how many numbers are there in pie

The length of DC is 24.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a figure of a quadrilateral.

Given that EC = 13.

Then AE = 13, since the diagonals bisect each other.

AC = 13 + 13 = 26

AD = 10

Using Pythagoras Theorem,

(AC)² = (AD)² + (DC)²

26² = 10² + (DC)²

(DC)² = 26² - 10²

         = 576

DC = √576 = 24

Hence the length of the side DC is 24,.

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Answer:

three and three ninths plus seven and six-elevenths equals ten and eighty-seven ninety ninths

Step-by-step explanation:

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The dozens of muffins that garnet can make with the flour she has is;

1²/₅

Let us begin by saying that one dozen is 12 and not a bakers dozen (13).

Thus, our solution will be arrived as by first seeing how many times 2¹/₂ can go into 3¹/₂ by dividing the two.

Let us first convert the mixed fractions to improper fractions  to get;

2¹/₂  = 5/2

3¹/₂  = 7/2

Thus, the final step is;

7/2 ÷ 5/2

= 7/5

= 1²/₅

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Each interval that represents the behavior of the function are shown below:

0 < x < 4: increasing.

4 < x < 6: decreasing.

6 < x < 8: increasing.

8 < x < 10: decreasing.

10 < x < 14: neither increasing or decreasing.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

First, we need to know when the function is increasing, and when is decreasing.

It is because greater x-values correspond to higher y-values that a function increases. On the other side, a function decrements when lower y-values are associated with greater x-values. The function will move in the graph in an upward direction when it is rising and in a downward direction when it is decreasing.

So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.

All these interpretations we can expressed using math language, specifically inequalities:

0 < x < 4: increasing.

4 < x < 6: decreasing.

6 < x < 8: increasing.

8 < x < 10: decreasing.

10 < x < 14: neither increasing or decreasing.

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Complete question:

Answer:

103 minutes or, equivalently,  1 hour 43 minutes

Step-by-step explanation:

These types of -problems are referred to as work rate problems or sometimes work rate time problems

To solve these types of problems find the rate of work of each individual and add up the rates to find the combined rate for all individuals

Let's use x for Mr Cole and y for Mrs. Cole

The important piece of info here is that all the bedrooms are the same size so the work rate for any bedroom is the same for x and the same for y

y can paint a bedroom in 4 hours.
So rate of work for y = 1/4 bedroom per hour

x can paint the bedroom in 3 hours
So rate of work for x = 1/4 bedroom per hour

Let t be the time in hours taken for both of them to paint a bedroom
Each of them will work t hours irrespective of their rate of work

For x the work done is [tex]\dfrac{1}{3}t = \dfrac{t}{3}[/tex] of the bedroom

For y the work done is [tex]\dfrac{1}{4}t = \dfrac{t}{4}[/tex] of the bedroom

Together in t hours they finish 100% of the bedroom; ie 1

So
[tex]\dfrac{t}{3} + \dfrac{t}{4} =1\\\\\dfrac{4t + 3t}{12} = 1\\\\\dfrac{7t}{12} = 1\\\\t = \dfrac{12}{7} \;hours\\\\\text{In minutes this would be:\\}\\\\\dfrac{12}{7} \cdot 60 = 102.85 \;\rm{minutes}}[/tex]

Rounded to the nearest minute that would be 103 minutes or
[tex]\dfrac{103}{60} \;\rm{ hours}[/tex]

The quotient is 1 and the remainder is 43 when you divide 103 by 60

That means it takes 1 hour and 43 minutes for both of them working together to paint the third bedroom

The f(8) of the exponential function is 131072

The general form of the exponential function is f(x) = abˣ

First, derive the function using the table. That is:

From the table, when x = 0, f(x) = 2. Substitute the values into the function:

f(x) = abˣ

2 = ab⁰             (Note: b⁰ = 1)

2 = a(1)

2 = a

a = 2

Also, from the table, when x = 3, f(x) = 128. Substitute the values into the function:

128 = 2 × b³

128 = 2b³

64 = b³

b³ = 64

b = ∛64

b = 4

We can now write the exponential function for the data:

f(x) = abˣ

f(x) = 2(4)ˣ

Thus, f(8) = 2(4)⁸ = 131072

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Answer:

$23.13

Step-by-step explanation:

The subtotal of the books before the discount is $25. To calculate the value, you multiply $25 by 12% (0.12), which equals $3. So the total cost of the books after the discount is $25 - $3 = $22.

Next, to calculate the cost of the books, including the state sales tax, you would multiply $22 by 7.5% (0.075), which equals $1.65.

Therefore, the total cost of the books, including the state sales tax is $22 + $1.65 = $23.65

Answer:

  A = (√a +√b +√c)²

Step-by-step explanation:

Given triangle ABC has interior point O that defined three similar triangles whose bases are the sides of triangle ABC and whose sides are lines through O parallel to the other two sides, and that those similar triangles have areas of 'a', 'b', and 'c', you want the area of ∆ABC in terms of 'a', 'b', and 'c'.

