Verify the equation: (cos x + 1)/(sin^3 x) = (csc x)/(1 - cos x)

A confidence interval for the population mean (BMI) based on a

random

sample of 45 people, a normal distribution should be used because the sample is random and the population is known.

In this scenario, the sample size is sufficiently large (n = 45), and the population standard

deviation

(σ = 6.16) is known. When these conditions are met, the appropriate distribution to construct a confidence interval for the population mean is the normal distribution. The central limit theorem states that when the sample size is large, the distribution of the sample mean approaches a

normal

distribution regardless of the shape of the population distribution.

Using the normal distribution, we can calculate the

standard

error of the mean (SEM) by dividing the population standard deviation by the square root of the sample size: SEM = σ / √n. In this case, the SEM would be 6.16 / √45. The confidence

interval

can then be calculated by multiplying the SEM by the appropriate critical value for the desired level of confidence (e.g., 95%) and adding/subtracting it to/from the sample mean.

Therefore, to construct a confidence interval for the population mean BMI, we would use a normal

distribution

because the sample is random, and the population standard deviation is known.

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Answer:

sorry

Step-by-step explanation:

i can't understand your question

there is no clarity

Answer:

0.075 inches per year

Step-by-step explanation:

The average rate of change is measured as

( difference in diameter ) ÷ ( difference in years )

= ( 251 - 248 ) ÷ ( 2005 - 1965 )

= 3 inches ÷ 40 years

= 0.075 inches per year

Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

The solution is given as follows;7. x² - 12x + y² + 6y = - 9.

We start by grouping the x and y terms separately, then completing the square by adding half of the coefficient of the respective variable and squaring the result. x² - 12x + y² + 6y = - 9(x² - 12x + __) + (y² + 6y + __) = - 9 + __ + __

Now, we'll fill in the blanks in the parentheses so that the trinomials are perfect squares: (x² - 12x + 36) + (y² + 6y + 9) = - 9 + 36 + 9.

This simplifies to: (x - 6)² + (y + 3)² = 36.

The center of the circle is (6, −3), and its radius is 6.9. x² + y² + 14x - 20y - 20 = 0.

First, we group the x terms and the y terms separately:x² + 14x + y² - 20y = 20.

Now, we'll complete the square in both x and y. x² + 14x + y² - 20y = 20(x² + 14x + __) + (y² - 20y + __) = 20 + __ + __.

We'll fill in the blanks so that the trinomials are perfect squares.

To find the terms to add, we take half of the coefficient of the variable and square it. (x² + 14x + 49) + (y² - 20y + 100) = 20 + 49 + 100

Simplifying, we get (x + 7)² + (y - 10)² = 169.

The center of the circle is (-7, 10), and its radius is 13.x - 2x + y + 3/2y = -1

We first rearrange the terms. x - 2x + y + 3/2y = -1-x - 1/2y = -1

We then complete the square in x and y as follows. x - 2x + y + 3/2y = -1(x - 1) - (1/2)(y + 2) = -1/2(x - 1)² - 1/4(y + 2)² = 1/2

The center of the circle is (1, -2) and its radius is 1/2.8. - 3x² - 3y² + 27y + 61 = 0

We rearrange and group the terms. - 3x² - 3y² + 27y = -61

We then complete the square. - 3x² - 3(y² - 9y + 81/4) + 27(81/4) = -61 - 3(81/4)(x² + (y - 9/2)² = 405/4

The center of the circle is (0, 9) and its radius is 3/2.10. x² + y² - 7x - 3y - 1 = 0

We rearrange and group the terms. x² - 7x + y² - 3y = 1

We then complete the square. x² - 7x + 49/4 + y² - 3y + 9/4 = 1 + 49/4 + 9/4(x - 7/2)² + (y - 3/2)² = 25/4

The center of the circle is (7/2, 3/2), and its radius is 5/2.12. 4x² - 16x + 4y² + 16 = 0

We rearrange and group the terms. 4x² - 16x + 4y² = -16

We then complete the square. 4(x² - 4x + 4) + 4y² = 0(x - 2)² + y² = 1

The center of the circle is (2, 0), and its radius is 1.

Completing the square is a method used to turn quadratic expressions in standard form into perfect squares. It’s often used to find the center and radius of circles.

