a street light is at the top of a pole that is 15 feet tall. a woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. how fast is the length of her shadow moving when she is 25 ft from the base of the pole?

Step-by-stepAnswer:

∠4 and ∠5

Step-by-step explanation:

Both angels seem to add up to 180°

A multiplier of 1.2 means the value is multiplied or increased by a factor of 1.2.

A multiplier is a term used to represent a factor by which a value is multiplied or increased. It is a numeric value that indicates the extent of the increase or expansion of a given quantity. Multiplication by a multiplier results in scaling or changing the magnitude of the original value.

A multiplier of 1.2 indicates that a value will be increased by 20% or multiplied by a factor of 1.2. This means that when the multiplier is applied to the original value, the resulting value will be 1.2 times the original.

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Based on this estimation method, the closest answer choice to the number of people that arrive at the box office during the time interval Osts 202 is (B) 150

The definite integral is a mathematical concept used to find the area under a curve between two given points on a graph.

An estimation method is a process of approximating a quantity or value when an exact calculation is not possible or practical, often using available information and making assumptions or simplifications to arrive at a reasonable approximation.

According to the given information:

Unfortunately, the graph mentioned in the question is not provided. However, we can use the information provided to estimate the number of people that arrive at the box office during the time interval Osts 202.

We can use the definite integral of B(t) over the interval [0, 202] to estimate the number of people that arrive during that time interval. This is given by:

∫[0,202] B(t) dt

Since we don't have the graph of B(t), we cannot calculate the definite integral exactly. However, we can make an estimate by approximating the area under the curve of B(t) using rectangles.

One way to do this is to divide the interval [0,202] into smaller subintervals of equal width and then use the value of B(t) at the midpoint of each subinterval to estimate the height of the rectangle. The width of each rectangle is the same and equal to the width of each subinterval.

Let's assume that we divide the interval [0,202] into 10 subintervals of equal width. Then, the width of each subinterval is:

Δt = (202 - 0) / 10 = 20.2

We can then estimate the height of each rectangle using the value of B(t) at the midpoint of each subinterval. Let's call the midpoint of the ith subinterval ti:

ti = (i - 0.5)Δt

Then, the height of the rectangle for the ith subinterval is:B(ti)

We can then estimate the area under the curve of B(t) over each subinterval by multiplying the height of the rectangle by its width. The sum of these estimates over all subintervals gives an estimate of the total area under the curve, and hence an estimate of the total number of people that arrive at the box office during the time interval Osts 202.

The estimate of the total number of people is given by:

∑[i=1,10] B(ti)Δt

We can use a calculator to compute this sum. Since we don't have the graph of B(t), we cannot calculate the sum exactly. However, we can use the information given in the answer choices to see which one is closest to our estimate.

Based on this estimation method, the closest answer choice to the number of people that arrive at the box office during the time interval Osts 202 is (B) 150

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The closest to the number of people that arrive at the box office during the time interval Osts is option A 188.

Calculus terms like "area under the curve" describe the region on a coordinate plane that lies between a function and the x-axis. Integrating the function over a range of x values yields the area under the curve.

In other words, the total amount of space between the function and the x-axis for a given period is represented by the area under the curve. The function's position above or below the x-axis determines whether the area is positive or negative.

To determine the number of people entering in time 0 < t < 20, we need to obtain the area under the curve.

The curve can be divided into two triangles and one rectangle thus:

Area of Rectangle = Length * Breadth = 15 * 5 = 75

Area of Blue Triangle = 1/2 * Base * height = 1/2 * 15 * 10 = 75

Area of Green Triangle = 1/2 * Base * height = 1/2 * 5 * 15 = 75/2

The total area is thus,

75 + 75 + 75/2 = 187.5 = 188

Hence. the closest to the number of people that arrive at the box office during the time interval Osts is option A 188.

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The complete question is:

Answer:

  (a)  Point R is at (−40, 40), a distance of 70 units from point Q

Step-by-step explanation:

Point Q is on the same horizontal line as P, but is 30 -(-40) = 70 units away. If point R is 70 units above point Q, its y-coordinate will be -30 +70 = 40.

