Answer:
7/36
Step-by-step explanation:
1 die has 6 faces
When two dice are rolled, the total number of outcomes
= 6 × 6 = 36
The Probability of having(5) =
(1 & 4), (2 & 3) , ( 3 & 2), (4 & 1)
= 4
The probability of having (10) =
(5 & 5), (4 & 6) , ( 6 & 4)
= 3
The probability that the score on the dice is either 5 or 10.
P(5) + P(10)
= 4/36 + 3/36
= 7/36
Answer: 7/36
Step-by-step explanation:
36 outcomes
4 chances of getting 5 (1+4, 2+3, 4+1, 3+2)
3 chances of getting 10 (4+6, 5+5, 6+4)
4+3=7
so 7/36 chance
Find the distance between points P(5, 1) and Q(3, 4) to the nearest tenth.
3.6
5
9.4
13
Answer:
≈ 3.6
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)
d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]
= [tex]\sqrt{(-2)^2+3^2}[/tex]
= [tex]\sqrt{4+9}[/tex]
= [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )
Answer:
3.6
Step-by-step explanation:
Look above bru
find the domain of the graphed function.
pls help:Find all the missing elements:
Answer:
B = 48.7° , C = 61.3° , b = 12Step-by-step explanation:
In order to find B we must first angle C
To find angle C we use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) } [/tex]
From the question
a = 15
A = 70°
c = 14
So we have
[tex] \frac{15}{ \sin(70) } = \frac{14}{ \sin(C) } [/tex]
[tex] \sin(C) = \frac{14 \sin(7 0 ) }{15} [/tex]
[tex]C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} ) [/tex]
C = 61.288
C = 61.3° to the nearest tenthSince we've found C we can use it to find B.
Angles in a triangle add up to 180°
To find B add A and C and subtract it from 180°
That's
A + B + C = 180
B = 180 - A - C
B = 180 - 70 - 61.3
B = 48.7° to the nearest tenthTo find b we can use the sine rule
That's
[tex] \frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) } [/tex]
[tex] \frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) } [/tex]
[tex] |b| = \frac{15 \sin(48.7) }{ \sin(70) } [/tex]
b = 11.9921
b = 12.0 to the nearest tenthHope this helps you
Find a polar equation r for the conic with its focus at the pole and the given eccentricity and directrix. (For convenience, the equation for the directrix is given in rectangular form.)
Conic: Parabola Eccentricity: e = 1 Directrix: y = 4
Answer:
The equation is [tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
Step-by-step explanation:
From the equation we are told that
The Eccentricity: e = 1
The Directrix is y = 4
Generally the polar equation for e = 1 and y = + c is mathematically represented as
[tex]r = \frac{e * c }{ 1 + ecos (\theta )}[/tex]
So
[tex]r = \frac{1 * 4 }{ 1 + 1 * cos (\theta )}[/tex]
[tex]r = \frac{4 }{ 1 + cos (\theta )}[/tex]
How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145
Answer:
Mean: 169.4
Median: 171
Mode: 181
Step-by-step explanation:
I first sorted the numbers by value, least to greatest.
145 147 153 153 167 170 170 172 181 181 181 182 185 185
We can see that 181 occurs the most, 3 times, so it's the mode.
The median of this set will be the middle number(s).
When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.
We can add all the numbers and divide by 14 to get the mean.
[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]
Hope this helped!
A researcher measures daily driving distance from college and weekly cost of gas for a group of commuting college students. What kind of correlation is likely to be obtained for these two variables?
Answer:
There is a positive correlation between these two variables.
Step-by-step explanation:
Positive correlation is an association amid two variables in which both variables change in the same direction.
A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
As the distance covered by the vehicle increases the amount of gas consumed also increases. Thus, the weekly cost of gas will also increase.
Thus, there is a positive correlation between these two variables.
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55, then P( A| B) is:_________.
a. .19
b. 1.57
c. .64
d. .91
Answer:
P( A| B)= 0.35. None of the options are correctStep-by-step explanation:
Two events A and B are said to be independent if the occurrence of one of the events does not affect the other occurring. For example, the event of tossing two coins is an independent event since they occur simultaneously. Two events are therefore independent if the following are true.
P(A|B) = P(A)
P(B|A) = P(B)
P(A and B) = P(A)P(B)
If A and B are independent events with P( A) = 0.35 and P( B) = 0.55,
then P( A| B) is a probability of A occurring provided that B has occurred. This is known as conditional probability for an independent event.
From the condition above for independent events, P(A|B) = P(A) and since P(A) = 0.35, hence P(A|B) =0.35
The grade appeal process at a university requires that a jury be structured by selecting individuals randomly from a pool of students and faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of students and faculty
Correct question is ;
The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of nine students and eleven faculty. (a) What is the probability of selecting a jury of all students? (b) What is the probability of selecting a jury of all faculty? (c) What is the probability of selecting a jury of six students and two faculty?
Answer:
A) 7.144 × 10^(-5)
B) 0.00131
C) 0.0367
Step-by-step explanation:
We are given;
Number of students = 9
Number of faculty members = 11
A) Now, the number of ways we can select eight students from 9 =
C(9, 8) = 9!/(8! × 1!) = 9
Also, number of ways of selecting 8 individuals out of the total of 20 = C(20,8) = 20!/(8! × 12!) = 125970
Thus, probability of selecting a jury of all students = 9/125970 = 7.144 × 10^(-5)
B) P(selecting a jury of all faculty) = (number of ways to choose 8 faculty out of 11 faculty)/(Total number of ways to choose 8 individuals out of 20 individuals) = [C(11,8)]/[C(20,8)] = (11!/(8! × 3!))/125970 = 0.00131
C) P(selecting a jury of six students and two faculty) = ((number of ways to choose 6 students out of 9 students) × (number of ways to choose 2 faculty out of 11 faculty))/(Total number of ways to choose 8 individuals out of 20 individuals) = [(C(9,6) × C(11,2)]/125970
This gives;
(84 × 55)/125970 = 0.0367
The cost in dollars y of producing x computer
desks is given by y = 40x + 4000
X
100
200
300
a. Complete the table
y
b. Find the number of computer desks that can be produced for $6200. (Hint: Find x when y = 6200.)
a. Complete the table.
х
100
200
300
y
b. For $6200,_ computer desks can be produced
Answer:
a.
y= 40x +4000
x= 100 --> y= 40(100)+4000= 4000+4000=8000
x=200 --> y= 40(200)+4000= 6000+4000= 10000
x=300 --> y= 40(300)+4000= 12000+4000= 16000
(in $)
b.
y= 40x+4000
6200= 40x+4000
6200-4000= 40x
2200= 40x
2200/40= x
55= x
(in unit)
Step-by-step explanation:
I hope this helps
if u have question let me know in comments ^_^
If AD=2/3AB, the ratio of the length of BC to the length of DE is A. 1/6 B. 1/4 C. 3/2 D. 3/4
Answer:
The correct answer is c
Step-by-step explanation:
Answer:
C.) 3/2
Explanation:
PLATO
if P(x)=1+6x-5x^2 represents the profit in selling x thousand Boombotix speakers, how many speakers should be sold to maximize profit?
Answer:
600
Step-by-step explanation:
[tex]p(x) = 1 + 6x - 5x^2[/tex]
x max = [tex]-b/2a[/tex]
a = -5
b = 6
-6/2(-5) = 6/10 = 3/5 = .6
.6 thousand = 600
600 speakers should be sold.
Alternatively, you can check the vertex of the parabola formed.
algebra and trigonometry difference
Answer:
Algebra deals with knowing the value of unknown variables and functional relationships, while trigonometry touches on triangles, sides and angles and the relationship between them.
Algebra is more on polynomial equations, x and y while trigonometry more on sine, cosine, tangent, and degrees.
Trigonometry is much more complicated than algebra but algebra has its uses in our daily lives, be it calculating distance from point to another or determining the volume of milk in a milk container.
Step-by-step explanation:
Answer:
Although both Algebra II and Trigonometry involve solving mathematical problems, Algebra II focuses on solving equations and inequalities while Trigonometry is the study of triangles and how sides are connected to angles.
hope this answer helps u
pls mark as brainliest .-.
Find the product of the roots of the equation
xl-5x - 36 = 0
Answer:
Step-by-step explanation:
Hello, I assume that you mean
[tex]x^2-5x-36[/tex]
The product is -36.
[tex]x_1 \text{ and } x_2 \text{ are the two roots, we can write}\\\\(x-x_1)(x-x_2)=x^2-(x_1+x_2)x+x_1\cdot x_2[/tex]
So in this example, it means that the sum is 5 and the product is -36.
Thank you
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time it takes to produce the product using the new machine is significantly less than the production time using the old machine. To test the claim, independent random samples were taken from both machines. You are given the following results.
New Machine Old Machine
Sample Mean 25 23
Sample Variance 27 7.56
Sample Size 45 36
As the statistical advisor to Ajax, would you recommend purchasing Allied's machine? Explain.
Answer:
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
Step-by-step explanation:
We must evaluate the differences of the means of the two machines, to do so, we will assume a CI of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).
