Find the probability of getting two heads and three tails in a
single throw of five unbiased coins?

37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1

Learn more about Trigonometric functions:

brainly.com/question/6904750

#SPJ11

Answer:

22

Step-by-step explanation:

10+11=21

.05+.05=1

1+21=22

a) The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.

b) The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.
c) The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.

Evaluate the following expressions. Your answer will be an angle in radians and in the interval [-π/2, π/2]
(a) sin^-1 (1) = π/2
(b) sin^-1 (√2 / 2)= π/4
(c) sin^-1 (- √2 / 2)= -π/4


(a) sin^-1 (1) = π/2
The inverse sine of 1 is π/2 radians, which is equivalent to 90 degrees.

(b) sin^-1 (√2 / 2)= π/4
The inverse sine of √2 / 2 is π/4 radians, which is equivalent to 45 degrees.

(c) sin^-1 (- √2 / 2)= -π/4
The inverse sine of - √2 / 2 is -π/4 radians, which is equivalent to -45 degrees.

Learn about Angle in radians and interval

brainly.com/question/30305712

#SPJ11

Answer: What else? Is that the whole sentence to this story i dont get it?

Step-by-step explanation:

The mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

A cuboid is a three-dimensional geometric shape that has six rectangular faces. It is also known as a rectangular parallelepiped. A cuboid has six rectangular faces, where opposite faces are congruent and parallel. The cuboid has eight vertices, twelve edges, and six rectangular faces.

To calculate the mass of a cuboid, you need to know its volume and density. The volume of a cuboid is the product of its length, width, and height. The density of a material is its mass per unit volume. Once you have these values, you can use the following formula to calculate the mass of the cuboid:

Mass = Density x Volume

where Mass is the mass of the cuboid, Density is the density of the material of which the cuboid is made, and Volume is the volume of the cuboid.

In the given question,

Using the given values, we can now calculate the mass of the solid copper cuboid in kg.

The volume of the copper cuboid is:

Volume = Length × Breadth × Height = 10 cm × 5 cm × 3 cm = 150 cm³

The mass of the copper cuboid can be calculated by multiplying its volume with its density. We are given that the density of copper is 9.86 g/cm³. Therefore, we have:

Mass = Volume × Density = 150 cm³ × 9.86 g/cm³ = 1479 g

To convert the mass in grams (g) to kilograms (kg), we need to divide the mass by 1000. Therefore:

Mass in kg = Mass in g / 1000 = 1479 g / 1000 = 1.479 kg

Therefore, the mass of the solid copper cuboid with dimensions length = 10cm, breadth = 5cm, and height = 3cm, is 1.479 kg.

To know more about cuboid,visit:

https://brainly.com/question/29568631

#SPJ9

The expression that represents the width of the rectangle is 6x^5y^2

We know that the area of a rectangle is given by the formula:

Area = Length x Width

We can rearrange the formula for the area to solve for the width:

Width = Area / Length

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

Area = 54x^8y^6

Length = 9x^3y^4

Substituting the given values, we get:

Width = (54x^8y^6) / (9x^3y^4)

Evaluate the quotient expression

Width = 6x^5y^2

Hence, the width expression is 6x^5y^2.

Read more about area at

https://brainly.com/question/22972014

#SPJ1

The frequency of a repeated event is its number of instances for every unit of time. In below given way frequency table can be constructed.

The frequency of a repeated event is its number of instances for every unit of time. It differs from angular frequency and is sometimes made reference to as temporal resolution for clarification. The unit of frequency is hertz (Hz), or one occurrence per second.

The time elapsed between events is measured by the period, which is the opposite of the frequency. For instance, the period, T—the time between beats—is equal to half a second if a heart beats 120 times per minute. Frequency tables to represent the morning and afternoon dogs as two sets of data are:

range        frequency

0- 9             2

10- 19           3

20-29         1

30-39         2

40-49         1

50-59         1

Therefore, in above given way frequency table can be constructed.

To know more about frequency, here:

https://brainly.com/question/30053506

#SPJ1

The simplified expression after doing this calculation is -1/3. To perform the addition or subtraction and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator for x and 3 is 3x.

