Task 1: Two Brothers Race
31
2.5
Distance (Miles),
2
81.5
1
0.5
0
5
10 15 20 25 30
Time (Minutes)
After running 10 minutes, Ryan was...
winning
losing
tied
Explain your thinking.
√
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The expression for the probability density function of the Weibull distribution will be: f(x) = k * x^(k-1) * e^(-x^k)

The expression for the probability density function (pdf) of a Weibull distribution is given by:

f(x) = k * x^(k-1) * e^(-x^k)

where:

x is the random variable

k is the shape parameter, which determines the shape of the distribution

e is the base of the natural logarithm

The shape parameter can take on any positive value, and the distribution is typically characterized by a shape that is either increasing or decreasing, depending on the value of k.

If the value of the k is less than 1, the distribution has a decreasing hazard rate, indicating that the failure rate decreases over time.

If the value of the k is greater than 1, the distribution has an increasing hazard rate, indicating that the failure rate increases over time.

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The final solution for the given equation is ln(f(x)) = ln{x²(31n(x) - 1) + 18[(3x-In(x))(3x+In(x))] + 9x + 18 In(x²))

The given equation is f(x) = x²(31n(x) - 1) 18 9x²-In(x) 27 + 18 In(x) 9(x + 2x In(x)).

Explanation:

We need to simplify the given equation, f(x) = x²(31n(x) - 1) 18 9x²-In(x) 27 + 18 In(x) 9(x + 2x In(x))

We have 2x In(x) = In(x²), substitute it in the given equation.

So,

f(x) = x²(31n(x) - 1) + 18(9x²-In(x) + 2In(x²)) + 9x + 18 In(x²)

Factorize 9x²-In(x), 9x²-In(x) = (3x-In(x))(3x+In(x))

So, f(x) = x²(31n(x) - 1) + 18[(3x-In(x))(3x+In(x))] + 9x + 18 In(x²)

Here we have to take natural logarithm of the above equation to obtain the final answer. Taking natural logarithm on both sides of the equation, we get

ln(f(x)) = ln{x²(31n(x) - 1) + 18[(3x-In(x))(3x+In(x))] + 9x + 18 In(x²))}

So, this is the final answer:

ln(f(x)) = ln{x²(31n(x) - 1) + 18[(3x-In(x))(3x+In(x))] + 9x + 18 In(x²))

Conclusion: The final answer for the given equation is ln(f(x)) = ln{x²(31n(x) - 1) + 18[(3x-In(x))(3x+In(x))] + 9x + 18 In(x²))

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Answer:

y = 5x + 11

Step-by-step explanation:

- first rearrange -5x + y = 2 and you'll have y = 5x + 2

- the slopes of parallel lines are equal so the slope of the line is 5

so far we have y = 5x + b

- to get b, replace the values in the equation by the values of the given point

(1) = 5(-2) + b

- rearrange and calculate, b = 11

y = 5x + 11

Given

A = (3.5, 2.2)

B = (1.5, -4.8)

Procedure

A midpoint is a point on a line segment that divides the segment into two equal segments.

Answer:

-------------------------------

John types at a rate of 16 words per minute.

With the stable rate, in 4 minutes he types:

The range of the function y = 3√(x) + 8 is [8, ∞).

To find the range of the function y = 3√(x) + 8,
Identify the base function:

In this case, it's the square root function √(x).
Determine the transformations:

The function is vertically stretched by a factor of 3, and then vertically shifted up by 8 units.

So the transformed function is y = 3√(x) + 8.
Find the range of the base function:

For the square root function, the range is all non-negative real numbers or [0, ∞).
Apply the transformations to the range:

First, vertically stretch the range by a factor of 3: [0 × 3, ∞ × 3) = [0, ∞).

Then, vertically shift the range up by 8 units: [0 + 8, ∞ + 8) = [8, ∞).

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The missing number in the median set is 6.

