A principal of $1900 was invested at 3.75% interest, compounded annually. Let be the number of years since the start of the investment. Let y be the value of the investment, in dollars.
Write an exponential function showing the relationship between y and t?

Answer:

(a-1) 22 rookies receiving a rating of 4 or better.

(a-2) 14 rookies received a rating of 2 or worse.

(b-1) Constructed below in explanation.

(b-2) 8% of total rookies received a rating of 5.

Step-by-step explanation:

We are provided the rating of Fifty pro-football rookies on a scale of 1 to 5 based on performance at a training camp as well as on past performance.

The frequency distribution constructed is given below:

 Rating          Frequency

     1                       4

     2                     10       where ranking of 1 indicate a poor prospect whereas

     3                     14         ranking of 5 indicate an excellent prospect.

     4                     18

     5                      4

(a-1) Rookies receiving a rating of 4 or better = Rating of 4 + Rating of 5

       So, by seeing the frequency distribution 18 rookies received a rating of

         4 and 4 rookies received a rating of 5.

Hence, Rookies receiving a rating of 4 or better = 18 + 4 = 22 rookies.

(a-2) Number of rookies received a rating of 2 or worse = Rating of 2 +

                                                                                                 Rating of 1

     So, by seeing the frequency distribution 10 rookies received a rating of

      2 and 4 rookies received a rating of 1.

Hence, Rookies receiving a rating of 2 or worse = 10 + 4 = 14 rookies.

(b-1) Relative Frequency is calculated as = Each frequency value /

                                                                         Total Frequency

   Rating        Frequency(f)        Relative Frequency

     1                       4                          4 / 50 = 0.08

     2                     10                         10 / 50 = 0.2

     3                     14                          14 / 50 = 0.28

     4                     18                          18 / 50 = 0.36

     5                     4                           4 / 50  = 0.08

                     [tex]\sum f[/tex]= 50                

Hence, this is the required relative frequency distribution.

(b-2) To calculate what percent received a rating of 5 is given by equation :

             x% of 50 = 4 {Here 4 because 4 rookies received rating of 5}

         x = [tex]\frac{4*100}{50}[/tex] = 8% .

Therefore, 8% of total rookies received a rating of 5.

22 rookies received a performance rating of 4 or better, and there are 14 rookies that received a rating of 2 or worse. The relative frequency distribution rounded to 2 decimal places for ratings 1, 2, 3, 4, and 5 is 0.08, 0.2, 0.28, 0.36, and 0.08 respectively. Finally, 8% of rookies received a rating of 5.

To answer question a-1, we add the frequencies of the ratings 4 and 5 together. So 18 (the number of rookies who received a 4) plus 4 (the number of rookies who received a 5) equals 22. Therefore, 22 rookies received a rating of 4 or better.

For question a-2, we add the frequencies of the ratings 1 and 2 together. So 4 (the number of rookies who received a 1) plus 10 (the number of rookies who received a 2) equals 14. Thus, 14 rookies received a rating of 2 or worse.

Next, for question b-1, we find the relative frequency distribution by dividing each frequency by the total number of players (50). So, the relative frequency for 1 would be 4/50 ≈ 0.08, for 2 it's 10/50=0.2, for 3 it's 14/50 ≈ 0.28, for 4 it's 18/50 = 0.36, and for 5 it's 4/50 ≈ 0.08. These are all rounded to 2 decimal places.

Finally, for question b-2, to find the percent of players who received a rating of 5, we take the frequency of 5 which is 4, and divide it by the total number of rookies, which is 50, then multiply by 100 to convert it to a percentage (4/50 * 100). The answer is 8%.

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Answer:

$95.78

Step-by-step explanation:

f(t) = 300t / (2t² + 8)

t = 0 corresponds to the beginning of August.  t = 1 corresponds to the end of August.  t = 2 corresponds to the end of September.  So on and so forth.  So the second semester is from t = 5 to t = 10.

