# Binomial theorem Questions and Answers

Math

Binomial theoremQuestion 4 of 25 A study of immunizations among school age children in California found that some areas had rates of unvaccinated school age children as high as 13 5 in 2014 Imagine a classroom of 20 children in one such area where 13 5 of children are unvaccinated If there are no siblings in the classroom we are willing to consider the vaccination status of the 20 unrelated children to be independent a Obtain the probability that none of the 20 children in such a classroom would be unvaccinated Enter your answer rounded to three decimal places I P None of the 20 children are unvaccinated b Obtain the probability that at least one of the 20 children in such a classroom would be unvaccinated Enter your answer rounded to three decimal places

Math

Binomial theoremSuppose the binomial expansion of (x - y)^n includes the term - 84x^6y^3.
The x^5y^4 term in the expansion will be
The x^6y^8 term in the expansion will be

Math

Binomial theoremConsider the binomial expansion of (4x + 3y)^n. Suppose the expansion includes a x^4y^8 term. Then n = ___
Check ALL of the following which will NOT in the simplified expansion of (4x + 3y)^n.
x^8y^4
x^8y^6
x^9y^3
x^6y^8

Math

Binomial theoremUse the Binomial Theorem and Pascal's Triangle to find the expanded form of the binomial expression.
(2x+3y)
A. (2x) +6(2x)³ (3y)+15(2x)*(3y)² +20(2x)³ (3y)³ +15(2x)² (3y)* +6(2x)(3y)³ +(3y)
B. (2x)+7(2x)³ (3y)+21(2x)*(3y)² +35(2x)³ (3y)² +21(2x)²(3y)* +7(2x)(3y)³ +(3y)

Math

Binomial theoremThe time between breakdowns of an alarm system is exponentially distributed with mean 10 days. What is the probability that there is less than 1 breakdown on a given day?
.9048
.3679
.0952
.000

Math

Binomial theoremSuppose the binomial expansion of (4x + 5y)^n includes the term 1400000x³y⁴.
(A) The x³y⁴ term in the expansion will be?
(B) The x⁵y⁴ term in the expansion will be?

Math

Binomial theoremThe polynomial (x + 9)⁷ (x – 5)² (- 3x² + 7x + 2)³ has degree?
The leading term will be?

Math

Binomial theoremSuppose the binomial expansion of (x - y)n includes the term – 84x6y3
The x5y4 term in the expansion will be ___
The x6y8 term in the expansion will be ___

Math

Binomial theoremSuppose the binomial expansion of (x + y)^n includes the term 3003x⁶y⁸.
The x⁵y⁹ term in the expansion will be?
The x⁴y³ term in the expansion will be?

Math

Binomial theoremSuppose the binomial expansion of (2x – 3y)n includes the term –15120x4y3
The x4y3 term in the expansion will be
The x5y3 term in the expansion will be

Math

Binomial theoremFind the coefficient of the a³y¹¹ term in the expansion of (a + y)¹⁴.
In the expansion,
(a + y)¹⁴ = a¹⁴ + ... +___________ a³y¹¹ + ... +y¹⁴
(Enter ONLY the coefficient)

Math

Binomial theoremFind the indicated terms in the expansion of
(4x² + x - 2)(4x² + 5x – 10) (5x² + 4x + 3)
The degree 5 term is ___
The degree 1 term is ___

Math

Binomial theoremWhich one of the following options is true when considering the expansion of
the binomial expression (x + y)5?
A. The expansion of (x + y)5 will yield 5 terms.
B. The first term of the expansion of (x + y)5 is x5y5.
C. The sum of the exponents of each term of the expansion of
(x + y)5 is 5.
D. The coefficients of the expansion of (x + y)5 are: 5, 10, 10, 5.

Math

Binomial theoremWhich of the following terms appear in the expansion of (x+y)^10? The letter a in each term represents a real constant.
A. ax^4y^6
B. ax^5
C. ax^6y^4
D. ax³y^7

Math

Binomial theoremA cat has a litter of 7 kittens. Find the probability that exactly 4 of the kittens are female. Assume
that male and female births are equally likely. Estimate the probability to five decimal places if necessary.
A) 0.00781
B) 0.54688
C) 0.27344
D) 2.1875

Math

Binomial theoremSuppose 3 out of 10 game pieces reads "Free candy bar". Which answer below would correctly find the probability that you win exactly 1 free candy bar with 4 game pieces if the events are independent?
4C₁ (.3)¹ (7)³
10C3 (-25)¹(.75)³
10C3 (.25) ³ (.75)¹
1C₁ (-3)¹ (7)³

Math

Binomial theoremA member of the American Kennel Club is researching Irish Wolfhounds, and measures ninety of them to find a sample average height of 33.0 Inches, with a 90% confidence interval of [32.7, 33.3] Inches. If the researcher finds twenty other ninety-dog samples, about how many of those samples will have an average outside this Interval?
1
2
4
5

Math

Binomial theoremThree boxes colored red, orange, and blue are to be randomly ordered from left to right. What is the probability that the end boxes will be orange and blue, in either order?
1/3
1/6
1/2
2/3

Math

Binomial theoremWhich of the following can be classified as a binomial probability experiment?
A coin is tossed 10 times. The random variable X is the number of heads that appear.
A bag contains 20 marbles. Eight marbles are red, nine marbles are blue, and three marbles are yellow. Three marbles are drawn out of the bag without replacement. The random variable X is the number of blue marbles.
Five customers walk into a store. The random variable a represents the number of customers who buy at least one product.
A random sample of 30 cars selected from a used car lot and their mileages are recorded.

Math

Binomial theoremA new type of grass seed was developed by an agricultural research company. It was determined that the probability of a seed germinating Is 0.92 (given the correct soll conditions, water, and sunlight). If 5 seeds are planted, what is the probability that at least 3 seeds will germinate?
0.045
0.995
0.92
0.08

Math

Binomial theoremThe average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. Do twenty-year-old have fewer cavities? The data show the results of a survey of 16 twenty-year-old who were asked how many cavities they have had. Assume that the distribution of the population is normal. 11, 8, 5, 6, 10, 9, 6, 9, 11, 9, 6, 10, 11, 7, 6, 11 What can be concluded at the a = 0.01 level of significance? Write hypothesis, give test stat and p-value. Write conclusions about HO and claim.

Math

Binomial theoremFind the mean, variance, and standard deviation of the binomial distribution with the given values of n and p.
n = 50, p=0.9
The mean, µ, is
The variance, σ2, is
The standard deviation, σ, is (Round to the nearest tenth as needed.)

Math

Binomial theoremMagnetic resonance imaging (MRI) is a process that pro- duces internal body images using a strong magnetic field. Some patients become claustrophobic and require sedation because they are required to lie within a small, enclosed space during
the MRI test. Suppose that 21% of all patients undergoing MRI testing require sedation due to claustrophobia. If 7 patients are selected at random, find the probability that
Note: Please keep 4 decimal places in your final answer.
a. exactly 2 patients require sedation.
b. less than 2 patients require sedation.
c. exactly 5 patients require sedation.
d. at least 5 patients require sedation.

Math

Binomial theorem11% of all Americans live in poverty. If 47 Americans are randomly selected, find the probability that
a. Exactly 3 of them live in poverty.
b. At most 4 of them live in poverty.
c. At least 2 of them live in poverty.
d. Between 4 and 12 (including 4 and 12) of them live in poverty.

Math

Binomial theoremThe commute times for students from home to school varies according to a distribution that
is approximately Normal with mean 28 minutes and standard deviation 18 minutes. What percent of the students commute between 30 and 60 minutes?
0.5438
0.3139
0.1091
0.7486
0.8577

Math

Binomial theoremA study of immunizations among school-age children in California found that some areas had rates of unvaccinated school-age children as high as 13.5% in 2014. Imagine a classroom of 20 children in one such area where 13.5% of children are unvaccinated. If there are no siblings in the classroom, we are willing to consider the vaccination status of the 20 unrelated children to be independent.
(a) Obtain the probability that none of the 20 children in such a classroom would be unvaccinated. (Enter your answer rounded to three decimal places.)
P(None of the 20 children are unvaccinated) =
(b) Obtain the probability that at least one of the 20 children in such a classroom would be unvaccinated. (Enter your answer rounded to three decimal places.)
P(At least one of the 20 children are unvaccinated) =

Math

Binomial theoremIf we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not
independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution.
If a population has A objects of one type, while the remaining B objects are of the other type, and if n objects are sampled without replacement,
then the probability of getting x objects of type A and n-x objects of type B under the hypergeometric distribution is given by the following
formula. In a lottery game, a bettor selects five numbers from 1 to 45 (without repetition), and a winning five-number combination is later
randomly selected. Find the probabilities of getting exactly two winning numbers with one ticket. (Hint: Use A = 5, B = 40, n=5, and x = 2.)
P(x) =
A!
B!
(A + B)!
(A-x)!x! (B-n+x)!(n-x)! (A+B-n)!n!
*****

Math

Binomial theoremAbout 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below.
(a) Company A has 284 employees. What is the probability that Company A will get the discount?
(Round to four decimal places as needed.)

Math

Binomial theoremA drug tester claims that a drug cures a rare skin disease 70% of the time. The claim is checked by testing the drug on 100 patients. If at least 68 patients are cured, the claim will be accepted.
Find the probability that the claim will be rejected assuming that the manufacturer's claim is true. Use the normal distribution to approximate the binomial distribution if possible.
The probability is
(Round to four decimal places as needed.)
*****

Math

Binomial theoremFind the 4th term in the expansion of (a + b) in simplest form.
Answer:
Submit Answer

Math

Binomial theoremUsing the Binomial distribution,
If n=10 and p=0.7, find P(x-7)
Question Help: D Post to forum

Math

Binomial theoremIn each of 12 races, the Democrats have a 60% chance of winning. Assume the races are independent of each other. Round your answers to three decimal places.
a. What characteristics of this scenario indicate that you are working with Bernoulli trials?
(3 points)
b. What is the mean and standard deviation of the number of races won? (3 points)
c. What is the probability that the Democrats will win the 7th race? (1 point)
d. What is the probability that the Democrats will win all 12 races? (2 points)

Math

Binomial theoremYou operate an auto store that sells tires. You are concerned about warranty returns on the tires. Company records show that the probability warranty repair for a tire in the first 90 days is .05. You are tracking the sales of three tires. What is the mean for this binomial distribution? .15
.19
.25
.35

Math

Binomial theorem9-49. Consider the polynomial x^4 - 6x^3 - 6x² + 6x - 7.
a.Using only integers, list all of the possible linear factors.
b.Is (x + 1) a factor of the polynomial? Is (x - 1) a factor? Show how you know without graphing.

Math

Binomial theoremExplain how to multiply a monomial and a polynomial that is not a monomial. Give an example,
CELLID
Choose the correct answer below.
OA. To multiply a monomial and a polynomial, use the distributive property to multiply each term of the polynomial by the monomial. For example, 3x (2x²+5) = 6x³ + 15x.
OB.
To multiply a monomial and a polynomial, use the commutative property to add the monomial to the polynomial. For example, 3x (2x²+5)=2x²+3x+5.
OC. To multiply a monomial and a polynomial, use the associative property to add the monomial to each term of the polynomial. For example, 3x (2x+5) = (2x²+3x)+(5+3x).
OD. To multiply a monomial and a polynomial, use the distributive property to subtract the monomial from each term of the polynomial. For example, 3x (2x²+5) = (2x²-3x) + (5-3x).

Math

Binomial theoremUse the Binomial Theorem to expand (c-11)4.
Oc4-44c³+726c²-5324c + 14641
11c4 +44c³ + 726c² +5324c + 14641c
4
C
0 c4
+44c³+726c² + 5324c + 14641
c4 +44c³ + 726c² +5324c + 14641

Math

Binomial theoremUse Pascal's triangle to expand each binomial.
(x - 5y)³
Oy5-5y4x+25y³x²-125y²x³+625x4-3125x³
Ox5 +5xy + 10x³y² + 10x²y³ + 5xy4+y5
Ox5-25x4y +250x³y² - 1250x²y³ +3125xy4-3125y³
Ox5-5xy + 25x³y²-125x²y³+625xy¹ - 3125y5

1