HELP ASAP PLSSSSSSS
Clara surveyed the students at her school to find out if they like pies and/or sandwiches. The results of her survey are shown in the two-way table below:



Like Pies

Do Not Like Pies

Total

Like Sandwiches

25

43

68

Do Not Like Sandwiches

26

6

32

Total

51

49

100



If a student does not like sandwiches, what is the probability that student also does not like pies?
81.3%
26.0%
23.1%
18.8%

HELP ASAP PLSSSSSSSClara Surveyed The Students At Her School To Find Out If They Like Pies And/or Sandwiches.

Answers

Answer 1

Answer:

18.8%

Step-by-step explanation:

For calculating this, focus on one part of the table :

The row where students do not like sandwiches

There are 32 students who do not like sandwiches, and 6 of them do not like pies. Take this a proportion :

P (does not like pies, do not like sandwiches) = 6/32P = 3/16P = 18.8%
Answer 2

Students who don't like sandwiches also don't like pie is the 2 nd box on 2 nd line

Probability

P(E)=6/32P(E)=6/32×100=3/16×100=18.8%

Option D


Related Questions

A graph shows the horizontal axis numbered 1 to 5 and the vertical axis numbered 1 to 5. points and a line show a downward trend. which is most likely the correlation coefficient for the set of data shown? –0.83 –0.21 0.21 0.83

Answers

The  most likely correlation coefficient for the set of data shown is: -0.21.

Correlation coefficient

We would be using CORREL in excel to determine the correlation coefficient by inputting the set data below

X Y

A (1,4)

B (2, 1.5)

C (3,3)

D (4,4)

E (5,2)

Hence:

Correlation coefficient=-0.20801

Correlation coefficient=-0.21 (Approximately)

Therefore the  most likely correlation coefficient for the set of data shown is: -0.21.

Learn more about correlation coefficient here:https://brainly.com/question/2735094

#SPJ4

Answer:

B) -0.21.

Step-by-step explanation:

Explain what the following statement means:
Polynomials are closed under the operations of addition and subtraction.
Provide one addition example and one subtraction example to demonstrate.
a set is closed under certain operation if the operation performed on two elements of the set gives an element of the same set
addition,subtractio sa well as multiplication of polynomials result into another polynomial.Therefore,the set of polynomials is closed under addition,subtraction and multiplication.
division of a polynomial need not be a polynomial (sometimes it is ,but not always).Therefore,the set of polynomials is not closed under division.see the example in the box beside.
Sample Response: If you add two polynomials, the sum is always a polynomial. Example: (2x2 + 3x) + (8x2 - 4x) = 10x2 - x If you subtract two polynomials, the difference is always a polynomial. Example: (2x2 + 3x) - (8x2 - 4x) = -6x2 + 7x
Compare your response to the sample response above. Did your response …

… explain what closure means for addition and give an example?

… explain what closure means for subtraction and give an example?

Answers

Polynomials are the algebraic expressions that consist of variables and coefficients.

How to explain the polynomial?

The Closure property of addition states that in a defined set, for example, the set of all positive numbers is closed with respect to addition since the sum obtained adding any 2 positive numbers is also a positive number which is a part of the same set.

Closure property of subtraction states that if any two real numbers a and b are subtracted from each other, the difference or result will be a real number as well. For example, 9 - 4 = 5.

Learn more about polynomial on:

https://brainly.com/question/2833285

#SPJ1

A map has a scale of 1 cm: 10 km. If Centerville and Greenwood are 40 km apart, then they are how far
apart on the map?
(Pls answer quick)

Answers

Answer:

4 cm

Step-by-step explanation:

1 cm : 10 km (given)

-> 1*4 cm = 10*4 km (Multiply both sides by 4)

-> 4 cm = 40 km

Scale

1cm:10km

Scale factor=10

Distance of Greenwood=40km

Now apart in map

40/104cm

3. If you are just building your payment history, how many points from a perfect score will you possibly miss
A. 280 points
B.
80 points
240 points
D. 120 points

Answers

a) 280 points

b) 80 points

c) 240 points

d) 120 points

correct option :A) 280 points

Which graph represents f of x equals square root of the quantity x plus 3 end quantity minus 2?

The graph shows a curve with an end point at 2 comma 3 that increasing to the right
The graph shows a curve with an end point at 3 comma 2 that increasing to the right
The graph shows a curve with an end point at negative 3 comma negative 2 that increasing to the right
The graph shows a curve with an end point at negative 2 comma negative 3 that increasing to the right

Answers

The obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis. None of the option is correct.

What exactly is a function?

A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.

