Helen draws a random circle, she then measures the circumference and diameter.
She gets a circumference C of 405mm correct to 2 significant figures
She gets a diameter D of 130mm correct to 2 significant figures
Helen wants to find the value of [tex]\pi[/tex] using the formula [tex]\pi[/tex] = C÷D
Calculate the lower and upper bound for Helens value of [tex]\pi[/tex]
Give your answer correct to 3 decimal places

Answers

Answer 1

The value of π can be written with upper and lower limits as -

3.12 ± 0.062.

What are significant figures?

Significant figures of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something.

Given is that Helen draws a random circle, she then measures the circumference and diameter. She gets a circumference {C} of 405mm correct to 2 significant figures She gets a diameter {D} of 130mm correct to 2 significant figures.

We can write -

Circumference {C} = (405 ± 2) mm

Diameter {D} = (130 ± 2) mm

The value of π can be calculated as -

π = {C}/{D}

π = (405 ± 2)/(130 ± 2)

Now, divide the numbers without errors first -

405/130

3.12

Now, we will calculate the relative errors in each number -

2/405 = 0.004

2/130 = 0.016

Adding the relative errors -

0.004 + 0.016

0.02

Absolute error = 0.02 x 3.12 = 0.062

The value of π can be written with upper and lower limits as -

3.12 ± 0.062

Therefore, the value of π can be written with upper and lower limits as -

3.12 ± 0.062.

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Related Questions

Helpp!! Solve the system by graphing.

Answers

Answer - solution to the equations ( 3, -2)

See attached graph showing where the two lines intersect, that is your solution

Goran wants to build a square picture frame with sides that are 5.25 inches long. Natalie wants to build a square sandbox and needs 11 times the amount of wood that Goran needs to build his frame. They have 4 pieces of wood that are each 65.5 inches long. How much wood will they have left over after making the frame and sandbox?

Answers

After constructing the frame of the sides 5.25 and sandbox, there is 10 inches of wood left over.

What is a square?

A square is a closed, two-dimensional shape that has four equal sides and four vertices. Parallel to one another are its opposing sides. A square is also equivalent to an equal-length and-width rectangle. A square is a regular quadrilateral with four equal-length sides and four equal-length angles. The square's angles are 90 degrees or at right angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. A square is a two-dimensional shape with four equal-length sides. A square's opposing sides are parallel to one another, and its four internal angles are all right angles.

given,

The total amount of wood.

= 4 x 65.5

= 262 inches.

Frame:

Side = 5.25 inches

The perimeter of the frame.

= 4 x 5.25

= 21 inches

Now,

Sandbox:

The wood used for the sandbox.

= 11 x 21

= 231 inches

The remaining wood.

= 262 - (21 + 231)

= 262 - 252

= 10 inches

The wood left over after making the frame of sides 5 .25 inches and the sandbox is 10 inches.

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Just before a referendum on a school​ budget, a local newspaper polls 417 voters to predict whether the budget will pass. Suppose the budget has the support of ​54% of the voters. What is the probability that the​ newspaper's sample will lead it to predict​ defeat?

Answers

Answer:

The probability here is 62%

The probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.

What is probability?

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Let X be the number of voters in the sample who do not support the budget (i.e., who will vote against it). Then X follows a binomial distribution with parameters n = 417 (the sample size) and p = 1 - 0.54 = 0.46 (the probability that a voter does not support the budget).

The probability that the sample will lead the newspaper to predict defeat is the probability that X is greater than half the sample size (since the budget will be defeated if more than half of the voters in the population vote against it). In other words, we need to calculate:

P(X > 0.5n) = P(X > 0.5 × 417) = P(X > 208.5)

We can use a normal approximation to the binomial distribution to estimate this probability. The mean of the binomial distribution is np = 417 × 0.46 = 191.82, and the standard deviation is √(np(1-p)) = √(417 × 0.46 × 0.54) = 10.04.

To apply the normal approximation, we standardize the random variable X as follows:

Z = (X - np) / √(np(1-p))

Then we can use a standard normal distribution table or calculator to find the probability:

P(X > 208.5) = P(Z > (208.5 - 191.82) / 10.04) = P(Z > 1.65) ≈ 0.0495

Therefore, the probability that the newspaper's sample will lead it to predict defeat is approximately 0.0495, or about 5%.

