Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green, four pieces are yellow, two pieces are purple, and three pieces are red. She draws one piece of candy from the bag at a time and eats it.
A. What is the probability that Chelsey will draw out three pieces of candy in this order: red, green, yellow?
B. What is the probability that Chelsey will draw out three pieces of candy in this order: green, yellow, red?
C. What is the probability that Chelsey will draw out three pieces of candy in this order: yellow, red, green? D. Make a conclusion about how the order in which she draws out the red, green, and yellow pieces affects the probability.

Answer:

a. [tex]-( 4\sqrt{3} + 3)[/tex]

b.  [tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]

c.  [tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]

d. [tex]45 + 12\sqrt{5y} + 4 y[/tex]

e. [tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]

Step-by-step explanation:

a.

[tex]\sqrt{12} - \sqrt{108} - \sqrt[3]{27}[/tex]

Expand each expression

[tex]\sqrt{4*3} - \sqrt{36 * 3} - \sqrt[3]{3*3*3}[/tex]

Split the first two surds

[tex]\sqrt{4}*\sqrt{3} - \sqrt{36} * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3*3*3}[/tex]

Apply law of indices

[tex]2*\sqrt{3} - 6 * \sqrt{3} - \sqrt[3]{3^3}[/tex]

Apply law of indices

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{3*\frac{1}{3}}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3^{1}[/tex]

[tex]2*\sqrt{3} - 6 * \sqrt{3} - 3[/tex]

[tex]2\sqrt{3} - 6\sqrt{3} - 3[/tex]

[tex]- 4\sqrt{3} - 3[/tex]

Factorize

[tex]-( 4\sqrt{3} + 3)[/tex]

The expression cannot be further simplified

b.

[tex](\frac{x^{\frac{-3}{4}}y^{\frac{2}{3}}}{x^{\frac{-1}{3}}y^{\frac{-5}{8}}})[/tex]

Expand the expression

[tex](\frac{x^{\frac{-3}{4}} * y^{\frac{2}{3}}}{x^{\frac{-1}{3}} * y^{\frac{-5}{8}}})[/tex]

Apply the following law of indices;

[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]

[tex]x^{{\frac{-3}{4} - \frac{-1}{3}}} * y^{{\frac{2}{3} - \frac{-5}{8}}}}[/tex]

[tex]x^{{\frac{-3}{4} + \frac{1}{3}}} * y^{{\frac{2}{3} + \frac{5}{8}}}}[/tex]

Add the exponents

[tex]x^{\frac{-9+4}{12}} * y^{{\frac{16+15}{24}}}}[/tex]

[tex]x^{\frac{-5}{12}} * y^{{\frac{31}{24}}}}[/tex]

[tex]x^{\frac{-5}{12}} y^{\frac{31}{24}}[/tex]

The expression cannot be further simplified

c.

[tex]\frac{8}{\sqrt{x} - \sqrt{5}}[/tex]

Rationalize the denominator

[tex]\frac{8}{\sqrt{x} - \sqrt{5}} * \frac{\sqrt{x} + \sqrt{5}}{\sqrt{x} + \sqrt{5}}[/tex]

[tex]\frac{8(\sqrt{x} + \sqrt{5})}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]

Simplify the numerator

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{(\sqrt{x} - \sqrt{5})(\sqrt{x} + \sqrt{5})}[/tex]

Simplify the denominator by difference of two squares

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{\sqrt{x}^2 - \sqrt{5}^2}[/tex]

[tex]\frac{8\sqrt{x} + 8\sqrt{5}}{x - 5}[/tex]

The expression cannot be further simplified

d.

[tex](3\sqrt{5} + 2\sqrt{y})^2[/tex]

Expand the expression

[tex](3\sqrt{5} + 2\sqrt{y})(3\sqrt{5} + 2\sqrt{y})[/tex]

Open the bracket

[tex]3\sqrt{5} (3\sqrt{5} + 2\sqrt{y})+ 2\sqrt{y}(3\sqrt{5} + 2\sqrt{y})[/tex]

Open both brackets

[tex]3\sqrt{5} *3\sqrt{5} + 3\sqrt{5}*2\sqrt{y}+ 2\sqrt{y}*3\sqrt{5} + 2\sqrt{y}*2\sqrt{y}[/tex]

