who in 1706 first gave the greek letter pi its current mathematical definition

Answer:

Option D.

Step-by-step explanation:

To find hypotenuse [tex]c[/tex] use formula:

                                    [tex]\text{Cos(B)}=\frac{a}{c}[/tex]

       After substituting [tex]B=62^0[/tex]  and a = 7 we have:

                                 [tex]\text{cos}(62^o)=\frac{7}{c}[/tex]

                                     [tex]0.4695=\frac{7}{c}[/tex]

                                         [tex]c=\frac{7}{0.4695}[/tex]

                                          [tex]c=14.9104[/tex]

Answer:

Step-by-step explanation:

yes

The variables in the equations are aligned as follows:   2x - 3y = 9 and

2x - 3y = 8/3

When we talk about aligning a system of linear equations, we mean rearranging the equations so that the variables are in the same order and have the same coefficients. This is done to make it easier to apply methods for solving systems of equations, such as substitution or elimination.

In a system of linear equations, each equation typically involves two or more variables. The variables may have different coefficients in each equation, and they may appear in a different order. Aligning the system involves rearranging the equations in a way that puts the variables in the same order, with the same coefficients.

Align the variables in given the system of linear equations :

To align the variables in the given equations, we need to rearrange the second equation so that the coefficients of  and  are the same as in the first equation.

To align the variables in the equations, we need to rearrange the terms so that the x, y, and constant terms are all grouped together.

Starting with the first equation:

2x - 3y = 9

We can rearrange this as:

2x = 3y + 9

Now we can divide both sides by 2 to get x by itself:

x = (3/2)y + 4.5

Now let's move on to the second equation:

1-6x +9y = -7

We can rearrange this as:

-6x + 9y = -8

Next, we'll divide both sides by -3 to get x by itself:

2x - 3y = 8/3

Now both equations are in the form of:

ax + by = c

where a, b, and c are constants. The aligned equations are:

2x - 3y = 9

2x - 3y = 8/3

To know more about variables visit :

brainly.com/question/29583350

#SPJ1

the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:

Area = 1/2 x base x height

We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:

14 = 1/2 x base x 6

Multiplying both sides by 2/6 (or simplifying to 1/3) gives:

14 x 3/2 = base

21 = base

Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.

This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.

In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.

To know more about  dimension  click here:

brainly.com/question/8286598

#SPJ4

a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.

b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.

c) The online sales were of 227 billion in the year of 2013.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:

b = 191.

In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:

m = 54/3

m = 18.

Hence the function modeling the sales in x years after 2011 is given as follows:

y = 18x + 191.

The sales were of 227 billion x years after 2011, for which y = 227, hence:

227 = 18x + 191

18x = 36

x = 2.

2 + 2011 = 2013.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

In Triangle ABC, we can draw a circle around each vertex of the triangle.

If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.

Radii is the plural form of radius. It is half of the diameter and the length of the radius is used to calculate the area and circumference of the circle.

To determine whether a triangle is an equilateral triangle, we can use circles.

In this method, we draw three circles, one around each vertex of the triangle.

We then measure the radii of the circles, ensuring that they are all equal. If the radii of the three circles are equal, then the triangle is an equilateral triangle.

In Triangle ABC, we can draw a circle around each vertex of the triangle. Then, we could use a measuring tool to measure the radii of each circle. If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.

This method of using circles to determine whether a triangle is an equilateral triangle is simple and efficient. It does not require any complex calculations, and it is easy to understand.

For more questions related to equilateral triangle

https://brainly.com/question/17264112

#SPJ1

Answer:

false, 216° turns 3/5 in a 360° rotation

In the multiple regression model with k regressors, the variance of the stochastic errors in the population can be estimated by the residual mean square (MSE).

         Multiple regression is a statistical tool that allows the researcher to estimate the relationship between multiple independent variables and a dependent variable. It measures the impact of a given independent variable on the dependent variable after controlling for the other independent variables.

        In simple linear regression, there is only one independent variable, whereas, in multiple linear regression, there is more than one independent variable.

         Residual mean square (MSE) is the variance of the error term (the difference between the predicted and observed values). It represents the average variance of the errors or the average deviation of the dependent variable from its predicted value.

         The MSE can be used to estimate the variance of the stochastic errors in the population. It is calculated by dividing the sum of squared residuals by the degrees of freedom (n-k-1)

           Where n is the sample size and k is the number of regressors.

Learn more about stochastic errors and multiple regression at: https://brainly.com/question/28178214

#SPJ11

The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached

Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are

The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.

