solve the ratio 2.4:3/4:1 2/3​

The Fundamental Pythagorean Identity in trigonomety sin²(x)+cos²(x)=1

Using  the Pythagorean Identity: [tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex] ,

Hence prove.

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

We know that the Pythagorean theorem,

sin²(x)+cos²(x)=1

We have

1-2cos²x = sin²(x)+cos²(x) -2cos²x

1-2cos²x = sin²(x)-cos²(x)

[tex]\frac{1-2cos^2x}{sinxcosx}=tanx-cotx[/tex]

To prove this take the right-hand sides

[tex]\frac{sin^2x}{sinxcosx}-\frac{cos^2x}{sinxcosx}\\\\=\frac{sinx}{cosx}-\frac{cosx}{sinx}\\\\= tanx-cotx[/tex]

learn more about  Fundamental Pythagorean Identity

https://brainly.com/question/2625528

#SPJ1

A random sample of students at a middle school shows that 10 students prefer listening to rock, 15 students prefer listening to hip hop and 25 students prefer no music, while they exercise. the given sample is unbiased.

Ten students at a middle school like to listen to rock, fifteen students prefer to listen to hip-hop, and twenty-five students prefer no music when they exercise.

The given sample is unbiased.

The term "biassed samples" refers to those that were created using biassed sampling methods. A biased sample is most likely not representative of the population. On the other hand, an "unbiased sample" is a sample that was created using a non-biased sampling method. An impartial sample is more likely to produce a representative sample. As was previously stated, a representative sample may not always be produced by an unbiased sampling technique, especially if the sample size is too small.

learn more about a random sample

https://brainly.com/question/29852583

#SPJ1

The total amount of juice in 16 servings is 2/3 + 1/3 = 1 cup, so the total amount of juice is 16 x 1 = 16 cups. This means there are 16 cups of fruit punch in 16 servings.

This question shows how to calculate the total quantity of a combination by multiplying the amount of each component by its respective ratio and then combining them together. It also emphasizes the need of understanding ratios and unit conversions while preparing recipes and measuring food.

To determine how many cups of fruit punch are in 16 servings, multiply the total amount of juice in 16 servings by 16.

For each serving, there are 2/3 cup of pineapple juice and 1/3 cup of cranberry juice, so the total amount of juice in each serving is:

2/3 + 1/3 = 1 cup

Therefore, the total amount of juice in 16 servings is:

16 x 1 = 16 cups

So there are 16 cups of fruit punch in 16 servings.

To know more about amount, visit

brainly.com/question/31538664

#SPJ1

Answer:

90°

Step-by-step explanation:

Given the vectors:

[tex]\displaystyle{\vec v = \langle -6, -3\rangle \ \: \text{and} \ \: \vec u = \langle 4, -8 \rangle}[/tex]

You can find the angle between two vectors by solving for θ in the equation:

[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}[/tex]

Where:

[tex]\displaystyle{\vec v \times \vec u = v_xu_x + v_yu_y}\\\\\displaystyle{|\vec v| = \sqrt{v_x^2 + v_y^2}}\\\\\displaystyle{|\vec u| = \sqrt{u_x^2+u_y^2}}[/tex]

Therefore:

[tex]\displaystyle{\vec v \times \vec u = |\vec v | |\vec u| \cos \theta}\\\\\displaystyle{(-6)(4)+(-3)(-8) = \sqrt{(-6)^2+(-3)^2} \cdot \sqrt{4^2+(-8)^2} \cos \theta}\\\\\displaystyle{-24+24=\sqrt{36+9}\cdot \sqrt{16+64}\cos \theta}\\\\\displaystyle{0=\sqrt{45}\cdot \sqrt{80}\cos \theta}\\\\\displaystyle{\dfrac{0}{\sqrt{45}\cdot \sqrt{80}}=\cos \theta}\\\\\displaystyle{0=\cos \theta}\\\\\displaystyle{\theta = 90^{\circ}}[/tex]

Therefore, the angle between two vectors is 90 degrees.

Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring, expressed as a number between 0 and 1. It is used to analyze and quantify the uncertainty associated with random events or processes.

To find the probability of choosing a number from the sample space that contains both 5 and 7, we need to count the number of outcomes that satisfy this condition and divide by the total number of possible outcomes in the sample space.

From the tree diagram, we can see that there are four possible two-digit numbers that contain both 5 and 7: 57, 75, 56, and 65.