The given equation of the function is;

[tex]y = -(x+2)^{1/3}+5[/tex]

Hence,the obtained graph is having is passes though the point (0,3.74 )on y-axis and (123,0) on the x-axis.

To learn more about the function refer:

https://brainly.com/question/5245372

#SPJ1

Answer:

The function f(x) = sqrt(x - 2) + 3 represents a square root function that is shifted 2 units to the right and 3 units up from the parent function f(x) = sqrt(x).

The endpoint of the function occurs when the radicand (x - 2) is equal to zero, which means x = 2. So, the function has an endpoint at (2, 3).

Since the function involves a square root, the value of y cannot be negative. Therefore, the function is increasing to the right.

The correct graph that represents the function f(x) = sqrt(x - 2) + 3 is the one that shows a curve with an endpoint at (2, 3) that increases to the right.

Therefore, the answer is: The graph shows a curve with an endpoint at 2 comma 3 that increases to the right. A.

What's the mean, median, mode, and range of 8, 10, 8, 14, 8 and 15

Answers

Answer: Mean: 10.5, Median: 9 Mode: 8 Range: 7

Step-by-step explanation  

mean put the numbers in order, so 8,8,8,10,14,15 the mean is adding all numbers together and dividing by the number so 8 + 8 + 8 + 10 + 14 + 15 divided by 6 is 10.5,

median is middle so 9 since theres two middle numbers u add them both and then divide by 2

mode is the most so its 8 since 8 is there 3 times

range is the highest number and lowest number and u subtract them so 15 - 8 = 7

sorry if this is long but the answers are at the top

Answer:

Below in bold.

Step-by-step explanation:

Mean = ( 8 + 10 + 8 + 14 + 8 + 15) /  6

=  10.5.

Arrange in ascending order to find the median:

8 8 8 10 14 15

Median = mean of the middle 2 numbers

= (8 + 10)/2

= 9.

Mode = most occurring number = 8.

Range = greatest - least = 15 - 8 = 7.

Solve the math:

Elsa is 2 years older than Bella. Emma is twice as old as Elsa. So, what will be the sum of their ages in 1 years time. And then also find out what was the summation of their ages before 5 years from now.

Answers

Answer:

Step-by-step explanation:

Let Emma's age be 2x years, then:

Elsa's age is x years, also:

Bella's age is x - 2 years.

In one years time the sum of their ages

=  2x + 1 + x + 1 + x - 2 + 1

= 4x + 1  where x = Elsa's age now.

5 years before now

Sum of their ages

=  2x -5 + x - 5 + x - 2 - 5

= 4x - 17 where x = Elsa's age now,

7829y[tex]\frac{-69}{56x}[/tex] Find the exact value!

Answers

[tex]\\ \rm\Rrightarrow 7829y\times \dfrac{-69}{56x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{7829(69)y}{56x}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{540201y}{56x}[/tex]

[tex]\\ \rm\Rrightarrow 9646.4y/x[/tex]

Kelly plants 45 tulips in 30 minutes what is the unit rate?

Answers

Answer:

1.5 per minute

Step-by-step explanation:

unit rate is how many in 1 minute so 45 divided by 30 is 1.5 and if you want to check your answer do 1.5 x 30 which is 45

Graph the line 2x – 3y = 12.


Answers

Decided by 12 is 2 your welcome

Answer:

-6, -4

Step-by-step explanation:

I got it right

Which of the following expressions is equivalent to ab2 + 6ab + 7a3 – 14a?

Answers

Answer:

−4a^2+2ab+8a

Step-by-step explanation:

−4a^2+2ab+8a is expressions of equivalent to ab2 + 6ab + 7a3 – 14a.

Which expression is equivalent to st6?

1 Answer. s(6) × t(6) is equivalent to (st)(6).

Which expression is equivalent to FG )( 4 )?

Thus, the expression (f + g)(4) is equal to f(4) + g(4).

Learning more about expressions is equivalent at

https://brainly.com/question/24734894

#SPJ2

the factory makes light bulbs the probability that a bulb is defective is 1/15 if 300 light bulbs are tested about how many are expected to be defective

a 20

b 66

c 15

d 30

Answers

defective : working = 1/15 ( x20 ) 20/300
so the answer is 20 light bulbs
A) you can make a ratio of 1/15 = x/300

300x1 = 300

300/15 = 20

Given that l is the centroid of triangle CDE, find CH.
A. 3
B. 4
C. 8
D. 12

Answers

Answer:

D. 12.

Step-by-step explanation:

As I is the centroid G is the midpoint of CE, so

2x + 5 = 5x - 4

5+4 = 5x - 2x

3x = 9

x = 3.

x + 5 =  2/3 * CH   (Properties of the centroid of a triangle).

