(100 POINTS!!!) Find the minimum sample size n needed to estimate for the given values of​ c, o ​, and E.
c=0.95​, o=7.6 ​, and E=2. Assume that a preliminary sample has at least 30 members.
n=?

Answer:

  10 meters

Step-by-step explanation:

You want the width of the path surrounding an 18 meter by 24 meter pool if the total area of pool and path is 1672 square meters.

The total area of the rectangular shape is the product of its length and width:

  A = LW

  1672 = (24 +2x)(18 +2x)

  418 = (12 +x)(9 +x) . . . . . . . . divide by 4

  418 = 108 +21x +x² . . . . . . eliminate parentheses

  420.25 = 110.25 +21x +x² . . . . . . add 2.5 to complete the square

  20.5 = (10.5 +x) . . . . . . . . . . take the positive square root

  10 = x . . . . . . . . . . . . . . subtract 10.5

The width of the path is 10 meters.

__

Additional comment

The attached graph shows the two solutions of the original equation written so the solutions are the x-intercepts:

  (24 +2x)(18 +2x) -1672 = 0

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The (x, y) coordinates for the image of each point after each transformation include the following:

A' (-3, -4)         A" (1, 1)         A'" (2, 2).

B' (1, -4)           B" (1, 5)        B'" (10, 2).

C' (-1, -1)           C" (4, 3)       C''' (6, 8).

In order to apply a translation of four units to the left and five units down to triangle ABC, we would use this transformation rule;

(x, y)                               →                  (x - 4, y - 5)

A (1, 1)                         →                    A' (-3, -4).

B (5, 1)                         →                    B' (1, -4).

C (3, 4)                         →                    C' (-1, -1).

Next, we would reflect triangle ABC across the line y = x;

(x, y)                            →                      (y, x)

A (1, 1)                         →                    A" (1, 1).

B (5, 1)                         →                    B" (1, 5).

C (3, 4)                         →                    C" (4, 3).

Lastly, we would dilate triangle ABC with scale factor of 2​;

(x, y)                            →                      (2x, 2y)

A (1, 1)                         →                    A'" (2, 2).

B (5, 1)                         →                    B'" (10, 2).

C (3, 4)                         →                    C''' (6, 8).

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Answer:

P = 9 + 9 + 4 + 4

Step-by-step explanation:

P=2(lxw) or l+l+w+w

Therefore, 9+9+4+4 is right.

The angle of elevation of the sun to the nearest degree is: 34°

The angle of elevation is defined as an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is referred to as an angle of elevation.

There are three main trigonometric ratios which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

In this case, the dimensions given will warrant the use of the tangent function to get:

tan θ = 101/147

tan θ = 0.6871

θ  = tan⁻¹(0.6871)

θ  = 34°

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The probability that a randomly selected point within the square falls in the red-shaded square is 0.36

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

The areas of the above shapes are

Red square = 3² = 9

White square = 5² = 25

The probability is then calculated as

P = Red square/White square

So, we have

P = 9/25

Evaluate

P = 0.36

Hence, the probability that a randomly selected point within the square falls in the red-shaded square is 0.36

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Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The range of the margin of error is 1 pound, which means that the actual weight of the box could be off by a maximum of 1 pound.

Beatriz measured the weight of a box and determined the margin of error as 23.5 pounds to 24.5 pounds. The greatest possible error for her actual measurement can be determined by finding the range of the margin of error.

The range of the margin of error can be determined by finding the difference between the upper limit and the lower limit. Therefore, the range of the margin of error is 24.5 - 23.5 = 1 pound.

This means that the actual weight of the box could be off by a maximum of 1 pound. This is the greatest possible error for her actual measurement.

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Answer:

The volume of the buoy can be calculated by finding the volumes of the cone and hemisphere separately and then adding them together.

The volume of the cone is given by:

Vcone = (1/3)πr^2h

where r is the radius of the base of the cone and h is the height of the cone.

Substituting the given values, we get:

Vcone = (1/3)π(0.95)^2(1.2) = 1.08 m^3 (rounded to two decimal places)

The volume of the hemisphere is given by:

Vhemisphere = (2/3)πr^3

where r is the radius of the hemisphere.

Substituting the given value, we get:

Vhemisphere = (2/3)π(0.95)^3 = 1.05 × 10^-3 m^3 (rounded to two decimal places)

Therefore, the total volume of the buoy is:

Vbuoy = Vcone + Vhemisphere = 1.08 + 1.05 × 10^-3 = 1.08 m^3 (rounded to two decimal places)

Probabilities are:
Even number = 0.5
Odd Number = 0.5
Number 1 face up = 1/6

Number 2 face up = 1/6

Number 3 face up = 1/6

Number 4 face up = 1/6

Number 5 face up = 1/6

Number 6 face up = 1/6

The correct options are:

Esmerelda converted the mixed number to the wrong improper fraction.

Esmerelda added the numerators.

Esmerelda did not divide –24 by 6 correctly.