New machine
Sample mean x₁ = 25
Sample variance s₁ = 27
Sample size n₁ = 45
Old machine
Sample mean x₂ = 23
Sample variance s₂ = 7,56
Sample size n₂ = 36
Test Hypothesis:
Null hypothesis H₀ x₂ - x₁ = d = 0
Alternative hypothesis Hₐ x₂ - x₁ < 0
CI = 90 % ⇒ α = 10 % α = 0,1 z(c) = - 1,28
To calculate z(s)
z(s) = ( x₂ - x₁ ) / √s₁² / n₁ + s₂² / n₂
s₁ = 27 ⇒ s₁² = 729
n₁ = 45 ⇒ s₁² / n₁ = 16,2
s₂ = 7,56 ⇒ s₂² = 57,15
n₂ = 36 ⇒ s₂² / n₂ = 1,5876
√s₁² / n₁ + s₂² / n₂ = √ 16,2 + 1.5876 = 4,2175
z(s) = (23 - 25 )/4,2175
z(s) = - 0,4742
Comparing z(s) and z(c)
|z(s)| < | z(c)|
z(s) is in the acceptance region. We accept H₀ we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine
The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean
A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.
(a) If the initial distribution for states A, B, and C is P0 = ( 1／3 , 1／3 , 1／3 ), find the distribution of X2
(b) Find the steady state distribution by solving πP = π.
Answer:
A) distribution of x2 = ( 0.4167 0.25 0.3333 )
B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]
Step-by-step explanation:
Hello attached is the detailed solution for problems A and B
A) distribution states for A ,B, C:
Po = ( 1/3, 1/3, 1/3 ) we have to find the distribution of x2 as attached below
after solving the distribution
x 2 = ( 0.4167, 0.25, 0.3333 )
B ) finding the steady state distribution solving
[tex]\pi p = \pi[/tex]
below is the detailed solution and answers
y - 4= -2(x + 3)
Complete the missing value in
the solution to the equation.
(-3, _ )
Answer:
4
Step-by-step explanation:
i distributed the -2 to what's in the parentheses. that equal 0. I then moved the 4 to the zero so that it becomes positive. I just assumed that you were ask for Y
Step-by-step explanation:
y-4=-2(x+3)....eq(1)
y- 4= -2x-6
y=-2x-2...eq(2)
subtituting equation 2 in equation 1
(-2x-2)-4=-2x-6
-2x-6=-2x-6
=0
Algebra Review
Write an algebraic expression for each verbal expression.
1. the sum of one-third of a number and 27
2. the product of a number squared and 4
3. Write a verbal expression for 5n^3 +9.
Answer:
Step-by-step explanation:
1. The sum of one-third of a number and 27
= [tex]\frac{1}{3}\times x +27\\= 1/3x +27[/tex]
2. The product of a number squared and 4
[tex]Let\:the\:unknown\: number\: be \:x\\\\x^2\times4\\\\= 4x^2[/tex]
3.Write a verbal expression for 5n^3 +9.
The sum of the product and of 5 and a cubed number and 9
If f(x)=4x-6 and g(x) vx+2 what is (f*g)(7)
Answer: The value of (f*g)(7) is 66.
Step-by-step explanation:
Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]
Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]
[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]
[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]
Hence, the value of (f*g)(7) is 66.
a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent
Answer
$25.59
Step-by-step explanation:
subtract by percentage or you can also do:
100% - 4.5% = 95.5%
95.5% x $26.80 = $25.594
IF ROUNDED: $25.59
Answer:
$25.65
Step-by-step explanation:
Let the original hourly rate be r.
Then 1.045r + $26.80/hr.
Dividing both sides by 1.045, we get:
$26.80/hr
r = ------------------ = $25.65 This was the before-raise pay rate.
1.045
What is the rise over run for the slope -11/9
Answer: 11 down and 9 right
Step-by-step explanation:
Slope IS rise over run where the top number of the fraction (numerator) determines the vertical distance --> positive is up, negative is down
and the bottom number of the fraction (denominator) determines the horizontal distance --> positive is right, negative is left.
Given slope = -11/9
the numerator is -11 so the "rise" is DOWN 11 units
the denominator is 9 so the "run" is RIGHT 9 units
Select the best with the least expensive corn per ounce The choices are in the image
Answer:
B
Step-by-step explanation:
Option A:
1.50÷18≈0.0833
3.00÷36≈0.0833
4.50÷54≈0.0833
Option B:
0.75÷15=0.05
Option C:
2.20÷15=0.146
Use the model to show to help find the sum 0.34 plus 0.49
Answer/Step-by-step explanation:
The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.
Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.
The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].
