A bag contains 3red, 4white, 5green balls. Three balls are selected without replacement. Find the probability that the three balls chosen are:
A) all red
B) all green
C)one of each color
Answers
Answer:
A. 1/220 B. 1/22 C. 3/11
Step-by-step explanation:
This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).
Notations for combinations:
The number of ways to select r things from a set of n things is
[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex] where the exclamation points mean factorial.
[tex]n!=1\cdot2\cdot3\ldots\cdot n[/tex] and 0! is defined to be 1.
There are two other commonly used symbols for this:
[tex]_nC_r[/tex] and [tex]n \choose x[/tex].
In all three parts, the number of ways to choose 3 balls from a set of 12 is
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}[/tex]
Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving
[tex]C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220[/tex]
A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.
B) The number of ways to choose 3 green balls from the set of 5 green balls is [tex]C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10[/tex] out of 220, so the probability is 10/220 = 1/22.
C) The number of ways to choose 1 red is C(3, 1) = 3. Choose 1 green in C(5, 1) = 5 ways. Choose 1 white in C(4, 1) = 4 ways.
The probability is [tex]\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}[/tex]
Answer:
a) 1/220
b) 1/22
c) 3/11
Step-by-step explanation:
Check the attachment.
Related Questions
a rectangle has an area of 72 square inches and a width of 9 inches what is its perimeter?
Answers
Answer:
34 inches.
Step-by-step explanation:
In order to ger perimeter you need to find the value of all sides. We know one side is 9 inches. To find the other side length you divide the area by the side length (72/9=8). This is because the formula for area is length times width. To find permiter you add all the side lengths together. A rectangle has 4 sides, so you would do 9+9+8+8
This weekend, Paul earned $42 selling
handmade drawings. He sold some
posters for $9 each and a drawing for
$15. Which equation represents this
situation?
A 42 = (9 + p) - 15
B 42 = (9+ p) + 15
c 42 = (9 x p) + 15
D 42 = (9 x p) - 15
Answers
Answer:
C
Step-by-step explanation:
lol
Find the area using the given image.
Answers
54
Explanation:
Area of a triangle: 1/2 * base * height
1/2 * 18 * 6 = 54
Hope this helped you! :)
What is the correct answer NEED ANSWER ASAP
Answers
Answer:
Your answer is
x-int: (3 , 0) , (-3/2 , 0)
y-int: (0 , -9)
Step-by-step explanation:
Which angles are vertical to each other? Select all that apply.
Answers
Answer:
Answer is D. angle DGF and AGC
Given circle E with diameter CD and radius EA. AB is tangent to Eat A.
If AD = 14 and CD = 26, solve for AC. Round your answer to the nearest
tenth if necessary. If the answer.cannot be determined, click "Cannot be
determined."
Answers
The triangle ACD is the right angle since it is a triangle in a semicircle. The length of AC from the diagram is 21.9feet
Application of pythagoras theoremThe theorem states that the square of the hypotenuse is equal to the square of the other two sides
From the given circle, the triangle ACD is right angle since it is a triangle in a semicircle
Given the following
Hypotenuse = 26 feet = CD
Base side = AD = 14ft
Required
Length AC
Use the theorem
26^2 = 14^2 + AC^2
AC^2 = 676 - 196
AC^2 = 480
AC = 21.9feet
Hence the length of AC is 21.9feet
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x^2-2x-15>0; use -5,0 and 7 to help find the solution
Answers
I don't know what is given when I 8th May but if you can please send the answers
5/root of 7 - 2 is rationalized by multiplying the numerator and denominator by what?
Answers
The considered fraction is ationalized by multiplying the numerator and denominator by the expression as given by: Option A: √7 + 2
How to rationalize a fraction?Suppose the given fraction is [tex]\dfrac{a}{b+c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}[/tex]
(we used the identity [tex](b-c)(b+c) = b^2 - c^2[/tex])
We actually rationalize just for the use of that later denominator or numerator(if they seem to be helpful).
Remember that
[tex]\dfrac{b-c}{b-c} = 1[/tex]
thus, multiplying it with the fraction doesn't change its value, and just change the way how it looks. We assume that b-c is not 0
For this case, the given fraction is:
[tex]\dfrac{5}{\sqrt{7} - 2}[/tex]
Thus, here we will multiply the denominator with [tex]\sqrt{7} + 2[/tex] so that we can use the identity [tex](b-c)(b+c) = b^2 - c^2[/tex].
Thus, we get:
[tex]\dfrac{5}{\sqrt{7} - 2} \times \dfrac{\sqrt{7} + 2}{\sqrt{7} + 2} = \dfrac{5(\sqrt{7} + 2)}{(\sqrt{7})^2 - 2^2} = \dfrac{5(\sqrt{7} + 2)}{3}[/tex]
See, the denominator now looks a bit better. We try to make it look smooth and simplified because division is more complex than multiplication, so its better to have square root term in numerator than in denominator.