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what is the cosine of π/3

Answers

Answer: 1/2

I recommend printing out a sheet of exact trigonometric functions or using a unit circle to answer problems like these if you haven’t memorized some of them. Or just use a calculator in radians mode if you’re allowed to.

Please help will mark Brainly (please answer all the drop down questions)

Answers

Step-by-step explanation:

system 1 :

3x + 2y = 7

4x + 7y = 17

system 2 :

12x + 2y = 28

4x + 7y = 17

the first equation in the second system is not a multiple of either equation in the first system, and the second equation in the second system is the same as the second equation in the first system.

thus, the systems are not equivalent.

"12x" gives us the idea what the factor would have to be (4 or 3), if the second equation of the second system would be a multiple of any of the equations in the first system.

as we would have to multiply 3x by 4 to get 12x, and 4x by 3 to get 12x.

but then 2y×4 = 8y, or 2y×3 = 6y, and that is not the same as 2y (part of the first equation of the second system).

that is why this first equation of the second system is not a multiple of either equation in the first system.

and that makes it impossible for both systems to be equivalent. that the second equations are identical, is then not relevant anymore.

Use the long division method to find the result when 4x^3+13x^2+17x+8 is divided by x+1

Answers

Step-by-step explanation:

please refer to the sketch

The sum of two numbers is 210 and their difference is 30. What are the two numbers?

Answers

Answer:

120 and 90

Step-by-step explanation:

let one number be x and the other y

x + y = 210 (sum = 210)

x - y = 30 (difference = 30)

add the two equations together

2x = 240

divide both sides by 2 to isolate x

x = 120

plug into 1st equation

120 + y = 210

subtract 120 from both sides

y = 90

Solution :

We take the 2 numbers as 'x' and 'x-30' in order to find those numbers

We plug the values into the given equation

[tex]x + x - 30 = 210\\2x - 30 = 210\\\\2x = 240\\x = \frac{240}{2} \\x = 120\\x - 30 = 120 - 30 = 90\\[/tex]

[tex]120 - 90 = 30[/tex]

Hence , the two numbers are 120 and 90

Help Please!!!!!!!!!​

Answers

Answer:

what's the question?

Step-by-step explanation:

help pls fractionsss tyy

Answers

The amount of syrup she needs is 3/4 cups of syrup. Option A

What is a fraction?

A fraction can be described as the part of a whole variable, element or number.

The several types of fractions are;

Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractions

Also, proportion can be defined as a mathematical comparison between two numbers

From the information given, we have that;

6 cups of soap = 1 /4 cup of syrup

Then 18 cups of soap = x cups of syrup

cross multiply, we get;

6x = 18(1/4)

multiply the values

6x = 18/ 4

Divide both sides by the coefficient of x , we get;

x = 18/ 4 × 1/6

x = 3/ 4 cup of syrup

Hence, the value is 3/4

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please help me answer this question.

Answers

The distance between points E(-8, 7) and L(-1, 4) on the coordinate plane is √58 units

What is an equation?

An equation shows how two or more numbers and variables are related to each other.

The distance between two points in the coordinate plane is given as:

[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

The distance between points E(-8, 7) and L(-1, 4) is:

[tex]EL = \sqrt{(4-7)^2+(-1-(-8))^2}=\sqrt{58}[/tex]

The distance is √58 units

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7.89 divided by 2 step by step

Answers

Answer:

3.945

Step-by-step explanation:

PLEASE HELP WITH EASY FRACTIONS APPRECIATED MUCH!!!

Answers

Answer: 3/4 is right

Step-by-step explanation:

A construction company is building a fence that is 1 1/3 miles long. They can building the fence 1/6 Mile every hr. How long to build the fence?

Answers

The time to build the fence will be 10 hours.

How to calculate the time?

The fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since construction company is building a fence that is 1 1/3 miles long and they can building the fence 1/6 Mile every hr.

The time to build the fence will be:

= 1 1/3 ÷ 1/6

= 5/3 × 6/1

= 30 / 3

= 10 hours.