Here are the solutions to each problem, which include the center and radius for each circle:7. Center: (6, -3); Radius: 6.9. Center: (-7, 10); Radius: 13.11. Center: (1, -2); Radius: 1/2.8. Center: (0, 9); Radius: 3/2.10. Center: (7/2, 3/2); Radius: 5/2.12. Center: (2, 0); Radius: 1.

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Answer:

A.  g(x) = -[tex]x^{2}[/tex] - 4

Step-by-step explanation:

f(x) is flipped, so [tex]x^{2}[/tex] becomes -[tex]x^{2}[/tex].

After being flipped, the graph is move down 4 units.

Therefore, g(x) = -[tex]x^{2}[/tex] - 4

Im gonna label the long side of a rectangle a and the smaller side b.

For the perimeter, 2a + 2b = 34

For the area, a x b = 66

if a is 11 and b is 6, the equation for perimeter would be 22 + 12 = 34.

So a = 11 and  b = 6

Answer:

Longer side = 11

Shorter side = 6

Step-by-step explanation:

L x W = 66,  then W = 66/L

2L + 2W = 34

substitute for W:

2L + 2(66/L) = 34

2L + 132/L = 34

multiply both sides of the equation by L:

2L² + 132 = 34L

divide both sides by 2:

L² + 66 = 17L

L² - 17L + 66 = 0

factor:

(L - 11)(L - 6) = 0

L = 11 or L = 6

if L = 11, then W = 6

if L = 6 then W = 11

Answer:

B

Step-by-step explanation:

equation for volume of a cone = [tex]V=\frac{1}{3}\pi r^2h[/tex]

plug in - [tex]V=\frac{1}{3} \pi (4)^2(7)[/tex]

Answer:

we have

volume of cone =1/3 πr²h=1/3×π×4²×7ft³

so

v=1/3 π(4²)(7)ft³

Answer:

Answer:

Area of a CIRCLE with radius of 3 inches is

PI * radius^2 =

3.14159265 * 3^2 =

28.27433385  square inches.  

Since we are dealing with a SEMI-CIRCLE, we divide that by 2 and get:

14.137166925  square inches which rounds to about

14.14 square inches

Step-by-step explanation:

Answer: 30pi^2 divided by 2

Explanation:

To find the area of a circle, it is pi x radius ^2

Since it is a semicircle 30 is the radius.

pi x radius ^ 2 = 30pi^2

the area would be 30pi^2 divided by 2

a) There are 9! (9 factorial) orders of shows John can watch if he watches one episode of each of the 9 different television shows.

b) There are 126 combinations for John to download 5 random episodes from the 9 shows.

c) There are 1,320 different ways to select a captain, equipment manager, and sound manager from a group of 12 students without any person holding two positions.

a) If John watches one episode of each of the 9 different television shows, the number of orders of shows he can watch is 9!.

b) If John wants to download 5 random episodes of these 9 shows, the number of combinations is given by the binomial coefficient:

C(9, 5) = 9! / (5!(9-5)!) = 126

c) To select a captain, equipment manager, and sound manager from a group of 12 students without any person holding two positions, the number of different ways is given by the product of the choices for each position:

12 * 11 * 10 = 1,320

Therefore, there are 1,320 different ways to select a captain, equipment manager, and sound manager in this scenario.

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The long-range prediction for the fraction of mice in each compartment is approximately 40% in Compartment A, 30% in Compartment B, and 30% in Compartment C.

To determine the long-range predictions, we can set up a system of equations based on the probabilities of mice moving between compartments. Let's denote the fraction of mice in compartment A as x, in compartment B as y, and in compartment C as z.

For compartment A, the fraction of mice in the next step will be 0.2x (moving to B) and 0.4x (moving to C). Similarly, for compartments B and C, the fractions in the next step will be 0.25y + 0.4z and 0.45y + 0.3z, respectively.

Setting up the equations, we have:

x = 0.2x + 0.4z
y = 0.25y + 0.4z
z = 0.45y + 0.3z

Simplifying and solving the equations, we find:

x = 0.4
y = 0.3
z = 0.3

Therefore, the long-range prediction for the fraction of mice in compartment A is 0.4, in compartment B is 0.3, and in compartment C is 0.3. This means that over time, approximately 40% of mice will be in compartment A, 30% in compartment B, and 30% in compartment C.

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Step-by-step explanation:

f(x) = x^2 represents a quadratic function, where the input value (x) is squared and the resulting output value is equal to the square of x.

g(x) = (x+3)^2 - 1 represents another quadratic function, where the input value (x) is first added to 3, then squared, and the resulting output value is equal to the square of (x+3) minus 1.

To evaluate these functions for a specific value of x, we simply substitute that value into the function in place of x. For example, if we want to find f(4), we would replace x with 4 to get:

f(4) = 4^2 = 16

Similarly, if we want to find g(-2), we would replace x with -2 to get:

g(-2) = (-2+3)^2 - 1 = 1^2 - 1 = 0

We can also graph these functions on a coordinate plane by plotting points for various values of x and their corresponding values of f(x) or g(x). The graph of f(x) = x^2 is a parabola that opens upwards, while the graph of g(x) = (x+3)^2 - 1 is also a parabola, but it has been shifted 3 units to the left and 1 unit downwards compared to the graph of f(x).

The volume of the room with the given dimensions is 84 cubic meters.

The volume of a room can be calculated by multiplying its length, width, and height. In this case, the given dimensions are:

Length (L) = 7 m

Width (W) = 4 m

Height (H) = 3 m

To find the volume, we can use the formula:

Volume = Length × Width × Height

Substituting the given values:

Volume = 7 m × 4 m × 3 m

Simplifying:

Volume = 84 m³

Therefore, the volume of the room with the given dimensions is 84 cubic meters.

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The combination of food A and food B that meets the requirements and has the greatest amount of protein is 2 units of food A and 1 unit of food B, with a total of 30 grams of protein.

We can approach the problem of finding the combination of food A and food B that meets the requirements and has the greatest amount of protein using linear programming.

1) Variables:

Let x be the number of units of food A.
Let y be the number of units of food B.

2) Organizational chart:

Food A:
Sodium: 120 mg/unit
Fat: 1 g/unit
Protein: 5 g/unit

Food B:
Sodium: 60 mg/unit
Fat: 1 g/unit
Protein: 4 g/unit

Meal requirements:
Sodium: ≤ 480 mg
Fat: ≤ 6 g

Objective: Maximize protein

3) Objective equation:

Maximize z = 5x + 4y

4) Constraint inequalities:

120x + 60y ≤ 480 (sodium constraint)
x + y ≤ 6 (fat constraint)
x ≥ 0, y ≥ 0 (non-negative constraint)

5) Graph the constraints:

To graph the constraints, we can first graph the boundary lines.

120x + 60y = 480
x + y = 6

Then we can shade the feasible region, which is the region that satisfies all the constraints.

The feasible region is a polygon with vertices at (0,0), (4,2), (6,0), and (3,3).

6) Find the vertices:

The vertices of the feasible region are (0,0), (4,2), (6,0), and (3,3).

7) Test the vertices:

We can test each vertex by substituting its coordinates into the objective equation and finding the maximum value.

(0,0): z = 0
(4,2): z = 30
(6,0): z = 30
(3,3): z = 27

The maximum value of the objective function is 30, which occurs at the points (4,2) and (6,0).

8) Write the complete solution:

To maximize protein while satisfying the sodium and fat constraints, we need to use 4 units of food A and 2 units of food B, or 6 units of food A and 0 units of food B. Both of these combinations have a total of 30 grams of protein.

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1. Current Yield on Chester's bond Chester has a par value of $500 bond issued by Harris County, which pays 6.2% yearly interest. When Chester bought it, the market rate of Harris County bonds was 101.760. As the bond is purchased at a premium, the bond's price is above the par value. It is trading above the face value of $500 per bond.Using the current market rate formula, C = (I/PV) + (FV/PV)n

Where ,C = Current YieldI = Yearly Interest PV = Current Market RateFV = Par Value ($500)n = Number of Years Then,

98.626 = (6.2/ PV) + (500 / PV)101.760

[tex](PV) = $498.70PV = $4.90[/tex]

Therefore, the current market price of the bond is $4.90.Using the current yield formula, Current Yield = (Yearly Interest/Current Market Price) x 100Current

Yield [tex]= (6.2/4.90) x 100 = 126.53[/tex]