Thus, the considered fraction is ationalized by multiplying the numerator and denominator by the expression as given by: Option A: √7 + 2
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Juliana bought 3 bags of chips for 0.85 each and 3 sodas for herself and two friends and spent exactly $6 (before tax.) write an equation to find the price of each can of soda.
Answers
Step-by-step explanation: Cost of 3chips =$0.85×3= $2.55
Cost of 3 soda will be $6-$2.55
Cost of 1soda will be ($6-$2.55)/3
Help
What is the change in the breaking weight of the pennies, for each increase in one unit of the length of the bridge?
Answers
Using linear function concepts, it is found that the change in the breaking weight of the pennies was of -6 units of weight.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the function is:
y = -6x + 136.
The slope is of m = -6, hence the change in the breaking weight of the pennies was of -6 units of weight.
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Find the equation of the line shown (first one to do it gets brainlist)
Answers
Answer:
y = 1/4x + 2
Step-by-step explanation:
We do y = mx + b
slope = rise over run = 1/4
Y-intercept = 2
Equation is y = 1/4x + 2
Answer:
y = -0.25x + 2
Step-by-step explanation:
When x=0, y = 2
When y=0, x = 8
X = 0 – 4 = -4
Y = 2 – 1 = 1
[tex]Slope\:(m)=\frac{y}{x} =\frac{1}{-4} =-0.25[/tex]
Please help
Below is a list of the steps used to construct a square inscribed in a circle. Step M-Place the compass point at the endpoint of the diameter and the pencil at the center of the circle to construct an arc. Step N - Draw in two diameters using the points where the small arc intersects the line segments and the center. Step O Construct a small arc by placing the compass point where the diameter intersects the line segment and the pencil on the center of the circle. Step P- Construct a line segment between the two points where the arc intersects the circle Step Q-Draw line segments between the four points where the two constructed diameters intersect the circle. Which list shows these steps in the correct order?
○M, N, O, P, Q
○M, P, O, N, Q
○ O, P, M, Q, N
○P,O,M,Q,N
Answers
O,p,m,q,n
Evaluate the expression for A=3
32-4a
Answers
Hi ! Dude
Answer:
20 is the correct answer
Step-by-step explanation:
Given :a = 3 and ,An expression = 32 - 4aWhat we have to do :After reading question we can understand that we have to find the value of expression by plugin the value of a .
Solution Starts :[tex] \qquad \: \rightarrow 32 - 4a [/tex]
Plugin value of a ,
[tex] \qquad \:\rightarrow \: 32 - 4(3)[/tex]
[tex]\qquad \: \rightarrow \: 32 - 12[/tex]
[tex]\qquad \: \rightarrow \: \underline{ \underline{20}}[/tex]
Hence , 20 is the answer .
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[tex]\blue\textsf{\textbf{\underline{\underline{Question:-}}}}[/tex]
Evaluate the expression for a=3
32-4a
[tex]\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}[/tex]
Provided Information:-
a=3The expression [tex]\bold{32-4a}[/tex]
To Find:-
Simplify the expression 32-4a
In order to do that, we should
Substitute 3 in lieu of a:-[tex]\tt{32-4(3)}[/tex]
Multiply:-
[tex]\tt{32-12}[/tex]
Subtract:-
[tex]\dashrightarrow\bigstar\boxed{\boxed{\underline{\bold{20}}}}\dashleftarrow[/tex]
So our final solution is 20.
Good luck.- - -- - - - - - - - - - - - - - - - - -- - - - - - - - - - -- -- - - - - -- - - - - - - - - - - - -
Sammy makes $2,362/month as a baseball coach. he is making a budget, and has created the following chart in order to divide his monthly paycheck into his various accounts: expense type frequency account monthly amount items essential (fixed) monthly checking $1,292 rent, car, insurance essential (variable) monthly checking $420 basic groceries, telephone, electricity, cable tv, batting practice non-essential monthly cash $260 snack items, restaurants, gifts, movies other (predictable) annual savings $130 health exams, clothing, food, baseball coach magazine other (unpredictable) annual emergency savings $210 non-insured healthcare, repairs, and income replacement other (long-term) 5 years vacation savings $50 vacation total $2,362 sammy makes monthly deposits from each paycheck into the various accounts, and then spends from those accounts only for their defined purposes. he knows that it is not a perfect system, but thinks that it will help to assure coverage for future expenses. using his essential expenses as a guideline, how much will sammy need to save if he wants to have 3 times the amount of his living expenses in the bank as part of his emergency savings. how long will it take him to achieve his goal? a. $1,712; approximately 8 months b. $5,136; approximately 24 months c. $6,486; approximately 30 months d. $2,162; approximately 6 months
Answers
The amount of time it would will it take him to achieve his goal is B. $5,136; approximately 24 months.