[tex](3\sqrt{5} *3\sqrt{5}) + (3\sqrt{5}*2\sqrt{y})+ (2\sqrt{y}*3\sqrt{5}) + (2\sqrt{y}*2\sqrt{y})[/tex]

Multiply each expression in the bracket

[tex](3*3\sqrt{5*5}) + (3*2\sqrt{5*y})+ (2*3\sqrt{5*y}) + (2*2\sqrt{y*y})[/tex]

[tex](9\sqrt{25}) + (6\sqrt{5y})+ (6\sqrt{5y}) + (4\sqrt{y^2})[/tex]

Solve like terms

[tex](9\sqrt{25}) + (12\sqrt{5y}) + (4\sqrt{y^2})[/tex]

Take square root of 25 and y²

[tex](9 * 5) + (12\sqrt{5y}) + (4 * y)[/tex]

[tex](45) + (12\sqrt{5y}) + (4 y)[/tex]

Remove the brackets

[tex]45 + 12\sqrt{5y} + 4 y[/tex]

The expression cannot be further simplified

e.

[tex]-\sqrt{\frac{3}{5x}}[/tex]

This expression can not be simplified; However, it can be rewritten, by applying law of indices as

[tex]-(\frac{3}{5x})^{\frac{1}{2}}[/tex]

Answer:

Step-by-step explanation:

First, we can figure out how many additional inches of rope are needed.  If there are 8 knots, 16 additional inches will be needed. Peter would need 9 feet 4 inches of rope, or 112 inches.

The formula for finding the length of the rope needed would be 8+2n.

Hope this helps!

Answer:

112 inches

Step-by-step explanation:

Each knot needs 2 inches of rope

There are 2 knots

2*8 = 16 inches

He wants 8 ft from the ground, but he wants it in inches

8 ft* 12 inches per foot = 96 inches for the rope

96+ 16 =112 inches of rope

Answer:

B (from down below) They are similar but your q does not match up with the picture

Step-by-step explanation:

to determine if two triangles are similar you have to make sure the ratios are the same. So 10 / 8 = 1.25, so all sides should have this ratio. 15 / 12 is also 1.25 so you know to sides are similar and also the triangles ARE SIMILAR. So The statement would be KMN is similar to KLP.

Answer:

a. m<A = 35°

b. m<CBD = 61°

c. m AD is  sin55 = AD/40     AD = 32.77

d. m BC is sin 29 = 22.94/BC   BC = 47.32

e. m CD is tan 29 = 22.94/CD    CD = 41.38

f. m BD is cos 55 = BD/40    BD = 22.94

Step-by-step explanation:

The solution is,

a. m<A = 35°

b. m<CBD = 61°

c. m AD is  sin55 = AD/40     AD = 32.77

d. m BC is sin 29 = 22.94/BC   BC = 47.32

e. m CD is tan 29 = 22.94/CD    CD = 41.38

f. m BD is cos 55 = BD/40    BD = 22.94

In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

here, we have,

from the given figure, we get,

a) ∠D = 90

i.e.  ∠A= 90 - 55 = 35

b)  similarly,

∠CBD = 90-29

          =61

c) m AD is  sin55 = AD/40

i.e.  AD = 32.77

d) m BC is sin 29 = 22.94/BC  

i.e.  BC = 47.32

e)  m CD is tan 29 = 22.94/CD    

   i.e. CD = 41.38

f) m BD is cos 55 = BD/40  

  i.e. BD = 22.94

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Answer:

40

Step-by-step explanation:

if you add all the numbers up it becomes 96 and 96 goes Into. 480 5 times so you multiply 5 times the number of giant swallow tails

Answer:

If they are proportional we can expect 40

lol iready

Answer:

Data set A {41,19,29,12,49,30} = 30

Data set B {28,22,10,30,15} = 21

Data set C{49,24,18,53,38} = 36.4

Step-by-step explanation:

Data set A {41,19,29,12,49,30} =

Mean = Sum of terms/ number of terms

Number of term = 6

Mean = 41 + 19 + 29 + 12 + 49 + 30/ 6

= 180/6 = 30

Data set B {28,22,10,30,15} =

Mean = Sum of terms/ number of terms

Number of term = 5

Mean = 28 + 22 + 10 + 30 + 15/ 5

= 105/5 = 21

Data set C{49,24,18,53,38} =

Mean = Sum of terms/ number of terms

Number of term = 5

Mean =49 + 24 + 18 + 53 + 38/ 5

= 182/5 = 36.4

=============================================

Explanation:

Note that m + 1/m and m^2 + 1/(m^2) are very similar. If we square (m + 1/m), then we end up with something in the form (a+b)^2 = a^2 + 2ab + b^2, where a = m and b = 1/m. The 2ab portion is equal to 2*m*(1/m) = 2 which allows us to isolate m^2 + 1/(m^2) fully.

