Let tk be the number of ways to choose k beads from a drawer that contains 10 red beads, 8 blue beads, and 11 green beads. Find the generating function for the sequence {tk} 29 k = 0. Do not find a formula for tk.
Answer:
[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]
Step-by-step explanation:
From the given information;
The total number of beads = 10 + 8 + 11 = 29
To choose k beads out 29 beads, let assume that [tex]t_k[/tex] be the no. such that:
[tex]t_k = ( ^{29}_{k}) \ \ \ where; k =0,1,2,3,....,29[/tex]
∴
The sequence [tex]\{ t_k\}^{29}_{k=0} = (^{29}_{k})[/tex]
The generating function for [tex]\{ a_k \}^n_{k=0}[/tex] is:
[tex]G(x) = a_o +a_1x +a_2x^2 +...+a_nx^n[/tex]
[tex]G(x) = \sum \limits ^{n}_{k=0} \ a_k x^k[/tex]
For the sequence above;
[tex]G(x) = \sum \limits ^{29}_{k =0 } (^{29}_{k}) x^k[/tex]
By applying binomial series [tex](1+x)^n = \sum \limits ^n_{k=0} ( ^n_k) x^k[/tex]
Thus:
[tex]\mathbf{G(x) = (1 + x)^{29}}[/tex]
i am a decimal number less than 1. the digit in my tenths place is an even prime number. my hundredths digit is twice my tenths digit, and my hundred thousandths digit is twice my hundredths digit. the thousandths digit is three less than my hundredths digit. my ten thousandths digit is the sum of my tenths and thousandths digit. what number am i?
Answer:
.
Step-by-step explanation:
Answer:
0.24857
Step-by-step explanation:
Less than 1 is 0. and
only even prime is 2
A sporting goods store sells two types of bicycles, in two colors. The table
shows its sales over the last year.
Road bike
Mountain bike
Total
Silver
81
39
120
Black
54
26
80
Total
135
65
200
Are buying a road bike and buying a silver bike independent events?
A. Yes, because P(road bike) = 0.675 and P(road bike | silver) = 0.675.
B. No, because P(road bike) = 0.675 and P(road bike | silver) = 0.6.
C. Yes, because P(road bike) = 0.405 and P(road bike | silver) = 0.675.
O D. No, because P(road bike) = 0.675 and P(road bike | silver) = 0.675.
Answer:
Answer D
Step-by-step explanation:
120 + 81+ 39=240 silver bikes
80+54+26= 160 black bikes
Total 200 + 135 + 65= 400
240+ 160=400
Answer:
Answer is C
Step-by-step explanation:
ap3xxx
I WILL GIVE BRAINLIEST TO WHOMEVER ANSWERS FIRST
Please explain how to do this please show work
Answer:
(x-1)(x+4)
I.e x(x+4)-1(x+4)
Xsquare +4x -x -4
Xsquare +3x -4
Divide: 1.98 divided by 0.09
Find the distance between the points. Round to the nearest tenth.
(1, 3) and (5.0)
Who is good at math?
Answer:
me depending on what kind of math it is
Step-by-step explanation:
Solve x^2 + 6x + 15 = 0 using the Quadratic Formula
Which of the following are two-step equations? Choose more than
one answers
Answer:
i think a b d f
Step-by-step explanation:
A and B are independent events.
P(A) = 0.6
P(B) = 0.4
What is P(AB)?
O A. 0.24
O B. 0.6
O C. 0.4
D. Not enough information
Answer:
Not enough information
By the Exterior Angle Theorem, which of the following is a true statement?
Answer:
2nd option is the correct answer
Step-by-step explanation:
[tex]m \angle 1 > m \angle 3 \: \& \: m \angle 1 > m \angle 7 \\ [/tex]
According to the Exterior Angle Theorem, the true statement should be considered as the option b.
What is an Exterior Angle Theorem?The exterior angle theorem defined that at the time when a triangle's side should be extended, the resultant exterior angle formed should be equivalent to the sum of the measures of the two opposite interior angles of the triangle.
So based on this, we can say that the option b is correct.
learn more about an angle here: https://brainly.com/question/6150811
What is the range in interval notation?
Answer:
The blue box
Step-by-step explanation:
Youre talking about range which takes place on the y-axis (domain is the x-axis).
The top point is an open circle which indicates in the math world the parentheses and the bottom point 1 in a bracket as its a closed circle.
In a certain chemical, the ratio of zinc to copper is 4 to 19. A jar of the chemical contains 760 grams of copper. How many grams of zinc does it contain?
1) 760 grams
2) 3,610
3) 30,400
4) 190 or 160 grams
if you answer this you are a genius.
Answer:
Question 1: 3380g
Question 2: 2g/cm^3
Step-by-step explanation:
I used online mass and density calculators. Hope this helps :)!
What expression is equivalent to 12y + (7y)(3)
Answer:
I got 33y
Step-by-step explanation:
hi if its right but here
Answer:
57y
Step-by-step explanation:
Guys I need some help
Black friday sale on TVs were 50 in tv for $148.00 or 65 in for $199.00 which is the better buy this is not worth a grade just some understanding
Answer:
i personally think the 65 in. one
Step-by-step explanation:
max is thinking of a number which he calls n
Answer:
what are you trying to ask?
Step-by-step explanation:
Choose the equation that represents the asymptote of the graph f(x) = 2^x +3.
y = 0
y = 3
x = 0
x = 3
Answer:
x = 0Step-by-step explanation:
The horizontal asymptote occurs at x = 0, Hence the equation that represents the asymptote of the graph is at x = 0
f(x) = 2^x +3.
0 = 2^x +3.
2^x +3. = 0
2^x = -3
log 2^ x = log(-3)
x log2 = log(-3)
x = log(-3)/log 2
Hence the required function is when x = 0
distance from -3 to 0
HELP ME PLEASEEEE :)
Answer:
I believe it to be C
Step-by-step explanation:
Write the ratio as a fraction in lowest term: 15 to 36
Answer:
5/12
Step-by-step explanation:
15 to 36 can also be written as 15/36.
Divide by common values to simplify.
15÷3/36÷3
5/12
Best of Luck!
if f(x) = x^2 + x , find f(-3) a)-12 b)3 c)6
In a recent year, 6% of cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 124 cars, 29 had manual transmissions. Estimate the proportion of college students who drive cars with manual transmissions with 90% confidence.
Answer:
The estimate the proportion of college students who drive cars with manual transmissions with 90% confidence is
[tex]0.171 < p < 0.297 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 124
The population proportion p = 0.06
The number of cars with manual transmissions is k = 29
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally the sample proportion is mathematically represented as
[tex]\^ p = \frac{ 29 }{124 }[/tex]
=> [tex]\^ p = 0.234[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.234 (1- 0.234 )}{124} } [/tex]
=> [tex]E = 0.063 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.234 - 0.063 < p < 0.234 + 0.063 [/tex]
=> [tex]0.171 < p < 0.297 [/tex]
Use the balanced hanger diagram to choose the equations
that best represents how to find the mass of the square.
A. 5t = 42
b. x + 27 = 4x + 15
C. 5t = 36
d. x + 15 = 4x + 12
Answer:jkcv
ijfklgjk
Step-by-step explanation:
vn vvcxkhvxcl
During final exam weeks, many college students exercise to fuel their study sessions. Data from a recent survey are shown in the Venn diagram. Let M be the event that the student exercises in the morning and let A be the event that the student exercises in the afternoon.
A Venn diagram titled exercise habits. One circle is labeled M, 0.25, the other circle is labeled A, 014, the shared area is labeled 0.37, and the outside area is labeled 0.24.
What is the probability that a randomly chosen college student exercises in the morning or afternoon?
0.37
0.39
0.62
0.76
Answer:
WARNING! .39 AND .76 IS WRONG.
THE PEOPLE ABOVE ARE INCORRECT.
THE ANSWER IS EITHER .37 OR .62
I believe the correct answer is .62 --> .25 + .37 = .62 . This also makes sense.
(C)
ED2021
The probability that a randomly chosen college student exercises in the morning or afternoon are 0.37.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomesFrom the given Venn diagram, we see that
Probability that the student exercises in the afternoon
P(A) = 0.14 + 0.37 = 0.51
Probability that the student exercises in the morning
P(M) = 0.25 + 0.37 = 0.61
Now, the probability that a randomly chosen college student exercises in the morning or afternoon
P(A ∩ M) = 0.37
Learn more about probability here;
https://brainly.com/question/11234923
using the order of operations, what should be done first to evaluate 8² + 10 (-5) (3) - 5?
A. Subtract 5 From 3.
B. Divide 10 by -5.
C. Add 6 and 10.
D. Evaluate 8².
Answer:
D
Step-by-step explanation:
Find the unit rate. Round to the nearest hundredth, if necessary.
$5.99 for 18 lb
The unit rate is ?/b
Please help I’ll mark u <3
Answer:
x>-4
Step-by-step explanation: