Prove the identity. \[ \frac{1}{\tan x(1+\cos 2 x)}=\csc 2 x \] Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Ruie, select the More inf

To solve the equation x^(3) = -13, we need to take the cube root of both sides of the equation. The cube root of x^(3) is x, and the cube root of -13 is -2.3513 (rounded to 4 decimal places). Therefore, the solution to the equation is x = -2.3513.

Here are the steps to solve the equation:

1. Start with the equation x^(3) = -13
2. Take the cube root of both sides of the equation: (x^(3))^(1/3) = (-13)^(1/3)
3. Simplify the left side of the equation: x = (-13)^(1/3)
4. Calculate the cube root of -13: x = -2.3513 (rounded to 4 decimal places)

So the solution to the equation is x = -2.3513.

Note: The original question had some typos and irrelevant parts, so I ignored those and focused on the main equation to solve.

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Answer: 75% of $13.50 is 10.125

Step-by-step explanation:

Answer:

10.125

Step-by-step explanation:

13.50 x .75 = 10.25

To find the missing quantity, we will plug in the given values into the formula for simple interest and solve for the unknown variable. The formula for simple interest is I = Pxrxt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Given:
P = $4000
r = 8% = 0.08
t = 3 years

Plugging in the given values into the formula, we get:

I = $4000 x 0.08 x 3

Simplifying the equation, we get:

I = $960

Therefore, the missing quantity is the interest, I, which is equal to $960.

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The value of the expression −16 + 12 is −4.  

Subtraction is a basic arithmetic operation that involves finding the difference between two numbers. It is denoted by the minus sign (-) and is performed by subtracting the second number from the first number.

We can subtract fractions, decimals, and negative numbers by following the same principles of subtraction.

Here we have

The numerical expression −16 + 12    

As we know

12 is 4 greater than 16 and 16 has a negative sign

Therefore,

The value of the expression −16 + 12 is −4.  

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Answer:

On June 1, 2013, Anchorage, Alaska experiences 18 and 1/4 hours of daylight.

In a 24-hour day, there are 24 - 18 and 1/4 = 5 and 3/4 hours without daylight.

Therefore, the number of hours without daylight on June 1, 2013 in Anchorage, Alaska was 5 and 3/4 hours.

Answer:

24-18.4=5 and3/4

Step-by-step explanation:

The researcher's study aims to examine how exercise and diet affect weight loss. The researcher collected data from 12 volunteers with similar weights and health conditions and randomly assigned them to one of three programs: Program I with diet only, Program II with exercise only, and Program III with a combination of diet and exercise. After three months, the weight loss of each participant was recorded and summarized. The researcher wishes to carry out nonparametric tests at a significant level of 0.05 to examine the effectiveness of the three programs and to compare the effectiveness of Program III to Program I.

a) To examine the effectiveness of the three programs, we can use the Kruskal-Wallis test, a nonparametric test that compares the medians of three or more groups. The null hypothesis is that the medians of the three programs are equal, and the alternative hypothesis is that at least one of the medians is different. We can use the R function kruskal.test() to carry out the test:

```
> weight_loss <- c(2,0,1,1,1,2,1,3,2,1,4,4)
> program <- factor(c(rep("I",4), rep("II",3), rep("III",5)))
> kruskal.test(weight_loss ~ program)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of the three programs.

b) To compare the effectiveness of Program III to Program I, we can use the Wilcoxon rank-sum test, a nonparametric test that compares the medians of two groups. The null hypothesis is that the medians of Program III and Program I are equal, and the alternative hypothesis is that the medians are different. We can use the R function wilcox.test() to carry out the test:

```
> weight_loss_I <- c(2,0,1,1)
> weight_loss_III <- c(3,2,1,4,4)
> wilcox.test(weight_loss_I, weight_loss_III)
```

The output shows the test statistic and the p-value. If the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the medians of Program III and Program I.

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The distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles, which can be calculated using the Pythagorean theorem.

The Pythagorean Theorem is an equation in geometry which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In other words, a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse.

Weather station A is 34 miles away from the thunderstorm located at point c. To measure the distance between weather station A and the storm, we must calculate the hypotenuse of a right triangle. The right triangle is formed by the two points of the storm and weather station A, with the 34 miles between them forming the base of the triangle. The hypotenuse of the triangle is the distance between the two points, which can be calculated using the Pythagorean theorem. The equation for the Pythagorean theorem is a² + b²= c², where a and b are the sides of the triangle, and c is the hypotenuse.

Therefore, the distance between weather station A and the storm is  [tex]\sqrt{(34^2 + 34^2)}[/tex], which is 48.48 miles.

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This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.

In order to graph the line whose equation is y=5/2x+2, we need to begin by plotting the point (0,2) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.

Similarly, to graph the line whose equation is y=5/2x+3, we need to begin by plotting the point (0,3) on the graph. This is the y-intercept of the equation, which is where the line crosses the y-axis. From this point, we need to move 5 units up (the rise) and 2 units to the right (the run). This will give us another point on the line. We can then draw a straight line through these two points to graph the equation.

In both cases, the slope of the line is 5/2, which is the coefficient of x in the equation. The slope tells us how much the line rises or falls for every unit it moves to the right. In this case, the line rises 5 units for every 2 units it moves to the right. This is why we move 5 units up and 2 units to the right from the y-intercept to find another point on the line.

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The diameter of the opening of the cone is approximately 8.92 units.

We can use the formula for the volume of a cone:

V = (1/3) × π × r^2 × H

where V is the volume, H is the height, and r is the radius of the base.

In this case, we are given the volume V = 196 and the height H = 12. We want to find the diameter of the opening, which is 2r.

First, we can rearrange the formula for the volume to solve for r

r = sqrt((3V) / (πH))

Plugging in the values, we get

r = sqrt((3 × 196) / (π × 12)) ≈ 4.46

So the radius of the base of the cone is approximately 4.46 units.

Finally, we can find the diameter of the opening:

d = 2r ≈ 8.92 units

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The given question is incomplete, the complete question is:

The volume of the cone is 196 cubic units. If the height of the ice cream cone is H=12 what is the diameter of the opening of the cone?

Answer: To find the number of stamps on each page, we can divide the total number of stamps by the number of pages:

263 stamps ÷ 9 pages = 29.22 stamps per page (rounded to two decimal places)

Since we want to place the same number of stamps on each page with as few left over as possible, we can round down to the nearest whole number:

29 stamps per page

To find out how many stamps were left to put in an envelope, we can multiply the number of pages by the number of stamps per page, and then subtract from the total number of stamps:

263 stamps - (29 stamps per page x 9 pages) = 8 stamps left over to put in an envelope

Therefore, the completed sentences are:

29 stamps were placed on each page.

8 stamps were put in an envelope.

Step-by-step explanation:

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

Surface area is the total area that the surface of an object occupies. It is a measure of how much area is covered by the exterior of an object. The formula for the surface area of a cylinder is:

Where r = radius of the base and h = height of the cylinder.

Here we have

Diameter of the cylinder = 2.8 cm

Radius of the cylinder = 2.8/2 = 1.4 cm

Height of the cylinder = 3.7 cm  

Using the formula,

The surface area of a cylinder SA= 2πr² + 2πrh

The surface area of the cylinder

= 2π(1.4)² + 2π(1.4)(3.7)