In the problem, the graph plotted is that of cosine function and the amplitude of is 8

The 5 points marked are

(-π/16, 0) - the first point

(0, 8) - showing the amplitude and 1/4 cycle

(π/16, 0) - 1/2 cycle

(-π/16, -8) - 3/4 cycle

(3π/16, 0) - one complete cycle

Learn more about trigonometric graph at:

https://brainly.com/question/24329125

#SPJ1

We can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

The matrix product of two matrices, A and B, is defined as the matrix C, where C = AB. To calculate the product of two matrices, we must take the dot product of each row of A and each column of B. If we are given a matrix product A1B, then we can calculate B1A without necessarily knowing what A and B are.

To do so, we must first invert the matrix A1B. We can do this by solving a system of equations. We can set up this system of equations by treating the entries of A1B as the coefficients in a system of equations, and solving for the entries of B1A. Once we have found the inverse, we can calculate the matrix B1A.

Finally, once we have the matrix B1A, we can calculate its product by taking the dot product of each row of B1A and each column of A1B. In this way, we can calculate B1A without knowing the values of A and B.

See more about matrix at: https://brainly.com/question/14414517

#SPJ11

Answer:

16

Step-by-step explanation:

When we divide the entire equation by 1/-2 to get rid of the coefficient of n we get n = 16.

The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

See more about probability at: https://brainly.com/question/14904900

#SPJ11

The volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant is π units cubed. The curve is not provided here. Therefore, it is impossible to solve this question. We are unable to determine the function whose graph is being revolved around the y-axis based solely on the information given.If the curve had been given, we would have used the disk method, which states that the volume of a solid of revolution generated by rotating a plane figure about a line is equal to the sum of the volumes of an infinite number of infinitesimally thin disks perpendicular to that line. If f(x) is a non-negative function defined on [a, b], then the volume V of the solid generated by revolving the region between the curve y = f(x), the x-axis, x = a, and x = b about the y-axis is given by:V = π∫ab[f(x)]2 dxWhere π is the constant π = 3.14159..., a and b are the limits of integration, and f(x) is the function whose graph is being revolved.

It is also important to avoid ignoring any typos or irrelevant parts of the question and to not repeat the question in the answer unless necessary. Finally, when using math terminology or solving math problems, it is important to show all work and use proper notation.

For example, when solving a problem such as "find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places," one might use the formula for finding the volume of a solid of revolution:V=π∫abf(x)2dxwhere f(x) is the function defining the curve, and a and b are the limits of integration. The limits a and b can be found by setting the equation defining the curve equal to zero and solving for x.

Once the limits are found, the function can be integrated and the result can be multiplied by π to find the volume of the solid. The answer should then be rounded to four decimal places and, if the answer does not exist, the answer should be entered as dne.

Learn more about notation:

https://brainly.com/question/29218346

#SPJ11

The probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is used to quantify uncertainty and to make informed decisions in the face of incomplete or uncertain information.

We can assume that the heights of male passengers follow a normal distribution with a mean of 69.0 in and a standard deviation of 2.8 in. Let X be the height of a male passenger in inches. Then, we need to find the probability that X is less than or equal to 74 in, which represents the height of the airliner's doors.

(a) Using the standard normal distribution, we can standardize X as follows:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation of the distribution, and z is the corresponding z-score.

Substituting the values, we get:

z = (74 - 69.0) / 2.8 = 1.75

Using a standard normal distribution table or calculator, we can find the probability that a standard normal random variable is less than or equal to 1.75:

P(Z ≤ 1.75) ≈ 0.9599

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9599, or 95.99%.

To learn more about probability visit:

https://brainly.com/question/13604758

#SPJ1

Answer: 16x+3x^3−8

Please mark me brainliest :)

Answer:

Step-by-step explanation:

[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]    

[tex]7 (x+\frac{9}{28} )=60[/tex]     (multiplied both sides by 3)

[tex]x+\frac{9}{28} =\frac{60}{7}[/tex]          (divided both sides by 7)

[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex]     (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)

Experiment Random Variable (x)Possible values of the random variable Discrete or Continuous.

a) Take a 20-question examination Number of questions answered correctly Discrete (0, 1, 2, 3, ..., 20)

b. Observe cars arriving at a tollbooth Number of cars arriving at tollbooth for 1 hour Discrete (0, 1, 2, 3, ...)

c. Audit 50 tax returns Number of returns containing errors Discrete (0, 1, 2, 3, ...)

d. Observe an employee’s work Number of nonproductive hours in an eight-hour workday Continuous

e.Weigh a shipment of goods Number of pounds Continuous Random variables are numerical values that are a result of a random experiment. Random variables are generally classified into two categories

Solution:

discrete random variables and continuous random variables

.Discrete random variables

 When a random variable can assume only a countable number of values, it is called a discrete random variable.