The steps below show this

[tex]m + \frac{1}{m} = \sqrt{71}\\\\\left(m + \frac{1}{m}\right)^2 = \left(\sqrt{71}\right)^2\\\\m^2 + 2*m*\frac{1}{m} + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} = 71\\\\m^2 + 2 + \frac{1}{m^2} - 2 = 71-2\\\\m^2 + \frac{1}{m^2} = 69\\\\[/tex]

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

Alternatively, you can isolate m in the equation [tex]m + \frac{1}{m} = \sqrt{71}[/tex] to get two irrational solutions. Plug either solution into m^2 + 1/(m^2) and you should get the same result as above.

Answer:

121

Step-by-step explanation:

This is an arithmetic sequence.

First term  a = -15

Common difference [d] = second term - first term

                                  = -11 - [-15] = -11 + 15 = 4

nth term = a + (n-1) * d

35th term = -15 + (35 - 1) * 4

                = -15 + 34 * 4

                = - 15 + 136

                = 121

Answer:

121 and 257

Step-by-step explanation:

So we would have our equation for arithmetic sequences which is [tex]a_{n} =a_{1} +(n-1)d[/tex] a1 is the first term, n is the term we want to know, and d is the common difference. We would plug in the numbers into the equation so we would get [tex]a_{n} =-15+(35-1)4[/tex]. And if you simplify you would get [tex]a_{n} =121[/tex].

Than for the other one we would do the same thing so you would get [tex]a_{n} = 121+(35-1)4[/tex] and if you simplify you would get [tex]a_{n} =257[/tex].

Answer: $20 <= X < = $21

Step-by-step explanation:

According to the question, you are told that he loses by going over $21 or by buying all items and being less than $20.

That means the total amount of the items bought must be equal to 20 dollars or 21 dollars or be within the two amount of money.

If Mikel buys six bottles of shampoo, let x represent the total amount for the six bottles of shampoo. Then, the compound inequalities for this expression will be x less than or equal to 21 dollars and x greater than or equal to 20 dollars. That is,

$20 <= X < = $21

Answer:

The given system of equations has "No solution” means that the constants are the numbers without variables. If the coefficients are the equal on both sides then their constants will not equal,they did not satisfy the given equations and therefore it said to have no solution

The given system of equations has "infinitely many solutions" if the given linear system of equations has both the equations represents to the same line.

Step-by-step explanation:

No solution would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable. Infinite solutions would mean that any value for the variable would make the equation true.

Answer:

domain: x cant be equal to 3.75

Step-by-step explanation:

I don't know if the problem is in my calculations or the question itself, but the result I got is irrational.

Anyway, here are my calculations. If the help you somehow to solve the question - great!

If not,srry to disappoint you

Answer:

its quite simple...

the formula to find volume= width x height x length ( or area x length)

Step-by-step explanation:

of A

of B

length of whole prism= 4

Volume (A)= w x h x l

                 =  5 x 9 x 4

                = 180 cm³

volume (B)= w x h x l

                = 3 x 2 x 4

                = 24 cm³

add both values to get the volume of whole prism = 180 + 24

                                                                                    = 204 cm³

Answer:

  P''(1, 7)

Step-by-step explanation:

4 units right and 1 left will add a net of +3 to the x-coordinate.

2 down and 5 up will add a net of +3 to the y-coordinate.

The coordinates of P with 3 added to each are ...