The errors made by Esmerelda are as follows:

1. Esmerelda converted the mixed number to the wrong improper fraction.

2. Esmerelda added the numerators.

3. Esmerelda did not divide –24 by 6 correctly.

Let's go through each error:

1. Esmerelda converted the mixed number to the wrong improper fraction:

Esmerelda incorrectly converted "Negative 5 and one-fourth" to "Negative StartFraction 21 over 4 EndFraction." The correct conversion would be "Negative StartFraction 5 over 4 EndFraction" since the mixed number -5 1/4 can be expressed as -5 + 1/4 = -5  (1/4) = -5 (4/4) + (1/4) = -5 (4 + 1)/4 = -5 (5/4) = -5 (5 over 4).

2. Esmerelda added the numerators:

Esmerelda incorrectly added the numerators of the fractions, resulting in "Negative StartFraction 21 over 4 EndFraction" instead of the correct numerator of -5 * 4 = -20.

3. Esmerelda did not divide –24 by 6 correctly:

Esmerelda made an error in dividing -24 by 6, resulting in "StartFraction 24 over 6 EndFraction" instead of the correct value of -24 divided by 6, which is -4.

Therefore, the correct options are:

- Esmerelda converted the mixed number to the wrong improper fraction.

- Esmerelda added the numerators.

- Esmerelda did not divide –24 by 6 correctly.

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To find f(g(x)), we need to substitute g(x) into the function f(x). Given that g(x) = x - 4, we substitute it into f(x) as follows:

[tex]f(g(x)) = f(x - 4) = (x - 4)^2 + 4[/tex]

To simplify this expression, we can expand the square:

[tex]f(g(x)) = (x - 4)(x - 4) + 4\\ = x^2 - 8x + 16 + 4\\ = x^2 - 8x + 20[/tex]

Therefore, f(g(x)) simplifies to[tex]x^2 - 8x + 20.[/tex]

Next, let's find g(f(x)). We substitute f(x) into the function g(x):

[tex]g(f(x)) = g(1/x^2 + 4) = 1/x^2 + 4 - 4\\ = 1/x^2[/tex]

Hence, g(f(x)) simplifies to 1/x^2.

In summary, f(g(x)) simplifies to[tex]x^2 - 8x + 20[/tex], and g(f(x)) simplifies to 1/x^2.

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Answer:

55

Step-by-step explanation:

[tex]\displaystyle MOE = z\biggr(\frac{\sigma}{\sqrt{n}}\biggr)\\\\4=1.96\biggr(\frac{15}{\sqrt{n}}\biggr)\\\\4=\frac{29.4}{\sqrt{n}}\\\\\sqrt{n}=\frac{29.4}{4}\\\\\sqrt{n}=7.35\\\\n=54.0225\\\\n\approx55\uparrow[/tex]

Make sure to always round up the required sample size to the nearest integer!

Answer:

50.75

Step-by-step explanation:

We have:

[tex]E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\[/tex]

[tex]=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74[/tex]

Answer:

60°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

48° + 11x - 5 + 9x - 3 = 180°

40° + 20x = 180°

20x = 140°

x = 7

To find m∠A, replace x with 7:

m∠A = 9x - 3

9×7-3 = 60°

Shan performed better in his science test than in his math test based on the respective scores of 15 out of 20 and 7 out of 10.

To determine which test Shan achieved better results in, we need to compare the scores he obtained in both the math and science tests.

Shan scored 7 out of 10 in his math test, which can be written as a fraction 7/10. This fraction can also be converted to a decimal by dividing 7 by 10, resulting in 0.7.

Similarly, Shan scored 15 out of 20 in his science test, which can be written as a fraction 15/20. This fraction can also be simplified by dividing both the numerator and denominator by 5, resulting in 3/4. Converting this fraction to a decimal by dividing 3 by 4 yields 0.75.

Comparing the decimal values, we can see that 0.75 (science test) is greater than 0.7 (math test). Therefore, Shan achieved better results in his science test compared to his math test.

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The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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The angle BAM is 40°. as the correct angle based on the given values is not 160°, but rather 40°.

To solve this problem within the topic of inscribed and circumscribed circles, we can utilize the property of angles subtended by the same arc on a circle.

Let's consider triangle ABC and point M within angle ABC. Since triangle ABC is isosceles with AB = AC, we can draw the circumcircle passing through points A, B, and C. Let O be the center of this circumcircle.

Based on the property mentioned earlier, angle BAM will be equal to half the measure of arc BC on the circumcircle, subtended by chord BM.

Given that ∠ABC = 50° and ∠BMC = 40°, we can deduce that arc BC on the circumcircle will have a measure of 2 * ∠BMC = 2 * 40° = 80°.

Since angle BAM is half the measure of arc BC, we have:

∠BAM = 0.5 * 80° = 40°

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Answer:

A.

Step-by-step explanation:

Let's think of this as a clock.  We can see that the 2 lines start in the same place, around 3 o'clock.  Next, one of the line segments shifts down to around 6 o'clock.  Next, it shifts to about 9 o'clock.  Logically, the next step (in a clock) would be 12 o'clock, making A the correct choice.

We can also just use a regular circle, with one of the line segments moving 90 degrees each time.

