Why should there be a number corresponding to the length of every line we draw?

The math shows the world is designed, and that design is symmetry and spirals.

How is math found in nature What is the significance of mathematical patterns in nature?

Mathematics is seen in many beautiful patterns in nature, such as symmetry and spirals. Both are aesthetically appealing and proportional. Symmetry can be radial, where the lines of symmetry intersect a central point such as a daisy or a starfish.

Here,

If Hailey used math to describe the design in nature: the number of legs insects and spiders have, the number of petals on flowers, and even the patterns of spots on some animals. The math shows the world is designed, and that design is symmetry and spirals.

Hence, the math shows the world is designed, and that design is symmetry and spirals.

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The table complete table that shows equivalent ratios is:

Toss     Dollars  

5             2

30           12

45           18

See image in the attachment that shows the points on a coordinate plane.

The ratios that give the same value when we compare them together are regarded as equivalent ratios.

For example, 2:3 is an equivalent ratio to 4:6, because 4/6 can be simplified as 2/3.

If it cost $12 to toss 30 rings, the ratio of dollars to number of toss would be: 12:30 = 2:5.

Let x = number of toss

Let y = amount in dollars

The equation that models the equivalent ratios can be written as y = 2/5x.

Therefore, when we have 2 dollars (y = 2):

2 = 2/5(x)

10 = 2x

10/2 = x

x = 5 toss

When we have 45 tosses (x = 45):

y = 2/5(45)

y = 18 dollars

The table of equivalent ratios would be:

Toss     Dollars  

5             2

30           12

45           18

The points, (5, 2), (30, 12), and (45, 18) are shown on the coordinate axes in the diagram below, where y = dollars, and x = toss.

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The  mean height of the low tides is 1.21 ft

The heights of the low tides for four days are -0.22 ft, 2.64 ft, -0.22 ft, and 2.64 ft

The mean of a sample is given by the formula =

summation of all observation / number of observation

mean = (x₁ + x₂ + x₃ + x₄)/ 4

mean = -0.22 + 2.64 - 0.22 + 2.64 / 4

mean = 4.48 / 4 = 1.21

Therefore, the  mean height of the low tides is 1.21 ft

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The value of dy/dx is ( v du/dx - u dv/dx)/v²

From the question, we have

y = (1+x)u/(1+x)v

y = u/v

dy/dx = d/dx(u/v)

d/dx(u/v) = ( v du/dx - u dv/dx)/v²

Derivatives:

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilized. The derivative is used to assess how sensitive a dependent variable is to an independent variable (independent variable). In mathematics, a quantity's instantaneous rate of change with respect to another is referred to as its derivative. Investigating the fluctuating nature of an amount is beneficial. In calculus, a function's derivative measures how sensitively its output value changes in response to changes in its input value.

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Answer The answer is 96 but as a fraction 96 8/13

Step-by-step explanation: There are 1256 rubber bands and 13 games to distribute them according to the problem; therefore, to divide to give an equal amount per each group for each game, you would give out 96 rubber bands each time, so 96 is the answer or 96 8/13.

Answer:

d the last one I think

Step-by-step explanation:

I am not really sure

Answer:

D.) 6.67 X 10^2

Answer:

1st Table : Linear

2nd Table : Non-Linear

Step-by-step explanation:

To determine if the function is Linear or not , we find the change in y with a certain change in x

So for the 1st Table:

When x changes from x = 2 to x = 4 increased by 2

Then  y changes from y = 3 to y = 0 decreases by 3

When x changes from x = 4 to x = 6 increased by 2

Then  y changes from y = 0 to y = -3 decreases by 3

Since change in y is the same for the same change in x , Then the Function is Linear

So for the 2nd Table:

When x changes from x = 1 to x = 2 increased by 1

Then  y changes from y = 1 to y = 4 increased by 3

When x changes from x = 2 to x = 3 increased by 1

Then  y changes from y = 4 to y = 9 increased by 5

Since change in y is not the same for the same change in x , Then the Function is Non-Linear

Glad to Help

The equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the following statement - "4 less than a number is given w".

Assume the number to be [x].

We can write the equation representing the statement -

"4 less than a number is given w" as a mathematical expression as -

[w] = x     where x ∈ (- ∞, 4)

Therefore, the equation representing the statement - "4 less than a number is given w" as -

[w] = x     where x ∈ (- ∞, 4)

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For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

As given in the question,

Given :

Pair of parallel lines are AG and BH.

CF is the transversal.

Transversal CF intersect line AG at point D and

Transversal CF intersect line BH at point E

Four pair of corresponding angles

Two pair of alternate interior angles

Corresponding pair of angles in the pair of parallel lines are congruent.

∠ADE ≅ ∠BEF

∠ADE and ∠BEF are corresponding angles.

Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.

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The mean score of all the students is 79.5 and it is round off into one decimal place.