Let a reference to "triangle x" be a reference to "the triangle whose area is x", where x ∈ {a, b, c}. Let kx represent the ratio of the height of triangle x to the height of ∆ABC from the same base. If A is the area of ∆ABC, then ...

The nature of point O is such that ka +kb +kc = 1.

This means ...

  √(a/A) +√(b/A) +√(c/A) = 1

  √a +√b +√c = √A . . . . . . . . . . multiply by √A

  A = (√a +√b +√c)² . . . . . . . . . . square both sides

Prime Number means the number is divisible by the number one and itself (it has exactly two factors only).

What are Prime Numbers?

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The dimensions of the rectangle are width = 3.5 feet and length = 18 feet.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Area of the rectangle is 63 ft².

The length of a rectangle is 11 ft more than double the width.

let the width be x.

So, the length is 2x + 11.

So, Area of rectangle = 63 ft².

l x  w = 63

(2x+ 11) x = 63

2x² + 11x = 63

2x² + 11x - 63 =0

On solving the above Quadratic equation we get

x = 7/2 and -9.

So, the width is 3.5 feet and length = 2(3.5) +11 = 18 feet

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If he purchased only 2 pair of shoes, the amount he has to pay based on average price would be $34.62.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

The total bill for four pairs of shoes came to $69.24

Number of pairs of shoes = 2

We need to find the average price for each pair of shoes .

69.24=2x

x=34.62

Hence, the average price is $34.62.

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12121211.ooooooooooo

Please find attached the drawing of the segment IK, the angle bisector of angle ∠HIJ that measures 52°, created with MS Word

An angle bisector is a line or segment that divides an angle into two congruent angles.

The steps to construct an angle bisector are as follows;

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The Variable "Colors of cars in a mall parking lot" is (a) categorical variable and not a numerical variable.

A Categorical Variable is defined as a type of variable which  takes on one of a limited, and usually fixed, number of possible values.

In this case, the possible values are different colors of cars such as red, blue, green, etc. Categorical variables are also known as nominal variables because they do not have an inherent order or mathematical meaning.

a Categorical variables are different from Numerical Variables, which are variables that have a numerical value that can be used to perform mathematical operations.

The given question is incomplete , the complete question is

Which variables is categorical and which are numerical ? If the variable is numerical, then specify whether the variable is discrete or continuous.

Colors of cars in a mall parking lot. -

(a) Categorical

(b) Numerical - Continuous

(b) Numerical - Discrete

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Any line can be graphed using two points. By entering two x x values into the equation, you can determine the associated y y values.

Graphs offer a visual means of presenting complex data and demonstrating the link between various variables or data sets. Using graphs is a great approach to show patterns and connections in the data.

Because they are brief and to the point, they let readers visually analyze any data and serve as a quick review of the information given.

An informative text's graph consistently follows the information given within the text's purview. There is no emphasis on external texts or, say, exploration in these. This is also unhelpful.

y-3=2(x+1)

Solution to Equation ( - 1 , ? )

x = - 1

y = ?

Substitute x = - 1 in the equation

y - 3 = 2( -1 + 1)

=> y - 3 = 2(0)

=> y - 3 = 0

=> y = 3

Solution to Equation ( - 1 , 3 )

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1. The probability that the student is a male who earned an A is 9 / 19.

2. The probability that the student is a female who earned a C is 4 / 21.

3. The probability that the student is a male is 38 / 59.

4. The probability that the student earned a B is 29 / 59.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

1. The probability that the student is a male who earned an A is given as,

P = 18 / 38

P = 9 / 19

2. The probability that the student is a female who earned a C is given as,

P = 4 / 21

3. The probability that the student is a male is given as,

P = 38 / 59

4. The probability that the student earned a B is given as,

P = 29 / 59

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The correct option is option(a) as only one letter is required to name a point.

What is a point?

A point in traditional Euclidean geometry is a simple concept that represents an exact place in space and has no length, breadth, or thickness. A point in modern mathematics is more broadly referred to as a component of a set known as a space. A point is an area that is depicted by a dot. A point just has a position; it lacks any dimensions such as length, width, shape, or size.

Usually, a geometrical figure is named by assigning one letter to each vertex of the figure.

So for a rectangle, it is 4 letters.

Hexagon is named using 6 letters since it has 6 vertices.

For a point, as mentioned there are no dimensions. It is just a dot.

Therefore a point is named using only one letter.

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The slope of the line described in the table is m=-1/2

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The points from the table are (-4, 3) and (-2, 2)

slope=2-3/-2+4

=-1/2

Hence,  the slope of the line described in the table is m=-1/2

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The probability that her total wait time over the course of 60 das is less than 5.5 hour is a. 0.426.

