The equation of the line of best fit of a scatter plot is y = 8x − 1. What is the slope of the equation?

Answer:

D.

Step-by-step explanation:

The answer is 3.

Bonus: Here is a fun challenge, try to decipher what Im saying here. (Use an online binary website.)

01001001 01100110 00100000 01111001 01101111 01110101 00100000 01100110 01101001 01101110 01100100 00100000 01101111 01110101 01110100 00100000 01110111 01101000 01100001 01110100 00100000 01110100 01101000 01101001 01110011 00100000 01110011 01100001 01111001 01110011 00101100 00100000 01001001 00100000 01110111 01101001 01101100 01101100 00100000 01100110 01101111 01101100 01101100 01101111 01110111 00100000 01111001 01101111 01110101 01110010 00100000 01100010 01110010 01100001 01101001 01101110 01101100 01111001 00100000 01100001 01100011 01100011 01101111 01110101 01101110 01110100 00100000 00111010 00101001

Answer:

$20.00 is the correct answer

Step-by-step explanation:

I promise this is correct

The inverse function of f(x) = 5x - 3 is found by switching x and y to solve for x, resulting in the inverse function f⁻¹(x) = (x + 3) / 5. This process is part of understanding function transformations that change a function's graph.

Finding the Inverse Function

Find the inverse function of f(x) = 5x - 3. To find the inverse, we need to switch the roles of x and y. So we first write  y = 5x - 3. We then solve this equation for x to get x as a function of y. Performing the steps:

Add 3 to both sides: y + 3 = 5x.

Divide both sides by 5: (y + 3) / 5 = x.

This new equation x = (y + 3) / 5 represents the inverse function. To use the proper notation, we replace y with f⁻¹(x) and x with y, giving us f⁻¹(x) = (x + 3) / 5.

Understanding Function Transformations

When considering transformations such as f(-x) or f(2x), these changes to the independent variable result in specific alterations to the graph of the function, such as reflections across the y-axis or horizontal shrinkage by half.

Answer:

2%

Step-by-step explanation:

Answer:

The answer is D. 52

Step-by-step explanation:

edg 2020

The horizontal distance between the balloon and the ship can be calculated using the tangent function is 1639 feet.

To find the horizontal distance between the balloon and the ship, we can use the tangent function in trigonometry. Let's denote the horizontal distance as x, and the distance between the balloon and the ship along the ground as y.

We have the angle of depression (21°) and the altitude of the balloon (2,000 feet). We can set up the equation:

tan(21°) = y / (2,000 + y)

Now, we need to solve for y:

tan(21°) * (2,000 + y) = y

y * tan(21°) = 2,000 * tan(21°) - y * tan(21°)

y * (1 - tan(21°)) = 2,000 * tan(21°)

y = (2,000 * tan(21°)) / (1 - tan(21°))

Now, calculate the value:

y ≈ (2,000 * 0.364) / (1 - 0.364)

y ≈ 728 / 0.636

y ≈ 1,148.17

Now that we have the value of y, we can find the horizontal distance x using the Pythagorean theorem:

[tex]x^2 + y^2 = (2,000)^2\\x^2 + (1,148.17)^2 = 4,000,000\\x^2 = 4,000,000 - 1,319,441.98\\x^2 = 2,680,558.02\\x = 1,638.84 (rounded)[/tex]

The horizontal distance between the balloon and the ship is approximately 1,639 feet.

Horizontal distance = height of balloon / tangent(angle of depression) = 2000 / tan(21°) ≈ 5243.87 feet.

To find the horizontal distance between the balloon and the ship, we can use trigonometry, specifically the tangent function.

Let's denote:

- [tex]\( h \)[/tex] as the height of the balloon above the ground (2,000 feet in this case).

- [tex]\( \theta \)[/tex] as the angle of depression (the angle formed between the line of sight from the balloon to the ship and the horizontal ground).

Given that the angle of depression [tex]\( \theta \)[/tex] is 21°, we can use the tangent function:

[tex]\[ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \][/tex]

In this case, the opposite side is the height of the balloon above the ground (2,000 feet), and we want to find the adjacent side, which represents the horizontal distance between the balloon and the ship.

So, we have:

[tex]\[ \tan(21°) = \frac{2000}{\text{horizontal distance}} \][/tex]

To find the horizontal distance, we rearrange the equation:

[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \][/tex]

Now, we can calculate this:

[tex]\[ \text{horizontal distance} = \frac{2000}{\tan(21°)} \approx \frac{2000}{0.381} \approx 5243.87 \text{ feet} \][/tex]

So, the horizontal distance between the balloon and the ship is approximately 5243.87 feet.

Answer:

Step-by-step explanation:

"A system of linear equations" covers a lot of territory. In Algebra 1, it usually means two linear equations in two unknowns. Each of those equations will graph as a line on a coordinate plane.

A solution is a point that satisfies all the equations. That is, it is a point that is on all the lines described by the system of equations.

The geometry of lines on a plane comes into play with regard to solutions.

Answer:

The area of rectangle =21 sq units .

Step-by-step explanation:

Given the four vertices of rectangle are 1+4i,-2+4i, -2-3i and 1-3i.

Consider ABCD is  a rectangle and its vertices are 1+4i,-2+4i,-2-3i and 1-3i.