Using the model, we can solve 0.34 + 0.49.
Add both fractions together.
[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]
[tex] \frac{83}{100} = 0.83 [/tex]
About how many feet are in 3.6 kilometers? 1 m = 39.37 in
Answer:
11811 feet
Step-by-step explanation:
Hope it helps!
There are about 11,812 feet in 3.6 kilometers.
To convert kilometers to feet, we need to use the conversion factor:
1 kilometer = 3,280.84 feet.
Now, to find how many feet are in 3.6 kilometers,
we can multiply 3.6 by the conversion factor:
So, 3.6 kilometers x 3,280.84 feet/kilometer
= 11,811.504 feet.
Thus, Rounded to a whole number, there are about 11,812 feet in 3.6 kilometers.
Learn more about Unit Conversion here:
https://brainly.com/question/14573907
#SPJ6
(-1, 4) and (-2, 2).
Answer:
Slope : 2
slope-intercept: y = 2x + 6
Point-slope (as asked): y - 4 = 2 (times) (x + 1)
standered: 2x - y = -6
Step-by-step explanation:
Find the distance between the points. Give an exact answer and an approximation to three decimal places.
(3.1,0.3) and (2.7. - 4.9)
The exact distance is
(Simplify your answer. Type an exact ans
Answer: sqrt(27.2) =approx 5.215
Step-by-step explanation:
The distance between 2 points can be calculated using Phitagor theorem
L= sqrt( (x1-x2)²+(y1-y2)²)
Where x1, y1 are the coordinates of the first point and x2, y2 are the coordinates of the 2-nd point.
L=sqrt((3.1-2.7)²+(0.3-(-4.9))²)= sqrt(0.4²+5.2²)=sqrt(27.2) - this is exact answer.
sqrt(27.2)=5.21536...=approx 5.215
A researcher at the University of Washington medical school believes that energy drink consumption may increase heart rate. Suppose it is known that heart rate (in beats per minute) is normally distributed with an average of 70 bpm for adults. A random sample of 25 adults was selected and it was found that their average heartbeat was 73 bpm after energy drink consumption, with a standard deviation of 7 bpm. In order to test belief at the 10% significance level, determine P-value for the test.
Answer:
Step-by-step explanation:
Given that:
mean μ = 70
sample size = 25
sample mean = 73
standard deviation = 7
level of significance = 0.10
The null hypothesis and the alternative hypothesis can be computed as follows:
[tex]\mathtt{H_o : \mu = 70} \\ \\ \mathtt{H_1 : \mu > 70 }[/tex]
The z score for this statistics can be calculated by using the formula:
[tex]z = \dfrac{X- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{73- 70}{\dfrac{7}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3}{\dfrac{7}{5}}[/tex]
[tex]z = \dfrac{3 \times 5}{{7}{}}[/tex]
z = 2.143
At level of significance of 0.10
degree of freedom = n -1
degree of freedom = 25 - 1
degree of freedom = 24
The p - value from the z score at level of significance of 0.10 and degree of freedom of 24 is:
P - value = 1 - (Z < 2.143)
P - value = 1 - 0.9839
P - value = 0.0161
Decision Rule: since P value is lesser than the level of significance, we reject the null hypothesis.
Conclusion: We conclude that energy drink consumption increases heart rate.
Kelvin wants to know whether he skied without falling more than twice as long as anyone else in his family. His dad tells him that he can check by using the inequality 2f < 223, where f is the time skied in seconds for each person. Plug the values for the time skied by each person into the inequality to find the answer.
Lori 55
Vanessa 265
Devon 172
Celia 112
Arnold 356
Answer:
Kelvin did not skied without falling more than twice as long as anyone else in his family.
Step-by-step explanation:
The inequality representing the event where Kelvin skied without falling more than twice as long as anyone else in his family is:
[tex]2f<223[/tex]
Here 223 is the time for Kelvin.
Check for Lori as follows:[tex]2f<223[/tex]
[tex]2\times 55=110<223[/tex]
Kelvin skied without falling more than twice as long as Lori.
Check for Vanessa as follows:[tex]2f<223[/tex]
[tex]2\times 265=530>223[/tex]
Kelvin skied without falling less than twice as long as Vanessa.
Check for Devon as follows:[tex]2f<223[/tex]
[tex]2\times 172=344>223[/tex]
Kelvin skied without falling less than twice as long as Devon.
Check for Celia as follows:[tex]2f<223[/tex]
[tex]2\times 112=224>223[/tex]
Kelvin skied without falling less than twice as long as Celia.
Check for Arnold as follows:[tex]2f<223[/tex]
[tex]2\times 356=712>223[/tex]
Kelvin skied without falling less than twice as long as Arnold.
