Work out the circumference of this circle. Take n to be 3.142 and write down all the digits given by your calculator. 10 cm​

A quadrilateral with at least one pair of parallel sides is called, in American and Canadian English, a trapezoid. In British and other forms of English, a (North American) trapezoid is called a trapezium. The transposition of these two terms was a result of an error in Charles Hutton's mathematical dictionary.

In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. As opposed to the particular examples below, a scalene trapezoid is a trapezoid without equal sides.

The Greek mathematician Euclid identified five different quadrilateral shapes, of which four had two sets of parallel sides (the square, rectangle, rhombus, and rhomboid in English) and one did not (a trapezia, meaning "a table," which comes from "four" and means "a foot; end, boundary, edge").

In his commentary on the first book of Euclid's Elements, Proclus (412–485) developed two varieties of trapezia: one pair of parallel sides, or a trapezium (v), divided into isosceles (equal legs), and scalene (unequal) Similar to how cuboid and rhomboid both mean "resembles," trapezia with no parallel sides is a trapezoid, trapezoeidé, or literally "trapezium-like."

English followed Proclus's arrangement until the late 18th century, when a prominent mathematical lexicon produced by Charles Hutton in 1795 endorsed a transposition of the terms without providing an explanation. Although this error was fixed in British English around 1875, it remained in American English till the present..

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Answer:

3811

Step-by-step explanation:

37X100= 3700

37X3=111

so 3700+ 111= 3811

Answer:

700 is your answer i am pretty sure. If not i am super sorry

Answer:

630

Step-by-step explanation:

If she owns 70 and each went up by 10 then 70*10=700

700-70=630

I am sure it is correct but if not,sory if it is wrong

The  system of equations that could be used to determine the price of each pound of raspberries and the price of each pound of grapes is:  44 x + 43 y = 217 , 45x + 18y = 144 .  Each pound of peaches cost $2 and each pound of grapes cost $3

x = price of each pound of peaches

y = price of each pound of grapes.

Given that yesterday,  he sold 44 pounds of peaches and 43 pounds of grapes for a total revenue of $217

So 44 x + 43 y = 217 be equation 1.

Also given that today he sold 45 pounds of peaches and 18 pounds of grapes for a total revenue of $144.

So 45x + 18y = 144 equation 2.

Multiplying equation 1 with 18 gives us,

792x +774y = 3906

Multiplying equation 2 with 43 gives us,  

1935x+774y = 6192

Solving these,

792x +774y = 3906

1935x+774y = 6192

---------------------------------------------

-1143 x=- 2286

x = 2286/ 1143

x = 2

Plug this value of x in equation 1 and solve for y, to get,

44 x + 43 y = 217

44 (2) + 43 y = 217

43 y = 217 − 88

43 y =129

y = 129/43

y = 3

Therefore each pound of peaches cost $2 and each pound of grapes cost $3

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Answer:

A. The perimeter of the image is 4 times as large as the perimeter of the pre-image.

Explanation:

To answer this question, we use an example.

Given the pre-image:

• A square with side length 1 cm

• Perimeter = 4 x 1 = 4cm

If the square is dilated by a scale factor of 4:

• Side length = 4cm

• Perimeter = 4 x 4 =16cm

We see therefore that 'The perimeter of the image is 4 times as large as the perimeter of the pre-image.'

The correct choice is A.

Answer:

x = 5, y = 25

Step-by-step explanation:

I use the substitution method to solve. (I hope I got the equations correct)

6x + y = 55 ---1

10x + 3y = 125 ---2

From 1: y = 55 - 6x ---3

Substitute 3 into 2:

10x + 3(55 - 6x) = 125

10x + 165 - 18x = 125

- 8x = - 40

x = 5

Substitute x into 3

y = 55 - 6(5) = 25

Answer:

[2005]=25.29

Step-by-step explanation:

[tex]y = 7.41 + 2.98x[/tex]

Answer:

(a) Fermat's little theorem states that for any prime p , we have

a^p-1 = 1 (mod p).

for any integer ,a. Then

999999 = 1000000 - 1 = 10^6 - 1 = 1 - 1 = 0 (mod 7)

so 7 does indeed divide 999,999.

(b) Generalizing, we have

10^12n - 1 = 999...999 (12n nines) = (10^n)^12 - 1 = 0 (mod 13)

for positive integer, n. Now, since 1 = 1001 - 1000 and -1 = (mod 1001) , it follows that 10^3 is its own inverse modulo 1001, i.e.