First we find sides of rectangle

AB=vertices of B- vertices of A

AB= -2+4i-(1+4i)=-3

BC= Vertices of C - vertices of B

BC=-2-3i-(-2+4i)=-7i

Length of BC=[tex]\sqrt{(-7)^2}[/tex]=7 ( Magnitude always positive)

CD= vertices of D- vertices of C

CD= 1-3i-(-2-3i)=3

Length of CD= [tex]\sqrt{3^2}[/tex]=3 ( Magnitude  always positive)

DA= vertices of A - vertices of D

DA= 1+4i-(1-3i) =7i

Length of DA= [tex]\sqrt{7^2}[/tex]=7 ( Magnitude always positive)

AB=CD and DA= BC

Length BC=7 units

Breadth AB=3 units

Area of the rectangle = [tex]length\times breadth[/tex]

Area of rectangle =[tex]AB\times BC[/tex]

The [tex]95\%[/tex] confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.

Further Explanation:

Explanation:

The formula for confidence interval can be expressed as follows,

[tex]\boxed{{\text{Confidence interval}}=\left( {\overline X  \pm ME} \right)}[/tex]

ME represents the Margin of Error.

The confidence interval has two limits.

(1). Upper Limit

(2). Lower Limit

The upper limit can be calculated as follows,

[tex]{\text{Upper limit}}=\left( {X + ME}\right)[/tex]

The lower limit can be calculated as follows,

[tex]{\text{Lower limit}} = \left( {X - ME}\right)[/tex]

The given confidence interval is [tex]\left( {6.93,11.45}\right).[/tex]

The upper limit of the confidence interval is 11.45.

The lower limit of the confidence interval is 6.93.

The 95\% confidence interval for the population mean is [tex]\left( {6.93,11.45}\right)[/tex] means that there are [tex]95\%[/tex] chances of the population mean lies in the interval.

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949

2. Learn more about standard normal distribution https://brainly.com/question/13006989

3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: Z-score, Z-value, confidence interval, confidence limit, 95 percent, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.

Answer: The expression for the given statement is [tex]t-7[/tex]

Step-by-step explanation:

We are given a statement:

7 less than a number t

Let the number be considered as 't'

'Less' in the above statement means subtraction operation.

The numerical value written before the 'less' operation is written after in the expression.

Thus, the expression for the given statement is [tex]t-7[/tex]

The algebraic expression for '7 less than a number t' is t - 7. This represents taking the number t and subtracting 7 from it.

The question requires an algebraic expression. '7 less than a number t' translates to t - 7 in algebraic terms. The phrase 'less than' is a clear indication to subtract in math context. So, take the number t and subtract 7 from it, hence, t - 7 is our answer. This is a common way to express relative quantities and operations in algebra.

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Final answer:

To solve for 'r' in the given equation, add 9s to both sides and then divide by 4, resulting in r = (9s + K) / 4.

Explanation:

To solve for r in the equation 4r - 9s = K, we need to isolate r on one side of the equation. Here's how we can do this:

The measure of the subtended angle by the arc is approximately 1.20 radians or 68.75 degrees. This is determined using the formula θ = s/r to find the subtended angle.

To find the subtended angle, we need to use the formula θ = s/r, where s is the arc length and r is the circle's radius. The area of the circle with radius r, is πr², and given that it is 78.5 cm², we first need to find the radius. By solving the area equation, we get r = √(78.5/π), or approximately 5.00 cm. Using the radius in the angle formula (θ = 6/5.00), we get θ to be approximately 1.20 radians. However, if the question is asking for the result in degrees, we need to convert the result from radians to degrees by using the conversion factor 180/π. Thus, θ = 1.20 * (180/π) which gives approximately 68.75 degrees.

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Calculate the circle's radius first from the given area. Then, find the circumference of the circle and compare the arc length to the circumference to obtain the subtended angle. Therefore, the subtended angle is approximately 68.79 degrees.

The subject of this question falls under the domain of geometry in Mathematics, where we identify the measure of angle subtended by a certain arc. In order to achieve this, we must understand that a complete circle with a 360-degree angle covers an arc length equivalent to its circumference. If we know the radius of the circle, calculated from the area, we can compare the known arc length to the circumference of the circle to find the angle subtended.

First, we find the radius using the given circle area using the formula [tex]A=\pi r^2[/tex], which gives r= √(A/π). So r= √(78.5 cm² / 3.14) =approx. 5cm. Now, the full circumference of a circle (C) is 2πr, which gives [tex]C = 2*3.14*5 cm = 31.4 cm.[/tex] The full angle covered by the circumference is 360 degrees. To find the angle subtended by an arc of length 6cm, we calculate as follows: (6 cm / 31.4 cm) * 360 degrees = approx. 68.79 degrees.

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Answer:

Option C. Obtuse

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

If [tex]c^{2}=a^{2} +b^{2}[/tex] ----> is a right triangle

If [tex]c^{2}>a^{2} +b^{2}[/tex] ----> is a obtuse triangle

If [tex]c^{2}<a^{2} +b^{2}[/tex] ----> is an acute triangle

where

c is the greater side

Verify

[tex]c^{2}=26^{2}= 676[/tex]

[tex]a^{2} +b^{2}=7^{2} +24^{2}=625[/tex]

therefore

[tex]676>625[/tex]

[tex]c^{2}>a^{2} +b^{2}[/tex] -----> is a obtuse triangle

Answer:

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