Point R is at (−40, 40), a distance of 70 units from point Q

Answer:

13 storage boxes is the least

Step-by-step explanation:

What we know:

- We have 127 cd's

- We have boxes only able to hold 10

What we need to figure out:

- how many boxes at the least are we going to need

Step 1: Divide

Since we need to figure out how many times 10 goes into 127 we divide 127 by 10 so...

127/10 = 12 with a remainder of 7.

Step 2: Figure out the remainder

Since there are seven left over and you cannot put them in boxes already being used then we put them in a new box, not yet used. That would make it a total of 13 boxes needed at the least.

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Answer:

16 inches.

PS:

Can I have Brainliest?

Answer:

Your answer is : 16 inches

Step-by-step explanation:

12 ÷ 3 = 4

4 inches for 1/4 of the year

= 4 × 4 = 16

hence, it would grow 16 inches in 1 year

Answer: The value of f/5 is 4.

Step-by-step explanation:  This question can be solved by using substituting the value of f( which is 20) in the earlier given expression ( which is f/5).

Here are the steps to solve this question:-

Step 1. Expression = f/5 ( according to the question)

Step 2. Value of f=20 ( according to the question)

Step 3. Using the value of f in step 2 in the equation given in step 1,

                        f/5=20/5

                         f/5=4

Thus, the value of expression f/5 is 4.

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We have that because the central angle is 90°, the sector represents 1/4 of a circle with a radius of 10 yd.

So, length of the safety rail is given by:

Where:

r = 10 yd

pi = 3.14

Substitute, we have:

The Answer is 15.7 yd

Next, area of the deck is given by:

Substitute the values:

The answer is 78.5 yd^2

The other point where the tangent line is horizontal is (-5, 17).

To find where the tangent line is horizontal, we need to find the value of t that corresponds to that point on the curve.

First, we can find the derivative of y with respect to x using the chain rule:

dy/dx = dy/dt / dx/dt = (-30 sin(t)) / (5(cos(t) - sin(t))) = -6 tan(t)

Now we need to find the value of t that makes the derivative equal to zero, which is where the tangent line is horizontal:

-6 tan(t) = 0

tan(t) = 0

t = 0, π

So we need to find the corresponding values of x and y for t = 0 and t = π.

When t = 0, we have:

x = 5(sin(0) + cos(0)) = 5

y = 47 - 15cos²(0) - 30sin(0) = 32

So one point where the tangent line is horizontal is (5, 32).

When t = π, we have:

x = 5(sin(π) + cos(π)) = -5

y = 47 - 15cos²(π) - 30sin(π) = 17

So the other point where the tangent line is horizontal is (-5, 17).

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10 packages

First find the perimeter

perimeter = 2 × (length+width)

2 × (20 + 40)

2 × 60 = 120

4 yards = 12 feet

120 ÷ 12 = 10 packages

The probability of choosing a green balloon is 0.25. The probability of choosing a yellow balloon is 0.15. The probability of choosing a red balloon is 0.2. The probability of choosing a pink balloon is 0.4.

These probabilities indicate the likelihood of selecting each color of balloon when randomly reaching into the package.

The probability of each event when choosing one balloon at random from the package can be determined as follows:

Probability of choosing a green balloon:

The package contains a total of 5 green balloons. Therefore, the probability of selecting a green balloon is 5/(5+3+4+8) = 5/20 = 1/4 = 0.25.

Probability of choosing a yellow balloon:

The package contains a total of 3 yellow balloons. Thus, the probability of selecting a yellow balloon is 3/(5+3+4+8) = 3/20 = 0.15.

Probability of choosing a red balloon:

The package contains a total of 4 red balloons. Hence, the probability of selecting a red balloon is 4/(5+3+4+8) = 4/20 = 0.2.

Probability of choosing a pink balloon:

The package contains a total of 8 pink balloons. Consequently, the probability of selecting a pink balloon is 8/(5+3+4+8) = 8/20 = 0.4.

To summarize:

The probability of choosing a green balloon is 0.25.

The probability of choosing a yellow balloon is 0.15.

The probability of choosing a red balloon is 0.2.

The probability of choosing a pink balloon is 0.4.

These probabilities indicate the likelihood of selecting each color of balloon when randomly reaching into the package.

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Answer:

Step-by-step explanation:

The arcs that are congruent are:

Two geometric figures can be described as congruent if on can be superpose on the other.

Conclusively, congruent' is said to be a word that connote 'exactly equal' when looking at the shape and size of the angles. The options chosen above are congruent because they have the sides to be equal.

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Answer:

2.1

Step-by-step explanation:

Answer:

I watched cobra Kai and loved it. Still waiting on Netflix new season. Watched to where Miyagi-do and Eagle Fang members joined up. So wonderful that Demetrius and Hawk made up.

Step-by-step explanation:

Hope this helps.

Answer:

Yes i have watched the show.

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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Aristotle was the first to draw the conclusion that the Earth is round from actual data.

The first people to reach the empirically supported conclusion that the Earth was spherical were the ancient Greeks. In the sixth century BCE, Pythagoras originally put out the notion of a spherical Earth, which was further expanded by his disciples Parmenides and Plato. Yet in the fourth century BCE, the Greek philosopher Aristotle offered the strongest factual support for a spherical Earth.

Aristotle noted that the Moon experiences a bent shadow from the Earth during lunar eclipses. He understood that the Earth would have to be a sphere for this to happen. Aristotle also observed that the North Star's height fluctuates as one moves north or south, which could only be justified if the Earth were curved. Aristotle came to the conclusion that the Earth was a spherical based on these and other observations, which was a commonly held belief in the ancient world and has subsequently been supported by a wealth of data.

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Answer:

1,00000000

Step-by-step explanation:

ganda ko HAHAGAGGAGAGAGA

Answer:

Step-by-step explanation:

Given the expression (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we are to take the product of all the complex values. We must note that i² = -1.

Rearranging the expression [(3 - i)(3 + i)] [(2 + i)(1 - i)](1 + 2i)

On expansion

(3 - i)(3 + i)

=  9+3i-3i-i²

= 9-(-1)

= 9+1

(3 - i)(3 + i) = 10

For the expression (2 + i)(1 - i), we have;

(2 + i)(1 - i)

= 2-2i+i-i²

= 2-i+1

= 3-i

Multiplying 3-i with the last expression (1 + 2i)

(2 + i)(1 - i)(1 + 2i)

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

= 3+6i-i-2i²

= 3+5i-2(-1)

= 3+5i+2

= 5+5i

Finally,  [(3 - i)(3 + i)] [(2 + i)(1 - i)(1 + 2i)]

= 10(5+5i)

= 50+50i

Hence,  (3 - i)(3 + i)(2 + i)(1 - i)(1 + 2i) is equivalent to 50+50i

Answer:

I think ur teacher need to learn this problem before making the right choice

Step-by-step explanation:

The value of the given integral is: v = [(4√(3) - 5)π/3]

To evaluate the given integral, let's calculate it step by step:

First, let's integrate with respect to z from 1 to √(4 - x² - y²):

∫[1, √(4 - x² - y²)] dz = √(4 - x² - y²) - 1

Next, let's integrate the above expression with respect to y from -√(3 - x²) to √(3 - x²):

∫[-√(3 - x²), √(3 - x²)] (√(4 - x² - y²) - 1) dy

To simplify the integration, let's convert to polar coordinates:

x = r cosθ

y = r sinθ

The bounds of integration in polar coordinates will be:

r: 0 to √(3)

θ: 0 to 2π

Now, we can rewrite the integral in terms of polar coordinates:

∫[0, 2π] ∫[0, √(3)] (√(4 - r²) - 1) r dr dθ

Evaluating the inner integral with respect to r:

∫[0, 2π] [(-1/3) (4 - r²)\(^{3/2}\) - (1/2) r²] | [0, √(3)] dθ

∫[0, 2π] [(2√(3)/3) - (1/3)(4 - 3)\(^{3/2}\) - (1/2)(√(3))²] dθ

Simplifying further:

∫[0, 2π] [(2√(3)/3) - (1/3) - (3/2)] dθ

∫[0, 2π] [(2√(3)/3) - (5/6)] dθ

Now, integrating with respect to θ:

[(2√(3)/3)θ - (5/6)θ] | [0, 2π]

[(2√(3)/3)(2π) - (5/6)(2π)] - [(2√(3)/3)(0) - (5/6)(0)]

[(4√(3)/3)π - (5/3)π] = [(4√(3) - 5)π/3]

Therefore, the value of the given integral is: v = [(4√(3) - 5)π/3]

Complete Question:

Evaluate the integral:

v = ∫∫∫ [−√3, √3] [−√(3−x²), √(3−x²)] [1, √(4−x²−y²)] dz dy dx

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Answer:

around 66.56? i might have missed a side.