We are given that;

Median set=18

Now,

To find the missing number, you need to know the number of elements in the set and their order. The median is the middle value of a set when it is arranged in ascending or descending order. If the set has an odd number of elements, the median is the exact middle value. If the set has an even number of elements, the median is the average of the middle two values.

For example, if the set is {2, 4, 6, 8, 10}, the median is 6 because it is the middle value. If the set is {3, 5, 7, 9}, the median is (5 + 7) / 2 = 6 because it is the average of the middle two values.

Therefore, by median the answer will be 6.

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The ball hits the ground approximately 29.26 meters away from the player.

(a) To find the maximum height above the ground that the ball reaches, we can analyze the vertical motion of the ball. Let's consider the upward direction as positive.

Initial vertical velocity (v0y) = 18 m/s * sin(32°)

v0y = 9.5 m/s (rounded to one decimal place)

Acceleration due to gravity (g) = -9.8 m/s^2 (downward)

Using the kinematic equation for vertical motion:

v^2 = v0^2 + 2aΔy

At the maximum height, the final vertical velocity (v) is 0, and we want to find the change in height (Δy).

0^2 = (9.5 m/s)^2 + 2(-9.8 m/s^2)Δy

Solving for Δy:

Δy = (9.5 m/s)^2 / (2 * 9.8 m/s^2)

Δy ≈ 4.61 m (rounded to two decimal places)

Therefore, the maximum height above the ground that the ball reaches is approximately 4.61 meters.

(b) To find the total time the ball is in the air before it hits the ground, we can analyze the vertical motion. We need to find the time it takes for the ball to reach the ground from its initial height of 1 meter.

Using the kinematic equation for vertical motion:

Δy = v0y * t + (1/2) * g * t^2

Substituting the known values:

-1 m = 9.5 m/s * t + (1/2) * (-9.8 m/s^2) * t^2

This is a quadratic equation in terms of time (t). Solving this equation will give us the time it takes for the ball to hit the ground. However, since we are only interested in the positive time (when the ball is in the air), we can ignore the negative root.

The positive root of the equation represents the time it takes for the ball to hit the ground:

t ≈ 1.91 s (rounded to two decimal places)

Therefore, the ball is in the air for approximately 1.91 seconds.

(c) To find how far from the player the ball hits the ground, we can analyze the horizontal motion of the ball. Let's consider the horizontal direction as positive.

Initial horizontal velocity (v0x) = 18 m/s * cos(32°)

v0x ≈ 15.33 m/s (rounded to two decimal places)

The horizontal motion is not influenced by gravity, so there is no horizontal acceleration.

Using the formula for distance traveled:

Distance = v0x * t

Substituting the known values:

Distance = 15.33 m/s * 1.91 s

Distance ≈ 29.26 m (rounded to two decimal places)

Therefore, the ball hits the ground approximately 29.26 meters away from the player.

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I think your answer would be 64, if im wrong, im sorry! Hope this helps! :D

Answer:

Basically the statment is saying that in order to get P (A and B) you have to multiply P(A) by P(B).

Answer:

I think it means the probability of selecting (AnB) is equal to Probability of selecting A × probability of selecting B

Step-by-step explanation:

Please rate bainliest if you think I deserve

Answer:

a) adjacent angles, complementary angles

b) vertical angles, congruent angles

c) supplementary angles, adjacent angles

d) supplementary angles, adjacent angles

Step-by-step explanation:

Adjacent angles are angles that share a common vertex, ( usually angles that are right next to each other )

Complementary angles are angles that form a 90 degree angle  (  right angle )

Supplementary angles are angles that form a straight line

Vertical angles are angles that are vertically aligned with each other ( vertical angles are congruent )

The point on the graph where the tangent plane is parallel is (52, 52, -5382).

What is the tangent plane?