Hope this helps! :)

Answer:

0.5(x)(x + 2) = 24

x² + 2x - 48 = 0

x² + (x + 2)² = 100

Answer:

1. The solution to the differential equation is y = (4*t/3 + 2/3*t + C)/(t**2 + 4), where C is the constant of integration.

2. The general solution to the differential equation is y = (3/4)*exp(t/6) + C*exp(-t/2), where C is the constant of integration.

3. The solution to the initial value problem is y = t^2 + 4/3.

3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

Let's start by breaking down the information given:

- Three-fourths of the yard is covered with grass.

- One-fourth of the yard is used as a garden.

- The sprinkler could only water 1/5 of the yard.

To find out how much of the grass died, we need to determine the portion of the grass that was not watered by the sprinkler.

Let's assume the total area of the yard is represented by the value 1. Therefore, we can calculate the area of the grass as 3/4 of the total yard, which is (3/4) * 1 = 3/4.

The sprinkler can only water 1/5 of the yard, so the portion of the grass that was watered is (1/5) * (3/4) = 3/20.

To find the portion of the grass that died, we subtract the watered portion from the total grass area:

Portion of grass that died = (3/4) - (3/20) = 15/20 - 3/20 = 12/20.

Simplifying, we get:

Portion of grass that died = 3/5.

Therefore, 3/5 or 60% of the grass died because the sprinkler could only water 1/5 of the yard.

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Answer:

18

Step-by-step explanation:

Look at the values

2   184

7    94

Difference in volume: 184 liters - 94 liters = 90 liters

Difference in time: 7 minutes - 2 minutes = 5 minutes

rate in liters/minute: (90 liters) / (5 minutes) = 18 liters/minute

Answer:

3 units to the left of the y-axis

Step-by-step explanation:

Since all answers involve 3, I believe we are looking at the x-axis. To answer your question, a negative x value means that it is to the left of the origin. Therefore the answer would be 3 units to the left of the y-axis.

Answer:

Step-by-step explanation:

To determine the share of Winta in the profit, we need to calculate the ratio of her initial investment to the total initial investment and then apply that ratio to the total profit.

Winta's initial investment: Birr 21,000

Lensa's initial investment: Birr 17,500

Total initial investment: Birr 21,000 + Birr 17,500 = Birr 38,500

To find the share of Winta in the profit, we calculate:

Winta's share = (Winta's initial investment / Total initial investment) * Total profit

Winta's share = (Birr 21,000 / Birr 38,500) * Birr 24,600

Simplifying the calculation:

Winta's share = (0.5455) * Birr 24,600

Winta's share ≈ Birr 13,414.55

Therefore, Winta's share in the profit is approximately Birr 13,414.55.

[tex]\huge\blue{\fbox{\tt{Solution:}}}[/tex]

We can simplify the expression using trigonometric identities.

First, we can use the double angle formula for sine to write sin(2x) = 2sin(x)cos(x).

Next, we can use the double angle formula for cosine to write cos(2x) = cos^2(x) - sin^2(x) = 1 - 2sin^2(x). Rearranging this equation gives 2sin^2(x) - 2cos^2(x) = -cos(2x) + 1.

Substituting these identities into the original expression gives:

tan(x-1) ( sin2x-2cos2x) = tan(x-1) [2sin(x)cos(x) - 2(1 - 2sin^2(x))]

= 2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

We can use the identity tan(x) = sin(x)/cos(x) to simplify this expression further:

2tan(x-1)sin(x)cos(x) - 2tan(x-1) + 4tan(x-1)sin^2(x)

= 2sin(x)cos(x)/(cos(x-1)) - 2sin(x)/(cos(x-1)) + 4sin^2(x)/(cos(x-1))

Multiplying both sides of the equation by cos(x-1) gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x-1) = 2(1-2sin(x)cos(x))

Expanding the left-hand side of the equation gives:

2sin(x)cos(x) - 2sin(x) + 4sin^2(x)cos(x) - 4sin^2(x) = 2 - 4sin(x)cos(x)

Simplifying this equation gives:

4sin^2(x) - 2sin(x) - 2 = 0

This is a quadratic equation in sin(x), which can be solved using the quadratic formula.

Answer:

1) 4630 L = 4.63 kL

2) 2 L 360 mL = 2360 mL

3) 2700 g = 2.7 kg (rounded to nearest 0.1 kg)

4) 2.705 kg = 2.71 kg (rounded to nearest 0.01 kg)

5) 9.597 kg = 10 kg (rounded to nearest kg)

The correct step when using the median-fit method for modeling data is to fit a function to the median of the data.

The median-fit method can be used to model data by following these steps:

1. Arrange the data set in ascending order.

2. Find the median of the data set.

3. Divide the data set into two groups: one group that is below the median, and another group that is above the median.

4. Compute the median of each group.

5. Fit a function to the median of the data.

6. Use the fitted function to estimate values for the original data set.

The median-fit method is a statistical method used to model data. It involves fitting a function to the median of the data. This method is often used when the data set is skewed or has outliers.

The median-fit method is more robust to outliers than the mean-fit method. It is also less sensitive to the shape of the data distribution than other methods.

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Answer:

it answer is

P=2(l+b)

P=l + l + b + b