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There is a pair of parallel sides in the following shape.

Answers

Answer:

A = 38.5 units²

Step-by-step explanation:

the figure has one pair of parallel sides and is therefore a trapezium.

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

b₁ and b₂ are the parallel bases and h the perpendicular height between them.

here h = 7 , b₁ = 5 , b₂ = 6 , then

A = [tex]\frac{1}{2}[/tex] × 7 × (5 + 6) = 3.5 × 11 = 38.5 units²

Which of the following best describes the difference in the results for the special products( A+B)^2 and ( A-B)^2

Answers

The difference between the expansions of (A + B)^2 and (A - B)^2 is the sign of the middle term. In the second case it is negative, due to the negative sign on B.

Which is the difference between the two expressions?

Here we have two perfect square trinomials, these are:

(A + B)^2

(A - B)^2

Notice that the only difference between these is the sign of the second element.

Now we can expand these two expressions as:

(A + B)^2 = (A + B)*(A + B) = A^2 + 2AB + B^2

The second expression gives:

(A - B)^2 = (A - B)*(A - B) = A^2 + 2*A*(-B) + (-B)^2

                                       = A^2 - 2AB + B^2

There we can see that the only difference between these two expansions is the sign of the middle term. Where in the second case it is negative, due to the negative sign on B.

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-15 POINTS-
What’s the length of GH

Answers

Answer = 22

To find the length of GH find the distance from G to 0 and 0 to H. The distance from -14 to 0 is 14 and the distance from 0 to 8 is 8. Add these distances since they make the distance of GH like 14 + 8 = 22.

7. Write the standard form of the
the foci.
equation of the ellipse shown in the following graph. Identify

Answers

On solving the provided question we cans ay that -  equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

What is equation?

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).

equation of ellipse is given by (x2/a2) + (y2/b2) = 1.

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The diameter of a circle measures 18yd . What is the circumference of the circle? Use3.14 for pie , and do not round your answer. Be sure to include the correct unit in your answer.

Answers

Solution

Given ,

The diameter of a circle measures 18yd

To Find : The Circumference of a circle

Radius can be the determined by the formula

[tex]r = \frac{d}{2} \\r = \frac{18}{2} \\r = 9yd[/tex]

Now we can apply the formula of the circumference of a circle which is,

[tex]Circumference = 2\pi r[/tex]

[tex]Circumference = 2X3.14X9[/tex]

[tex]Circumference = 56.52[/tex]

Hence , the Circumference of a circle is 56.52yd

8-2z+3(x+y), when x=4, y=9, Z=3

Answers

[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3

Substitute:

[tex]8-2(3)+3(4+9)[/tex]

[tex]8-6+39[/tex]

Solve:

[tex]8-6+39\\=\fbox{23}[/tex]

[tex]\huge\text{Hey there!}[/tex]


[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]

[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]

[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]

[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]

[tex]\mathsf{= 2 + 12 + 27}[/tex]

[tex]\mathsf{= 14 + 27}[/tex]

[tex]\mathsf{= 41}[/tex]


[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]


[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]


~[tex]\frak{Amphitrite1040:)}[/tex]

Can someone solve this please

Answers

Answer:

u=37

Step-by-step explanation:

u+41= u+4 + u (sum of 2 interior angles is equal to exterior angle)

u+41= 2u+4

2u-u= 41-4

u=37

An octagon has a perimeter of 27 feet. If the sides of the octagon shrink by a scale factor of 8/9, what will the perimeter of the new octagon be

Answers

The perimeter of the new octagon be 24 feet.

What is the perimeter of octagon?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.

The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.

Given that the perimeter of an octagon is 27 feet

so the length of its side is 27/8 feet

if the side of the octagon shrink by a scale factor of 8/9

The side of new octagon is (27/8) * (8/9)

The side of new octagon is 3 feet.

So the perimeter of new octagon is 8 * side

⇒ the perimeter of new octagon = 8 * 3 feet

⇒ the perimeter of new octagon = 24 feet

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Find one value of x so that x + 3 is equal to 2x.

Answers

Answer:

-4

Sorry if this is wrong.

A map has a scale of 1 inch=35 miles. What is the actual distance if the distance on the map is 3.5 inches

Answers

Answer:

112.5 miles

Step-by-step explanation:

scale: 1 inch= 35 miles

this means that for every inch on a map, that is 35 miles in real life.

if the distance on a map is 3.5 inches, and you want to find out how much the distant would be in real life, all you have to do is:

3.5 x 35 = 112.5

I don’t understand this ssshh

Answers

After evaluating the given expressions the results could be 245 / 89 , 43/6, 33/4 .

What is expression ?

expression can be defined as with the minimum of two variables or numbers and at least one math operation.

Given that ,

7/ 8  * 14  / (3/8 * 6 ) + 2  1/5

= (7/8 * 14 )/ ((18 / 8) + 11/5)

= (98/ 8 ) / (90 + 88) / 40

= (98/ 8 ) /  (178/ 40)

= (98 * 40) / (8* 78)

= 245/89

Hence the final value could be 245/53.

7/ 8  + (6*7/8 - 4 * 3/16 ) / (3/4 )

(7/8 + (21/4 - 3/4 ) )  / (3/4)

(7/8 + 18/4)  / (3/4)

(43/8) / (3/4)

43/6

Hence the final value could be 43/6.

3  1/7  * (3 1/3 * (2/3 + 1/6 ) - 5/18 ) / 2 (3/7)

11/7 * (10/6 - 5/18) / (17/7)

(11/7 )* (27/ 18) /( 17/7)

(11* 27/18 )/ (17)

33/34.

Hence the final value could be 33/34.

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please help !!!!!!!!

Answers

8.96848786347

i think this should be right i did it with my 5th grade math skills and dont wory i have an a+

A pilot must log at least 1100 hours to fly an aircraft. Jabari logged 300 hours. How many more hours must he log to qualify

Answers

Answer: 800 more hours is required to fly an aircraft

Step-by-step explanation:

helppppppppo please

Answers

Step-by-step explanation:

the area of a trapezoid is

(a + b)/2 × x

a and b being the 2 bases. and x, as requested, is the height.

A

it does not matter which base is which, as long as we keep using them consistently.

so, let's assume a is the first base :

a = x + 5

and then for the second base

b = 2x - 1

now we use that in the main formula :

(x + 5 + 2x - 1)/2 × x = (3x + 4)/2 × x = (3x² + 4x)/2

A = (3/2)x² + (4/2)x = (3/2)x² + 2x ft²

B

now the height is increased by 4 ft.

that means we need to replace x by x + 4.

(3/2)(x+4)² + 2(x+4) = (3/2)(x² + 8x + 16) + 2x + 8 =

= (3/2)x² + (24/2)x + (48/2) + 2x + 8 =

= (3/2)x² + 12x + 24 + 2x + 8 =

= (3/2)x² + 14x + 32 ft²

with x being the original height, of course.

please please help so desperate

Answers

Answer:

The objective of the PACER is to run as long as possible while keeping a specified pace. Students run back and forth across a 20-meter space at a pace that gets faster each minute. A point is scored for each 20-meter distance covered. The test is easier in the beginning but progressively gets more difficult.

Step-by-step explanation:

Ricky went to sleep at 9:45 pm and woke up at 6:30 the next morning. For how long did he sleep?​

Answers

Answer:

8 hours and 45 minutes.

Step-by-step explanation:

Write the word sentence as an equation.

11 3/4 is the quotient of a number y and 6 1/4


An equation that represents this sentence is ?

Answers

The equation that represents the sentence is y ÷ 6₄¹ = 11₄³

What is quotient?

The word quotient is the outcome when dividend is divided by a divisor.

The result that comes from a division process is termed as quotient. While writing an equation quotient is placed on the right-hand side of the equal sign.

The number that is divided by other number is called dividend and this other number is called divisor.

Write the word sentence as an equation given in question?

11³₄ is the quotient of a number y and 6¹₄.

47/4 is the quotient of a number y and 25/4

hence, y is the dividend and 25/4 is the divisor

y ÷ 25/4 = 47/4

y × 4/25 = 47/4

y = 1175/16

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