The surface that contains all tangent lines of the curve at a point, $P$, that lies on the surface and passes through the point is represented by the tangent plane. We discovered earlier in our talks of derivatives and tangent lines that we can use tangent lines to mimic the behavior of a graph. We may employ tangent planes for a similar reason now that we're working with multivariable functions and three-dimensional coordinate systems.

Here, we have

Given: Let P be the tangent plane to the graph of g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286). Let f(x, y) = 26 – x² - y².

We have to find the point on the graph where the tangent plane is parallel.

Let P be the tangent plane to the graph z = g(x, y) = 26 – 13x² – 26y² at the point (4, 2, –286).

φ(x,y,z) = 13x² + 26y² + z - 26

Δφ = 26xi + 52yj + k

Δφ(4, 2, –286) = 104i + 104j + k

Then,

P: 104(x-4) + 104(y-2)+1(z+286) = 0

104x + 104y + z = 338...(1)

Now, Let

ψ(x,y,z) =  x² + y² + z - 26

Δψ = 2xi + 2yj + k

Let (x₀,y₀,z₀) be the point of the graph z = f(x,y) = 26 – x² - y² where the tangent plane in the plane is parallel to equation (1).

Δψ (x₀,y₀,z₀)  =  (2x₀,2y₀,1)

= 2x₀/104 = 2y₀/104 = 1/1

x₀ = 52 = y₀

Now, z₀ = 26 – x₀² - y₀² = 26 – 52² - 52²= -5382

Hence,  the point on the graph where the tangent plane is parallel is (52, 52, -5382).

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Answer:

B.

Step-by-step explanation:

they are congruent because they are the same shape and a 90° rotation about the origen counterclockwise will may the shape in Quadrent 2 onto the shape in Quadret 3

Answer:

2.80

Step-by-step explanation:

Answer= 2.8

Step-by-step explanation:

y+5.41=8.21

y= 8.21-5.41

y= 2.8

Answer:

120 degrees

Step-by-step explanation:

The expression sin(Tan⁻¹(-1)) evaluates to √2/2.

The trigonometric expression is sin(Tan⁻¹(-1)). To evaluate this expression, we need to understand the principal value of the inverse tangent function, Tan⁻¹.

The principal value of Tan⁻¹ is the angle whose tangent is equal to the given value. In this case, Tan⁻¹(-1) represents the angle whose tangent is -1. We know that the tangent function is negative in the second and fourth quadrants.

In the second quadrant, the reference angle whose tangent is 1 is π - π/4, which is 3π/4. In the fourth quadrant, the reference angle is -π/4.

Since the expression is sin(Tan⁻¹(-1)), we need to find the sine of the angle whose tangent is -1. The sine function is positive in the second quadrant, so the sine of 3π/4 is √2/2.

Therefore, sin(Tan⁻¹(-1)) is equal to √2/2.

In summary, the expression sin(Tan⁻¹(-1)) evaluates to √2/2, which represents the sine of the angle whose tangent is -1 in the second quadrant.

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Answer:

2

Step-by-step explanation:

(y1-y2)/(x1-x2) = (-6-6)/(-4-2) = -12/-6 = 2

hope it helps

Line j is the transversal, and ∠1 and ∠2 are alternate exterior angles.

Line j and its Nature:

Line j is a line that intersects two other lines, creating angles at the intersection points. In this case, it intersects two other lines. Line j could be either a transversal (a line that intersects two or more lines) or a perpendicular bisector (a line that divides another line segment into two equal parts at a right angle).

∠1 and ∠2:

Alternate Exterior Angles: These are pairs of angles that are on opposite sides of the transversal (line j in this case) and outside the two intersected lines. When a transversal intersects two parallel lines, alternate exterior angles are congruent (equal in measure). This option aligns with the description of ∠1 and ∠2 being alternate exterior angles.

Corresponding Angles: These are pairs of angles that are on the same side of the transversal but are in different positions relative to the two intersected lines. Corresponding angles are congruent when the transversal intersects two parallel lines, but this is not the case in the given options.

Perpendicular Bisector and Corresponding Angles: This combination doesn't accurately describe the situation of angles ∠1 and ∠2 being alternate exterior angles.

Therefore, the correct choice is: Line j is the transversal, and ∠1 and ∠2 are alternate exterior angles.

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Answer:

C

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below

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The dimensions of the poster with the smallest area are as follows: The width is 20 cm, and the height is 16 cm.

To determine these dimensions, we need to consider the area of the printed material on the poster, which is fixed at 388 square centimeters. Let's assume the width of the printed material is x cm.

Since the side margins are each 2 cm, the total width of the poster (including the margins) becomes x + 2 cm + 2 cm = x + 4 cm.

Similarly, the total height of the poster is x + 4 cm as well because the top and bottom margins are both 4 cm.

To calculate the area of the entire poster, we multiply the width by the height: (x + 4 cm) * (x + 4 cm) = (x + 4)^2 cm^2.

According to the problem, the area of the printed material is 388 square centimeters. Therefore, we have the equation (x + 4)^2 cm^2 = 388 cm^2.

Solving this equation, we find x + 4 = 19 cm, which means x = 15 cm.

Hence, the dimensions of the poster, width is 15 cm + 4 cm = 19 cm, and the height is also 15 cm + 4 cm = 19 cm.

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a and b.

a unit rate has a certain value per 1 thing

Answer:

The answer is

c=-4+3b/a-1

The samples of size n = 2 that can be drawn from this population is 28

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

Population, N = 8

Sample, n = 2

The samples of size n = 2 that can be drawn from this population is calculated as

Sample = N!/(n! * (N - n)!)

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

Sample = 8!/(2! * 6!)

Evaluate

Sample = 28

Hence, the number of samples is 28

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Complete question

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

How many samples of size n = 2 can be drawn this population?

Answer:

y−3=−13(x−1), which we can rearrange to get y=−13x+103.

The most likely mean for the sample distribution is option c. negatively skewed.

Based on the given information, we know that the mean (M) is less than both the median and the mode. This suggests that the distribution is skewed to the left (negatively skewed), with a long tail on the left side of the distribution.

The mean of a sample distribution is the average value of all the observations or measurements in the sample. It is calculated by adding up all the values in the sample and dividing the sum by the total number of observations in the sample.

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Depends on the specific values of x, y, and the step size h used in the approximation.

What is differentiation ?

Differentiation is a concept in calculus that involves finding the rate of change of a function with respect to one of its variables. It is represented by the symbol ∂/∂x or ∂/∂y or ∂/∂t (where x, y and t are the variables of the function). The process of differentiation allows us to find the slope of a curve, the instantaneous rate of change, and the maximum or minimum points of a function.

The difference between dy and δy can be determined by subtracting dy from δy. The accuracy of dy in approximating δy depends on the specific values of x, y, and the step size h used in the approximation.

For example, if we consider dy = (f(x+h, y+k)-f(x,y))/h, and δy= f'(x)*δx.

Where f(x,y) is the given function for the system of differential equations and f'(x) is the derivative of the function f(x,y) with respect to x.

so the difference between dy and δy is δy-dy= f'(x)*δx - (f(x+h, y+k)-f(x,y))/h.

The accuracy of dy in approximating δy can be determined by taking the limit of the difference as h approaches 0.

In the end, it all depends on the specific problem and desired level of accuracy.

Depends on the specific values of x, y, and the step size h used in the approximation.

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Given:

The number of 100.

To find:

The given number as an exponential expression with 10 as the base.

Solution:

We have,

Given number = 100

It can be written as

\(100=10\times 10\)

\(100=10^{1+1}\)                   \([\because a^m\cdot a^n=a^{m+n}]\)

\(100=10^2\)

Here, base is 10 and exponent is 2.

Therefore, the given number can be written as \(10^2\).

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

C. p -> q

Step-by-step explanation:

Just did this on Edge2020. Hope this helps :)