Mean

Mean refers the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given,

In a psychology class, 30 students have a mean score of 87.7 on a test. Then 21 more students take the test and their mean score is 67.7.

Here we need to find the mean score of all students.

In order order to find the mean score, we have to calculate the total score of the students by multiplying the mean score by the number of students then we get,

=> 30 x 87.7 = 2631

Similarly, the total score for 21 students is,

=> 21 x 67.7 = 1421.7

So, the 51 students, cumulative score is

=> 2631 + 1421. 7 = 4052.7

Therefore, the mean score is calculated as,

=> 4052.7/51

=> 79.464

When we round off the value into one decimal place then we get

=> 79.5

Therefore, the mean value of all the students is 79.5.

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Answer:

84.6

Step-by-step explanation:

Answer:

Step-by-step explanation:

13+(-3)^2+4(-3)+1- {-10-(-6)}

_________________________

[4+5}/ [4^2-3^2(4-3)-8]+12

15/3=5

Answer:

.7 kg

Step-by-step explanation:

1. Convert answers in grams into kilograms

1000g = 1 kg

750g = .75kg

705g = .705 kg

2. Find smallest number of kg

= .7 kg

Answer:d

Step-by-step explanation:d

a. The numeric value at Thursday -> x = 4 is of 32 degrees, which agrees with the graph.

b. A numeric value of 35 degrees Fahrenheit is obtained on Monday and on Thursday, also agreeing with the graph.

To obtain the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

In this problem, the function is defined as follows:

f(x) = 3x² - 18x + 56.

Giving the temperature in degrees Fahrenheit in x days after Sunday.

The day that represents Thursday is given by:

x = 4.

Hence the temperature is the numeric value of the function at x = 4, replacing both instances of x on the function by 4, hence:

f(4) = 3(4)² - 18(4) + 56 = 32 ºF.

Which agrees with the graph, as the Thursday's bar is a value slightly above 30, which can be interpreted as 32.

The numeric value is of 35 when:

3x² - 18x + 56 = 35

The solutions to the quadratic equation are:

x = 1.6, x = 4.4.

Hence the days are:

Monday and Thursday.

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The focus of parabola is (4 , -1) and directrix is 5

The general equation of a parabola is: y = a(x-h)²+ k or x = a(y-k)² +h, where (h ,k) denotes the vertex. The standard equation of a regular parabola is y² = 4ax.

Focus: The point (a, 0) is the focus of the parabola

Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.

Given equation of parabola is :

y = - 1/12 (x - 4) - 2

Comparing it with standard equation,

h = 4

k = 2

a = -1/12

using Focus: (h, k+ (1/4a)) and Directrix: y = k - 1/4a)

=> focus = (4 , 2+(12/4×-1))

=> focus = (4 , 2-3)

=> focus = (4 , -1)

and directrix is : y = 2-(1/4×-1/12)

y = 2 + 12/4

y=2 + 3 => 5

So, the focus is (4,-1) and directrix is 5

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The counterexample for "Two supplementary angles are not congruent." is

angle 100° and angle 80° are supplementary angels

angle 90° and angle 90° are supplementary angels

The instances show supplementary angles that are not congruent

A specific situation that demonstrates that a statement is untrue is referred to as a counterexample.

Counterexamples provides instances that opposes the statement

In this case the two supplementary angles 100-and-80 and 90-and-90 are not congruent and hence a counterexample to the statement

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The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then

(x,y)=( (mx₂+nx₁)/m+n ,  (my₂+ny₁)/m+n )

Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3

Therefore, we have

P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))

P(x,y)=(2.6,6)

Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio  2:3 is  (8,4).

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Distance travelled by the particle from time t = 0 to t = 3 in x-direction and y-direction is 27 units and 54 units respectively.

How to get distance/displacement using velocity?

According to given data:

A particle moves with velocity (dx)/(dt) = 3t² in x- direction

and (dy)/(dt) = 12t in y-direction

Integrating both sides of these derivatives with respect to t

x=  ∫3t² dt = (3t³)/3 + A = t³ + A

where A is integration constant

y= ∫12t d t = (12t²)/2 + B = 6t² + B

where B is integration constant

At t = 0 we get x = A and at t = 3 we get x = 3³ + A = 27 + A.

Therefore, the difference in position of a from t = 0 t = 3 is

27 + A - (0 + A) = 27 units.

Similarly,

At t = 0 , we get y = B and at t = 3 we get

y = 6 * 3² + B = 54 + B

Therefore, the difference in position of y from t = 0 tot t = 3 is

54 + B - (0 + B) = 54 units.