$T₂ = ∫₅¹⁰ 300t / (2t² + 8) dt

$T₂ = ∫₅¹⁰ 150t / (t² + 4) dt

$T₂ = 75 ∫₅¹⁰ 2t / (t² + 4) dt

$T₂ = 75 ln(t² + 4) |₅¹⁰

$T₂ = 75 ln(104) − 75 ln(29)

$T₂ ≈ 95.78

Answer:

a) a

b) ab

e) bbbbb

Step-by-step explanation:

We are given the following in the question:

[tex]a, b \in S[/tex]

[tex]x \in S \Rightarrow xb \in S[/tex]

a) a

It is given that [tex]a \in S[/tex]

b) ab

[tex]\text{If }a \in S\\\Rightarrow ab \in S[/tex]

Thus, ab belongs to S.

c) aba

This does not belong to S because we cannot find x for which xb belongs to S.

d) aaab

This does not belong to S because we cannot find x for which xb belongs to S.

e) bbbbb

[tex]\text{If }b \in S\Rightarrow bb \in S\\\text{If }bb \in S\Rightarrow bbb \in S\\\text{If }bbb \in S\Rightarrow bbbb \in S\\\text{If }bbbb \in S\Rightarrow bbbbb \in S[/tex]

Thus, bbbbb belongs to S.

Answer:

The probability that the object will emerge from the + side of this device is 1/2

Step-by-step explanation:

Orienting the magnetic field in a Stern-Gerlach device in some direction(y - direction) perpendicular to the direction of motion of the atoms in the beam, the atoms will emerge in two possible beams, corresponding to ±(1/2)h. The positive sign is usually referred to as spin up in the direction, the negative sign as spin down in the explanation, the separation has always been in the y direction. There can be some other cases where magnetic field may be orientated in x-direction or z-direction.

Answer:

15 Nickels, 11 Pennies

Step-by-step explanation:

Simplify your life and take out the decimals

5*N + P = 86

P + 4 = N (4 more nickels than pennies)

By substitution of the second eq into the first: 5*(P+4) + P = 86

5*P + 20 + P = 86

6P = 66

P = 11, so N = 4 + 11 = 15

Answer:Ruby has 11 pennies and 15 nickels.

Step-by-step explanation:

The worth of a penny is 1 cent. Converting to dollars, it becomes

1/100 = $0.01

The worth of a nickel is 5 cents. Converting to dollars, it becomes

5/100 = $0.05

Let x represent the number of pemnies that Ruby has.

Let y represent the number of nickels that Ruby has.

She has 4 more nickels than pennies. This means that

y = x + 4

Ruby has $0.86 worth of pennies and nickels. This means that

0.01x + 0.05y = 0.86 - - - - - - - - - - - 1

Substituting y = x + 4 into equation 1, it becomes

0.01x + 0.05(x + 4) = 0.86

0.01x + 0.05x + 0.2 = 0.86

0.06x = 0.86 - 0.2 = 0.66

x = 0.66/0.06

x = 11

y = x + 4 = 11 + 4

y = 15

Answer:

The augmented matrix has been given in the attachment

Step-by-step explanation:

The steps for the determination of INCONSISTENCY  are as shown in the attachment.

The 76.53% percentage, which represents the rate at which the QFT-G test correctly identifies those without tuberculosis, can be represented using notation as P(POSc | Sc). This is a conditional probability noting the likelihood of a negative test result when the individual does not have tuberculosis.

In the context of probabilities and statistics, you've asked about the interpretation of the 76.53% correctly identified as non-tuberculosis afflicted individuals in terms of notation. Based on the notation you provided and the description of the problem, the 76.53% would be represented as P(POSc | Sc).

This can literally be translated as the probability that the QFT-G test will result as negative (i.e., no tuberculosis, or POSc), given that the person is indeed not afflicted with tuberculosis (i.e., Sc). This is a conditional probability, expressing how likely we are to get a negative test result, given that the person doesn't really have tuberculosis.

