7

➡️ Penyelesaian:

7 × 7

49 ✅

\( \: \)

Answer:

\( \: \: \: \: \: \: \: \: \)

Answer: 50 oranges

Step-by-step explanation:

1 kg = 1000 g - 4 kg = 4000 g 4000g/80g= 50 (This gives the number of oranges in the box since each orange weighs 80 grams.)

Answer: 6 miles

Step-by-step explanation:

If you picture this scene in your head, you will get a simple 3x4x5 right triangle. 4 times 2 is 8, 5 times 2 is 10, so Sarah should, by now, have traveled 3 times 2 miles.

Final answer: Beth has traveled 6 miles after an hour.

Hope this helped! :)

Helping tip: The reason it is not 4 is because they are not traveling west and east away from each other. They are traveling north and east, so they are moving in two directions to form a right triangle, and the hypotenuse would be 10 (miles). The side, or distance, that Beth has traveled is 8. So as this is a typical variation of a 3x4x5 triangle Beth will have traveled  6 miles.

T/F Solution that can be analytically obtained but is not an actual answer to the equation often due to restrictions in the type of function such as a negative in the log

This statement is true.

Because, Sometimes, when solving an equation using analytical methods, we may arrive at a solution that is mathematically correct but is not a valid answer due to the restrictions in the type of function used.

For example, if a negative value appears in the logarithmic function, the solution may not be valid because the logarithmic function is only defined for positive values.

In such cases, we need to go back and recheck our work and take into account the restrictions of the function to arrive at a valid solution.

Sometimes when solving an equation analytically, the resulting solution may not be a valid answer due to restrictions in the domain of the function.

For example, if we solve an equation involving a logarithmic function, we may end up with a negative value inside the logarithm, which is not defined for real numbers. In such cases, the solution obtained analytically is not a valid answer to the equation.

Another example is when solving for the roots of a quadratic equation using the quadratic formula, we may obtain complex solutions even though we are only interested in real solutions.

Thus, it is important to always check the solutions obtained to ensure that they satisfy any domain or range restrictions of the functions involved in the equation.

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Answer:

1 foot

Step-by-step explanation:

5+(0.5*4)-6 = 1

The x- and y-coordinates of the center of mass are; (20, 0)

The center of mass is the location where the sum of the relative position of the masses in a mass distribution is zero. It is the point where force can be applied on the distributed mass without causing a rotation of the system.

The mas of the steel plate = 800 g = 0.8 kg

The base length of the isosceles triangular plate = 20 cm = 0.2 m

The height of the isosceles triangular plate = 30 cm = 0.3 m

Considering a small strip of height, dx and width, I, we get

Area of small strip, dA = I·dx

Density of the plate for a unit thickness, ρ = M/A

Density of the small strip of mass dm = dm/dA

Considering the density of the plate as uniform, we get;

\(\displaystyle {\frac{dm}{dA} =\frac{M}{A}\)

Therefore;

\(\displaystyle {dm=\frac{M}{A}\times dA}\)

The area of the triangular plate, A = (1/2) × 0.2 m × 0.3 m = 0.03 m²

Mass of the plate, M = 0.8 kg

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx}\)

The width of the small strip, I, located at a distance x from the vertex of the triangular plate, using similar triangles, indicates;

\(\dfrac{I}{20} = \dfrac{x}{30}\)

\(I=20\times \dfrac{x}{30} = \dfrac{2}{3} \cdot x\)

Therefore;

\(\displaystyle {dm=\frac{0.8}{0.03}\times I\cdot dx} = \frac{0.8}{0.03}\times \dfrac{2}{3} \cdot x\cdot dx}\)

The center of mass, \(x_{cm}\), can be obtained with the formula; \(\displaystyle {x_{cm} = \dfrac{1}{M} \cdot \int\limits {x} \, dm }\)

Therefore; \(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx }\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \cdot \int\limits {x} \cdot \frac{0.8}{0.03} \cdot \frac{2}{3}\cdot x\, dx } = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx\)

\(\displaystyle {x_{cm} = \dfrac{1}{0.8} \times \frac{0.8}{0.03} \times \frac{2}{3}\cdot \int\limits^3_0 {x^2} \, dx = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0\)

\(\displaystyle {x_{cm} = \frac{200}{9} \cdot \left[\frac{x^3}{3} \right]^{0.3}_0=\frac{200}{9} \times \frac{0.027}{3} =0.2\)

The location of the x-coordinate center of mass, \(x_{cm}\) = 0.2 m = 20 cm from the vertex, which is the same location as the x-coordinate of the centroid of the plate of uniform density.

The plate is symmetrical about the x-axis, therefore, the y-coordinate of the center of mass is along the x-axis, which is \(y_{cm}\) = 0

The coordinate of the center of mass = (0.2, 0)

Part of the question requires the location of the coordinate of the center of mass of the triangular plate

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To find the particular solution of the differential equation x²y" - xy + y = 6x ln x using variation of parameters, we first need to find the Wronskian of the homogeneous solutions.