  P'' = P(-2, 4) +(3, 3) = P''(1, 7)

Answer:

The monthly cost for 9 HCF is $38.54

Step-by-step explanation:

The graph is missing; however, the question can still be solved

Given

Slope = 1.55

When monthly cost = $47.84, Amount of water = 15 HCF

Required

Determine the monthly cost for 9 HCF

From the question, we understand that it is a linear function;

Linear functions are of the form

[tex]y = mx + b[/tex]

Where y is the function of x and m is the slope

In this case; the function is the monthly water bill

and x is the amount of water

Solving for b

When monthly cost = $47.84, Amount of water = 15 HCF

The function is as follows;

[tex]47.84 = 1.55 * 15 + b[/tex]

[tex]47.84 = 23.25 + b[/tex]

Subtract 23.25 from both sides

[tex]47.84 - 23.25= 23.25 - 23.25 + b[/tex]

[tex]24.59 = b[/tex]

[tex]b = 24.59[/tex]

Solving for the monthly cost for 9 HCF

Here, we have that

[tex]x = Amount\ of\ water = 9[/tex]

[tex]m = Slope = 1.55[/tex]

[tex]b = 24.59[/tex]

Substitute these values in the linear function; [tex]y = mx + b[/tex]

[tex]y = 1.55 * 9 + 24.59[/tex]

[tex]y = 13.95 + 24.59[/tex]

[tex]y = 38.54[/tex]

Hence, the monthly cost for 9 HCF is $38.54

Answer:

Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Amount of the inheritance = $ 6,000

Interest rate of the first part = 4% simple

Interest rate of the second part = 7% simple

Interest of the accounts after the first year = $ 360

2. How much did he invest in each account?

For answering the question, we will use the following equation:

x = Amount invested in the first account

6,000 - x = Amount invested in the second account

0.04x + 0.07 * (6,000 - x) = 360

0.04x + 420 - 0.07x = 360

-0.03x = 360 - 420 (Subtracting 420 at both sides)

-0.03x = -60

x = -60/-0.03

x = 2,000 ⇒ 6,000 - x = 4,000

Mr. Weaver invested $ 2,000 in the 4% simple interest account and $ 4,000 in the 7% simple interest account.

Answer:

9

Step-by-step explanation:

because the angle is 45 deg, it is 1/8 of the full circle

the arc it intercepts will also be 1/8 the circumference of the full circle

72*1/8=9

Answer:

Hey there!

-6 ft is 6 ft below sea level.

Hope this helps :)

Answer:

y=x+-2

Step-by-step explanation:

Slope intercept form is y=mx+b

I plugged in the slope for m and y-intercept for b

sorry i did this real fast because it sounded urgent :)

Answer:

[tex]\large \boxed{\sf \ \ \ 2x-ln(1-x) \ \ \ }[/tex]

Step-by-step explanation:

Hello,

for any real x different from 1

[tex]\dfrac{3-2x}{1-x}=\dfrac{2-2x+1}{1-x}\\\\=\dfrac{2(1-x)+1}{1-x}\\\\=2\dfrac{1-x}{1-x}+\dfrac{1}{1-x}\\\\=2+\dfrac{1}{1-x}[/tex]

if f(x)=2x

   f'(x)=2

if g(x)=-ln(1-x)

   [tex]g'(x)=\dfrac{-1*-1}{1-x}=\dfrac{1}{1-x}[/tex]

So antiderivative of

[tex]\dfrac{3-2x}{1-x}=2+\dfrac{1}{1-x}[/tex]

Is

2x-ln(1-x)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

-7j-k-1

Step-by-step explanation:

10k + 17 - 7j -18 -11k

10k-11k

-1k

17-18

-1

-7j-k-1

Answer:

120

Step-by-step explanation:

The total number of triangles that can be made are 120.

We have a circle and 10 points are placed on it.

We have to find how many possible triangles can be made such that their vertices will be the given points.

A combination can be defined as the number of possible arrangements of elements without taking into consideration the order of selection. The number of possible combinations can be given by -

[tex]\frac{n!}{(n-r)!r!}[/tex]

In the question given to us - we have 10 points on circle. Only three points are needed to make a triangle. The order does not matter here, therefore -

[tex]\frac{10!}{(10-3)!3!}\\\\\frac{10!}{7!\times3!} \\\\\frac{10\times9\times8\times7!}{7!\times3\times2\times1}[/tex]

10 x 3 x 4 = 120

Hence, the total number of triangles that can be made are 120.