10^3 x = 1 (mod 1001) -----> x = 10^3

This means

10^12n = (10^3 x 10^3)^2n = 1^2n = 1 (mod 1001) ----> 10^12n - 1 = 0 (mod 1001)

In the picture there is a straight line which has a point where the 2 lines intersect. The angles are 90°, 30° and a is 60°.

Given that,

In the picture there is a straight line which has a point where the 2 lines intersect.

The angles are 90° and 30°.

We have to find the angle a.

A straight angle in geometry is an angle with a vertex point that is at 180 degrees. In essence, it creates a straight line with sides that face away from the vertex. "Flat angles" is another name for it.

So, we get,

90°+30°+a=180°

a=180°-90°-30°

a=180°-120°

a=60°

Therefore, the angle a is 60°.

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The ball to rise 45 meters in 3 seconds.

How do you find the solutions of a quadratic equation?

here

Function : [tex]H= 30t-5t^{2}[/tex]

height = 45m

then [tex]30t-5t^{2} = 45[/tex]

simplify the quadratic equation ⇒ [tex]6t-t^{2} -9=0[/tex]

⇒ [tex]t^{2} -6t+9=0[/tex]

⇒ [tex](t-3) (t-3)=0\\t=3.[/tex]

 time required to  reach 45m = 3 sec.

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The thing that P(W) represents is A. It denotes the probability of screening a driver and finding that he or she is not intoxicated.

The value is 0.99257

It should be noted that probability simply means the likelihood that something will happen or occur based on the information given.

From the information, the man observed a sobriety checkpoint conducted by a police department, he saw drivers were screened and were arrested for driving while intoxicated.

P(W) = 0.000743

Therefore, those that are not intoxicated will be:

= 1 - P(W)

= 1 - 0.000743

= 0.99257

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The equation y = - 2x + 4 matches the line

How to find the equation?

The line passes through two points .

[tex](x_1, y_1) = (2, 0)\\\\(x_2, y_2) = (0, 4)[/tex]

We know that slope (m) is given by,

[tex]m =\frac{y_2 -y_1}{x_2 -x_1} \\\\m =\frac{4-0}{0-2} \\\\m= -\frac{4}{2} \\\\m= -2[/tex]

We know the slope- intercept form of an equation is:

y = mx+ c    ----(1)

Let us substitute the point  [tex](x_1, y_1)[/tex]  and m in (1)

y = mx+ c

0 = -2(2) +c

c = 4

Let us substitute c and m in (1)

The slope- intercept form of the equation is:

y = -2x + 4

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The number of boxes that should be opened to find it is 98 boxes.

Probability simply means the likelihood of the occurence of an event.

When there is a 3 percent chance or finding something special in a box,the number of boxes that will be opened will be illustrated thus:

Let the number of boxes be 100.

Therefore, the number of boxes will be:

= Total boxes - Percentage given

= 100 - 3

= 97

In this case, the 98th box will give the person the chance of getting it.

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Answer:

4x-5

Step-by-step explanation:

Based on the distance of the race and the length of the sections, the number of people that Heather will need to be on her team are 26 people

The entire race has a length of 5 1/5 miles and this length will be divided into sections that are 1/5 miles long.

Only one member of the team can run in each of these sections so enough people are needed on Heather's team to run the 1/5 mile sections.

The number of people to be in a team can be found by the formula:
= Length of race / Length of sections

= 5 1/5 miles / (1/5)

= 26/5 ÷ 1/5

= 26/5 x 5/1

= 26 people

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Answer:

Step-by-step explanation:

45 degrees -67/6

The required polynomial function is y=3(x+3)⁴(x-4 ) for the conditions as mentioned fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only involves non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1.

The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.

Here the given conditions are:

Fifth degree, 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

Let y be the f(x) and x be the variable.

Now, x+3 is the first term and x-4 be the second term with their multiplicity 4 and 1.

y=3(x+3)⁴(x-4)

For the above-mentioned fifth-degree conditions, the necessary polynomial function is y=3(x+3)⁴(x-4); 3 is a zero of multiplicity 4,-4 is the only other zero, leading coefficient is 3.

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Answer:

32

Step-by-step explanation:

Since l and m are parallel, the value of 2x is equal to 64.