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The flowchart that is used to prove GR ║ F_K is presented as follows;

∠RND and ∠FDP are supplementary  ⇒    ∠RND + ∠FDP = 180°

Given                            [tex]{}[/tex]                                 Definition of supplementary

∠KDN  ≅ ∠FDP                 [tex]{}[/tex]                    ⇒    ∠KDN = ∠FDP

Vertical angles are congruent[tex]{}[/tex]                    Definition of congruent angles

∠RND and ∠KDN are same side interior angles [tex]{}[/tex] ⇒∠RND + ∠KDN = 180°    

Definition of same side interior angles[tex]{}[/tex]                    Substitution property

[tex]{}[/tex]                                           GR ║ F_K

The relationships between the angles formed by a transversal and two parallel lines are;

Definition of congruency;

Two lines, shape or figure are said to be congruent if they have the same size and shape.

Supplementary angles;

Supplementary angles are angles that have a sum of 180°

Substitution property of equality

The substitution property sates that if an expression a = b, then the expression b can replace a in any equation and the equation will remain valid.

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The value of x=20, according to the given question.

What is meant by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to the given data in the question,

We know that y varies directly with x like that,

y=kx..................(1)

y=12 when x=15.

Now, we have to find the value of x when y=16.

Then, putting the given values of x & y in the eq. (1), and determine the value of k.

12=k(15)

[tex]k=12/15\\k=4/5\\[/tex]

Now, putting the value of k in the second statement in eq.(1), where only y's value is given.

[tex]16=\frac{4}{5}x\\ x=16*\frac{5}{4} \\x=20[/tex]

Hence, the value of x=20.

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Answer:

20 mph

Step-by-step explanation:

If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph

The linear function g(z) = 4 · z + 7 is the result of applying the transformation rule g(z) = f(z) - 2 (Translation two units down) on the linear function f(z) = 4 · z + 9 . (Correct choice: C)

In this problem we find a linear function that is modified into another linear function by a transformation rule. We need to find if the function is modified by a horizontal translation, a vertical translation or a combined translation, that is, a combination of horizontal and vertical translations.

Horizontal translation

g(x) = f(x - k), where k > 0 for a translation in + x direction.

Vertical translation

g(x) = f(x) + k, where k > 0 for a translation in + y direction.

After a quick inspection, we notice that linear function f(z) = 4 · z + 9 is transformed into g(z) = 4 · z + 7 by using vertical translation 2 units down.  Then, we find the following transformation formula:

g(z) = f(z) - 2

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Answer:

-3

Step-by-step explanation:

we sure y2-y1/x2-x1 to find slope

6+6/-4+0

12/-4

-3 is the slope

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The conditional probability that a camper entering the Luray Caverns has Canadian license Plates is given by:

0.3214 = 32.14%.

Conditional probability is the probability of one event happening, considering the outcome of a previous event. The formula is given by the rule presented as follows:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

The probabilities that compose the formula are listed as follows:

The events in this problem are given as follows:

The probabilities are given as follows:

P(A) = 0.28, P(A and B) = 0.09.

Hence the conditional probability is obtained as follows:

P(B|A) = P(A and B)/P(A) = 0.09/0.28 = 0.3214 = 32.14%.

The probability asked is that a camper entering the Luray Caverns has Canadian license Plates.

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Answer: 3/4

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator

GCD of 12 and 16 is 4

Divide both the numerator and denominator by the GCD

12 ÷ 4

16 ÷ 4

Reduced fraction: 3/4

Therefore, 12/16 simplified to lowest terms is 3/4.

Answer:.

Step-by-step explanation:

Using the monthly payment formula, it is found that:

A. You can afford a car at a price of $13,742.36.

B. The monthly payments are of $109.15.

The monthly payments are given by the equation presented as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

The variables involved in the equation are listed and explained as follows:

For item a, the parameters are given as follows:

A = 250, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

Hence the maximum value of the car is obtained as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]250 = P\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

0.0181919241P = 250

P = 250/0.0181919241

P = $13,742.36

For item b, the parameters are given as follows:

P = 6000, r/12 = 0.035/12 = 0.002917, n = 5 x 12 = 60

(P = 6000 as the 2000 of the down payment are already paid, hence not subjected to interest).

Hence the monthly payments are given as follows:

[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]

[tex]A = 6000\frac{0.002917(1.002917)^{60}}{(1.002917)^{60} - 1}[/tex]

A = 6000 x 0.0181919241

A = $109.15.

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The true bearing at which Jasenio should aim his bow and arrow is; b) 11.31°

We have different trigonometric ratios such as;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

We are told the track is 50 meters away from Jasenio and that by the time the arrow reaches it, the paper rabbit will be at a point about 10 meters to the right of what would be directly in front of him.

This means that there will be a right angle triangle formed with the height as 50 m and the base length as 10m. Thus, by trigonometric ratios, we have;

tan θ = 10/50

where θ is the true bearing angle. Thus;

tan θ = 0.2

θ = tan⁻¹0.2

θ = 11.31°

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