Multiply each fraction by the necessary factor to get the common denominator. For the first fraction, we multiply by 3/3, and for the second fraction, we multiply by x/x.

3/3 * (x/x) - x/x * (4/3) = (3x - 4x)/3x = (-x)/3x. Now, we can simplify the expression by canceling out the common factor of x in the numerator and denominator. (-x)/3x = -1/3

The simplified expression is -1/3.

Know more about fraction here:

https://brainly.com/question/10354322

#SPJ11

Answer: The correct answer would be Graph H.

Step-by-step explanation:

Answer:

top right

Step-by-step explanation:

600 per 10 hours is a rate of 60/hour.

You need a graph that has a slope of 60 and includes the point (1, 60).

Answer: top right

The length of 2W in inches can be calculated by using the measurements of the parallelogram. Wxx is 2x+15, and xY is x+27. Since the length of W xx and xY is referring to the same line, x+27=2x+15. Solving for x, x=12. Knowing the value of x, Wxx=2(12)+15=39 inches and xY=12+27=39 inches. Therefore, 2W=2(39)=78 inches.

The length of a line in a parallelogram can be calculated by adding the two measurements of the two lines containing the same point. Since the line containing point W is the same line containing point x, the two measurements can be solved for the same variable, x. Once the variable is determined, the value of the two lines containing the same point can be determined. The value of the two lines can then be multiplied by 2 to determine the length of the line in the parallelogram.

Know more about parallelogram here

https://brainly.com/question/29147156#

#SPJ11

After watching "Nike an Example of a TNC (Transnational Corporation)" and reviewing the readings and notes, it is clear that Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the countries where it produces ("the global South") and in the countries where it sells its products ("the global North").

In the global South, Nike's production has led to the creation of jobs and an increase in income for workers. However, these workers often face poor working conditions and low wages, which can negatively impact their standard of living. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for workers and their communities.

In the global North, Nike's production has led to the availability of affordable and fashionable clothing and shoes. However, the low prices of these products are often achieved through the exploitation of workers in the global South, which can lead to ethical concerns for consumers. Additionally, the environmental impact of Nike's production can also have a negative effect on the standard of living for consumers and their communities.

Overall, Nike's production of shoes and clothing around the world has had a significant effect on the standard of living of workers in the global South and consumers in the global North. While there are some benefits, such as job creation and affordable products, there are also significant negative impacts, including poor working conditions, low wages, and environmental degradation.

Learn more about watching

brainly.com/question/11375960

#SPJ11

Answer:

3/4

Step-by-step explanation:

Answer:

~7.8

Step-by-step explanation:

side 1 = 5

side 2 = 6

hypotenuse = h

h² = 5² + 6²

h² = 25 + 36

h² = 61

h = [tex]\sqrt{61}[/tex]

h = 7.8102...

Answer:

Step-by-step explanation:

1

The closest answer choice to 26.25 cm² is G. 16.5 cm².

What is area ?

Area is a measurement of the amount of space inside a two-dimensional figure, such as a square, rectangle, triangle, parallelogram, or circle. It is expressed in square units, such as square centimeters (cm²), square meters (m²), square inches (in²), or square feet (ft²).

Based on the given image, we can use the ruler to measure the dimensions of the parallelogram.

From the ruler, we can see that the base of the parallelogram is approximately 7.5 cm, and the height is approximately 3.5 cm. Therefore, the area of the parallelogram is:

Area = base x height

Area = 7.5 cm x 3.5 cm

Area = 26.25 cm² (rounded to the nearest 0.5 cm)

Among the answer choices provided, the closest one to the calculated area of the parallelogram is 26.5 cm², which is not provided in the answer choices.

Therefore, The closest answer choice to 26.25 cm² is G. 16.5 cm².

To learn more about Area from given link.

https://brainly.com/question/12187609

#SPJ1

Answer:

36πmm^2

Step-by-step explanation:

6mm^2=36mm

36mm×π=36πmm^2

The inequalities seen on Cartesian plane are - 2 · x + y > 1 and - (1 / 2) · x + y ≤ 2, respectively.