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Answer:f

Step-by-step explanation:

Answer: 31 degrees

Step-by-step explanation:

Assuming he works at a constant rate, the daily rate Mark rakes lawns in the fall is 40% of the daily rate he mows lawns in the summer.

Fall:

5 neighbors' lawns / 2.5 hours = 2 lawns per hour

Summer:

6 neighbours' lawns / 1.2 hours = 5 lawns per hour

2 x 100% / 5 = 40%

2 is 40% of 5

Answer:

Length of transverse axis  = 2 b  = 10

Length of conjugate axis   = 2 a  = 4      

Step-by-step explanation:

Explanation:-

Given Hyperbola

                       [tex]\frac{(y+2)^{2} }{25} -\frac{(x-3)^{2} }{4} =1[/tex]

  Standard form of Hyperbola    

                  [tex]\frac{(y-(K))^{2} }{b^{2} } -\frac{(x-h)^{2} }{a^{2} } =1[/tex]

   Center (h , k ) = (3 , -2 )  , a = 2 and b = 5

Length of transverse axis  = 2 b = 2(5) = 10

Length of conjugate axis   = 2 a = 2 (2) = 4      

Answer:

Andy

Step-by-step explanation:

Let's say that x is Andy's speed, and d is the distance he traveled.

The time it takes Andy to reach his friend is d/x.

The time it takes Ashley to travel the first half is (d/2)/(x/2) = d/x.

The time it takes Ashley to travel the second half is (d/2)/(5x) = d/(10x).

The total time is d/x + d/(10x) = 1.1 d/x.

It takes Ashley 1.1 times longer to reach the friend.  Andy gets there first.

[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Probability.

Basically we have to know that, when there is a specific event for which a probability has to be done, there are always two possibilities that is,

Event favourable and Not Favourable.

the Sum of both always end up as 1.

thus sum of the probability distribution is 1.

The sum of the probabilities in a uniform probability distribution is 1.

Hence, option C is the right choice.

A uniform distribution is a probability distribution in which all events have the same probability.

Because the chances of drawing a heart, a club, a diamond, or a spade are equal, a deck of cards has uniform distributions.

The general formula for the probability density function (pdf) for the uniform distribution is: f(x) = 1/ (b - a) for a ≤ x  ≤ b.

To find the sum of all the probabilities in a uniform probability distribution, we do the integral over f(x).

[tex]\therefore SUM = \int_{a}^{b}f(x)dx\\or, SUM = \int_{a}^{b}\frac{1}{b-a}dx\\or, SUM = \frac{1}{b-a}\int_{a}^{b}dx\\or, SUM = \frac{1}{b-a}[x]_{a}^{b}\\or, SUM = \frac{1}{b-a}(b-a)\\or, SUM = 1[/tex]

The sum can also be found using the graph attached, calculating the area of the red rectangle.

∴ The sum of the probabilities in a uniform probability distribution is 1.

Hence, option C is the right choice.

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Answer:

5/12

Step-by-step explanation:

take the number of students who read under6 books (5) and divide by total amount of students (12)

5/12

Answer:

5/12

Step-by-step explanation:

there are a total of 12 books read and a frequency of 5 books read that is fewer than 6 books

*see the attachment below showing Lewis' work

Answer:

*He simplified √400 incorrectly. It should be 20 instead of 200.

*He found the difference between the hypotenuse and the short leg instead of the long leg

Step-by-step explanation:

=>Going through the work of Lewis, you'd observe that in the 5th line where Lewis was supposed to simplify √400, he made a mistake by writing 200 instead of 20. The square root of 400 is 20 not 200.

=>Also, the length of the longest leg of the right angled triangle that Lewis is supposed to subtract from the length of the hypothenuse is 16 NOT 12.

The difference between the length of the hypothenuse and the length of the longest Leg = 20 - 16 = 4

Answer: A & B homies...

person up top is correct also...

Step-by-step explanation: on edg 2020

Answer: 1 & 4

Step-by-step explanation:

Just did it

Answer:

A.The height of the new trapezoid will be 1 ft.

D.The area of the new trapezoid is StartFraction 1 Over 16 EndFraction times the area of the original trapezoid.

Step-by-step explanation:

edg2020

Answer:

Four books  because there are the most dots over that spot on the bottom number line thingy