Two observers are 200 feet apart in line with a tree containing a bird's nest. The angles of elevation to the bird's nest are 30° and 60°. How far is each observer from the base of the tree?

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

25000

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

Let's solve your equation step-by-step.

4x+10=30

Step 1: Subtract 10 from both sides.

4x+10−10=30−10

4x=20

Step 2: Divide both sides by 4.

4x /4 = 20/4

x=5

The value of x that satisfies the equation 4x + 10 = 30 is x = 5.

Here,

To solve the equation 4x + 10 = 30,

we want to find the value of x that makes the equation true.

Step 1: Isolate the variable term.

First, we want to get rid of the constant term 10 on the left side of the equation.

We can do this by subtracting 10 from both sides of the equation:

4x + 10 - 10 = 30 - 10

Simplifying:

4x = 20

Step 2: Solve for x.

Next, we want to isolate the variable x on one side of the equation.

Since 4 is multiplied by x, we can undo this by dividing both sides of the equation by 4:

4x / 4 = 20 / 4

Simplifying:

x = 5

Step 3: Check the solution.

To verify that our solution is correct, we can substitute the value of x back into the original equation:

4x + 10 = 30

Substitute x = 5:

4(5) + 10 = 30

Simplifying:

20 + 10 = 30

30 = 30

Since both sides are equal, our solution x = 5 is correct.

Therefore, the value of x that satisfies the equation 4x + 10 = 30 is x = 5.

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To solve this problem, we can use the formula for probability:

P(event) = number of favorable outcomes / total number of outcomes

First, let's find the total number of outcomes. We are selecting 4 balls from 11 without replacement, so the total number of outcomes is:

11C4 = (11!)/(4!(11-4)!) = 330

where nCr is the number of combinations of n things taken r at a time.

Now let's find the number of favorable outcomes for each part of the problem.

Part 1: Exactly two white balls and two red balls

To find the number of favorable outcomes for this part, we need to select 2 white balls out of 6 and 2 red balls out of 5. The number of ways to do this is:

6C2 * 5C2 = (6!)/(2!(6-2)!) * (5!)/(2!(5-2)!) = 15 * 10 = 150

So the probability of selecting exactly two white balls and two red balls is:

P(2W2R) = 150/330 = 0.45 (rounded to two decimal places)

Part 2: At least two white balls

To find the number of favorable outcomes for this part, we need to consider two cases: selecting 2 white balls and 2 red balls, or selecting 3 white balls and 1 red ball.

The number of ways to select 2 white balls and 2 red balls is the same as the number of favorable outcomes for Part 1, which is 150.

To find the number of ways to select 3 white balls and 1 red ball, we need to select 3 white balls out of 6 and 1 red ball out of 5. The number of ways to do this is:

6C3 * 5C1 = (6!)/(3!(6-3)!) * (5!)/(1!(5-1)!) = 20 * 5 = 100

So the total number of favorable outcomes for selecting at least two white balls is:

150 + 100 = 250

And the probability of selecting at least two white balls is:

P(at least 2W) = 250/330 = 0.76 (rounded to two decimal places)

Answer:

m a g i c  t h a t ' s  h o w

Answer:

A

Step-by-step explanation:

Answer:

Easy B                  

Step-by-step explanation: srry If It's Wrong

Answer:

true

Step-by-step explanation:

They are dependent because the outcome of the event affects them

Answer:

x = 3.4

Step-by-step explanation:

Use the sin formula, due to the fact of the hypotenuse being known, and the variable being across 70.

Sin(70) = x / 3.6

Sin(70) * 3.6 = x

3.3828934 = x

Round to nearest tenth, as question asked

3.4 = x

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

The volume is 997.62 cubic units..

Step-by-step explanation:

We are given the following details:

The pyramid has a regular hexagonal base i.e. each side of hexagon is equal.

Side of hexagonal base, a = 8 units

Altitude of pyramid, h = 18 units

We have to find the volume of pyramid.

Formula:

\(V = \dfrac{1}{3} \times B \times h\)

Where, B is the area of base of pyramid.

h is the height/altitude of pyramid

To calculate B:

Here, base is a hexagon with side 8 units.