64/2 = 32

Each label should be dragged to the correct location in the equation as follows:

100 yards/1 × (3) feet/1 yards × (12) inch/1 foot × (2.54) cm/1 inch × 1 (meter)/100 cm = (91.44) meter

A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.

Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.

Conversion:

1 yard = 0.9144 meter

100 yards = X meters

Cross-multiplying, we have:

X = 0.9144 × 100

X = 91.44 meters.

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All real numbers n that is less than 14 when plugged in for x will be less than 14 in inequality .

What is inequality in math?

inequality  = 4n+ 13 ≤ 69

                 = 4n ≤ 69 - 13

                 = 4n ≤ 56

                 = n ≤ 56/4

                 = n ≤  14

Thus, all real numbers n that is less than 14 when plugged in for x will be less than 14.

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The length of the missing side z would be 17 units which is determined by Pythagoras's theorem.

A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

According to Pythagoras's theorem,

⇒ a² + b² = c²

Here, a = 8  b = 15 and c = z

⇒ (8)² + (15)² = z²

⇒ 64 + 225 = z²

Apply the addition operation,

⇒ 289 = z²

⇒ z² = 289

⇒ z = √289

⇒ z = 17

Therefore, the length of the missing side z would be 17 units.

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The inequality expression given as 2 - |6 + 12x| > -28 has a solution of -3 < x < 2

From the question, the inequality is given as

2-|6+12x|>-28

Rewrite properly as

2 - |6 + 12x| > -28

Subtract 2 from both sides

- |6 + 12x| > -30

Divide both sides by -1

|6 + 12x| < 30

Remove the absolute bracket

So, we have the following representation

-30 < 6 + 12x < 30

Add -6 to all sides of the inequality

So, we have

-36 < 12x < 24

Multiply through by 1/12

So, we have

-3 < x < 2

Hence, the solution to the expression is -3 < x < 2

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Answer:

Point of intersection is the point where two lines or two curves meet each other. The point of intersection of two lines of two curves is a point.

Step-by-step explanation:

Hope it helps! =D

2 lines intersect at:

A point

In a plane, crossed lines square measure any 2 or a lot of lines that cross each other. The purpose of intersection, which may be found on all crossed lines, is wherever the crossed lines share a standard purpose.

Perpendicular lines square measure 2 lines that cross at associate angle of right angles.

Since the purpose of intersection is that the solely location wherever the 2 graphs meet once the lines cross, the coordinates of that location offer the solution to the equations involving the 2 variables.

There are not any solutions once the lines square measure parallel.

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Answer:

(0, 6)

(-1 , 5)

Step-by-step explanation:

No, the given procedure doesn't result in a binomial distribution.

We can identify if a given procedure results in binomial distribution by observing whether these four conditions are met or not.

1: Each observation should be independent, it must not depend on the result of previous observation.

2: The probability of success should stay same from trial to trial.

3: n is fixed (the number of observations)

4: There are only two outcomes success or failure.

Surveying 2828 people to determine which statistics courses they have taken.

3 is satisfied since n is fixed

1 is satisfied since each observation is independent

4 is not satisfied since there can be more than 2 answers from the people (statistics courses can be many).

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The ratio of boys to girls in the 9th grade is 7 : 9. Girls are 218

proportion of girls in total students are [tex]\frac{218}{9}[/tex] = 24.2

According to the question, given that

In class ratio of boys and girls is 7 : 9

and girls in the class are 218

Proportion of girls in total class = [tex]\frac{218}{9}[/tex]

                                                    = 24.2

Therefore, we get proportion of girls in the class is 24.2

When determining if two ratios or fractions are equivalent, the proportion formula is utilized. The proportional formula is as follows:

a : b :: c : d = a/b = c/d

Proportion Formula

a:b::c:d = a/b = c/d

where,

a, d = Extreme terms

b, c = Mean terms

The product of means equals the product of extremes is one of the various proportional formulas. You can write this as ad = bc.

Two additional proportional formulas that depend on direct or indirect variation are available. When two quantities x and y are in direct proportion, y = k x, and when x and y  are in indirect proportion, y = k/x, with k serving as the proportionality constant in both cases.

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Answer: 3 5/8 hours

Step-by-step explanation:

2 + 1 = 3

1 / 4 = 2 / 8

3 / 8 + 2 / 8 = 5 / 8