In this problem we find two graphs by inequalities on Cartesian plane, whose definitions are listed below:

Case 19:

f(x) > y

Case 20:

f(x) ≤ y

Each inequality has a function of the form:

y = m · x + b

Where:

And the slope can be determined by secant line formula:

m = Δy / Δx

Now we proceed to determine each inequality:

Case 1:

Slope

m = 4 / 2

m = 2

Intercept

b = 1

Inequality

y > 2 · x + 1

- 2 · x + y > 1

Case 2:

Slope

m = 1 / 2

Intercept

b = 2

Inequality

y ≤ (1 / 2) · x + 2

- (1 / 2) · x + y ≤ 2

To learn more on inequalities: https://brainly.com/question/27989101

#SPJ1

The coordinates of point D are (-2,5) and the points given have been plotted. The solution has been obtained by using the distance formula.

What is distance formula?

The distance between two points can be calculated using the xy-plane distance formula.

We are given that ABCD should form a rectangle.

We know that opposite sides of a rectangle are equal.

So, AB = CD

Using the distance formula which is

d = √(x₂ - x₁)² + (y₂ - y₁)²

We get

⇒AB = √(3 - (-6))² + (-8 - (-4))²

⇒AB = √(3 + 6)² + (-8 + 4)²

⇒AB = √(9)² + (-4)²

⇒AB = √81 + 16

⇒AB = √97        ...(1)

Let the coordinates of Point D be (x, y)

So, similarly

⇒CD = √(x - 7)² + (y - 1)²   ...(2)

On equating (1`) and (2), we get

⇒√97 = √(x - 7)² + (y - 1)²

On squaring both sides, we get

⇒97 = (x - 7)² + (y - 1)²

⇒97 = x² + 49 - 14x + y² + 1 - 2y

⇒97 = x² + 50 - 14x + y² - 2y

⇒47 = x² - 14x + y² - 2y       ...(3)

Also, AC = BD as these are the opposite sides of the rectangle.

Using the distance formula, we get

⇒AC = √(7 - (-6))² + (1 - (-4))²

⇒AC = √(7 + 6)² + (1 + 4)²

⇒AC = √(13)² + (5)²

⇒AC = √169 + 25

⇒AC = √194     ...(4)

Similarly,

⇒BD = √(x - 3)² + (y - (-8))²

⇒BD = √(x - 3)² + (y + 8)²        ...(5)

On equating (4`) and (5), we get

⇒√194 = √(x - 3)² + (y + 8)²  

On squaring both sides, we get

⇒194 = (x - 3)² + (y + 8)²  

⇒194 = x² + 9 - 6x + y² + 64 + 16y

⇒194 = x² + 73 - 6x + y² + 16y

⇒121 = x² - 6x + y² + 16y    ...(6)

On subtracting (3) and (6), we get

8x + 18y = 74

On dividing by 2, we get

4x + 9y = 37

From this, we get

x = (37 - 9y) / 4

Substituting this in (3), we get

⇒47 = [(37 - 9y) / 4]² - [14 * [(37 - 9y) / 4]] + y² - 2y

On solving this, we get

y = 5

On substituting this in x, we get

x = (37 - 9(5)) / 4

x = (37 - 45) / 4

x = -8 / 4

x = -2

Hence, the coordinates of point D are (-2,5) and the points given have been plotted.

Learn more about distance formula from the given link

https://brainly.com/question/30395212

#SPJ1

The difference in area between a circle with a radius of 10cm and regular pentagon inscribed in it is  142cm².

The difference in area between a circle with a radius of 10cm and a regular pentagon inscribed in it can be found by first finding the area of the circle and then the area of the pentagon, and then subtracting the two values.

To find the area of the circle, we use the formula

A = πr²,

where r is the radius of the circle. In this case, r = 10cm, so the area of the circle is:

A = π(10cm)²
A = 100π cm²

To find the area of the regular pentagon, we can use the formula

A = (1/4)n*a² * cot(π/n),

where n is the number of sides of the polygon and a is the length of one side. Since the pentagon is inscribed in the circle, we can use the radius of the circle to find the length of one side of the pentagon.

