Knowing that this number, the Golden Ratio, is present not just in mathematics, but may also be present within your own brain and body (at the atomic or subatomic level), what do you think it means? Is this number evidence of a grand design, a massive freak coincidence or something else?

Answers

Answer 1

The Golden Ratio is a mathematical relationship that exists in art, shapes, nature and the human body. The golden ratio can be present in your body, from the length of your arms and legs when compared to your torso. Fingers is another example because the length of our fingers, each section from the tip of the base to the wrist is larger than the preceding.

The measurement of the human navel to the floor and to the top of the head to the navel is also the Golden ratio. Plastic surgeons and dental surgeons use it to reconstruct the human face. It also appears in everything around us like in the nature and science. It appears on in flower petals because it is believed that each petal is placed to so that each petal gets the best exposure to sunlight. Dolphins, starfish, sea urchins and honeybees also exhibit the proportion like humans. DNA molecules measures 34 angstroms by 21 angstroms at each full cycle of the double helix spiral, these two number are successive numbers. I think that the Golden Ratio is just a freak coincidence that happened.

Related Questions

A home pregnancy test is not always accurate. suppose the probability that the test indicates that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates that a woman is not pregnant when she really is, is 0.03. assume that the probability that a woman who takes the test is actually pregnant is 0.7. what is the probability that a woman is pregnant if the test yields a not pregnant result?

Answers

Set Events:
T=tests positive~T=tests negativeP=subject is pregnant~P=subject is not pregnant
We are givenP(T n ~P)=0.02P(~T n P)=0.03P(P)=0.7
recall by definition of conditional probabilityP(A|B)=P(A n B)/P(B)

Need to find P(P|~T)
First step: make a contingency diagram of probabilities (intersection, n)
P ~P sum
T 0.67 0.02 0.69=P(T)
~T 0.03 0.28 0.31=P(~T)
sum 0.70 0.30 1.00
=P(P) =P(~P)

therefore
P(P|~T)=P(P n ~T)/P(~T)=0.03/0.31 [ both read off the contingency table ]
=0.0968

Final answer:

The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.

Explanation:

The subject of this question is based on conditional probabilities. From the question we know that:

The probability of the test indicating a woman is pregnant when she's not (false positive) is 0.02 i.e., P(Positive|Not Pregnant) = 0.02 The probability of the test indicating a woman is not pregnant when she actually is (false negative) is 0.03 i.e., P(Negative|Pregnant) = 0.03 The probability that a woman who takes the test is actually pregnant is 0.7 i.e., P(Pregnant) = 0.7

From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:

P(A|B) = P(B|A) * P(A) / P(B)

So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).

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HELP!! A spherical ball just fits inside a cylindrical can, 16 centimeters tall, with a diameter of 16 centimeters. Which expression gives the volume of the sphere in cubic centimeters?

Answers

formula for volume of a sphere is V=4/3 x pi x R63

if diameter = 16 than radius = 16/2 = 8

so the equation would be 4/3 x pi x 8^3

Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?

it's ((cos theta) * (cot theta))/(1-sin theta) - 1 = csc theta

Answers

[tex]\bf cot(\theta)=\cfrac{cos(\theta)}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)} \\\\\\ sin^2(\theta)+cos^2(\theta)=1\\\\ -------------------------------\\\\[/tex]

[tex]\bf \cfrac{cos(\theta )cot(\theta )}{1-sin(\theta )}-1=csc(\theta )\\\\ -------------------------------\\\\ \cfrac{cos(\theta )\cdot \frac{cos(\theta )}{sin(\theta )}}{1-sin(\theta )}-1\implies \cfrac{\frac{cos^2(\theta )}{sin(\theta )}}{\frac{1-sin(\theta )}{1}}-1\implies \cfrac{cos^2(\theta )}{sin(\theta )}\cdot \cfrac{1}{1-sin(\theta )}-1 \\\\\\ \cfrac{cos^2(\theta )}{sin(\theta )[1-sin(\theta )]}-1\implies \cfrac{cos^2(\theta )-1[sin(\theta )[1-sin(\theta )]]}{sin(\theta )[1-sin(\theta )]}[/tex]