The homogeneous solutions are Yc = C₁x + C₂ ln(x), where C₁ and C₂ are constants. The Wronskian, denoted as W(x), is given by the determinant: W(x) = |x ln(x)|= |1 1/x |. Calculating the determinant, we get: W(x) = x(1/x) - ln(x)(1) = 1 - ln(x). Next, we find the particular solution using the variation of parameters formula: yp = -Y₁ ∫(Y₂ * g(x)) / W(x) dx + Y₂ ∫(Y₁ * g(x)) / W(x) dx. where Y₁ and Y₂ are the homogeneous solutions, and g(x) is the non-homogeneous term (6x ln x). Substituting the values, we have: yp = -(C₁x + C₂ ln(x)) ∫((C₁x + C₂ ln(x)) * 6x ln x) / (1 - ln(x)) dx + (C₁x + C₂ ln(x)) ∫(x * 6x ln x) / (1 - ln(x)) dx. Integrating these expressions will yield the particular solution. However, due to the complexity of the integrals involved, it is not possible to provide an exact expression in this format.

Therefore, the particular solution using variation of parameters is given by integrating the above expressions and simplifying.

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Kaelyn wants to use yarn to make hats and scarves. Each hat requires 0.2 kg of yarn, while each scarf requires 0.1 kg. She plans to make 333 times more scarves than hats and use a total of 555 kg of yarn.

Let h be the number of hats and s be the number of scarves Kaelyn makes. The first equation represents the total yarn used, which is 0.2h (for hats) plus 0.1s (for scarves) equal to 555 kg. The second equation represents the ratio of scarves to hats, where s is 333 times greater than h, i.e., s = 333h. So the system of equations is:

0.2h + 0.1s = 555

s = 333h

Kaelyn plans to use her yarn to make hats and scarves, with hats requiring 0.2 kilograms of yarn and scarves needing 0.1 kilograms. She aims to make 333 times more scarves than hats using a total of 555 kilograms of yarn.

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Using the z table, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

In the given question,

We have to find that the probability that a standard normal random variable will be between 0.3 and 3.2 .

We firstly learn about a standard normal random variable which is expressed with a mean and standard deviation.

Since we have to find the probability that a standard normal random variable will be between 0.3 and 3.2 .

So The probability should be

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

From the standard value of z

P(0.3<z<3.2)=0.9993−0.6179

Simplifying

P(0.3<z<3.2)=0.3814

Hence, the probability that a standard normal random variable will be between 0.3 and 3.2 is 0.3814.

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Answer:

my guess is 1?

Step-by-step explanation:

I just guess

(a) The total work done in stretching the 450 mm-long sheet with a cross-sectional area of 320 mm² until θ = 22° is approximately 6.84 kJ.

(b) The maximum stress before necking begins is approximately 397.89 MPa.

(a) To find the total work done, we need to integrate the area under the stress-strain curve.

Given: Length of the sheet (L) = 450 mm Cross-sectional area (A) = 320 mm² True-stress-true-strain curve equation: σ = 750 × ε^0.35

To calculate the work done, we can use the equation: Work = ∫σ dε

First, we need to find the limits of integration for strain (ε). Since the material is stretched until θ = 22°, we can convert this angle to strain using the equation: ε = tan(θ)

Therefore, ε = tan(22°) ≈ 0.404

Next, we can calculate the work done by integrating the stress-strain equation over the strain range: Work = ∫σ dε = ∫(750 × ε^0.35) dε

Evaluating the integral, we get: Work = [(750/0.86) × (ε^1.35)] | from 0 to 0.404 ≈ (750/0.86) × [(0.404)^1.35 - 0] ≈ 6.84 kJ

Therefore, the total work done is approximately 6.84 kJ.

(b) The maximum stress before necking begins can be determined by finding the stress corresponding to the strain value at necking.

Given the true-stress-true-strain curve equation, we can substitute the strain value at necking into the equation to find the corresponding stress: ε_necking = 0.404

σ_necking = 750 × (ε_necking)^0.35 ≈ 397.89 MPa

Therefore, the maximum stress before necking begins is approximately 397.89 MPa.

(a) The total work done in stretching the 450 mm-long sheet with a cross-sectional area of 320 mm² until θ = 22° is approximately 6.84 kJ.

(b) The maximum stress before necking begins is approximately 397.89 MPa.

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Answer:

I think it is 20%.

Step-by-step explanation:

35 * 0.2 = 7

35 + 7 = 42

Answer:

  j = 19.6

  k = 25.9

  J = 49°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationships between sides and angles in a right triangle.

The given side is opposite the given angle. We want to find the other acute angle and the missing sides: the hypotenuse, and the adjacent side. The relations involving the opposite side are ...

  Sin = Opposite/Hypotenuse   ⇒   Hypotenuse = Opposite/Sin

  Tan = Opposite/Adjacent   ⇒   Adjacent = Opposite/Tan

Of course, the acute angles in a right triangle are complementary, so we can use that fact to find the missing angle.

  Hypotenuse = Opposite/Sin

  IJ = 17/sin(41°) ≈ 25.9

  Adjacent = Opposite/Tan

 IK = 17/tan(41°) ≈ 19.6

  Angle J = 90° -41° = 49°

In summary, ...

  j = 19.6

  k = 25.9

  J = 49°

Answer:

The number that goes in the green box would be -3y^2

Step-by-step explanation:

There are no like term with the same variable y with an exponent of 2.

-Hope this helped

The given expression is,

→ -3y² - 3y + 4y + 100

Simplifying the given expression,

→ -3y² - 3y + 4y + 100

→ -3y² + (-3y + 4y) + 100

→ -3y² + y + 100

Hence, answer is -3y² + y + 100.

Answer:

C.

(I double-checked on m4thway, so don't worry. I'm sure i'm right.)

Hope this helped!! :) Now, good luck !!