The length of one side of the pentagon is:

a = 2r * sin(π/n)
a = 2(10cm) * sin(π/5)
a = 11.756cm

Now we can plug this value into the formula for the area of the pentagon:

A = (1/4)(5)(11.756cm)² * cot(π/5)
A = 172.047cm²

Finally, we can subtract the area of the pentagon from the area of the circle to find the difference in area:

Difference in area = 100π cm² - 172.047cm²
Difference in area = 314.159cm² - 172.047cm²
Difference in area = 142.112cm²

To the nearest whole, the difference in area between the circle and the pentagon is 142cm².

Learn more about circle here:

https://brainly.com/question/10209400

#SPJ11

The Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.

The null hypothesis states that a population parameter is equal to a value. The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.

Null Hypothesis (H0): The wait time for a new roller coaster is equal to or less than 90 minutes (H0: μ ≤ 90).

Alternative Hypothesis (Ha): The wait time for a new roller coaster is greater than 90 minutes (Ha: μ > 90).

In words, the null hypothesis states that the average wait time for the new roller coaster is equal to or less than 90 minutes.

The alternative hypothesis states that the average wait time is greater than 90 minutes.

We use the symbol μ to represent the population means of wait times for the new roller coaster.

Therefore, the Null Hypothesis (H0: μ ≤ 90) and Alternative Hypothesis (Ha). of the wait time for a new roller coaster is at least 90 minutes.

To learn more about Null Hypothesis and Alternative Hypothesis visit:

https://brainly.com/question/25263462

#SPJ1

Assuming the lines, which appear to be diameters, are actual diameters. The value of x is 10.63.

Any straight line that connects two points on a circle's circumference and goes through the circle's center. The length of such a line in geometry. The greatest separation possible between any two points in a metric space (geometry).

Exterior angles are 128, 32, and 45

Interior angles are 11x+4 and 85

Exterior angles = interior angles

128 + 32 + 45 = 11x+4 + 85

205 = 11x + 88

11x = 205 - 88 = 117

x = 117/11

x = 10.63

Therefore, the value of x is 10.63.

Learn more about diameter, here:

https://brainly.com/question/20293543

#SPJ1

The solution to the all given equations is that they have infinite many real solutions

Equation (a)

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

√(x^2-14x+49)=x-7

When both sides of the equations are squared, we have:

x^2 - 14x + 49 = x^2 - 14x + 49

Evaluate the like terms

0 = 0

This represents infinite many solutions

Equation (b)

Here, we have:

√(4x^2-20x+25)=5-2x

When both sides of the equations are squared, we have:

4x^2-20x+25 = 25 - 20x + 4x^2

Evaluate the like terms

0 = 0

This represents infinite many solutions

For the remaining expressions, we have the following (using the above steps)

Equation (c)

√(y^4+2y^2+1) = y^2 + 1

y^4 + 2y^2 + 1 = y^4 + 2y^2 + 1

0 = 0

Equation (d)

√(x^2+2x+1)=x+1

x^2 + 2x + 1 = x^2 + 2x + 1

0 = 0

Equation (e)

√(y^2-20y+100)=y-10

y^2 - 20y + 100 = y^2 - 20y + 100

0 = 0

Equation (f)

√(y^6-2y^3+1)=y^3-1

y^6-2y^3+1 = y^6-2y^3+1

0 = 0

Hence, the equations have infinite solutions

Read more about equations at

brainly.com/question/18831322

#SPJ1

Answer:

Step-by-step explanation:

216

The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.

An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷.  They can be used to find unknown values, such as the area of a circle or the speed of a moving object.

The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.

Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.

For more questions with distributive property,

https://brainly.com/question/6276874

#SPJ1

The value of 4x - 3y when x=1/2 and y=-5 is -13. The given equation can be simplified by using the distributive property.

An mathematical equation is a statement that states that two expressions are equal. It is usually written using symbols such as +, -, x, and ÷.  They can be used to find unknown values, such as the area of a circle or the speed of a moving object.

The equation 4x - 3y = 0 can be rearranged to 4x = 3y. We can substitute 1/2 for x and -5 for y to determine the value of the equation. The equation becomes 4(1/2) (4) -3 (-5). This equation can be simplified by using the distributive property. The equation simplifies to 4/2 - 15. 4/2 simplifies to 2 and -15 simplifies to -15. The final answer is 2 - 15 = -13.