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Answer:

13.5

Step-by-step explanation:

7 1/2=7.5

7.5/5*9=13.5

Answer:

99.7% of the distribution will be between 600 hours and 900 hours.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 750

Standard deviation = 50

What percent of the distribution will be between 600 hours and 900 hours?

600 = 750 - 3*50

600 is 3 standard deviations below the mean

900 = 750 + 3*50

900 is 3 standard deviations above the mean

By the Empirical Rule, 99.7% of the distribution will be between 600 hours and 900 hours.

Answer:

Car A. would travel the farthest

Answer:

Step-by-step explanation:

i need help to show the work

Answer:

P(A) = 400/924 = 100/231 or 0.4329

Step-by-step explanation:

The probability that both groups will have the same number of men P(A);

For the two groups to have the same number of men they must include 3 men and 3 women in each group.

P(A) = Number of possible selections of 3 men from 6 and 3 women from 6 into each of the two groups N(S) ÷ total number of possible selections of members into the two groups N(T).

P(A) = N(S)/N(T)

Since order is not important, we will use combination.

N(S) = 6C3 × 6C3 = 20 × 20 = 400

N(T) = 12C6 = 924

P(A) = 400/924 = 100/231 or 0.4329

The probability that both groups will have the same number of men is 0.43.

When dividing the group into two equal-sized groups of 6 each, the total number of ways to do this is represented by the binomial coefficient C(12, 6), which is equal to 924.

Now, to ensure that both groups have the same number of men, we need to consider the ways in which we can choose 3 men from the 6 available men, which is represented by C(6, 3), and similarly, we can choose 3 women from the 6 available women, which is also represented by C(6, 3).

The total number of ways to choose 3 men and 3 women for both groups is C(6, 3) * C(6, 3) = 20 * 20 = 400.

Since there are 2 equally likely outcomes (either both groups have the same number of men or they don't), the probability is 400/924, which simplifies to 0.43.

In summary, the probability that both groups will have the same number of men is 0.43 because there are 400 ways to select 3 men and 3 women for each group out of a total of 924 possible ways to divide the 12 people into two groups.

This results in a 0.43 probability for the desired outcome.

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The correct statements regarding the secant function are as follows:

It is one divided by the cosine, that is:

[tex]\sec{x} = \frac{1}{\cos{x}}[/tex]

The vertical asymptotes are when the cosine is 0, that is, [tex]x = k\frac{\pi}{2}, k = 1, 2, ...[/tex]

As for the values of the function:

[tex]\sec{\left(\frac{\pi}{4}\right)} = \frac{1}{\cos{\left(\frac{\pi}{4}\right)}} = \sqrt{2}[/tex]

[tex]\sec{\left(\frac{\pi}{3}\right)} = \frac{1}{\cos{\left(\frac{\pi}{3}\right)}} =  2[/tex]

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Answer: the last option is the correct answer.

Step-by-step explanation:

When x = 3, height = 2 × 3 = 6

When x = 3, base = π × 3² = 9π

Volume = 1/3 × 6 × 9π = 18π

Therefore,

The formula for determining the volume of the cone is

Volume = 1/3 × height × area of base

Height is f(x) = 2x

Area of base is g(x) = πx²

Therefore, the equation that can be used to the volume of the cone, V(x) would be

1/3(f.g)(x)

Final answer:

The student needs to find an equation V(x) representing the volume of a cone. Using the volume formula V(x) = kx² and the given volume of 18 when x is 3, the constant k can be calculated. Thus, the equation for the volume is V(x) = 2x².

Explanation:

The student is asking for an equation that represents the volume of a cone, V(x), based on a given volume when x equals 3. The general formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone. Since the volume is given as a quadratic function of x, and we know that when x equals 3 the volume is 18, a possible representation for the volume as a function of x could be V(x) = kx², where k is a constant that we would solve for using the given volume at x = 3.

To find the constant k, we substitute x with 3 and V(x) with 18 in the equation V(x) = kx² and solve for k. Therefore, the equation becomes 18 = k(3²), which simplifies to 18 = 9k. Solving for k gives us k = 2, so the equation for the volume of the cone as a function of x is V(x) = 2x².

The probability that at least one member of a married couple will vote is 0.34 or 34%. The probability of a wife voting given that her husband will vote is approximately 0.7143 or 71.43%. The probability of a husband voting given his wife will not vote is 0.06 or 6%.

The subject of this question is probability within the realm of mathematics. To find the probability of at least one member of a married couple voting, we can use the formula P(A or B) = P(A) + P(B) - P(A and B).

Therefore, the probability is 0.21 (husband voting) + 0.28 (wife voting) - 0.15 (both voting), which equals 0.34.

For (b), the probability that the wife will vote, given that her husband will vote, is P(Wife|Husband) = P(Wife and Husband)/P(Husband).

So, this probability is 0.15/0.21, which equals approximately 0.7143.

For (c), the probability that the husband will vote, given that his wife will not vote, is P(Husband|Wife not voting) = P(Husband) - P(Husband and Wife).

So, this probability is 0.21 - 0.15, which yields 0.06 or 6%.

Hello, you haven't provided the system of equations, therefore I will show you how to do it for a particular system and you can follow the same procedure for yours.

Answer:

For E1 -> Exactly one

For E2 -> None

For E3 -> Infinitely many

Step-by-step explanation:

Consider the system of equations E1:  y = -6x + 8 and 3x + y = 4, replacing equation one in two 3x -6x +8 = 4, solving x = 4/3 and replacing x in equation one y = 0. This system of equations have just one solution -> (4/3, 0)

Consider the system of equations E2:  y = -3x + 9 and y = -3x -7, replacing equation one in two -3x + 9 = -3x -7, solving 9 = -3. This system of equations have no solution because the result is a fallacy.

Consider the system of equations E3:  2 = -6x + 4y and -1 = -3x -2y, taking equation one and solving y = 1/2 + 3/2x, replacing equation one in two -1 = -3x -1 +3x, solving -1 = -1. This system of equations have infinitely many solution because we find a true equation when solving .

Answer:

[tex]240cm^2[/tex]

Step-by-step explanation:

The area of the rectangular face with dimension 8 by 8 is [tex]8*8=64cm^2[/tex]

The area of the rectangular face with dimension 10 by 8 is [tex]10*8=80cm^2[/tex]

The area of the rectangular face with dimension 6 by 8 is [tex]6*8=48cm^2[/tex]

The area of the two rectangular faces is [tex]2*\frac{1}{2}*8*6=48cm^2[/tex]

The total surface area is [tex]64+80+48+48=240cm^2[/tex]

Answer:

a) The person traveled 2.83 hours.

b) The person travels 220.17 kilometers.

Step-by-step explanation:

We have that the speed is the distance divided by the time. Mathematically, that is

[tex]s = \frac{d}{t}[/tex]

(a) how much time is spent on the trip and

The peron's average speed is 77.8 km/h, which means that [tex]s = 77.8[/tex]

The person distance traveled is:

22 min is 22/60 = 0.37h.

So for  the time t1, the person traveled at a speed of 89.5 km/h. Which has a distance of 89.5*t1.

For 0.37h, the person was at a stop, so she did not travel. This means that the total distance is

[tex]d = 89.5t1 + 0 = 89.5t1[/tex]

The total time is the time traveling t and the stoppage time 0.37. So

[tex]t = t1 + 0.37[/tex]

We want to find t1, which is the time that the person was driving.

So

[tex]s = \frac{d}{t}[/tex]

[tex]77.8 = \frac{89.5t1}{t1 + 0.37}[/tex]

[tex]77.8t1 + 77.8*0.37 = 89.5t1[/tex]

[tex]11.7t1 = 28.786[/tex]

[tex]t1 = \frac{28.786}{11.7}[/tex]

[tex]t1 = 2.46[/tex]

The total time is

[tex]t = t1 + 0.37 = 2.46 + 0.37 = 2.83[/tex]

The person traveled for 2.83 hours.

(b) how far does the person travel?

The person traveled 2.46 hours at an average speed of 77.8 km/h. So

[tex]s = \frac{d}{t}[/tex]

[tex]77.8 = \frac{d}{2.83}[/tex]

[tex]d = 77.8*2.83 = 220.17[/tex]

The person travels 220.17 kilometers.

Answer:

The value of n is 5.

Step-by-step explanation:

It is provided that in there are n black and n white balls in an urn.

Three balls are selected at random without replacement.

And if all the three balls are white the probability is [tex]\frac{1}{12}[/tex]

The probability of selecting 3 white balls without replacement is:

[tex]P(3\ white\ balls)=\frac{n}{2n}\times \frac{n-1}{2n-1}\times \frac{n-2}{2n-2} \\\frac{1}{12}=\frac{n(n-1)(n-2)}{2n(2n-1)(2n-2)} \\\frac{1}{12}=\frac{(n-1)(n-2)}{2(2n-1)(2n-2)} \\2(4n^{2}-6n+2)=12(n^{2}-3n+2)\\8n^{2}-12n+4=12n^{2}-36n+24\\4n^{2}-24n+20=0\\n^{2}-6n+5=0\\[/tex]

Solve the resultant equation using factorization as follows:

[tex]n^{2}-6n+5=0\\n^{2}-5n-n+5=0\\n(n-5)-1(n+5)=0\\(n-1)(n-5)=0[/tex]

So the value of n is either 1 or 5.

Since 3 white balls are selected the value of n cannot be 1.

So the value of n is 5.

Check:

[tex]P(3\ white\ balls)=\frac{n}{2n}\times \frac{n-1}{2n-1}\times \frac{n-2}{2n-2} \\=\frac{5}{2\times5}\times \frac{5-1}{(2\times5)-1}\times \frac{5-2}{(2\times5)-2}\\=\frac{1}{2}\times\frac{4}{9}\times\frac{3}{8} \\=\frac{1}{12}[/tex]

Thus, the value of n is 5.

Answer: each sheet of cardboard provides 2 pieces of smaller pieces of cardboard

Step-by-step explanation:

The area of each rectangular sheet of cardboard that the factory makes is 2 1/2 square feet. Converting

2 1/2 square feet to improper fraction, it becomes 5/2 square feet.

Each sheet of cardboard can be cut into smaller pieces of cardboard measuring 1 1/6 square feet. Converting

1 1/6 square feet to improper fraction, it becomes 7/6 square feet.

Therefore, the number of smaller pieces of cardboard that each sheet of cardboard provides is

5/2 ÷ 7/6 = 5/2 × 6/7 = 15/7

= 2 1/7 pieces

answer is 15 smaller pieces  Step-by-step explanation:

Mar 10, 2012 - Markups and Markdowns Word Problems - Independent Practice Worksheet. $6640. $3.201 ... 2) Fred buys a video game disk for $4. There was a discount of 20%.What is the sales price? 20% of 1 pay 8090 ... 5) Timmy wants to buy.a scooter and the price was $50. When ... at a simple interest rate of 54%.

Answer:

Correct option is (B) descriptive statistical method

Step-by-step explanation:

Descriptive statistics branch in statistics deals with the representation of the data using distinct brief coefficients. These coefficients are used as either the representative of the sample or the population.

The descriptive statistics branch is divided into two sub branches:

The three measures of central tendency are:

The measures of dispersion are:

The education researcher computes the average number of hours student study at various local colleges.

The average of a data is the mean value which is the measure of central tendency.

Thus, the researcher is using descriptive statistical method to summarize the data.

Final answer:

The education researcher is using descriptive statistical methods by calculating an average of study hours, which is a measure of central tendency, a fundamental aspect of descriptive statistics.

Explanation:

An education researcher who collects data on how many hours students study at various local colleges and then calculates an average to summarize this data is using descriptive statistical methods. Descriptive statistics involve organizing and summarizing data to provide a clear overview of its characteristics. Examples of descriptive statistics include measures of central tendency (mean, median, mode), which indicate the typical value within a data set, and measures of variability (range, variance, standard deviation), which show how spread out the data points are. The calculation of an average, or mean, falls under the measure of central tendency, making it a key component of descriptive statistics.

The given statement is true, and the further discussion can be defined as follows:

That's why the given statement is "true".

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Final answer:

True. Parental care is considered a moderating variable that can influence the relationship between eating a hot breakfast and a child's school performance.

Explanation:

Research indicates that children who eat a hot breakfast at home tend to perform better in school. However, this outcome is not solely based on the meal itself, but also on the parental care provided before the child goes to school. In this context, parental care acts as a moderating variable, potentially influencing the relationship between having a hot breakfast and a child's school performance. A moderating variable is one that affects the strength or direction of the relationship between an independent variable (hot breakfast) and a dependent variable (school performance). Therefore, the statement is True.

Answer:

P(A&B) = 0.4

Explanation:

Because it is a random process and there are no special constraints the probability for everybody is the same, the probability of choosing a particular site is 1/7, the person originally seated in chair number seven has 5/7 chance of not seating in chair number six and seven, the same goes for the person originally seated in chair number six; Because we want the probability of the two events happening, we want the probability of the intersection of the two events, and because the selection of a chair change the probability for the others (Dependents events) the probability P(A&B) = P(A) * P(B/A) where P(A) is 5/7 and the probability of choosing the right chair after the event A is 4/7, therefore, P(A&B) = 4/7*5/7 = 0.4.

If the events were independent the probability would be 0.51.

n = 15

Step-by-step explanation:

For 2^-6*2^n=2^9, a = 2, m = -6 and m + n = 9

⇒ -6 + n = 9

⇒ n = 15

⇒ 2³ × 4³ can also be written as 2³ × (2²)³ = 2³ × 2^6 [This is based on the law of exponents (a^m)^n = (a)^m×n]

⇒ 2³ × 2^6 = 2^ (3 + 6) = 2^9 [Using the law of exponents a^m × a^n = a^m+n]

Answer:

0.5 week

Step-by-step explanation:

The time spent by a pound of meat in this system is given by the average number of pounds of meat on inventory (2500 pounds) divided by the average weekly meat consumption (5000 pounds per week).

The time, in weeks, is:

[tex]t=\frac{2500\ pounds}{5000\ pounds/week} \\t= 0.5\ week[/tex]

The average time spent by a pound of meat in production is 0.5 week.

Answer:

Cross-sectional study.

Step-by-step explanation:

- In a cross-sectional study, data are observed, measured, and collected at one point in time.

- In a prospective (or longitudinal) study, data are collected in the future from

groups sharing common factors.

- In a retrospective (or case-control) study, data are collected from the past by going

back in tirme (through exanmination of records, interviews, arıd so on).

Hope this Helps!!

Answer:

[tex]5.796\times 10^{-29}m^3[/tex]

Step-by-step explanation:

Atomic radius of metal=0.137nm=[tex]0.137\times 10^{-9}[/tex]m

[tex]1nm=10^{-9}m[/tex]

Structure is  FCC

We know that

The relation between edge length and radius  in FCC structure

[tex]a=2\sqrt 2r[/tex]

Where a=Edge length=Side

r=Radius

Using the relation

[tex]a=2\sqrt 2\times 0.137\times 10^{-9}=0.387\times 10^{-9}m[/tex]

We know that

Volume of cube=[tex](side)^3[/tex]

Using the formula

Volume of unit cell=[tex](0.387\times 10^{-9})^3=5.796\times 10^{-29} m^3[/tex]

The volume of a unit cell is approximately 0.0580 nm³.

To find the volume of the unit cell for a metal with a face-centered cubic (FCC) crystal structure given an atomic radius of 0.137 nm, follow these steps:

Thus, the volume of the unit cell is approximately 0.0580 nm³.

1 inch on the map = 50 miles on the Earth.

A certain trip on the map is 2-3/4 inches.

-- first inch = 50 miles

-- second inch = another 50 miles

-- 3/4 inch = 3/4 of 50 miles (37.5 miles)

Total:

Here's an equation;

1 map-inch = 50 real-miles

Multiply each side by 2-3/4 :

2-3/4 inches = (2-3/4) x (50 miles)

2-3/4 map-inches = 137.5 real-miles

The actual distance between Houston and Austin is 137.5 miles.

We are given that;

The distance between Houston and Austin = 2 3/4 inches

Now,

To find the actual distance between Houston and Austin, we need to multiply the map distance by the scale factor.

The map distance is 2 3/4 inches, which is equivalent to 11/4 inches. The scale factor is 1 inch = 50 miles, which means that every inch on the map corresponds to 50 miles in reality. So, we have:

11/4 x 50 = (11 x 50) / 4

= 550 / 4

= 137.5

Therefore, by unit conversion answer will be 137.5 miles.

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Answer:

(a) P (X ≥ 4) = 0.972

(b) E (X) = 20

Step-by-step explanation:

Let X = number of people tested to detect the presence of gene in 2.

Then the random variable X follows a Negative binomial distribution with parameters r (number of success) and p probability of success.

The probability distribution function of X is:

[tex]f(x)={x-1\choose r-1}p^{r}(1-p)^{x-r}[/tex]

Given: r = 2 and p = 0.1

(a)

Compute the probability that four or more people will have to be tested before two with the gene are detected as follows:

P (X ≥ 4) = 1 - P (X = 3) - P (X = 2)

              [tex]=1-[{3-1\choose 2-1}(0.1)^{2}(1-0.1)^{3-2}]-[{2-1\choose 2-1}(0.1)^{2}(1-0.1)^{2-2}]\\=1-0.018-0.01\\=0.972[/tex]

Thus, the probability that four or more people will have to be tested before two with the gene are detected is 0.972.

(b)

The expected value of a negative binomial random variable X is:

[tex]E(X)=\frac{r}{p}[/tex]

The expected number of people to be tested before two with gene are detected is:

[tex]E(X)=\frac{r}{p}=\frac{2}{0.1}=20[/tex]

Thus, the expected number of people to be tested before two with gene are detected is 20.

The farmer will need:

[tex]\boxed{191\frac{11}{12}yd}[/tex]

In order to enclose the area shown in the figure below.

The diagram below shows the representation of this problem. Let:

[tex]x: The \ length \ of \ the \ rectangular \ pastures \\ \\ y: The \ width \ of \ the \ rectangular \ pastures[/tex]

We know that:

[tex]x=5\frac{5}{8}yd \\ \\ y=30\frac{2}{9}yd[/tex]

So the fencing the farmer needs can be calculated as the perimeter of the two adjacent rectangular pastures:

[tex]P=2(x+y)+y \\ \\ P=2(50\frac{5}{8}+30\frac{2}{9})+30\frac{2}{9} \\ \\ P=100\frac{10}{8}+60\frac{4}{9}+30\frac{2}{9} \\ \\ P=100\frac{10}{8}+90\frac{6}{9} \\ \\ P=100\frac{5}{4}+90\frac{2}{3} \\ \\ P=190(\frac{15+8}{12}) \\ \\ P=190(\frac{23}{12}) \\ \\ \\ Expressing \ as \ a \ mixed \ fraction: \\ \\ P=190+1+\frac{11}{12} \\ \\ P=191+\frac{11}{12} \\ \\ \boxed{P=191\frac{11}{12}yd}[/tex]

Enclosing areas: https://brainly.com/question/1904034

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