What are Savings?This refers to the emergency funds that are set aside for situations that were not initially budgeted for.
Hence, because Sammy makes about $2,362/month
Rent, car insurance $1,292
Basic groceries, telephone $420
Snack items $260
Annual Savings $130
Annual emergency savings $210
5 years of vacation savings $50
Total= $2,362
Using Sammy's method of putting these budgets into separate checking accounts, the amount which Sammy needs to save to have x3 of his living expenses and the length of time it would take is $5,136; approximately 24 months.
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Stu takes a job with a starting salary of $65,000 for the first year. he earns a 2% increase each year. to the nearest dollar, how much does stu make over the first five years? $325,000 $331,500 $338,263 $358,826
Answers
Answer:
$338,263
Step-by-step explanation:
first year stays the same, then multiply the years salary x 1.02 for the following years
year 1 = $65000
year 2 = 66300
year 3 = 67626
year 4 = 68978.52
year 5 = 70358.09
total for 5 years = $338262.61
rounded to 338,263.
Omar rented a truck for one day. There was a base fee of $14.99, and there was an additional charge of 80 cents for each kilometer driven. Omar had to pay
S111.79 when he returned the truck. For how many kilometers did he drive the truck?
Answers
Answer: 121 kilometers
Step-by-step explanation:
14.99 + .80x (-14.99) = 111.79 (-14.99)
.80x (/.80) = 96.8 (/.80)
x = 121
If p p and q q vary inversely and p is 17 when q is 4, determine q when p p is equal to 2.
Answers
Answer:
[tex]q = 34[/tex] when [tex]p = 2[/tex].
Step-by-step explanation:
Variables [tex]p[/tex] and [tex]q[/tex] ([tex]p \ne 0[/tex], [tex]q \ne 0[/tex]) are inversely proportional to one another if one variable- for example, [tex]p[/tex]- is proportional to the reciprocoal of the other variable- [tex](1/q)[/tex].
In other words, if [tex]p[/tex] and [tex]q[/tex] ([tex]p \ne 0[/tex], [tex]q \ne 0[/tex]) are inversely proportional to one another, there would exist a constant [tex]k[/tex] ([tex]k \ne 0[/tex]) such that:
[tex]\displaystyle p = k\times \left(\frac{1}{q}\right)[/tex].
The value of [tex]k[/tex] is constant and is independent of [tex]p[/tex] and [tex]q[/tex]. Given that [tex]p = 17[/tex] when [tex]q = 4[/tex], rearrange the equation above to find the value of [tex]k\![/tex]:
[tex]k = p\, q = 68[/tex].
Rewrite the equation again to find [tex]q[/tex] in terms of [tex]k[/tex] (which doesn't change) and [tex]p[/tex] (which might change):
[tex]\begin{aligned}q &= \frac{k}{p}\end{aligned}[/tex].
Since [tex]k = 68[/tex], given that [tex]p = 2[/tex], the value of [tex]q[/tex] would be:
[tex]\begin{aligned}q &= \frac{k}{p} \\ &= \frac{68}{2} = 34\end{aligned}[/tex].
Which of the following are solutions to the equation below?
Check all that apply.
x2 + 4x + 4 = 12
A. x= -22/3 - 2
O B. X = -V2+12
O c. X= V2 +12
O D. x = 213-2
O E. x = 2,5 + 2
O F. x= -2-43 +2
Answers
The solution is, x_1 = -2 + 2√3 and, x_2 = -2 - 2√3, are solutions to the equation below.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
1) Since we've been given the equation x²+4x +4=12 then let's solve it to find the roots
2) Applying the resolutive formula
x²+4x +4=12
x²+4x +4-12 =0
x²+4x -8=0
now, we know, here,
D = b² - 4ac
so, solving we get,
D = 48
Now, the roots are,
x = -b ± √D / 2a
so, here, we get,
x_1 = -2 + 2√3
x_2 = -2 - 2√3
Hence, The solution is, x_1 = -2 + 2√3 and, x_2 = -2 - 2√3, are solutions to the equation below.
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h.e.l.p. m.e. p.l.s.
Answers
The answer: 3.15 ✅
Since the middle line between a farction is also division in some cases, divide forty-one by thirteen.
[tex]\frac{41}{13} = 3.15[/tex]
Answer:
3.15
Step-by-step explanation:
First you setup the problem for long division.