Therefore, the value of 4x - 3y when x=1/2 and y=-5 is -13.

For more questions with distributive property,

brainly.com/question/6276874

#SPJ1

Complete question -

Find the value of 4x - 3y when x=1/2 and y=-5.

Answer:

  [-4, 2]

Step-by-step explanation:

You want the range of the graph shown.

The range is the vertical extent of the graph. This graph has a minimum at y=-4 and a maximum of y=2. All values between these are represented, so the range is ...

  [-4, 2] . . . . or -4 ≤ y ≤ 2

The fourth term of the arithmetic sequence is -24.

An arithmetic sequence is a sequence of numbers in which each term after the first is formed by adding a constant, called the common difference, to the preceding term.

The fourth term of an arithmetic sequence with a1=3 and a recursive formula of an=an-1-9 can be found by using the recursive formula repeatedly until the fourth term is reached.

First, find the second term by plugging in n=2 into the recursive formula:

a2=a2-1-9=a1-9=3-9=-6

Next, find the third term by plugging in n=3:

a3=a3-1-9=a2-9=-6-9=-15

Finally, find the fourth term by plugging in n=4:

a4=a4-1-9=a3-9=-15-9=-24

To know more about arithmetic sequence click on below link:

https://brainly.com/question/15412619#

#SPJ11

Answer:

To find the shorter route, we need to calculate the distances for both routes and compare them.

Route through Towns P and Q:

The distance between Town A and Town P is 3 units to the right and 5 units up, so it is √(3² + 5²) = √34 km.

The distance between Town P and Town Q is 2 units to the right, so it is 2 km.

The distance between Town Q and Town B is 4 units to the right and 4 units down, so it is √(4² + 4²) = 4√2 km.

Therefore, the total distance for this route is √34 + 2 + 4√2 km.

Route through Town R:

The distance between Town A and Town R is 5 units to the right and 3 units up, so it is √(5² + 3²) = √34 km.

The distance between Town R and Town B is 5 units to the right and 7 units down, so it is √(5² + 7²) = √74 km.

Therefore, the total distance for this route is √34 + √74 km.

Comparing the distances, we can see that:

√34 + 2 + 4√2 km ≈ 10.2 km

√34 + √74 km ≈ 12.6 km

Therefore, the shorter route is the one that goes through Towns P and Q, which is approximately 10.2 km long.

Two comparations can be done:

I understand that we want to compare the numbers:

√144 and 12.9329...

Notice that the second number has infinite decimals after the decimal point (and there is no a clear pattern), so it is an irrational number.

For the first one, we know that:

12*12 = 144

So 144 is a perfect square, then when we apply the square root we will get:

√144 = 12

Then the two comparations are:

√144 is rational and 12.9329... is irrational.

And:

12.9329...> √144

Learn more about irrational numbers at:

https://brainly.com/question/20400557

#SPJ1

The probability of fraudulent applications are:

The given parameters are

n = 25

p = 0.12

The individual probability can be calculated as

P(x) = C(n, x) * p^x * (1 - p)^(n - x)

So, we have

Probability the number of fraudulent applications in the sample is 0

P(0) = C(25, 0) * 0.12^0 * (1 - 0.12)^(25 - 0)

P(0) = 0.0410

Probability the number of fraudulent applications in the sample is 3

P(3) = C(25, 3) * 0.12^3 * (1 - 0.12)^(25 - 3)

P(3) = 0.2387

Probability the number of fraudulent applications in the sample is 3 or less

P(x ≤ 3) = P(0) + ... P(3)

Using the formula above, we have

P(x ≤ 3) = 0.4088

Probability the number of fraudulent applications in the sample is 5 or more

P(x ≥ 5) = P(5) + ... P(25)

Using the formula above, we have

P(x ≥ 5) = 0.1734

Probability the number of fraudulent applications in the sample is more than 3

P(x > 3) = 1 - P(x ≤ 3)

By substitution, we have

P(x > 3) = 1 - 0.4088

P(x > 3) = 0.5912

Read mroe about probability at

https://brainly.com/question/251701

#SPJ1