[tex]\bf \cfrac{cos^2(\theta )-1[sin(\theta )-sin^2(\theta )]}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{cos^2(\theta )-sin(\theta )+sin^2(\theta )}{sin(\theta )[1-sin(\theta )]} \\\\\\ \cfrac{cos^2(\theta )+sin^2(\theta )-sin(\theta )}{sin(\theta )[1-sin(\theta )]}\implies \cfrac{\underline{1-sin(\theta )}}{sin(\theta )\underline{[1-sin(\theta )]}} \\\\\\ \cfrac{1}{sin(\theta )}\implies csc(\theta )[/tex]

2/3 of a number is 32, what is the number?

Answers

2/3×a=32
a=32×3/2
a=96/2
a=48
The number is 48

2/3n = 32
Integers:- 3/2•2/3 = 32/1 = 3/2 = 96/2 = 48

A study of sleep patterns randomly selected participants in the study to sleep in either a dark room or a room with light.

Which element of experiment design is known to be a part of this study?

A.
blinding

B.
replication

C.
randomization

Answers

the answer is c: randomization

Answer:

C. randomization

Step-by-step explanation:

We are told that the study randomly selects participants in the study to sleep in either a dark room or a room with light. This means that randomization is part of the study.

True or false: the difference between the lower limit of a confidence interval and the point estimate used in constructing the confidence interval is called the sampling error.

Answers

Its true.
Sampling error is an error which is calculated by finding the difference between the lower limit or upper limit of a confidence interval and the point estimate used in constructing the confidence interval.
As we can calculate the difference, so sampling error can be positive or negative.

What's the next value?
1 I 2 L 3 F 4

Answers

Based on the pattern, 1 I 2 L 3 F ... the number corresponds to the number of lines of the letter. 1 refers to the vertical line in I. 2 refers to the vertical and horizontal lines that form L. 3 refers to the vertical and 2 horizontal lines that form F. So, 4 will most likely refer to E, one vertical line and 3 horizontal lines.

On average, Donna's Cafe has 18 customers, which represents 36% of the total approved occupancy by the fire department. a. What is the total approved occupancy of the cafe by the fire department? Total approved occupancy = customers b. According to the fire department's occupancy approval, what percentage of the cafe is still available for customers? Available occupancy percentage = % c. According to the fire department's occupancy approval, how many seats are still available for customers? Seats still available =

Answers

Customers = 18
Because this number is 36% of total approved occupancy. the maximum number of customers is
18/0.36 = 50

Part a.
Total approved occupancy = 50 customers

This means that available seats for customers are 50 - 18 = 32.
The available occupancy is
32/50 = 0.64 = 64%

Part b.
Available occupancy percentage for customers = 64%

Part c.
Number of seats still available for customers = 32

jim sold 200 litters of soda at baseball game.How much is this in milliters?

Answers

1 liter = 1000 milliliter

1000 * 200 = 200000

So, 200000 milliliter is the answer.

Answer: 200,000 ml of soda

One liter is 1000 milliliters. To convert between them, multiply 200 by 1000 to get 200,000

Find the area of a triangle with legs that are: 15mm,10mm,20mm

Answers

To calculate the area of triangle with three sides we use Heron's formula,
Area=sqrt(s(s-a)(s-b)(s-c))
where:
s=(a+b+c)/2
thus,
s=(15+10+20)/2
=22.5
hence the area will be:
Area=sqrt(22.5(22.5-15)(22.5-10)(22.5-20))
Area=sqrt(22.5*7.5*12.5*2.5)
=sqrt5273.4375
=72.62 mm^2

The area of a triangle with legs that are 15 mm, 10 mm, and 20 mm is [tex]72.618 mm^{2}[/tex]

Further Explanation;Area Area is a measure of how much space is occupied by a given shape. Area of a substance is determined by the type of shape in question.

For example;

Area of a rectangle is given by; Length multiplied by width Area of a circle = πr². where r is the radius of a circle, Area of a square = S², Where s is the side of the square.etc.Area of a triangle The area of a triangle is given based on the type of the triangle in question.Right triangle.The area of a right triangle is given by;

= 1/2 x base x height

Scalene triangleIt is a triangle that with sides and angles that are not equal.Area of a scalene triangle depends on the features of the triangle given.