Like this: 41/--13 (cant really draw the thing)
After that you you solve it and get 3.15384+ which you round to 3.15 because it is the hundreth.
please please help me
Answers
a rope 33cm long has a mass of 561 g. what is the mass of 13 cm of this rope.? can some one please help
Answers
Step-by-step explanation:
[tex]33cm = 561g[/tex]
[tex]13cm = x[/tex]
[tex] \frac{13}{33} \times 561[/tex]
[tex]221g[/tex]
Answer: 221
Step-by-step explanation:
33cm = 561g
1cm = 561/33 = 17
13cm = 17 × 13
Which phrase describes the shape of the temperature data? symmetrical left-skewed right-skewed normal
Answers
In this distribution, the shape that describes the temperature data is left-skewed distribution.
What is left-skewed distribution?left-skewed distribution serves as a type of more values on the right side (tail) of the distribution graph .
Therefore, From the graph, majority of the data is to the right of the graph which is a left-skewed distribution.
Learn more about left-skewed distribution at;
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Answer:
B) left-skewed
Step-by-step explanation:
Find the equation of the line shown (first one to do it gets brainlist)
Answers
Answer:
y = 2x – 1
Step-by-step explanation:
When x=0, y = -1
When y=0, x = 0.5
Two angles (angle C and angle D) are
supplementary. The measure of angle C is
5x – 6 and the measure of angle D is 7x +
14. Find the measure in degrees of each
angle
Answers
Answer:
C= 65.5°
D= 114.1°
Step-by-step explanation:
5x - 6 + 7x +14 = 180
5x + 7x + 14 - 6 = 180
12x + 8 = 180
- 8 - 8
12x = 180
12x/12 = 180/12
x = 14.3
C= 5x - 6
5(14.3)-6
71.5 - 6
C=65.5°
D= 7x + 14
7(14.3) + 14
100.1 + 14
D= 114.1°
65.5 + 114.1 = 179.6°
When this is rounded up, you will get 180°
Hope this helps!
Give a pair of alternate interior angles, a pair of alternate exterior angles, and a pair of corresponding angles.
WILL MARK BRAINLIEST IF RIGHT!! Help
Answers
Answer:
Alternate Interior
∠3 and ∠6
Alternate Exterior
∠2 and ∠7
Corresponding
∠1 and ∠5
I hoped this helped :)
the least common multiple [l.c.m] of16,30and36
Answers
Answer:
720
Step-by-step explanation:
16=2^4
30=5*3*2
36=(2^2)*(3^2)
so
(2^4)*5*(3^2)=720
mayonaise on a escatlater going so fast so i will see you later
Answers
HELPP FOR BRIANLEST!!!
Answers
Answer:
Your answer Exterior C is 160°
Interior C is 20°
Step-by-step explanation:
<A + <B + <C = 180°
<Left C + <Right C = 180°
<A + <B = <Right C
(5x - 10)° + 12x° = 16x
17x - 10 = 16x
x = 10
<A = 5x - 10
<A = 5*10 - 10
<A = 50 - 10 = 40°
<B = 12x
<B = 12*10
<B = 120°
<A + <B = <Right C.
40° + 120° = 160°
Doug has a bag full of crayons. There are 6 red crayons, 7 blue ones, and 4 green crayons. Doug wants to color a blue sky. What is the probability that Doug will pull out a red crayon, put it back in the bag, and then get a blue crayon? Write your answer as a simplified fraction
Answers
Answer:
[tex]\sf \dfrac{7}{17}[/tex]
Step-by-step explanation:
Given information:
6 red crayons7 blue crayons4 green crayons⇒ total number of crayons = 6 + 7 + 4 = 17
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(red\:crayon) =\dfrac{\textsf{Number of red crayons}}{\textsf{Total number of crayons}}=\dfrac{6}{17}[/tex]
If the red crayon is put back in the bag, the drawing of the red crayon prior to drawing the blue crayon will not affect the probability of drawing a blue crayon.
[tex]\implies \sf P(blue\:crayon)=\dfrac{\textsf{Number of blue crayons}}{\textsf{Total number of crayons}}=\dfrac{7}{17}[/tex]
Solve the equation 3x-2y =7, x+2y= -3
Answers
Answer:
x=1y= -2Step-by-step explanation:
3x-2y =7x+2y= -34x=4x=4/4x=13x-2y=73(1)-2y=73-2y=7-2y=7-3-2y=42y=-4y=-4/2y= -2Verify solutionx+2y= -31+2y= -32y=-3-12y= -4y= -4/2y= -2Answer:
x = 1
y = -2
Step-by-step explanation:
adding both quation we get
3x -2y + x + 2y =7 + -3
4x = 4
x = 1
substituting this equation in the earlier equation we get
3 * 1 -2y = 7
3 - 2y = 7
-2y = 4
y = -2