Examples: the number of cars passing by a particular point of a highway in a day or the number of customers served by a shop in a day.

Continuous random variables: 

When a random variable can assume any value within a given range or interval, it is called a continuous random variable.

Examples: temperature, the weight of a person, or the height of a person.Tax returns: The random variable is discrete, as it can only take certain values (0, 1, 2, 3, and so on) since the number of tax returns containing errors is an integer.The shipment of goods: The random variable is continuous because it can assume any value between the minimum and maximum weight of the shipment, and the weight of the shipment can be any value.

To know more about random variables:

https://brainly.com/question/30789758

#SPJ11

The child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

The given problem requires us to determine the number of milliliters of a liquid medicine that a child should receive in order to obtain a specific dosage of the active ingredient. We are given that the medicine contains 100 mg of the active ingredient in 5 ml.

The child needs to receive 300 mg of the active ingredient, and there are 100 mg of the active ingredient in 5 ml of the medicine. Therefore, the child should be given:

[tex]\frac{300 mg}{100mg/5ml} = \frac{300\text{ mg} \times 5\text{ ml}}{100\text{ mg}} = 15\text{ ml}$$[/tex]

So the child should be given 15 ml of the medicine to receive 300 mg of the active ingredient.

Learn more about Liquid Measurements:

https://brainly.com/question/7744911
#SPJ4

Answer:

between 15 and 16

Step-by-step explanation:

31÷2=15.5 meaning 15.5 is between 15 and 16

The probability of winning is 1/17, which can also be expressed as a decimal (approximately 0.059) or as a percentage (approximately 5.9%).

The odds on a bet represent the ratio of the probability of winning to the probability of losing. In this case, the odds are 16:1 against winning, which means that the probability of winning is 1 out of 16.

To express this probability as a fraction, we can use the formula:

Probability of winning = 1 / (odds + 1)

Plugging in the given odds, we get:

Probability of winning = 1 / (16 + 1)

Probability of winning = 1/17

In this case, the odds of 16:1 against winning correspond to a probability of 1/17, which represents the chance of winning the bet.

To learn more about probability click on,

https://brainly.com/question/29111123

#SPJ4

The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

Learn more about   probability and betting:https://brainly.com/question/29061226

#SPJ11

Answer:

  4/33

Step-by-step explanation:

You want to write 0.1212...(repeating) as a simplified fraction.

A repeating decimal beginning at the decimal point can be made into a fraction by expressing the repeating digits over an equal number of 9s.

Here, there are 2 repeating digits, so the basic fraction is ...

  12/99

This can be reduced by removing a factor of 3 from numerator and denominator:

  [tex]0.\overline{12}=\dfrac{12}{99}=\boxed{\dfrac{4}{33}}[/tex]

__

Additional comment

Formally, you can multiply any repeating decimal by 10 to the power of the number of repeating digits, then subtract the original number. This gives the numerator of the fraction. The denominator is that power of 10 less 1.

  0.1212... = (12.1212... - 0.1212...)/(10^2 -1) = 12/99

Doing this multiplication and subtraction also works for numbers where the repeating digits don't start at the decimal point. Finding a common factor with 99...9 may not be easy.

You can also approach this by writing the number as a continued fraction. The basic form is ...

  [tex]x=a+\cfrac{1}{b+\cfrac{1}{c+\cdots}}[/tex]

where 'a' is the integer part of the original number, and b, c, and so on are the integer parts of the inverse of the remaining fractional part. The attachment shows how this works for the fraction in the problem statement.

A calculator cannot actually represent a repeating decimal exactly, so error creeps in and may eventually become significant.

Answer:

what's your exact question

Answer:

can u pls type the full question

Answer: 132 cubic centimeters

Step-by-step explanation:

To find the volume of the block of clay, we need to add the volumes of the two rectangular pieces.

The volume of a rectangular solid can be found by multiplying its length, width, and height. Let's call the first rectangular piece A and the second rectangular piece B. Then the dimensions of A are 6 cm (length), 4 cm (width), and 3 cm (height), and the dimensions of B are 5 cm (length), 4 cm (width), and 3 cm (height).

The volume of A is:

Volume of A = length x width x height = 6 cm x 4 cm x 3 cm = 72 cubic centimeters

The volume of B is:

Volume of B = length x width x height = 5 cm x 4 cm x 3 cm = 60 cubic centimeters

So the total volume of the block of clay is:

Volume of block = Volume of A + Volume of B = 72 cubic centimeters + 60 cubic centimeters = 132 cubic centimeters

Therefore, the volume of the block of clay is 132 cubic centimeters.

The solution to the equation is x = -2 if x ≠ 0.