So as x = 3

2/3 CH = 3 + 5

CH = 8 * 3/2

CH = 12.

1)we surveyed 760 people. 240 of them like
broccoli more than carrots and peas. 340 of them
like carrots more than broccoll and peas. The rest
prefer peas. What is the simplified ratio of people
who prefer peas to the total number of people?

Answers

I could be wrong, but I believe the answer is 90:380

There are 769 people surveyed in total, 240 and 340 of them are separate from the number of people who preferred peas,

240 + 340 is 580

In order to find put how many people preferred peas, subtract the number of people separated from the people who preferred peas and the total number of people surveyed:

760 - 580, which is 180

That would mean the ratio of people who preferred peas to the total amount of people surveyed would be 180:760 unsimplified

In order to simplify the ratio, we must find the highest common factor, the biggest possible number that these numbers both divide into evenly:

180 and 760 both divide evenly into 2, so the ratio simplified would be 90:380

Please let me know if this answer was wrong!

Please help don’t understand radical

Answers

Simplified

[tex]x\sqrt[3]{x}[/tex]

In a board game, there is a 29 chance of drawing a card that gives a player a double turn. The remaining cards are single-turn cards. A player wants to run a simulation to estimate the probability of drawing two double-turn cards in a row, assuming the first card is replaced, and the deck is shuffled afterward.

Answers

Probability helps us to know the chances of an event occurring. The probability of getting a double card in a row is 0.311.

What is Probability?

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The probability of drawing a single double turn card for the first time, therefore,

Probability = 29/52

Further, given the card is replaced and reshuffled, therefore, the probability of getting a double card again will be,

Probability = 29/52

Thus, the probability of getting a double card in a row can be written as,

Probability = (29/52)×(29/52) = 0.311

Hence, the probability of getting a double card in a row is 0.311.

Learn more about Probability:

https://brainly.com/question/795909

#SPJ1

20 points
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 216, 36,6 Find the 8th term.

Answers

Answer:

0.001

Step-by-step explanation:

Given (or we can find) :

First term : 216

Common ratio : 36/216 = 1/6

To find 8th term :

a₈ = ar⁸⁻¹

a₈ = (216)(1/6)⁷

a₈ = 216/279936

a₈ = 6³/6⁷

a₈ = 1/6⁴

a₈ = 1/1296

a₈ = 0.000771604938

a₈ = 0.001 (nearest thousandth)

write the equation of the line that passes through (-3,6) with a slope of -2

Answers

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

[tex]\diamond\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

       What is the equation of the line that passes through (-3, 6) and has a slope of -2?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond[/tex]

     

First, we need to write the equation of the line in point-slope form:-

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Replace y1 with 6, m with -2, and x1 with -3:-

[tex]\sf{y-6=-2(x-(-3)}[/tex]

On simplification,

[tex]\sf{y-6=-2(x+3)}[/tex]

On further simplification,

[tex]\sf{y-6=-2x-6}[/tex]

Add 6 on both sides:-

[tex]\it{y=-2x}[/tex]

Good luck with your studies.

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

The sum of two numbers is 12 and their difference is 4
write down two equations to describe given equation
solve the simultaneous equations to find the two numbers

Answers

Answer:

8 and 4

Step-by-step explanation:

let the 2 numbers be a nd b

equations :

a + b = 12

a - b = 4

Adding the two equations

a + b + a - b = 12 + 4

2a= 16

a = 8

b = 4

which term describes where the three angle bisecters of a a triangle intersect

Answers

the incenter. it forms a circle

Answer:

The incenter....

Step-by-step explanation:

The point at which all three of the angle bisectors of a triangle meet is known as the incenter

dont confuse it with the circumcenter and the centroid.

i hope this helps!!!

Question Write an equation in slope-intercept form of the line that passes through (6, −2) and (12, 1)

Answers

Answer:

[tex]y = \dfrac 12x -5[/tex]

Step-by-step explanation:

[tex]\text{Given that,}~ (x_1,y_1) = (6,-2)~ \text{and}~ (x_2,y_2) = (12,1)\\\\\text{Slope,}~ m = \dfrac{y_2 -y_1}{x_2 -x_1} = \dfrac{1+2}{12-6}= \dfrac{3}{6} = \dfrac 12\\\\\text{Equation of line,}\\\\~~~~~~~~y-y_1 =m(x-x_1)\\\\\implies y+2=\dfrac 12 (x-6)~~~~~~~~~~~~~~;[\text{Point -slope form}]\\\\\implies y = \dfrac 12 x -3 -2\\\\\implies y = \dfrac 12x -5~~~~~~~~~~~~~~~~~~~~~;[\text{Slope-intercept form.}][/tex]

Question is in the picture (I got it wrong)

Answers

Answer:

  (B)  38.4 m³

Step-by-step explanation:

The volume of a prism is given by the formula ...