Step-by-step explanation:

12.56+10+10+17+8+9

This region is bounded by the lines and the non-negativity constraints (x₁ ≥ 0, x₂ ≥ 0).

Let's start by graphing the constraint inequalities:

4x₁ + x₂ ≤ 100

x₁ + x₂ ≤ 80

x₁ ≤ 40

x₁ ≥ 0, x₂ ≥ 0

First, plot the lines corresponding to the equations:

4x₁ + x₂ = 100 (let's call it line A)

x₁ + x₂ = 80 (line B)

x₁ = 40 (line C)

Now, let's shade the feasible region determined by the constraints. This region is bounded by the lines and the non-negativity constraints (x₁ ≥ 0, x₂ ≥ 0).

The feasible region will be the area of the graph that satisfies all the constraints and lies within the boundaries.

Once we have the feasible region, we can identify the optimal solution point by evaluating the objective function at each corner point of the feasible region.

Finally, we select the corner point that gives the maximum value of the objective function.

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Answer: -1.8 and 11.4

Step-by-step explanation:

Trust me or don’t lol

Answer:

D. 2.6 and 7

Step-by-step explanation:

Plato course, did the test

Answer:

Hope it helps you☺️☺️

Step-by-step explanation:

-3(4x+3)+4(6x+1)=x+43-13x

or,-12x-9+24x+4=-12x+43

or,12x-5=-12x+43

or,12x+12x=43+5

or,x=48/24

so,x=4

Answer:

2,250

Step-by-step explanation:

negative times a negative equals a positive.

Answer:

-

The linear equation that is parallel to the line passing through (-4, -8) and (-4, 2) but passes through the point (2, -5) is given by:

x = 2.

A linear function is modeled by:

y = mx + b

In which:

The line passing through (-4, -8) and (-4, 2) has an undefined slope, hence it is given by:

x = -4.

When two lines are parallel, they have the same slope, hence the line that passes through the point (2, -5) is given by:

x = 2.

The graph at the end of the answer shows both vertical lines.

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p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

To express the given expression x^2 + 7x + 12 / (x + 2) in the form p(x) + k / (x + 2), we will perform polynomial division.

1. Divide the numerator (x^2 + 7x + 12) by the denominator (x + 2):

(x^2 + 7x + 12) ÷ (x + 2)

2. Perform long division:

       x + 5
       ________________
x + 2 | x^2 + 7x + 12
       - (x^2 + 2x)
       ________________
             5x + 12
             - (5x + 10)
       ________________
                 2

3. Write the result:

p(x) + k / (x + 2) = x + 5 + 2 / (x + 2)

So, p(x) = x + 5, and k = 2. The expression x^2 + 7x + 12 / (x + 2) can be written in the form p(x) + k / (x + 2) as:

x + 5 + 2 / (x + 2)

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Answer:

the answer is 6 hours and 30 minutes

There are 1680 ways the teaching assistants can be chosen to grade the exam.

To determine the number of ways the teaching assistants can be chosen to grade the exam, we need to consider the number of choices available for each question and multiply them together.

For the first question, there are eight teaching assistants available. Therefore, there are 8 choices for the first question.

For the second question, since one assistant has already been assigned to the first question, there are seven remaining assistants available. Thus, there are 7 choices for the second question.

Similarly, for the third question, there are six remaining assistants available after two have been assigned to the previous questions. Hence, there are 6 choices for the third question.

Lastly, for the fourth question, there are five remaining assistants available after three have been assigned to the previous questions. Therefore, there are 5 choices for the fourth question.

To determine the total number of ways, we multiply the number of choices for each question:

Total ways = 8 * 7 * 6 * 5 = 1680

Therefore, there are 1680 possible approaches to select the teaching assistants to grade the exam.

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