= 2π(1.4)² + 2.8π(3.7)

Here, the total surface area of the cylinder will equal the amount of wrapping paper needed to completely cover the cylinder

Therefore,

The equation to calculate the amount of wrapping paper is 2π(1.4)² + 2.8π(3.7) cm²

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hi i think its A. SA = 2π(1.4)2 + 2.8π(3.7) hope this helped have a nice day! :)

Answer:

C) Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank. Savings accounts provide a safe and secure way to store money for use in the future. They also offer the opportunity to earn interest over time, which can be used to grow your savings. As a result, savings accounts are a great way to save for long-term goals such as retirement, a child's education, or a down payment on a home.

Answer:

C)Savings accounts are designed to earn interest to encourage depositors to keep their money in the bank.

Step-by-step explanation:

Savings accounts are designed to keep your money safe and to hold it for as long as you want. Ex for the future, such as collage or something you really want like a car. A saving account will  will hold your money until you want to deposit it out of your account.

(a) The proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) The proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.

Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.

To find the proportion of observations in a standard normal distribution that satisfies each of the statements, we need to use a standard normal distribution table or calculator.

(a) z > -1.66

We need to find the area to the right of z = -1.66 on a standard normal distribution table or calculator. This is equivalent to finding the area to the left of z = 1.66 since the standard normal distribution is symmetrical.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525. Therefore, the area to the right of z = -1.66 is:

1 - 0.9525 = 0.0475

So, the proportion of observations in a standard normal distribution that satisfies z > -1.66 is 0.0475, or approximately 4.75%.

(b) -1.66 < z < 1.66

We need to find the area between z = -1.66 and z = 1.66 on a standard normal distribution table or calculator.

Using a standard normal distribution table or calculator, we find that the area to the left of z = 1.66 is 0.9525 and the area to the left of z = -1.66 is 0.0475 (as calculated in part (a)). Therefore, the area between z = -1.66 and z = 1.66 is:

0.9525 - 0.0475 = 0.9050

Therefore, the proportion of observations in a standard normal distribution that satisfies -1.66 < z < 1.66 is 0.9050, or approximately 90.50%.

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Points A and Q are connected by a line. To get the length of AR, measure the distance between A and Q and multiply that value by k. To find point R, mark off the length of AR along a ray that extends from point A in the direction of Q.

In mathematics, a ray is a segment of a line with a known starting point but no known endpoint. It can go on forever in that one direction. A beam cannot be measured since it lacks a terminal. fun facts A ray is similar to the sun's rays.

In geometry, a ray is a line that, starting from a single terminal, extends indefinitely in one direction (or point of origin). A ray is represented by a beam of sunlight travelling across space; while the sun is the ray's goal, it continues to travel forever.

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Complete question -

Answer: 207.1875

Step-by-step explanation:

side length a = 19.5 cm

side length b = 21.25 cm

diagonal p = q = 28.841159824112 cm

perimeter P = 81.5 cm

area of rectangle A = 414.375 cm2

area of rectangle divided into a triangle = 207.1875

hope this helps

Answer:

True both each.

Step-by-step explanation:

Your teacher would probably like you to remember the Trig Identities or allow you to have a cheat sheet for the Quiz or Test.

[tex]\frac{sin(\alpha )}{sin^{2}(\alpha) +cos2\alpha } \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +[cosx^{2} (\alpha)-sinx^{2} (\alpha )]} \\\\\frac{sin(\alpha )}{sin^{2}(\alpha) +cosx^{2} (\alpha)-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{[sin^{2}(\alpha) +cosx^{2} (\alpha)]-sinx^{2} (\alpha )}[/tex]

[tex]\frac{sin(\alpha )}{1-sinx^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos^{2} (\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )*cos(\alpha )}\\\\\frac{sin(\alpha )}{cos(\alpha )}*\frac{1}{cos(\alpha )} \\\\tan(\alpha )*sec(\alpha )\\\\\frac{1}{cot(\alpha )}*sec(\alpha )\\\\\frac{sec(\alpha )}{cot(\alpha )}[/tex]

The given statement " let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 will be denoted by P(X=8)" is true. Because In probability theory, P(X=8) denotes the probability that the random variable X takes on the value 8.