Therefore, the current yield on Chester's bond is 126.53%.2. Investment with a greater return after six years After six years, the return on stocks and bonds investment will be calculated as: Stocks

Return = [tex]1,000(1 + 0.053)^6 = $1,385.94[/tex]

Bonds Return = [tex]1,400(1 + 0.041)^6 = 1,734.69[/tex]

Therefore, the return on bonds investment is $1,734.69, and the return on stocks investment is $1,385.94. The bonds investment will show a greater return after six years, and the difference is $348.75.3. Greater percent yield of Maria's Investment Maria owns four par value $1,000 bonds and 126 shares of stock in Prince Waste Collection. The bonds pay a yearly interest of 7.7%, and Maria bought them when the market value was 97.917.The cost of one stock = $19.33 and the yearly dividend per stock is 85 cents.

Maria's total investment in stocks = [tex]126\times$19.33 = $2,439.18[/tex]

Maria's total investment in bonds = $1,000 x 4 = $4,000 When Maria bought bonds, the market value of the bond was [tex]979.17 ($1,000 x 0.97917).[/tex][tex]= (Yearly Interest / Purchase Price) \times 100= (7.7 / 979.17) \times 100 = 0.786%[/tex]

The stock's annual yield[tex]= (Dividend / Purchase Price) \times100= (0.85 / 19.33) \times 100 = 4.4%[/tex]

Therefore, the percent yield on stocks is greater, and the difference is 3.61%.

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Answer:

r = c / 2π

Step-by-step explanation:

c = 2πr is the formula for the circumference of a circle of radius r.

We can solve this for r:

r = c / (2pi)

or

r = c / 2π

Answer:

[tex]\implies\boxed{ 10^a = 300 }[/tex]

Step-by-step explanation:

We are provided logarithmic equation , which is ,

[tex]\implies log_{10}^{300}= a [/tex]

Say if we have a expoteintial equation ,

[tex]\implies a^m = n [/tex]

In logarithmic form it is ,

[tex]\implies log_a^n = m [/tex]

Similarly our required answer will be ,

[tex]\implies\boxed{ 10^a = 300 }[/tex]

Answer:

nope, an integer must be a whole number, no fractions / decimals

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

An integer is a whole number or a number that is not a fraction or decimal. So, since 41.77 is a decimal it cannot be an integer. Examples of integers are 41 or -2.

Answer:

324

Step-by-step explanation:

1 yards = 36 inches

36 x 9 = 324

Answer:

I think the answer is 49in^2

Answer: She ate 12 apples

Step-by-step explanation: 18 divided by 2 is 9 add 2 of 9 to the other 9 and you get 12 hope I helped

Answer:

she ate 10 apples

Step-by-step explanation:

I thought of it because there is only 18 apples all together

Answer:

3.25

Step-by-step explanation:because you have to divide the years with the inches so in each year i would grow about 3.25 inches

The position function is obtained by integrating the acceleration function twice and applying initial conditions: s(t) = -5/16 sin(4t) + 9/4t + 6.

To find the position function, we need to integrate the acceleration function twice with respect to time (t) and apply the initial conditions.

Given:

Acceleration function: a(t) = 5 sin(4t)

Initial velocity: v(0) = 1

Initial position: s(0) = 6

First, integrate the acceleration function to find the velocity function:

v(t) = ∫(a(t)) dt = ∫(5 sin(4t)) dt = -5/4 cos(4t) + C1

Next, apply the initial velocity condition to solve for the constant C1:

v(0) = -5/4 cos(0) + C1 = 1

C1 = 1 + 5/4 = 9/4

Now, integrate the velocity function to find the position function:

s(t) = ∫(v(t)) dt = ∫(-5/4 cos(4t) + 9/4) dt = -5/16 sin(4t) + 9/4t + C2

Finally, apply the initial position condition to solve for the constant C2:

s(0) = -5/16 sin(0) + 9/4(0) + C2 = 6

C2 = 6

Therefore, the position function is:

s(t) = -5/16 sin(4t) + 9/4t + 6 (Expression using t as the variable).

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Answer:

12 units

Step-by-step explanation:

got it right on edg

Answer:

A

Step-by-step explanation:

A line of best fit is a line that gives an estimate of where the line would be, therefore it is close to most of the data points.

Answer:

A)

Step-by-step explanation:

Answer:

325

Step-by-step explanation:

got it right on edg

The required equation of the circle that shown in the graph is,
(x + 1)² + (y - 2)² = 4 where (-1 , 2) is the center of the circle and 2 unit is the radius of the circle. Option C is correct.

A graph of the circle is shown, It is to determine the equation of the circle.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x  - h)² + (y - k)² = r²

where h, k is the coordinate of the circle's center on the coordinate plane and r is the circle's radius.

From the graph, the center is ( -1, 2) and the radius is  2. Now put these values in the standard equation of the circle.
(x - (-1))² + (y - 2)² = 2²
(x +1 )² + (y - 2)² = 4

Thus, the required equation of the circle that shown in the graph is,
(x + 1)² + (y - 2)² = 4 where (-1 , 2) is center of the circle and 2 unit is the radius of the circle. Option C is correct.

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Answer:

77

Step-by-step explanation:

7x10 is 70 plus 7 is 77

Answer:

11,000

Step-by-step explanation:

You would multiply 1,500 by 7 and then add 500.

a)The probability that 3 balls drawn have the same color=1/28.

b)The probability that 3 balls drawn have different colors= 3/14.

c)A and B are mutually exclusive events.

Explanation:

Given that a vase contains 9 balls: 3 blue, 3 red, and 3 green ones. Three random balls are drawn from the vase and are not put back in.

The events that are considered are: A = the 3 balls drawn to have the same color. B = the 3 balls drawn have different colors.

(a) Calculation of P(A), We need to find the probability that 3 balls drawn have the same color.

P(A) = probability of getting 3 blue balls + probability of getting 3 red balls + probability of getting 3 green balls.

The probability of getting 3 blue balls is 3/9 × 2/8 × 1/7 = 1/84.

The probability of getting 3 red balls is 3/9 × 2/8 × 1/7 = 1/84.

The probability of getting 3 green balls is 3/9 × 2/8 × 1/7 = 1/84

Therefore, P(A) = 1/84 + 1/84 + 1/84 = 3/84 = 1/28.

(b) Calculation of P(B), We need to find the probability that 3 balls drawn have different colors.

P(B) = probability of getting one ball of each color + probability of getting 2 balls of one color and one ball of another color.

The probability of getting one ball of each color is 3/9 × 3/8 × 3/7 = 27/252

The probability of getting 2 balls of one color and one ball of another color is 3(3/9 × 2/8 × 3/7) = 27/252

Therefore, P(B) = 27/252 + 27/252 = 54/252 = 3/14.

(c) Finding if are A and B independent,

A and B are not independent as P(A) = 1/28 and P(B) = 3/14.

The probability of both A and B occurring together is zero, as it is impossible to draw 3 balls that are of the same color and 3 balls of different colors at the same time. Hence, A and B are mutually exclusive events.

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a) The probability that the 3 balls drawn have the same color:

               P(A) =  0.0095 or 0.95%

b) The probability that the 3 balls drawn have different colors:

               P(B) = 0.2143 or 21.43%

c) A and B are not independent.

Explanation:

a)

P(A) = (3/9) × (2/8) × (1/7) + (3/9) × (2/8) × (1/7) + (3/9) × (2/8) × (1/7)

          = 0.0095 or 0.95%

Note: In the first fraction, the numerator is 3 because there are three blue balls. The denominator is 9 because there are 9 balls in total.

Since the first ball has been drawn, there are only 8 balls left, hence 2/8 in the second fraction. And so on.

b)

P(B) = (3/9) × (3/8) × (3/7) + (3/9) × (3/8) × (3/7) + (3/9) × (3/8) × (3/7)  

       = 0.2143 or 21.43%

Note: In the first fraction, the numerator is 3 because there are three blue balls. The denominator is 9 because there are 9 balls in total.

Since the first ball has been drawn, there are only 8 balls left, hence 3/8 in the second fraction. And so on.

c)

P(A)P(B) = 0.0095 × 0.2143

             = 0.00204

             ≈ 0.2%

P(A ∩ B) = 0 (because if you have 3 balls of different colors, then you cannot have 3 balls of the same color at the same time)

Therefore, A and B are not independent.

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