The equation  -1/x-1+2/x+5=1 can be rearranged to 2/x+1/x+5 = 0. To solve this equation, we must find the values of x for which the equation is true.
Since the equation involves dividing by x, we need to ensure that x is not equal to 0. Therefore, the restriction on the variable is x ≠ 0.
To solve the equation, we can first add -1/x to both sides to get 2/x + 5 = 1. Then, we can subtract 5 from both sides to get 2/x = -4. Finally, we can divide both sides by 2 to get x = -2.
Therefore, the solution to the equation is x = -2 if x ≠ 0.
To solve the given equation, we need to first find a common denominator. Here, the common denominator is (x - 1)(x + 5).-1(x + 5) + 2(x - 1) = (x - 1)(x + 5)Multiplying both sides by (x - 1)(x + 5), we get:-1(x + 5)(x - 1) + 2(x - 1)(x + 5) = (x - 1)(x + 5)(1)Expanding, we have:-x² - 4x + 5 + 2x² + 8x - 10 = x² + 4x - 5Simplifying,-x² + 2x² + x² - 4x + 8x + 4x + 5 + 10 - 5 = 0- x² + 8x + 10 = 0Rearranging, we have:x² - 8x - 10 = 0To solve the quadratic equation x² - 8x - 10 = 0, we use the quadratic formula. The formula is given byx = [-b ± sqrt(b² - 4ac)] / 2a Where a = 1, b = -8, and c = -10.Substituting these values, we get:[tex]x = [8 ± sqrt((-8)² - 4(1)(-10))] / 2(1)[/tex]

Simplifying = [8 ± sqrt(64 + 40)] / 2x = [8 ± sqrt(104)] / 2x = 4 ± sqrt(26)Therefore, the restrictions on the variable Are's ≠ 1 and x ≠ -5.

For more such questions on variable

https://brainly.com/question/28248724

#SPJ11

The angle ABD is 35 degrees, AC is 20 units long, and AB is 29 units long.

An angle is created by combining two rays (half-lines) that have a common terminal. The angle's vertex is the latter, while the rays are alternately referred to as the angle's legs and its arms.

Triangle ABD's angle ABC is one of its outside angles, making it equal to the sum of the opposing interior angles.

Angle ABC = Angle ABD + Angle ACD

replacing the specified values:

110° = Angle ABD + 75°

Simplifying:

Angle ABD = 110° - 75°

Angle ABD = 35°

Due of their shared angles, the two triangles are comparable. This fact can be used to establish a ratio between the corresponding sides:

AC / CD = AB / BD

replacing the specified values:

AC / 10 = 16 / 8

Simplifying:

AC = 20

To know more about angle visit:-

brainly.com/question/28451077

#SPJ1

Complete Question:

Find the angle ∠ABD jn the given figure

Answer:

A

Step-by-step explanation:

Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.

Answer: A

The value of x for the angle 100 + x under the top parallel line is equal to -10.

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.

The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:

100 + x = 90

subtract 100 from both sides

x = 90 - 100

x = -10.

Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.

Know more about angles here:https://brainly.com/question/24607467

#SPJ1

The equation of  line of reflection that transforms shape P into shape Q is y=7.

a reflection is known as a flip. A reflection is a mirror image of its shape. An image will reflect through the line, known as the line of reflection. Every point in a figure is said to mirror the other figure when they are all equally spaced apart from one another.

In the given figure, Shape P and Shape Q touches the line y=7 and Shape Q forms exact reflection of Shape P

Hence, the equation of the line of reflection that

transforms shape P into shape Q. is y=7.

To know more about line, visit:

https://brainly.com/question/2696693

#SPJ1

The probability that the first question she gets right is question number 4, is 0.1054.

Number of options there are for a single query = 4

P(guessing correct answer for a single question) = 1/4

P(guessing correct answer for a single question) = 0.25

Probability of getting correct answer P(correct) = 0.25

Probability of getting wrong answer P(wrong) = 1 - Probability of getting correct answer

Probability of getting wrong answer P(wrong) = 1 - 0.25

Probability of getting wrong answer P(wrong) = 0.75

So, the probability that the first question she gets right is question number 4 = Probability of getting 1st question wrong × Probability of getting 2nd question wrong × Probability of getting 3rd question wrong × Probability of getting 4th question right

The probability that the first question she gets right is question number 4 = 0.75 × 0.75 × 0.75 × 0.25

The probability that the first question she gets right is question number 4 = 0.1055

To learn more about probability link is here

brainly.com/question/31120123

#SPJ4

The complete question is:

In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. (Round your answers to four decimal places.)

What is the probability that the first question she gets right is question number 4?