The total number of possible outcomes in the sample space is the number of ways to arrange the four digits in a two-digit number, which is 4 × 3 = 12 (since there are 4 choices for the first digit and 3 choices for the second digit, once the first digit is chosen).

Therefore, the probability of choosing a number from the sample space that contains both 5 and 7 is:

4/12 = 1/3

So the probability of choosing a number from the sample space that contains both 5 and 7 is 1/3 or approximately 0.33.

To know more about probability

brainly.com/question/30034780

#SPJ9

There is 53.5 cubic feet of space left for water in the aquarium.

The volume of three-dimensional space occupied by an object or substance alone is referred to as volume.

The aquarium's total volume can be found by multiplying its dimensions:

Volume = Length x Width x Height

Volume = 6 ft x 3 ft x 3 ft

Volume = 54 cubic feet

However, Ms. Collins has already filled the bottom of the tank with gravel that takes up 0.5 ft of space. Therefore, the remaining space for water is:

Remaining space = Total volume - Gravel volume

Remaining space = 54 cubic feet - 0.5 cubic feet

Remaining space = 53.5 cubic feet

So, there is 53.5 cubic feet of space left for water in the aquarium.

know more about volume visit

brainly.com/question/1578538

#SPJ9

Answer:

The median increases to 7

Step-by-step explanation:

List the numbers in chronological order,

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5

As of now, the median is 6.75.

When a shoe size of 9 is added, we have

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9

Now, the median is 7.

The farmer can expect to calculate the surface area of the barn in units of m² or square meters. Thus, option B is correct.

Surface area is a two-dimensional measurement that represents the total area of all the faces or sides of a three-dimensional object. It is the sum of the areas of all the faces or surfaces that make up the object.

The surface area is typically expressed in square units, such as square meters (m²), square feet (ft²), or square centimetres (cm²), depending on the unit system used.

For example, the surface area of a cube with sides of length "s" can be calculated by finding the area of each face (which is s²), and then summing the areas:

Surface area of a cube = 6 x (side length)² = [tex]6s^2[/tex]

The farmer can expect to calculate the surface area of the barn in units of m² or square meters.

Surface area is a two-dimensional measurement that represents the total area of all the faces or sides of a three-dimensional object, such as a barn. The unit of measurement for surface area is always expressed in square units, such as m², ft², cm², etc.

Therefore, options (a) m, (c) ft, and (d) ft³ are incorrect, surface area

the farmer expect to calculate the surface area in [tex]m^2[/tex].

Learn more about area here:

https://brainly.com/question/27683633

#SPJ1

Answer:

u = 10ft

Step-by-step explanation:

7ft x 8ft = 56. 560 ÷ 56 = 10.
Therefore, u = 10ft

The identity using the Pythagorean Identity:

[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex]  , Hence proved

Trigonometry formulas can be used to address many different kinds of issues. These issues could involve Pythagorean identities, product identities, trigonometric ratios (sin, cos, tan, sec, cosec, and cot), etc. Many formulas, such as those involving co-function identities (shifting angles), sum and difference identities, double angle identities, half-angle identities, etc., as well as the sign of ratios in various quadrants,

the Fundamental Pythagorean Identity: sin²(x)+cos²(x)=1

Verify the identity using the Pythagorean Identity:

[tex]\frac{1-cosx}{sinx}=\frac{sinx}{1+cosx}[/tex]

To prove this take the right-hand side of the given identity.

We know that,

[tex]\frac{sinx}{1+cosx}*\frac{1-cosx}{1-cosx}\\\\=\frac{Sinx(1-cosx)}{1-cos^2x}\\\\=\frac{1-cosx}{sinx}[/tex]

Hence the left-hand sides.

learn more about Pythagorean identities,

https://brainly.com/question/2625528

#SPJ1

answer is b) y = - 3/4 * x - 8,The reason for this is that the slope of the line is -3/4 (since it goes down by 3 units for every 4 units to the right), and it passes through the point (-6,-8).

what is slope?

In mathematics, the slope of a line is a measure of how steep it is. It is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.

In the given question,

Based on the information provided, the equation that represents the straight line passing through -8 on the y-axis and -6 on the x-axis would be:

b) y = - 3/4 * x - 8

The reason for this is that the slope of the line is -3/4 (since it goes down by 3 units for every 4 units to the right), and it passes through the point (-6,-8) which can be verified by substituting these values into the equation.

To know more about slope , visit:

https://brainly.com/question/19131126

#SPJ1

A = π r² is the formula

r is the radius

Hope it helps ✨

Answer:

Step-by-step explanation:

[tex]A=\pi \times r^2[/tex]          where r is the circle's radius

The correct statement is that "P is above sea level and City R is below sea level True"

To determine the position of the points observe the given picture. Here we can observe that the point which has positive values are placed above the sea level and the points which have negative values are placed below the sea level.

The elevation in Feet of these 3 cities is marked on the number line

The point 0 on the number line represents the sea level.

From the figure,

The point P is above sea level and Q is at sea level  

The point R is below the sea level

Hence,  

The correct statement is that "P is above sea level and City R is below sea level True"

Learn more about Sea level at

https://brainly.com/question/21176136

#SPJ1

Complete Question:

The elevation in Feet of these 3 cities is marked on the number line shown below. The point 0 on the number line represents the sea level. Which statement must be true?

Which statement must be true?

A City P and City Q are above sea level.

B City Q and City R are below sea level.

C City P is above sea level and City Q is below sea level.

D City P is above sea level and City R is below sea level.

The statement " if we design a study to have no more than a 10% chance of a type 2 error, then the statistical power of the study equals 90%" is true because achieving a 10% chance of a type 2 error, or a 90% power, means that the study has a high probability of detecting a true effect if it exists

Statistical power is defined as the probability of correctly rejecting a false null hypothesis, or in other words, the probability of detecting a true effect if it exists. A type 2 error, on the other hand, occurs when we fail to reject a false null hypothesis, or when we fail to detect a true effect that actually exists.

Therefore, if we design a study to have no more than a 10% chance of a type 2 error (i.e., 90% power), then we are saying that the probability of detecting a true effect, if it exists, is 90%. This is equivalent to saying that the study has 90% power to detect the effect.

Learn more about statistical power here

brainly.com/question/29355073

#SPJ4

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

When an item or form is rotated about a fixed point, generally the origin or a specified point in the plane, the amount of rotation that takes place is referred to as the degree of rotation. Angles are measured in degrees, where one full rotation equals 360 degrees. The amount of angle shift, expressed in degrees, that occurs when an item or shape is rotated is known as the degree of rotation. A shape has been turned a quarter of a full rotation anticlockwise, for instance, if it is rotated 90 degrees in that direction. Similar to this, a form has completed one-half of a full rotation if it is rotated 180 degrees.

given

The graph suggests that the image was rotated 90 degrees anticlockwise and in the other manner to make.

Compare the figure's initial placement (the grey triangle) to its final placement to see this (the red triangle).

One of the vertices on the grey triangle is pointing upward, and the other two are pointing to the right and left.

The red triangle's up-pointing vertex remains after the transformation, but the other two vertices now point down and up-left, respectively.

This represents the direction and degree of rotation utilised to make the image, which is 90 degrees anticlockwise.

To know more about the degree of rotation visit :-

https://brainly.com/question/28485034

#SPJ1

Answer:

[tex] \ \frac{1}{2} (5 \frac{1}{4} + 7)(2) = 12 \frac{1}{4} [/tex]

A is correct.

The radius and volume of the cylinder are 4 cm and 754 cm³ respectively and volume of the cone is 216 cm³.

What the volume of a cone and cylinder?

Volume of cone and cylinder is V = (1/3)πr²h and V = (1/3)πr²h respectively

where r is the radius of the base of the cone, h is the height of the cone, and π is the mathematical constant π (approximately equal to 3.14).

For cone:

To use this formula, we first need to find the radius of the base of the cone. We know that the diameter of the base is 12 cm, so the radius is half of that:

r = d/2 = 12/2 = 6 cm

Now we can plug in the values we have into the formula:

[tex]V = \frac{1}{3} \pi {r}^{2} h \\ V = \frac{1}{3} π( {6}^{2} )(19) \\ V = ( \frac{1}{3} )π(36)(19) \\ V = ( \frac{1}{3} )(3.14)(36)(19) \\ V = 216.24 cm³[/tex]

So, volume of the cone is 216.24 cm³ or 216 cm³ ( approximately)

For cylinder:

We are given the diameter of the cylinder as 8 cm, so we can find the radius as half of that:

r = d/2 = 8/2 = 4 cm

We are also given the height of the cylinder as 15 cm.

Now we can plug in these values into the formula:

[tex]V = π {r}^{2} h\\ V = π( {4}^{2} )(15) \\ V = π(16)(15) \\ V = 240π \\ V ≈ 753.98 \: cubic \: centimeters[/tex]

Therefore, the volume of the cylinder is approximately 753.98 cubic centimeters or 754 cm³ (approximately).

Learn more about volume:

https://brainly.com/question/463363

#SPJ1

Based on the given information, Lola used 9/8 cups of rice for the rice pudding.

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another. It consists of two numbers separated by a horizontal line called a fraction bar or a vinculum. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator.

Lola has 4 1/2 cups of rice, which is equivalent to 9/2 cups of rice.

She uses 3/4 of the rice to make sushi rolls for dinner. So, the amount of rice she uses for the sushi rolls is:

(3/4) x (9/2) = 27/8 cups of rice

To find the amount of rice she uses for the rice pudding, we need to subtract the amount she used for the sushi rolls from the total amount she had:

9/2 - 27/8 = 36/8 - 27/8 = 9/8

So Lola used 9/8 cups of rice for the rice pudding.

To know more about fractions visit:

brainly.com/question/29766013

#SPJ1

Let a = 10, b = 6, c = 12, and d = x

ab=cd

x = ab/c

x = 10(6)/12

x = 5

Answer: well it could be

2/5 or 8/20 or 1/5 or 16/40

Step-by-step explanation:

The number that should be added to both sides of this quadratic equation to complete the square is (-3/2)² .

When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. Finding the function's highest or minimum value and the time it happens is one use for the square-root method.

We can solve quadratic equations that lack a factor by completing the square.

In order to make the left side of the formula a perfect square trinomial, the equation's form must be adjusted.

The given  quadratic equation:

1 = x² - 3x

This can be written as:

x² - 3x - 1 = 0

a = 1, b = -3 and c = -1.

using the formula: (b/2)² = (-3/2)²

The number added both side is:

(-3/2)² + 1 = x² - 3x + (-3/2)²  (required equation);

On simplification:

9/4 + 1 = (x -3/2)²

13/4 = (x -3/2)²

Thus, the number that should be added to both sides of this quadratic equation to completing square is (-3/2)² .

know more about the completing square'

https://brainly.com/question/13981588

#SPJ1

He received Glhf 25,967.23 as interest at the end of 7 years. The total amount he received at the end of 7 years is GhC 39,067.23.

Simple interest is the interest the lender pays the borrower on the loan. It includes principal only and does not include interest. Simple interest rates are not just for certain loans. This is also the type of interest that banks pay on customers' savings.

a. To find the interest he received at the end of 7 years, we first need to calculate the amount he had at the end of 4 years:

   A = P(1 + r/n) (nt)

⇒ A = 14100 (1+ 0.08)(1× 4)

⇒ A = 19628.61

So, he had GhC 19,628.61 at the end of 4 years. He then transferred this amount to another bank offering 12% compound interest per annum. We can use the same formula to find the amount he will have after 7 years:

 A = P(1 + r/n) (nt)

⇒ A = 19628.61( 1 + 0.12/1) (1×7)

⇒ A = 40067.23

Therefore, the amount he received at the end of 7 years is GhC 40,067.23.

To find the interest he received at the end of 7 years, we subtract the principal amount:

Interest = A - P

Interest = 40067.23 - 14100

Interest = 25,967.23

So, he received GhC 25,967.23 as interest at the end of 7 years.

b. The total amount he received at the end of 7 years is the sum of the principal and the interest:

Total amount = P + Interest

Total amount = 14100 + 25,967.23

Total amount = 39,067.23

Therefore, the total amount he received at the end of 7 years is GhC 39,067.23.

Learn more about Interest:

https://brainly.com/question/30955042

#SPJ1

The maximum point of this quadratic function f(t) = -16t² + 80t + 64 is equal to 164.

In this exercise, you are required to determine the maximum value of the given quadratic functions that is written in standard form. In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

y = a(x - h)² + k

Where:

For the given quadratic function f(t) = -16t² + 80t + 64, the axis of symmetry can be calculated as follows:

Axis of symmetry, Xmax = -b/2a

Axis of symmetry, Xmax = -(80)/2(-16)

Axis of symmetry, Xmax = -80/-32

Axis of symmetry, Xmax = 2.5

For the vertex, we have:

f(t) = -16t² + 80t + 64

f(2.5) = -16(2.5)² + 80(2.5) + 64

f(2.5) = 164.

