_____________ refers to the scenario in which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.

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:

Parameter                                            

Step-by-step explanation:

We are given the following in the question:

The average age of men who had walked on the moon was 39 years, 11 months, 15 days.

Population and sample:

Parameter and statistic:

Population of interest:

men who had walked on the moon

Value:

average age of men who had walked on the moon

Thus, the give value describes a population and hence, it is a parameter.

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.

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:

(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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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:

c₁ = 1/2

c₂ = - e²/2

y = (1/2)*(eˣ - e²⁻ˣ)

Step-by-step explanation:

Given

y = c₁eˣ + c₂e⁻ˣ

y(1) = 0

y'(1) = e

We get y' :

y' = (c₁eˣ + c₂e⁻ˣ)'  ⇒  y' = c₁eˣ - c₂e⁻ˣ

then we find y(1) :

y(1) = c₁e¹ + c₂e⁻¹ = 0

⇒  c₁ = - c₂/e² (I)

then we obtain y'(1):

y'(1) = c₁e¹ - c₂e⁻¹ = e    (II)

⇒  (- c₂/e²)*e - c₂e⁻¹ = e

⇒  - c₂e⁻¹ - c₂e⁻¹ = - 2c₂e⁻¹ = e

⇒  c₂ = - e²/2

and

c₁ = - c₂/e² = - (- e²/2) / e²

⇒  c₁ = 1/2

Finally, the equation will be

y = (1/2)*eˣ - (e²/2)*e⁻ˣ = (1/2)*(eˣ - e²⁻ˣ)

Applying the initial conditions, it is found that the solution is:

[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]

------------------------

The solution for the PVI is given by:

[tex]y = c_1e^{x} + c_2e^{-x}[/tex]

------------------------

The condition [tex]y(1) = 0[/tex] means that when [tex]x = 0, y = 1[/tex], and thus, we get:

[tex]c_1e + c_2e^{-1} = 0[/tex]

[tex]c_1e+ \frac{c_2}{e} = 0[/tex]

[tex]c_1e^{2} + c_2 = 0[/tex]

[tex]c_2 = -c_1e^{2}[/tex]

------------------------

The derivative is:

[tex]y^{\prime}(x) = c_1e^{x} - c_2e^{-x}[/tex]

Applying the condition [tex]y^{\prime}(1) = e[/tex], we get:

[tex]c_1e - \frac{c_2}{e} = e[/tex]

Considering [tex]c_2 = -c_1e^{2}[/tex]:

[tex]c_1e + c_1\frac{e^2}{e} = e[/tex]

[tex]c_1e + c_1e = e[/tex]

[tex]2c_1e = e[/tex]

[tex]2c_1 = 1[/tex]

[tex]c_1 = \frac{1}{2}[/tex]

------------------------

The second constant is:

[tex]c_2 = -c_1e^{2} = -\frac{e^2}{2}[/tex]

And the solution is:

[tex]y = \frac{1}{2}e^{x} - \frac{e^2}{2}e^{-x}[/tex]

A similar problem is given at https://brainly.com/question/13244107

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.

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:

a) Empty set

b)  [tex]\{x : x \in N \text{ and } x < 13\}[/tex]                                        

Step-by-step explanation:

Roster form is a comma separated list form of set.

a) The set of natural numbers x that satisfy x + 4 = 1.  

[tex]x + 4 = 1\\x = -3 \notin N[/tex]

Thus, x is an empty set.

b) set-builder notation for the set  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We use x to represent this set. Now x belongs to natural number and is less than equal to 12.

Thus, it can be written as:

[tex]\{x : x \in N \text{ and } x < 13\}[/tex]

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%.

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:

$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

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%.

Answer:

A. 0.52

Step-by-step explanation:

Let D be the event that person used Debit card and C b the event that person used coupon.

We have to find the probability of customer does not use coupons given that a customer does not pay with a debit card,

P(C'/D')=P(C')P(D'/C')/[P(C')P(D'/C')+P(D')P(D'/C')]

We are given that P(D)=0.35, P(C)=0.30 and P(D/C)=0.5.

P(D')=1-0.35=0.65

P(C')=1-0.3=0.7

P(D'/C')=0.5.

P(C'/D')=0.7(0.5)/[0.7(0.5)+0.65(0.5)]

P(C'/D')=0.35/[0.35+0.325]

P(C'/D')=0.35/[0.35+0.325]

P(C'/D')=0.35/0.675

P(C'/D')=0.5185=0.52

Thus, the probability of customer does not use coupons given that a customer does not pay with a debit card is 0.52.

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.

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.

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:

A = -10

Step-by-step explanation:

A/2 = -5

Multiply both sides by the denominator of the fraction

We have A/2 x2 = -5 x 2

A = -10

Answer:

-10

Step-by-step explanation:

It is the easiest equation.

A/2= -5

At first, we have to multiply both the sides by 2. Therefore, we can get,

[tex]\frac{A*2}{2}[/tex] = (-5 × 2)

or, A = -10

Therefore, the value of A is -10. It remains negative because we cannot multiply both the sides by -1. If we do that, we cannot determine the constant.

Answer: A = -10

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:

The variance of this distribution is 0.0036.

Step-by-step explanation:

The variance of n binomial distribution trials with p proportion is given by the following formula:

[tex]Var(X) = \frac{p(1-p)}{n}[/tex]

In this problem, we have that:

About 90% of defendants are found guilty in criminal trials. This means that [tex]p = 0.9[/tex]

Suppose we take a random sample of 25 trials. This means that [tex]n = 25[/tex]

Based on a proportion of .90, what is the variance of this distribution?

[tex]Var(X) = \frac{p(1-p)}{n}[/tex]

[tex]Var(X) = \frac{0.9*0.1}{25} = 0.0036[/tex]

The variance of this distribution is 0.0036.

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:

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.

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.

Learn more about the unit conversion here:

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Answer:

13.5

Step-by-step explanation:

7 1/2=7.5

7.5/5*9=13.5

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]

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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:

Answer:

The unit rate is 6 1/4 cups of soda per cup of pineapple juice

Step-by-step explanation:

we know that

To find out the unit rate of soda to pineapple juice in the punch, divide the cups of soda by the cups of pineapple juice

so

[tex]2\frac{1}{2} :\frac{2}{5}[/tex]

Convert mixed number to an improper fraction

[tex]2\frac{1}{2}=2+\frac{1}{2}=\frac{2*2+1}{2}=\frac{5}{2}[/tex]

substitute

[tex]\frac{5}{2} :\frac{2}{5}[/tex]

Multiply in cross

[tex]\frac{25}{4}= 6.25[/tex]

Convert to mixed number

[tex]6.25=6+0.25=6+\frac{1}{4}= 6\frac{1}{4}[/tex]

That means

The unit rate is 6 1/4 cups of soda per cup of pineapple juice

Answer:

6 1/4

Step-by-step explanation:

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:

(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.