For example;

Sine FormulaArea of a triangle = 1/2 ab sin θ, when given two sides of the triangle and the angle between themHeron's formulaArea of a triangle = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex] when given all the sides of the triangle. where [tex]s =\frac{(a+b+c)}{2}[/tex]

In this case we are given, a = 15 mm, b = 10 mm, c = 20 mm

Therefore, we use the Heron's formula;

Area= [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]s =\frac{(a+b+c)}{2}[/tex]

[tex]s= \frac{(15+10+20)}{2} \\s= 22.5[/tex]

Therefore;

Area = [tex]s\sqrt{s(s-a)(s-b)(s-c)}[/tex]

= [tex]22.5\sqrt{22.5(22.5-15)(22.5-10)(22.5-20)}[/tex]

=[tex]\sqrt{22.5(7.5)(12.5)(2.5)} \\\sqrt{5273.4375}[/tex]

[tex]= 72.618 mm^{2}[/tex]

Keywords: Area, Area of a triangle, Heron's formula, Sine formula, Scalene triangle.

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Level: Middle school

Subject; Mathematics

Topic: Area

Sub-topic: Area of a triangle

an actor gains 20pounds for a part and then losses 15 pounds during the filming of the movie to go along with the story.who do you write a addition expression to describe this situation

Answers

Let the actor's initial weight be 'x'

He is then gaining 20 pounds. The clue is in the word 'gaining' as it means 'increasing' or in Mathematics can be related as 'plus'

The expression is: x+20

He then loses 15 pounds. The clue is in the word 'losses' as it means 15 pounds is to be subtracted from the last value

Last value is x + 20
The weight now is x + 20 - 15 = x + 5

Gabrielle's age is three times Mikhail's age. The sum of their ages is 44. What is Mikhail's age?

Answers

g=gabby's age
m=micsdjfsdf's age

g=3m

sum is add
g+m=44

subsitute 3m for g
3m+m=44
4m=44
divide by 4 both sides
m=11

mikhail is 11 year old

Mikhail is 11 yrs old because 11 times 3 is 33. 33 plus 11 is 44

How can I use context clues and keywords to translate situations into inequalities? Explain with an example of your own.

Answers

Consider the following example:

Mira and Lola are looking to hire a hall for their 18th birthday party. They are expecting at least 50 guests and want a hire that will accommodate the party. Write this requirement as an inequality

Solution: the keyword here is 'at least' because it means that the hall must be able to accommodate a minimum of 50 people. It is a clue that Mira and Lola are expecting more than 50 guests. The inequality symbol for this context is 'more than or equal to' and as inequality, we have x ≥ 50

Final answer:

To translate situations into inequalities, use context clues and keywords. Start by understanding the relationships and factors involved. Then, represent the situation with variables and create an inequality based on the context clues. For example, if Bob earns $10 more than Alice, the inequality would be 'a < a + 10'.

Explanation:

In order to use context clues and keywords to translate situations into inequalities, it's important to understand the relationships and factors involved. Let's take an example:

Scenario: Suppose you have two friends, Bob and Alice. Bob earns $10 per hour more than Alice. In this case, we can use the following context clues:

The relationship between Bob and Alice: Their wealth is unequal.The factor involved: The difference in their earnings.

We can now translate this situation into an inequality:

Let's say Alice's earnings are represented by 'a'.Bob's earnings would be 'a + 10' (since he earns $10 more).The inequality can be represented as 'a < a + 10' (Alice's earnings are less than Bob's earnings).

By using the context clues and the keywords (earnings, difference), we were able to translate the situation into the inequality 'a < a + 10'.

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Multiply and Dividing Rational Numbers

8/9 ÷ 2/3

7/8 × 1/4

3/4×1/6

Answers

essentially is just

[tex]\bf \cfrac{8}{9}\div \cfrac{2}{3}\implies \cfrac{8}{9}\cdot \cfrac{3}{2}\implies \cfrac{8\cdot 3}{9\cdot 2}\implies \cfrac{24}{18}\implies \cfrac{4}{3} \\\\\\ \cfrac{7}{8}\cdot \cfrac{1}{4}\implies \cfrac{7\cdot 1}{8\cdot 4}\implies \cfrac{7}{32} \\\\\\ \cfrac{3}{4}\cdot \cfrac{1}{6}\implies \cfrac{3\cdot 1}{4\cdot 6}\implies \cfrac{3}{24}\implies \cfrac{1}{8}[/tex]

Which quantity is proportional to 20/5?

Answers

Well can you be a little more specific? There's an infinite amount. For example, there's 4, 8/2, 12/3, 16/4, and you get the idea.

An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees

Answers

0.3(8.59) = 2.577 rounds to 2.58 acres

amy has 72 sweets in bag.she keeps 1/4 of them for herself,but shares the remainder between 6 of her friends.how many sweets will she give to each of her friends?

Answers

Amy keeps 18 sweets. find this by dividing 72 by 4

she has 54 left to share

54 divided by 6 is how many sweets each friend will get

Each friend gets 9 sweets

Convert decimal +49 and +29 to binary, using the signed‐2’s‐complement representation and enough digits to accommodate the numbers. then perform the binary equivalent of (+29) + (-49), (-29) + (+49), and (-29) + (-49). convert the answers back to decimal and verify that they are correct.

Answers

To solve this problem, let us first find for the binary equivalents of the numbers. They are:

Decimal --> Binary

+ 29 --> 00011101

+ 49 --> 00110001

- 29 --> 11100011

- 49 --> 11001111

Now we apply the normal binary arithmetic to these converted numbers:

(+ 29) + (- 49) ---> 00011101 + 11001111 = 11101100 ---> - 20 (TRUE)

(- 29) + (+ 49) ---> 11100011 + 00110001 = 00010100 ---> + 20 (TRUE)

(- 29) + (- 49) ---> 11100011 + 11001111 = 10110010 ---> - 78 (TRUE)

Of the books in a library, 1/3 came from Robbie's collection and 15 came from Marta's. Of the rest, 15 were Elena's 1/5 were Winfield's, and 5 were purchased from the bookstore. How many book are there in the library?

Answers

library amount: l
Robbie: r=(1/3)l
Martha: m=15
rest of books: l-r-m=e+w+b
Elena: e=15
Winfield: w=1/5(e+w+b)
bookstore: b=5

w=(e+w+b)/5
w=(15+5+w)/5
w=4+w/5
(4/5)w=4
w=5

l-r-m=e+w+b
l-(1/3)l-15=15+5+5
(2/3)l=25+15
(2/3)l=40
l=60=amount of books

The total number of books in the library are 75.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.

What will be the equation for given scenario?

Let the total number of books in the library be x.

The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]

Collect the like terms,

[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]

On solving the equation for x we get x=75.

Therefore, the total number of books in the library are 75.

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If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?

Answers

In this question, the prices are Increased at a monthly rate of 2.3%. Since you are asked how much the percentage in a year and there is 12 month in a year, then you need to do the calculation 12 times.

The calculation would be (100%+2.3%)^12= 131.37344984%

That would be about 31.37% a year.

PLEASE HELP WITH SOME GEOMETRY
Prove the following statement by contradiction using an indirect proof. In a triangle angle A = 90°, then the triangle is a right triangle. Which of the following choices would be the first step to temporarily assume?
angle A = 90°
the triangle is a right triangle
the triangle is not a right triangle
angle A is not 90°

Answers

The contradiction proof should start with a negation:
"The triangle is not a right triangle angle and A is not 90°"
Then you proof that this statement is false

A pharmacist has 40% and 80% iodine solutions on hand .How many liters of each iodine solutions will be required to produce 6 liters of a 50% iodine mixture?

Answers

so... let's change the concentration percentage to decimal format. .. so 40% is just 4/100 or 0.4 and so on.

[tex]\bf \begin{array}{lccclll} &amount&concentration& \begin{array}{llll} concentration\\ amount \end{array}\\ &-----&-------&-------\\ \textit{40\% sol'n}&x&0.4&0.4x\\ \textit{80\% sol'n}&y&0.8&0.8y\\ -----&-----&-------&-------\\ mixture&6&0.5&3 \end{array}[/tex]

so... whatever "x" and "y" may be, we know the must add up to 6 liters.

and whatever 0.4x and 0.8y are, we also know, they must add up to a 3 of concentrated amount.

thus [tex]\bf \begin{cases} x+y=6\implies \boxed{y}=6-x\\ 0.4x+0.8y=3\\ ----------\\ 0.4x+0.8\left( \boxed{6-x} \right)=3 \end{cases}[/tex]

solve for "x", to see how much of the 40% solution will be needed.

what about "y"? well, y = 6 - x.

which algebraic expression represents the phase

Answers

The keyword here is product.

A product is the result when multiplying.

Therefore, the answer here is B.

A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price

Answers

Final answer:

The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.

Explanation:

To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:

$15 × 0.35 = $5.25

This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:

$15 + $5.25 = $20.25

Therefore, the selling price of the product would be $20.25.

Madison deposited a total of $5,000 between two saving accounts bearing simple interest. One of the accounts has an interest rate of 4% while the other rate is 5%. If the total interest earned after one year is $220, find the amount deposited into each of the accounts.

Answers

0.04x+0.05 (5000-x)=220
Solve for x to find the amount invested at 4%
0.04x+250-0.05x=220
0.04x-0.05x=220-250
-0.01x=-30
X=30÷0.01
X=3,000 invested at 4%

5000-3000=2000 invested at 5%

Find the area under the standard normal curve between z = −2.57 and z = 1.27. Round your answer to four decimal places, if necessary.

Answers

P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)

P(Z ≤ 1.27) = 0.8980
P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57) = 1 - 0.99488 = 0.00512

P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512 = 0.89288
0.8929 (4 d.p.)

The area under the standard normal curve between z = −2.57 and z = 1.27 is, 0.8929

What is meant by Probability?

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to give that,

To find the area under the standard normal curve between z = −2.57 and z = 1.27.

Now, the area under the standard normal curve is between z = −2.57 and z = 1.27 is,

P(-2.57 ≤ Z ≤ 1.27) = P(Z ≤ 1.27) - P(Z ≤ -2.57)

Since, P(Z ≤ 1.27) = 0.8980

And, P(Z ≤ -2.57) = 1 - P(Z ≤ 2.57)

= 1 - 0.99488

= 0.00512

Hence,

P(-2.57 ≤ Z ≤ 1.27) = 0.8980 - 0.00512

= 0.89288

= 0.8929

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Name the three different types of proof in math and give a description of each

Answers

I think the answer would be Paragraph Proof, The Flow Proof, and the Transformational proof. If you need the descriptions feel free to google it, or i can tell you that also!

How to solve 7.86 x 4.6

Answers

The answer is 34.156

Place the 7.86 on the top and the 4.6 on the bottom and multiply

If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the second equation is substituted into the first equation.

2x – 7y = 4

3x + y = –17

Answers

Equation 1: [tex]2x-7y=4[/tex]
Equation 2: [tex]3x+y=-17[/tex]

Rearranging equation 2 to make 'y' the subject

[tex]y = -17 - 3x[/tex] ⇒ Call this Equation 3

Substituting Equation 3 into Equation 1
[tex]2x-7(-17-3x)=4[/tex]
[tex]2x+119+21x=4[/tex]
[tex]23x+119=4[/tex]
[tex]23x=4-119[/tex]
[tex]23x=-115[/tex]
[tex]x=-5[/tex]

Then substitute x = -5 into either Equation 1 or Equation 2 to solve for 'y'

[tex]2x-7y=4[/tex]
[tex]2(-5)-7y=4[/tex]
[tex]-10-7y=4[/tex]
[tex]-7y=4+10[/tex]
[tex]-7y=14[/tex]
[tex]y=-2[/tex]

Note: the original question did not attach the option for the equation after substitution so you might want to follow the working out here carefully and match it with the options given.

let f(x)=4x-1 and g(x)=2x^2+3. perform the function operation and then find the domain. To
f(x) + g(x)

Answers

hello :
F(x)=4x-1 and g(x)=2x²+3.

f(x) + g(x) = 2x²+4x+2
the domain oh : f+g is : R

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