\(\text{Area of hexagon, B }= 6 \times \dfrac{\sqrt{3}}{4}a^{2}\)

Here, a = 8 units

\(\Rightarrow B = 6 \times \dfrac{\sqrt{3}}{4}\times 8^{2}\\\Rightarrow B = 166.27\text{ square units}\)

Putting values of B and h in Formula of volume:

\(\Rightarrow V = \dfrac{1}{3} \times 166.27 \times 18\\\Rightarrow V = \dfrac{2992.89}{3} = 997.62\text{ cubic units}\)

Hence, the volume is 997.62 cubic units.

Answer:

Fig C take reflection over horizontal axis (parallel to x axis) to be figure D

Fig D further take reflection over vertical axis -> fig D' -> reflection over horizontal axis -> F

Step-by-step explanation:

Step-by-step explanation:

When (x - 2) = 0, x = 2.

=> F(2) = -4(2)² + 14(2) - 23 = -11.

By Remainder Theorem,

The remainder of F(x) divided by (x - 2) is -11.

Answer:

Step-by-step explanation:

12 NO WELCOME

:)

The temperature drops by \(31\°C\) from day to night in this city.

To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: \(-40\°C\)

Average daily high temperature: \(-9\°C\)

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = \(-9\°C - (-40\°C)\)

Simplifying the equation:

Temperature drop = \(-9\°C + 40\°C\)

Temperature drop = \(31\°C\)

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by \(31\°C\) from day to night in this city.

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Answer:

Step-by-step explanation:

Answers:

(Check image below).

Answer:

(x + i) (x - i)

Step-by-step explanation:

The expression x^2 + 1 is a sum of squares, which means that it cannot be factored using real numbers. However, it can be factored using complex numbers.

To factor x^2 + 1, we can use the fact that i^2 = -1, where i is the imaginary unit.

We can rewrite x^2 + 1 as:

x^2 + 1 = x^2 - (-1)

Now, we can use the difference of squares formula to factor x^2 - (-1):

x^2 - (-1) = (x + i)(x - i)

Therefore, the factored form of x^2 + 1 is:

(x + i)(x - i)

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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The length of side X in simple radical form with a rational denominator is 10/√3.

In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.

This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):

Adjacent side = 5/√3

Hypotenuse, x = 2 × 5/√3

Hypotenuse, x = 10/√3.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Step-by-step explanation:

I there a picture for the problem ?

Answer:

point (5, 5) is in Quadrant: I  (1)

point (3, –2) is in Quadrant: IV   (4)

The point (–4, –4) is in Quadrant: III   (3)

Step-by-step explanation:

Answer:

The point (5, 5) is in Quadrant  

✔ I

    II

    III

    IV

The point (3, –2) is in Quadrant  

    I

    II

    III

✔ IV

The point (–4, –4) is in Quadrant

    I

    II

✔ III

    IV

Answer:

Number 3

Step-by-step explanation:

ur welcome

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

The given equation is x²+24x=33.

We need to factorise the equation using completing the square method.

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.

Now, x²+24x-33=0

Add and subtract (b/2)²=144 to the equation.

x²+24x-33+144-144=0

⇒x²+24x+144-33-144=0

⇒(x+12)²-177=0

⇒(x+12)²=177

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

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To find the sum or difference we must know what k is however you can simplify the expression by rewriting and removing the parenthesis furthermore collecting the like terms to get the solution.

Attached photo shows the steps to the solution :P

Answer:

The function domain is:

{x|x ≥ -4}

Hence, option 4 is correct.

Step-by-step explanation:

Given the expression of the function

\(f\left(x\right)=\sqrt{x+4}\)

We know that the domain of the function is the set of input values for which the function is real and defined

We know that the value inside the radical expression must be greater than or equal to 0 so that the function remains defined.

so

\(x+4\ge \:0\)

subtract 4 from both sides

\(x+4-4\ge \:0-4\)

simplify

\(x\ge \:-4\)

Therefore, the function domain is:

{x|x ≥ -4}

Hence, option 4 is correct.

Answer:

Step-by-step explanation:

The missing number is

y = 2x + 3

hope it helps :)