Read more on quadratic function here: brainly.com/question/13159926

#SPJ1

The linear equations are x + y = 679, 4x + 7y = 3370 and  586 non-students attended the play.

What is a linear equation, exactly?

A linear equation is a mathematical equation that describes a straight line when plotted on a graph. It is an equation in which the highest power of the variable is one. Linear equations are commonly written in the form of y = mx + b, where "x" and "y" are variables, "m" is the slope of the line, and "b" is the y-intercept. Linear equations can be used to model many real-world situations, such as distance and speed, cost and revenue, and temperature and time.

Now,

a) Let x = student tickets sold and y = number of non-student tickets sold. Then we have the following system of linear equations:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

b) To solve for y, we can use the first equation to get:

y = 679 - x

then,

4x + 7(679 - x) = 3370

Simplifying and solving for x, we get:

3x = 2363

x = 787

So 787 student tickets were sold. To find the number of non-student tickets sold, we can use the equation y = 679 - x:

y = 679 - 787 = -108

Since it doesn't make sense to have a negative number of non-student tickets sold, we made an error somewhere. Looking at the problem again, we realize that the equation should be:

x + y = 679 (the total number of tickets sold is 679)

4x + 7y = 3370 (the total revenue from ticket sales is $3370)

where y represents the number of student tickets sold and x represents the number of non-student tickets sold. With this correction, we get:

y = 679 - x

4(679 - x) + 7x = 3370

Simplifying and solving for x, we get:

3x = 1759

x = 586.33

x = 586

So 586 non-student tickets were sold.

Which means 586 non-students attended the play.

To know about linear equations visit the link

brainly.com/question/29739212

#SPJ1

Answer:

The answer is 41

Step-by-step explanation:

82 / 2

Tt represents the points 3 and 7 on the x-axis, since they are both 2 units away from 5 and equation form is | x - 5 | = 2.

What is equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

An absolute value equation that has a solution set containing the numbers 3 and 7 on the x-axis.

One possible equation is:

| x - 5 | = 2

This equation represents the set of all numbers on the x-axis that are 2 units away from the number 5.

In other words, it represents the points 3 and 7 on the x-axis, since they are both 2 units away from 5.

To learn more about equation visit:

https://brainly.com/question/2972832

#SPJ1

Answer:

|x+5|=2 is the equation

Pie chart is the  best to show the percentage of gases on earth's atmosphere.

A pie chart, sometimes known as a circle chart, is a circular statistical visual that shows numerical proportion through slices of data. Each slice's arc length in a pie chart is proportional to the quantity it shows, as are its center angle and area. Although it was given that name because it resembles a slice of pie, there are other ways to serve it.

Nitrogen accounts for 78% of the atmosphere, oxygen 21% and argon 0.9%. Gases like carbon dioxide, nitrous oxides, methane, and ozone are trace gases that account for about a tenth of one percent of the atmosphere.

The Pie chart is the best to show the percentage of gases on earth's atmosphere.

Learn more about Pie chart here:

brainly.com/question/9979761

#SPJ9

The scatter plot that shows correlation with causation is (c)

A scatter plot is a type of graph that displays the relationship between two variables. The position of each point on the plot represents the value of both variables.

If there is a strong positive correlation between two variables, it means that as one variable increases, the other variable also tends to increase.

If there is a strong negative correlation, it means that as one variable increases, the other variable tends to decrease.

The scatter plot with the mst positive or negative correlation is c

This is the scatter plot that shows correlation with causation

Read more about scatter plot  at

https://brainly.com/question/23202763

#SPJ1

Thus, the approximate area of lake whose shape is taken on the square of the grid is 8 sq. unit.

A grid area is a rectangular area just on grid that is made up of one or more grid cells. When you define an area using named grid areas or when you place an object using line-based placement, grid areas are produced.

By dividing the supplied figure in square grids and counting how many of these there are, it is easiest to determine the area of a typical two-dimensional shape.

For the following question:

Thus,

Total area = 4*1 + 8*(1/2)

Total area = 4 + 4

Total area = 8 sq. unit

Thus, the approximate area of the lake whose shape is taken on the square of the grid is 8 sq. unit.

know more about the area on grid

https://brainly.com/question/29165112

#SPJ1