Probability is a measure of the likelihood or chance that a certain event or outcome will occur. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.

In this case, X represents the number of male births between 1:00am and 3:00am at a hospital in Orange County. So, P(X=8) represents the probability that exactly 8 male births occur during that time period.

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--The given question is incomplete, the complete question is

"True or false let X be the number of male births between 1:00am and 3:00am at a hospital in orange county. The probability that X equals 8 is denoted by P(X=8)"--

(A). The chest has a volume of 17,600 cubic inches. (B). The cushion covers 880 square inches of the chest. (C). Whereas area is measured in square units, volume is measured in cubic units.

An object's area is determined by its shape. The amount of space a figurine or any other as double geometric shape takes up on a plane depends on its area.

(A). Chest volume is calculated as follows: 40 inches by 22 inches by 20 inches, or 17,600 cubic inches.

(B). The cushion's coverage area for the chest is 40 inches by 22 inches, or 880 square inches.

(C). The units for area are square units, while the units for volume are cubic elements (like as cubic feet or cubic meters) (such as square inches or square meters). This is so because area is the measure of space an item occupies in two dimensions, but capacity means the quantity of space an object occupies in three dimensions. As a result, area is expressed in feet or meters whereas volume is recorded in cubic units.

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The ordered pairs are the solution to the inequality as follows:

6) (-1,3) and 7) (1,4).

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

As per the question, we have:

5) (0,-1)

No, this ordered pair is not a solution to the inequality.

6) (-1,3)

Yes, this ordered pair is a solution to the inequality.

7) (1,4)

Yes, this ordered pair is a solution to the inequality.

8) (0,0)

No, this ordered pair is not a solution to the inequality.

9) (3,3)

No, this ordered pair is not a solution to the inequality.

10) (2, 1)

No, this ordered pair is not a solution to the inequality.

Thus, the ordered pairs are the solution to the inequality as follows:

6) (-1,3) and 7) (1,4).

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Answer:

See below.

Step-by-step explanation:

We are asked to "expand", rather distribute the expression.

We can Distribute due to the Distributive Property.

The Distributive Property is a property that allows us to distribute the multiplier into numbers in the parentheses.

Let's distribute for this expression.

Distribute:

[tex]-5(-2d + 6)=(-5 \times -2d)+(-5 \times 6)= 10d -30[/tex]

Our distributed expression is 10d - 30.

The following are the correct convertion for the units of mass:

8000 mg converted to gram is 8 g

80 g converted to kilogram is 0.08 kg

0.8 kg converted to g is 800 g.

Gram (g) is the base unit of mass in the metric system. The milligrams (mg) and kilograms (kg) are derived units.

1 gram = 1000 milligrams (mg)

1000 grams = 1 kilogram (kg)

8000 mg = (8000/1000) g

8000 mg = 8 g

80 g = (80/1000) kg

80 g = 0.08 kg

0.8 kg = (0.8 × 1000) g

0.8 kg = 800 g.

In conclusion, 8000 mg converted to gram is 8 g, 80 g converted to kilogram is 0.08 kg, and 0.8 kg converted to g is 800 g.

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The x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

R(x) cannot be at x=-1, -2, 2, 3 because these are the values of the function at these points. Additionally, R(x) cannot be at x=10 and x=1 because these are the holes of the function. Therefore, the x-values that R(x) cannot be are -1, -2, 2, 3, 10, and 1.

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The right rectangular prism's longest line segment measures around 14.79 cm in length.

We are aware that the rectangular prism's body diagonal makes up the longest line segment inside a right rectangular prism. The longest distance is that between points A and D. AD is the longest line segment as a result. To determine a line segment's length, use a scale. Straight line segments can be measured with it.

The Pythagorean theorem can be used to determine how long the space diagonal is:

a = length = 12.6 cm

b = width = 3.2 cm

c = height = 7 cm

You may determine the space diagonal (d) by using:

d = sqrt(a² + b² + c²)

Substituting the values, we get:

d = sqrt(12.6² + 3.2² + 7²) cm

d = sqrt(159.76 + 10.24 + 49) cm