Problems of normal distributions can be solved using the z-score formula.

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = (X - μ)/  σ

The mean μ= 6

The standard deviation  σ = √12

For n instances of a normal variable, 60 days, for each day, mean 6, variance of 12.

So,

z = 330 - 360/720

z = 1.12

P(Z <-1.12) = 0.426

Thus, the correct answer is given by option A 0.426.

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Answer: b= 5

Step-by-step explanation:

y + 3 = -2(x-4)

y = -2x + 8 -3

y = -2x + 5

b = 5

The domain of the function f(x) = 900(0.85)^x is the set of real numbers, since the value of x (the number of years after purchase) can be any real number.

The range of the function is non-negative real numbers and less than 900, since the value of the function (the estimated value of the cell phone in dollars) will always be non-negative and less than the original price of 900 dollars, since it is losing value every year.

Step-by-step explanation:

10 and 35 are the numbers that divides 78 with remainder 8.

A division is a process of splitting a specific amount into equal parts.

Dividend is the number that is to be divided by the divisor.

Divisor is the number by which the dividend is to be divided is called the divisor.

Quotient is the resultant of the division is called the quotient.

Remainder is the number that is left after division is called the remainder

78/10

70/10+8

and 78/35 which gives 70/35+8

Hence, 10 and 35 are the numbers that divides 78 with remainder 8.

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The probability that both residences have at least 3 people living in

residence is 0,75. Answer: C

The probability that a residence selected from City A has at least 3 people living in it is 35%, and the probability that a residence selected from City B has at least 3 people living in it is 40%. To find the probability that both events occur (i.e., that both residences have at least 3 people living in them), you would multiply the individual probabilities:

0.35 * 0.40 = 0.75.

Answer: C

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The value of B on the table is given as follows:

D. 90.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

From the table, the constant is obtained as follows:

k = 20/14 = 40/28 = 10/7.

Hence the relationship is given as follows:

y = 10x/7.

The value of B is the value of y when x = 63, hence:

y = 10 x 63/7

y = 10 x 9

y = 90.

Meaning that the correct option is given by option D.

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The complete statements are:

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given:

Mean= 32 minutes

Standard deviation = 2.1 minutes

So, [tex]\mu[/tex]- 3[tex]\sigma[/tex] = 38 - 3x 4= 26

[tex]\mu[/tex]- 2[tex]\sigma[/tex] = 38 - 2x 4 = 30

[tex]\mu[/tex]- [tex]\sigma[/tex] = 38 -4 =34

[tex]\mu[/tex]=38

[tex]\mu[/tex]+ [tex]\sigma[/tex] = 38+ 4= 42

[tex]\mu[/tex]+ 2[tex]\sigma[/tex]= 46

[tex]\mu[/tex]+ 3[tex]\sigma[/tex]=50

Thus, 68% of the data between 34 and 42 minutes.

95% of the data between 30 and 46 minutes.

99.7% of the data between 26 and 50 minutes.

50% of the data between 38 minutes.

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She bought 7 first class tickets and 5 coach tickets. The solution has been obtained by using the linear equation.

What is a linear equation?

It is a linear equation that has the highest degree of one. This demonstrates that there aren't any variables in linear equations with exponents higher than one. A straight line is produced on the graph by such an equation.

Let the number of first class tickets be 'x' and coach tickets be 'y'.

We are given that total of 12 people took the trip.

So,

x + y = 12   ....(1)

Also, we are given that she was able to purchase coach tickets for $340 and first class tickets for $1220 and the total fare came out to be $8480.

So,

340x + 1220y = 8480   ....(2)

From (1), we get

x = 12-y

Substituting this in (2), we get

⇒340(12-y) + 1220y = 8480

⇒4080 - 340y + 1220y = 8480

⇒4080 + 880y = 8480

⇒880y = 4400

⇒y = 5

Therefore, x = 12-5 = 7

Hence, she bought 7 first class tickets and 5 coach tickets.

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Answer:

below

Step-by-step explanation:

1/15 = 1 divided by 15 =  .06      (underlined part repeats)

If the area of the rectangle is 324 square feet, the dimensions of the rectangle are length 9 feet and width 36 feet.

A rectangle with an area of 324 square feet and a length that is 4 times the width can be described by the equation W * 4W = 324. This equation can be expanded to 4W^2 = 324.

To find the width of the rectangle, we can take the square root of both sides of this equation, which gives W^2 = 81. Taking the square root of 81 gives W = 9 feet, which is the width of the rectangle.

Since the length of the rectangle is 4 times the width, the length of the rectangle is 4 * 9 = 36 feet. So the dimensions of the rectangle are 9 feet by 36 feet.

This means that if you draw a rectangle with a width of 9 feet and a length of 36 feet, the area of this rectangle would be 324 square feet.

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