  V = Bh

where B is the area of the base, and h is the height.

__

The picture tells you the area of the pool is 24 m² and its height is 1.6 m. The volume formula tells you its volume is ...

  V = Bh = (24 m²)(1.6 m) = 38.4 m³

The volume of the prism is 38.4 cubic meters.

help me with this question please! it’s VERY URGENT and i dont know where to begin with❗️

Answers

Answer:

[tex] |x|1 | \: 2 | \: 3 | \: 4 | \: 5 | \\ |y| 5| \: 4 \: | 3 \: | 2 | 1| [/tex]

Step-by-step explaination:

We were told that:

[tex] x + y = 6 [/tex]

therefore to see if it is correct you can just input the values for x and y and see if they add up to 6 (add the vertical values). For example;when x = 1, y = 5 or when x = 2, y = 4

Need help please answer ASAP!
(20-21)

Answers

#20

1/2x+3<2x-61/2x-2x<-6-3-3/2x<-93/2x>9x>9(2/3)x>6

#21

Find LCD of 2,7x,x

x is most common

So

LCD is 2(7x)(x)=14x²

Answer:

20.  (4)  x > 6

21.  (3)  14x

Step-by-step explanation:

Question 20

[tex]\begin{aligned}\dfrac{1}{2}x+3 & < 2x-6\\\dfrac{1}{2}x+3-3 & < 2x-6-3\\\dfrac{1}{2}x & < 2x-9\\\dfrac{1}{2}x-2x & < 2x-9-2x\\-\dfrac{3}{2}x & < -9\\-\dfrac{3}{2}x \cdot 2 & < -9 \cdot 2\\-3x & < -18\\-\dfrac{3x}{3} & < -\dfrac{18}{3}\\-x & < -6\\\dfrac{-x}{-1} & < \dfrac{-6}{-1}\\x & > 6\end{aligned}[/tex]

Question 21

Rewrite all three fractions so that their denominators are the same:

[tex]\dfrac{1}{2}=\dfrac{1 \times 7x}{2 \times 7x}=\dfrac{7x}{14x}[/tex]

[tex]\dfrac{2}{7x}=\dfrac{2 \times 2}{7x \times 2}=\dfrac{4}{14x}[/tex]

[tex]\dfrac{5}{x}=\dfrac{5 \times 14}{x \times 14}=\dfrac{70}{14x}[/tex]

Therefore, the least common denominator is [tex]14x[/tex]

I need help on this please

Answers

Answer:

  9.45 ounces

Step-by-step explanation:

The formal definition of the standard deviation of a population is that it is the square root of the mean of the squares of the differences between the data values and their mean.

The calculation can be done more simply as the root of the difference between the mean of the squares and the square of the mean. That is the calculation shown in the attachment.

The population standard deviation is about 9.45 ounces.

_____

Additional comment

The easier way to do the calculation is to use the calculator or spreadsheet function that gives the result directly. For the Desmos calculator shown, that function is stdevp(w) for the definition of w that we used. The function has the same name in many spreadsheet programs.

The surface areas of two similar solids are 169 m2 and 81 m2. the volume of the larger solid is 124.92 m3. which proportion correctly shows how to solve for the volume of the smaller solid, x? = = = =

Answers

By finding the scale factor, we will see that the volume of the smaller solid is 86.75 m³.

How to get the volume of the smaller solid?

If the solids are similar, then there is a scale factor between the two. Then the relation between the areas is equal to the scale factor squared, and the relation between the volumes is equal to the scale factor cubed.

This means that if the areas are 169 m² and 81 m², then we can write:

169 m² = (k²)*81 m²

Solving for k, we get:

k = √(169 m²/81 m²) = 1.44

Then if the volume of the large solid is 124.92m³ we can write:

124.92m³ = k³*V

Replacing k and solving for V we get:

124.92m³ = (1.44)³*V

(124.92m³/ (1.44)³) = V = 86.75 m³

If you want to learn more about scale factors:

https://brainly.com/question/3457976

#SPJ4

Answer: Its C

Step-by-step explanation: Just did it

Consider the quadratic function shown in the table below. x y 0 0 1 3 2 12 3 27 Which exponential function grows at a faster rate than the quadratic function for 0< x < 3?