d = sqrt(219) cm

d ≈ 14.79 cm

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Question:

What is the measurement of the longest line segment in a right rectangular prism that is 12.6 centimeters long, 3.2 centimeters wide, and 7 centimeters tall, and that connects two vertices that are not on the same face of the prism?

The length of the rectangular prism is 13 centimetres.

The volume of a rectangular prism is 208 cm³. The area of one end is 16 cm². The length of the rectangular prism can be found as follows:

Therefore,

volume of a rectangular prism = lwh

where

Hence, let's find the length

volume of a rectangular prism = lwh

208 = 16 × l

16l = 208

divide both sides by 16

l = 208 / 16

l = 13 cm

Therefore,

length of the prism = 13 cm

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The expression  9-36x can be factorized as 9(1-4x)

An expression's factors are things that are multiplied by other things. A number, variable, phrase, or any other lengthier expression may be used. For instance, 2, x, and y are the factors of 2xy.

To factor the expression 9-36x completely, we need to find the greatest common factor (GCF) of the two terms and then use the distributive property to factor it out.

The GCF of 9 and 36 is 9, so we can factor out 9 from both terms:

9-36x = 9(1-4x)

Now the expression is factored completely.

So the final answer is:

9-36x = 9(1-4x)

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The roots in simplest form are x=-8+6i and x=-8-6i.

The question is asking you to find the roots of -5x^(2)-80x-140=0 in simplest form by completing the square.

To complete the square, follow the steps below:

1. Divide the coefficient of the x^2 term by 2 and add the result to both sides of the equation:
-5x^2/2 + 80x/2 + 140 = 0 + 5x^2/2

2. Square the coefficient of the x^2 term: (5x^2/2)^2

3. Add this result to both sides of the equation: 5x^2/2 + (5x^2/2)^2 + 80x/2 + 140 = 5x^2/2 + (5x^2/2)^2

4. Rewrite the equation as a perfect square on the left side of the equation: (5x^2/2 + 40x/2)^2 = (5x^2/2 + 40x/2)^2 + 140

5. Take the square root of both sides to solve for x:
5x^2/2 + 40x/2 = ± √140

6. Rewrite the equation as two equations in x:
x = -80 ± √140 / 10

7. Simplify:
x = -8 ± √14  / 1

Therefore, the roots of -5x^(2)-80x-140=0 in simplest form by completing the square are x = -8 ± √14 / 1.
To find the roots in simplest form by completing the square for the equation -5x^(2)-80x-140=0, we need to follow these steps:

1. First, we need to isolate the x terms on one side of the equation. We can do this by adding 140 to both sides of the equation:

-5x^(2)-80x=140

2. Next, we need to factor out the coefficient of the x^(2) term, which is -5:

-5(x^(2)+16x)=-140

3. Now we need to complete the square by adding the square of half of the coefficient of the x term to both sides of the equation:

-5(x^(2)+16x+64)=-140+320

4. Simplify the right side of the equation:

-5(x+8)^(2)=180

5. Divide both sides of the equation by -5:

(x+8)^(2)=-36

6. Take the square root of both sides of the equation:

x+8=±6i

7. Solve for x:

x=-8±6i

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The result of this synthetic division is the quotient (1 2/3 5/3)

To divide two polynomials using synthetic division, we need to write the dividend as a binomial of the form (x-r) and the divisor in its linear form. In this case, the binomial is (x+2) and the linear form is 3x2+7x+2.

Quotient:
3/3=1

2/3=2/3

Coefficients of dividend: 3 7 2

Quotient: 1 2/3

Product of quotient and binomial: (x+2)

(3x2+7x+2) - (x+2): 3x+5 2

Quotient:
3/3=1

2/3=2/3

5/3=5/3

The result of this synthetic division is the quotient (1 2/3 5/3).

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Answer:

D. The other solution to function g is 9 + √2i

Step-by-step explanation:

The roots of a quadratic equation of the form ax² + bx + c = 0

are

[tex]x = -\dfrac{b}{2a} + \dfrac{\sqrt{b^2-4ac}}{2a}\\and\\x = -\dfrac{b}{2a} - \dfrac{\sqrt{b^2-4ac}}{2a}\\[/tex]

If one of the roots is 9 - √2i then
[tex]-\dfrac{b}{2a} = 9[/tex]

and

[tex]\dfrac{\sqrt{b^2-4ac}}{2a} = 2i[/tex]

So if one root is 9 - √2i then the other root must be 9 -+ 2i

This is answer choice D

The identity cos²θ/2 is (1 + cosθ)/2

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We can use the half-angle identity for the cosine function to solve this problem:

cos²θ/2 = (1 + cosθ)/2

Therefore, to find cos²θ/2 , we need to know the value of cosθ.

If the value of cosθ is known, we can substitute it into the half-angle identity to find cos²θ/2

Hence, the identity cos²θ/2 is (1 + cosθ)/2

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