Thus, Kelvin did not skied without falling more than twice as long as anyone else in his family.
Answer:
Yes, Kevin skied 2x as long as Lori.
Step-by-step explanation:
Kevin's time was 223 seconds; Lori's time was 110 seconds.
110^2 = 220 or 110 multiplied by 2 equals 220 or 110 x 2 = 220 or
110 * 2 = 220
Thus, Kevin indeed, skied twice as long as Lori.
Solve for x: 3(x + 1)= -2(x - 1) + 6.
Answer:
x=1
Step-by-step explanation:
3(x + 1)= -2(x - 1) + 6.
Distribute
3x+3 = -2x+2+6
Combine like terms
3x+3 = -2x+8
Add 2x to each side
3x+3+2x = 8
5x+3 = 8
Subtract 3 from each side
5x =5
Divide by 5
x =1
A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?
Answer:
b = - 3.7
Step-by-step explanation:
here are the data values:
x y XY X²
14 46 644 196
15 49 735 225
16 37 592 256
17 42 714 289
18 37 666 324
19 31 589 361
20 25 500 400
21 23 483 441
22 20 440 484
23 15 345 529
24 12 288 576
now we are required to find the summation (total) of all values of X, Y, XY and X².
∑X = 209
∑Y = 337
∑XY = 5996
∑X² = 4081
The formular for finding b is given as:
b = n∑XY - (X)(Y) / n∑X² - (∑X)²
= 11(5996) - (209)(337) / 11(4081) - (209)²
= 65956 - 70433 / 44891 - 43681
= -4477/ 1210
= -3.7
The question asked us to find the value of b but we can go further to find the equation of the regression line:
a = ∑Y - b∑X / n
= 337 - (-3.7)(209)/ 11
=1110.3/11
= 100.94
the equation is:
Y = 100.94 - 3.7X
I hope you find my solution useful!
=
Consider a bag of jelly beans that has 30 red, 30 blue, and 30 green jelly beans. a) How many color combinations of 15 beans have at least 6 green beans
Answer:
680
Step-by-step explanation:
Number of red beans = 30
Number of Blue beans = 30
Number of green beans = 30
How many color combinations of 15 beans have at least 6 green beans?
Since at least 6 of the beans must be green,
Then (15 - 6) = 9
Then, the remaining 9 could be either red, blue or green.
Therefore, C(9 + (9 - 1), 3)
C(17, 3) = 17C3
nCr = n! ÷ (n-r)! r!
17C3 = 17! ÷ (17 - 3)! 3!
17C3 = 17! ÷ 14!3!
17C3 = (17 * 16 * 15) / (3 * 2)
17C3 = 4080 / 6
17C3 = 680 ways
Using the combination formula, it is found that there are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.
The order in which the beans are chosen is not important, hence, the combination formula is used to solve this question.
Combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Th total number of combinations of 15 beans from a set of 30 + 30 + 30 = 90 is:
[tex]C_{90,15} = \frac{90!}{15!75!} = 45795674000000000[/tex]
With less than 6 green, we have:
0 green:
[tex]C_{30,0}C_{60,15} = \frac{60!}{15!45!} = 53194089000000[/tex]
1 green:
[tex]C_{30,1}C_{60,14} = \frac{30!}{1!29!} \times \frac{60!}{14!46!} = 520376960000000[/tex]
2 green:
[tex]C_{30,2}C_{60,13} = \frac{30!}{2!28!} \times \frac{60!}{13!47!} = 2247585600000000[/tex]
3 green:
[tex]C_{30,3}C_{60,12} = \frac{30!}{3!27!} \times \frac{60!}{12!48!} = 5681396900000000[/tex]
4 green:
[tex]C_{30,4}C_{60,11} = \frac{30!}{4!26!} \times \frac{60!}{11!49!} = 9391696900000000[/tex]
5 green:
[tex]C_{30,5}C_{60,10} = \frac{30!}{5!25!} \times \frac{60!}{10!50!} = 10744101000000000[/tex]
Hence, the total for the number of combinations with less than 5 green is:
[tex]53194089000000 + 520376960000000 + 2247585600000000 + 5681396900000000 + 9391696900000000 + 10744101000000000 = 28638351000000000[/tex]
Subtracting the total amount of combinations from the number with less than 5 green, the number of combinations with at least 6 green is:
[tex]T = 45795674000000000 - 28638351000000000 = 17157323000000000[/tex]
There are 17,157,323,000,000,000 color combinations of 15 beans have at least 6 green beans.
A similar problem is given at https://brainly.com/question/24437717