Answers

So values are

(0,0)(1,3)(2,12)(3,27)

The rule is

3/1=312/2=627/3=9

Explicit formula

x(3x) where x is set of integers

Equation here is

y=3x²

Answer:

[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.

Step-by-step explanation:

Given table:

[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]

First Differences in y-values:

[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]

Second Differences in y-values:

[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]

As the second differences are the same, the function is quadratic.

The coefficient of [tex]x^2[/tex] is always half of the second difference.

Therefore, the quadratic function is:

[tex]f(x)=3x^2[/tex]

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]

An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3  is [tex]f(x)=4^x[/tex]

[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]

[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]

As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.

The volume of this rectangular prism is 48,608 cubic centimeters. What is the value of b?

Answers

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism = width × length × height

Given:

volume = 48,608 cm³width = 16 cmlength = bheight = 62 cm

Substituting the given values into the formula and solving for b:

⇒ 48608 = 16 × b × 62

⇒ 48608 = 992 b

⇒ b = 48608 ÷ 992

⇒ b = 49

Answer:

b = 49 cm

Step-by-step explanation:

Volume of a rectangular prism: length × width × height

V = L×W×H

v = 48,608 cm³l = b cmw = 16 cmh = 62 cm

Substitute the values above and solve for b:

48,608 = b × 16 × 62

48,608 = 992b

48,608/992 = 992b/992

49 = b

Final answer: 49 cm

Hope this helps!

1. Truncate the following numbers to the unit:
a) 25
b) 76
c) 10

Answers

Answer:

1 Truncation

Truncation is a method of approximating numbers. It is easier than rounding, but does not always give the best approximation to the original number. Truncation is used in computing when division is done with integers and the answer must be an integer.

Step-by-step explanation:

Instructions: find the marked angle in the triangle diagrams and explain how you figured it out.

(Image below) Also giving brainlyest to the person with a good explanation

Answers

Answer: 84 degrees

Step-by-step explanation:


this triangle is an isosceles triangle meaning two sides are of equal length ( the two sides in this case being the ones marked with the two lines // and // ) and that also means the triangle will have two equal angles (48 and 48) how do we know that? The triangle looks like this essentially: (see image below) where angle a = to angle b


a triangles angles added up always =180 degrees

Since we proved angle a is equal to angle b, we should be able to also subtract them from 180 to find angle c. 48+48=96


and simply subtract 96 from 180 to get 84 degrees.


therefore the angle is 84 degrees

Other Questions
Audrey is running for student council president. she estmates her chances of winning to be 1/5 chance. Which likelihood describes aubrey's estimated chances of winning? A. ImpossibleB. UnlikelyC. likelyD. Certain Please help me mi amor !!! I really need help x + 10Find the value of x Pa help po salamat, Some plant species and animal species depend on each other. Which of these animals help thousands of plant species to reproduce?. You spin the spinner once, what is P(not even)There is three parts to the spinner Which of the following methods helped Realist Winslow Homer to make the figuresappear lifelike in Prisoners from the Front?A. asking real soldiers to model in the studio during the painting processB. using the camera obscura to trace the reflections of soldiers onto canvasC. using photographs of soldiers to serve as models for the figuresD. using preparatory sketches of soldiers on the battlefield and in camp Need help please .The ares of the sector shown below is 59 yd^2 find the length of the radius. Round to the nearest whole number use 3.14 for pi QUESTION in the diagram below the following are rectangles. ACEG ;BCDJ ; JDEF and HJFG is a square AB =AH = x ;BC=5 ; HG=3 Area of a square= ss= s Area of a rectangle= lb Determine the area of ine following, some cases love answer terms of . DO NOT MEASURE THE DIAGRAM) 2.1.1 ABJHUnit 2.1.2 BCDJ: Units Units 2.1.3 DEFJ 2 2.1.4 HJFG Units 22 write in terms of the length of 2.2.1 AC 2.22 AC Units A triangle has sides with lengths of 55 feet, 65 feet, and 81 feet. Is it a right triangle?yesno Help please need quickly like rn Cuando te sientes asi Select the correct answer. what is the most significant benefit of exercising regularly? a. physical fitness b. less fatigue c. improved mood d. increased flexibility Move a number or variable to each line to create the expression. Please help with this question. what will be the change in momentum caused by a net force of 240 N acting on an object for 3 seconds ? what is the only type of lawyer guraranteed in the bill of rights Fill in the blanks in the following paragraph to correctly identify phenomena that help provide evidence for the particle nature of light Mom got way to intense with the circus tricks this afternoon. How you think and feel affects the way you: