A deck of 52 cards has only one queen of diamonds. The deck is well-shuffled and you draw the first and last card (without replacement). What is the chance that the first card is a queen of diamonds or the last card is a queen of diamonds

Answer:

City @ 2017 = 8,920,800

Suburbs @ 2017 = 1, 897, 200

Step-by-step explanation:

Solution:

- Let p_c be the population in the city ( in a given year ) and p_s is the population in the suburbs ( in a given year ) . The first sentence tell us that populations p_c' and p_s' for next year would be:

                                  0.94*p_c + 0.04*p_s = p_c'

                                  0.06*p_c + 0.96*p_s = p_s'

- Assuming 6% moved while remaining 94% remained settled at the time of migrations.

- The matrix representation is as follows:

                         [tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}p_c\\p_s\end{array}\right] = \left[\begin{array}{c}p_c'\\p_s'\end{array}\right][/tex]          

- In the sequence for where x_k denotes population of kth year and x_k+1 denotes population of x_k+1 year. We have:

                         [tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_k = x_k_+_1[/tex]

- Let x_o be the populations defined given as 10,000,000 and 800,000 respectively for city and suburbs. We will have a population x_1 as a vector for year 2016 as follows:

                          [tex]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o = x_1[/tex]

- To get the population in year 2017 we will multiply the migration matrix to the population vector x_1 in 2016 to obtain x_2.

                          [tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] x_o[/tex]

- Where,

                         [tex]x_o = \left[\begin{array}{c}10,000,000\\800,000\end{array}\right][/tex]

- The population in 2017 x_2 would be:

                         [tex]x_2 = \left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right]\left[\begin{array}{cc}0.94&0.04\\0.06&0.96\end{array}\right] \left[\begin{array}{c}10,000,000\\800,000\end{array}\right] \\\\\\x_2 = \left[\begin{array}{c}8,920,800\\1,879,200\end{array}\right][/tex]

The estimated populations in 2017 are approximately 9,792,000 for the city and 807,360 for the suburbs

To set up the difference equation for this situation, let's denote the city population in a given year as [tex]\( C_n \)[/tex] and the suburban population as [tex]\( S_n \),[/tex] where [tex]\( n \)[/tex] represents the number of years since 2015. The initial populations in 2015 are given as [tex]\( C_0 = 10,000,000 \)[/tex] and[tex]\( S_0 = 800,000 \)[/tex].

Each year, 6% of the city's population moves to the suburbs, which can be represented as [tex]\( 0.06C_n \)[/tex]. Similarly, 4% of the suburban population moves into the city, which is [tex]\( 0.04S_n \).[/tex]

The difference equations describing the change in population each year are:

[tex]\[ C_{n+1} = C_n - 0.06C_n + 0.04S_n \][/tex]

[tex]\[ S_{n+1} = S_n + 0.06C_n - 0.04S_n \][/tex]

Now, let's calculate the populations for 2016 (one year after 2015,[tex]\( n = 1 \))[/tex]:

[tex]\[ C_1 = C_0 - 0.06C_0 + 0.04S_0 \][/tex]

[tex]\[ S_1 = S_0 + 0.06C_0 - 0.04S_0 \][/tex]

Plugging in the initial values:

[tex]\[ C_1 = 10,000,000 - 0.06 \times 10,000,000 + 0.04 \times 800,000 \][/tex]

[tex]\[ S_1 = 800,000 + 0.06 \times 10,000,000 - 0.04 \times 800,000 \][/tex]

Calculating the values:

[tex]\[ C_1 = 10,000,000 - 600,000 + 32,000 \][/tex]

[tex]\[ S_1 = 800,000 + 600,000 - 32,000 \][/tex]

[tex]\[ C_1 = 9,432,000 \][/tex]

[tex]\[ S_1 = 1,368,000 \][/tex]

Next, we calculate the populations for 2017 [tex](\( n = 2 \)):[/tex]

[tex]\[ C_2 = C_1 - 0.06C_1 + 0.04S_1 \][/tex]

[tex]\[ S_2 = S_1 + 0.06C_1 - 0.04S_1 \][/tex]

 Using the populations from 2016:

[tex]\[ C_2 = 9,432,000 - 0.06 \times 9,432,000 + 0.04 \times 1,368,000 \][/tex]

[tex]\[ S_2 = 1,368,000 + 0.06 \times 9,432,000 - 0.04 \times 1,368,000 \][/tex]

Calculating the values:

[tex]\[ C_2 = 9,432,000 - 565,920 + 54,720 \][/tex]

[tex]\[ S_2 = 1,368,000 + 565,920 - 54,720 \][/tex]

[tex]\[ C_2 = 9,792,000 \][/tex]

[tex]\[ S_2 = 807,360 \][/tex]

Answer:

Step-by-step explanation:

I'm going to assume that the problem is -23x -214 = 274

And in that case...

1. First isolate the x-value by adding 214 to both sides of the equation:

-23x = 488

2. Then, divide both sides by -23 to truly get x alone:

x = [tex]-\frac{488}{23}[/tex] or -21.22

Answer:

 x = -18

Add the opposite of the constant on the left:

 -2/3x = 21/4 +27/4 = 48/4 = 12

Multiply the equation by the inverse of the coefficient of x:

 x = (-3/2)(12) = -18

The solution is x = -18.

Step-by-step explanation:

Answer:

1. Stratified Random Sampling

Step-by-step explanation:

Sampling is a technique of drawing small number of representative units from population.

Stratified Random Sampling is when population is divided into : heterogenous (different) groups, homogeneous (identical) within themselves - known as Strata.

Process of drawing Sample from each such strata group is called Stratified Random Sampling. This sampling makes sample better representative of various groups in population. Eg : Dividing population in strata based on gender , religion etc & then drawing sample from each strata.

Researcher dividing students into - freshman, sophomores & other groups ; then drawing sample from each group is an example of Stratified Sampling. It creates representative sample of each student body in school .

The researcher is practicing stratified random sampling by dividing the students into groups based on their class standing and randomly selecting a sample from each group.

The researcher is practicing stratified random sampling.

In stratified random sampling, the population is divided into homogeneous groups called strata. The researcher then randomly selects a sample from each stratum to create a representative sample of the entire population.

In this case, the researcher divided the students into groups based on their class standing and randomly selected 50 students from each group.

This ensures that the sample includes students from all class standings and accurately represents the entire student body of the Scion School of Business.

Answer: the diameter of the can is 2.8 inches

Step-by-step explanation:

The formula for determining the volume of a cylinder is expressed as

Volume = πr²h

Where

r represents the radius of the cylinder.

h represents the height of the cylinder.

π is a constant whose value is 3.14

From the information given,

height = 4.5 inches

Volume of can = 454 millilitres

1 cubic inch = 16.387 millilitres

Converting 454 millilitres to cubic inches, it becomes

454/16.387 = 27.7 cubic inches

Therefore

27.7 = 3.14 × r² × 4.5

27.7 = 14.13r²

r² = 27.7/14.13

r² = 1.96

r = √1.96

r = 1.4

Diameter = 2 × radius

Diameter = 2 × 1.4 = 2.8 inches

Solution:

The circumference of a circle is given as:

[tex]\text{circumference } = 2 \pi r[/tex]

Where,

"r" is the radius of circle

We know that,

[tex]diameter = 2 \times radius\\\\d = 2 \times r\\\\d = 2r[/tex]

Thus the circumference can also written as:

[tex]\text{circumference } = 2 \pi r\\\\\text{circumference } = \pi \times d[/tex]

Thus, the circumference is found by multiplying Pi by the diameter is correct statement

The true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.

Therefore, the true statement about the circumference of a circle is: circumference is found by multiplying Pi by the diameter.

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Answer:

(1)5 ft 4 in

(2)9.6 ft

Step-by-step explanation:

We are given that

AB=12 ft

BC=8 ft

All right triangles are similar

(1)Let BD=x

Triangle ABC and DBC are similar

When two triangle are similar then , the ratio of their corresponding sides are equal.

[tex]\frac{12}{8}=\frac{8}{x}[/tex]

[tex]x=\frac{8\times 8}{12}=\frac{64}{12}=5.3 ft[/tex]

[tex]x=\frac{64}{12}\times 12=64 inches[/tex]=5 ft 4in

1 feet=12 inches

(2)In triangle DBC

[tex]CD^2=BC^2+DB^2[/tex]

Using Pythagoras theorem  

[tex](hypotenuse)^2=(Base)^2+(perpendicular\;side)^2[/tex]

[tex]CD^2=(8)^2+(5.3)^2[/tex]

[tex]CD=\sqrt{64+28.09)}=9.6 feet[/tex]

Hence, the length of support wire=9.6 feet

The distance from point B that point D should be placed in the triangle is 5 feet 4 inches.

The distance from point B that point D should be placed in the triangle will be calculated thus:

Let the distance be represented by x

12/8 = 8/x

x = (8 × 8) / 12

x = 5 ft 4 in

The length of the support wire will be calculated thus:

CD² = 8² + 5.3²

CD² = 64 + 28.09

CD² = 92.09

CD = ✓92.09

CD = 9.6 feet

Therefore, the length of the support wire is 9.6 feet.

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Answer:(x,-14) (x+6)

Step-by-step explanation:

I think correct me if I am wrong.

Answer: the price of a bag of popcorn is $5.3

Step-by-step explanation:

Let x represent the price of one drink.

Let y represent the price of one bag of popcorn.

Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. This is expressed as

4x + 9y = 65.25- - - - - - - - - - - - - - -1

Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn.

This is expressed as

8x + 3y = 51.75- - - - - - - - - - - - - - -2

Multiplying equation 1 by 8 and equation 2 by 4, it becomes

32x + 72y = 522

32x + 12y = 207

Subtracting, it becomes

60y = 315

y = 315/60

y = 5.25

Answer:

Point B

Step-by-step explanation:

Because the x coordinate is -2

Move two to the left.

The y-coordinate is 2

After we are at -2 for x, then move up to reach the y=2 line. \

Then that will be your point.

Answer:

it would be point b

Answer:

The time the both trains have to travel for making a distance of 1162.5 miles apart  T = 7.75 hour

Step-by-step explanation:

Speed of the first train = 78 [tex]\frac{mi}{h}[/tex]

Speed of the second train = 72 [tex]\frac{mi}{h}[/tex]

Suppose the both trains have to travel for time = T hour

The distance traveled by first train ( [tex]D_{1}[/tex] ) = Speed × time

⇒ [tex]D_{1}[/tex] = 78 × T --------- (1)

The distance traveled by second train ( [tex]D_{2}[/tex] ) = 72 × T --------- (2)

Total distance D = [tex]D_{1}[/tex] + [tex]D_{2}[/tex]

⇒ D = 78 × T + 72 × T

⇒ 1162.5 = 150 T

⇒ T = 7.75 hour

This is the time the both trains have to travel for making a distance of 1162.5 miles apart.

Answer:

Step-by-step explanation:

It’s 34

Answer:

The answer to your question is Area = 9 yd²

Step-by-step explanation:

Data

Big square                        Small square

Area = 36 yd²                   Area = x

Side = 6 yd                       Side = 3 yd

Process

1.- Use the formula of Area of a square to find it

         Area = side x side

2.- Substitution

         Area = 3 x 3

3.- Simplification and result

         Area = 9 yd²

Answer:

A

Step-by-step explanation:

- Generally, the agent of a COMMA + VERBing modifier must be the nearest preceding SUBJECT.

- B and C: The 32 species...include the animal known as the killer whale, growing

- Here, COMMA + growing seems to refer to the 32 species -- the nearest preceding subject -- implying that the SPECIES are GROWING.

Not the intended meaning.

- The intended meaning of the original sentence is that THE KILLER WHALE can GROW.

Eliminate B and C.

- In D and E, includes (singular) does not agree with the 32 species (plural).

Eliminate D and E.

- the correct answer is A

The correct answer is option (A). include the animal known as the killer whale,which can grow to be 30 feet long

To determine this, we need to ensure the sentence maintains proper subject-verb agreement and logical consistency. The primary subject is 'The 32 species that make up the dolphin family,' which is plural.

Therefore, the verb 'include' is correct, rather than 'includes' which would be for a singular subject.

Additionally, 'which can grow to be 30 feet long and is' clearly and correctly describes the killer whale.

The correct answer to this question is (A) include the animal known as the killer whale, which can grow to be 30 feet long and is.

Answer:

Option 1) A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.  

Step-by-step explanation:

We are given the following in the question:

95% confidence interval of mean body mass index (BMI) for girls between 13 and 19 years of age is:

[tex](19.5, 26.3)[/tex]

Lower limit = 19.5

Upper limit = 26.3

1. A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.

The given statement is false. This is not the right interpretation for confidence interval.

2. The margin of error is 3.4

The confidence interval can be found as

[tex]\text{sample mean}\pm \text{Margin of error}[/tex]

Let x be the sample mean and y be the margin of error, thus, we can write

[tex]x - y =19.5\\x + y = 26.3\\2x =45.8 \\x = 22.9\\y = 22.9 - 19.5\\y = 3.4[/tex]

Thus, the margin of error is 3.4

Thus, the given statement is true.

3. The value z in the margin of error is 1.96.

The statement is true.

The z-multiplier for a 95% confidence interval used is 1.96

4. A total of 95% of all SRS of size n contain the true mean body mass index

The given statement is true. It is the right interpretation of 95% confidence interval.

Among the provided statements, 'A total of 95% of all teenage girls have BMI between 19.5 and 26.3' is NOT accurate. A 95% confidence interval does not indicate that 95% of the data is in that range.

In this case, the statement that is NOT true about the confidence interval for estimating the mean body mass index (BMI) for girls between 13 and 19 years of age is: 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3.

A 95% confidence interval does not claim that 95% of the population data falls within this range. Instead, it asserts that if we were to take many samples and build a confidence interval from each sample, then about 95% of the confidence intervals would contain the true mean BMI (this is the meaning of statement 4).

Statement 2 is incorrect since the margin of error is not 34. It is calculated as (26.3 - 19.5)/2 = 3.4.

Statement 3 is correct as the value for 'z' in a 95% confidence interval is indeed 1.96. This is because 1.96 is the z-score that cuts off the top 2.5% and bottom 2.5% of data in a standard normal distribution, leaving 95% of the data in between.

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Answer:

169/4

Step-by-step explanation:

x² - 13x + c

x² -2(x)(13/2) +(13/2)²

(13/2)² = 169/4 or 42 ¼

Out of a dozen eggs, with 4 being white, the fraction that represents the brown eggs is 8/12. Simplified, this fraction is 2/3.

The question is asking us to find what fraction of the eggs are brown if there are 4 white eggs out of a dozen in a basket. Since there are 12 eggs in a dozen, and we know 4 are white, we can subtract the 4 white eggs from the total to find out how many are brown.

12 eggs (total) - 4 white eggs = 8 brown eggs.

Therefore, the fraction of the basket that contains brown eggs is 8/12. To simplify this fraction, we look for the greatest common divisor of both the numerator (8) and the denominator (12), which is 4. Dividing both by 4, we get:

8 ÷ 4 = 2

12 ÷ 4 = 3

So the fraction of the eggs that are brown in simplest form is 2/3.

Answer:

Step-by-step explanation:

According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green.

Colour      Brown     Yellow      Red     Blue   Orange     Green   total

Prob           0.12          0.15         0.12     0.23    0.23         0.15        1  

The probability that a randomly selected peanut M&M is not yellow

=[tex]1-P(Yellow) = 0.85[/tex]

the probability that a randomly selected peanut M&M is orange or yellow.

= [tex]0.23+0.15=0.38[/tex]

the probability that three randomly selected peanut M&M's are all red.

= [tex](0.12)^3 = 0.001728[/tex]

(assuming large number of peanuts and thus independent )

If you randomly select two peanut M&M's, compute that probability that neither of them are red.

= [tex](1-0.12)^2\\= 0.7744[/tex]

If you randomly select two peanut M&M's, compute that probability that at least one of them is red

=[tex]1-P(both non red)\\= 1-0.88^2\\= 0.2256[/tex]

Answer:

42 games

Step-by-step explanation:

If the college basketball team has won 14 games and lost 6 games,

The Probability of recording a win is given as:

Probability(of a win)[tex]=\frac{Number of Outcomes }{Total Number o trials}[/tex]=[tex]\frac{14}{20}[/tex]

In experimental probability, this can also be taken as the Relative Frequency of a win.

Therefore: Number of Expected Wins

=Relative Frequency of  a win X Total Number of Trials

[tex]\frac{14}{20}X60=42[/tex]

The team would expect to win 42 games in a 60 game schedule

Final answer:

The team would win 35 games in a 50 game schedule.

Explanation:

To find out how many games the team would win in a 50 game schedule, we can use a proportion. The team has won 14 out of 20 games so far, which can be written as 14/20. We can set up a proportion with x representing the number of games the team would win in a 50 game schedule:

14/20 = x/50

Now we can cross-multiply and solve for x:

20x = 14 * 50

20x = 700

x = 700/20

x = 35

So, if they continue to win at this rate, the team would win 35 games in a 50 game schedule.

Answer: it would take 7 years more for Brianna's money to double than for Adam's money to double

Step-by-step explanation:

Considering Brianna's investment,

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = $480

r = 6.5% = 6.5/100 = 0.065

A = 2 × 480 = $960

Therefore,

960 = 1800 x 2.7183^(0.065 x t)

960/1800 = 2.7183^(0.065t)

2 = 2.7183^(0.065t)

Taking ln of both sides, it becomes

Ln 2 = 0.065tln2.7183

0.693 = 0.065t

t = 0.693/0.065

t = 10.66

Approximately 17 years

Considering Adam's investment, we would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

P = 480

A = 960

r = 6.75% = 6.75/100 = 0.0675

n = 4 because it was compounded 4 times in a year.

Therefore,.

960 = 480(1 + 0.0675/4)^4 × t

960/480 = (1 + 0.016875)^4t

960/480 = (1.016875)^4t

Taking log of both sides, it becomes

Log 2 = 4t log 1.016875

0.301 = 0.0291t

t = 0.301/0.0291

t = 10.34

Approximately 10 years

Answer:

there are 5 animals in each pack.

Step-by-step explanation:

if you add 9+6= 15 then divide 15 by 3 you will get 5 as your answer

Answer: there were 5 animals in each pack.

Step-by-step explanation:

Let x represent the number of toy animals in each pack.

Josiah has 3 packs of toy animals. Each pack has the same number of animals. This means that the number of animals in the 3 packs is

3x

Josiah gives 6 animals to his sister stephanie. This is expressed as 3x - 6. If she has 9 left, it means that

3x - 6 = 9

3x = 9 + 6

3x = 15

x = 15/3

x = 5

Answer:

I believe it is 2 for $5.08

Step-by-step explanation:

1.27 times 2 is 2.54

2.54 times 5 is 12.70

Answer:

D 2(1/2) for $6.25

Step-by-step explanation:

a. 5.08/2=2.54

b.12.7/5=2.54

c.1.27/0.5=2.54

d.6.25/2.5=2.5

Answer:

T = 25 + 12 * h

Step-by-step explanation:

To find the rate of the tuner it is necessary to go to an equation:

First would be the full rate that has a value of 25. And for every hour that is 12.

That is to say:

T = 25 + 12 * h

h being the hours it takes to tune the piano. And this equation would reprehend what the piano tuner

Answer: Noah paid $6591 on his car loan.

Step-by-step explanation:

The amount of money paid as down payment for the car is

20/100 × 25350 = 5070

Therefore, the amount paid to finance the remaining cost of the car is

25350 - 5070 = $20280

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

From the information given,

P = 20280

R = 6.5%

T = 5 years

I = (20280 × 6.5 × 5)/100 = $6591

Answer:its $6591

Step-by-step explanation:

The amount of money paid as down payment for the car is

20/100 × 25350 = 5070

Therefore, the amount paid to finance the remaining cost of the car is

25350 - 5070 = $20280

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount taken as loan

R represents interest rate

T represents the duration of the loan in years.

From the information given,

P = 20280

R = 6.5%

T = 5 years

I = (20280 × 6.5 × 5)/100 = $6591

Answer:

This would be quad III

Step-by-step explanation:

To graph the polar equation, plot points based on r and θ values. To express the quotient of complex numbers in rectangular form, operate division, simplify, then convert. To convert a rectangular equation to polar form, substitute x and y with their polar form.

1. To graph the polar equation, you would plot points based on the r (magnitude/distance) and θ (angle) values from the origin (0,0). As you've not provided the specific polar equation, I cannot provide a full step-by-step explanation.

2. To divide complex numbers and express the quotient in rectangular form, you multiply the numerator and the denominator by the conjugate of the denominator, simplify, and convert the result into rectangular coordinates (x+iy) form. For example,

2(cos150° + isin150°) / 8(cos210° + isin210°)

After calculating the division, you end up with the cosine and sine of an angle in the numerator. Then, convert this to rectangular form. Unfortunately, as Brainly platform constraints, computational solutions cannot be provided through this medium.

3. To convert the rectangular equation (x+5)^2+y^2=25 in polar form, replace x = rcosθ and y = rsinθ in the equation. Then simplify the equation to get a polar equation.

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Final answer:

The distance between two ships leaving a harbor can be calculated using vector addition and the cosine law formula, resulting in an approximate distance of 565 miles.

Explanation:

The distance between the two ships can be calculated using vector addition.

To find the distance apart, we can add the vectors representing the paths of the two ships. Using the cosine law formula, we calculate the magnitude of the resultant vector to be approximately 565 miles.

Option C: [tex]\frac{4}{5}[/tex] is the slope of the line

Explanation:

The line passes through the points [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]

We need to find the slope of the line.

The slope can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]

Let us substitute the points in the formula

Thus, we have,

[tex]m=\frac{-5-(-1)}{-2-3}[/tex]

Simplifying, we get,

[tex]m=\frac{-5+1}{-2-3}[/tex]

Adding the numerator and denominator, we have,

[tex]m=\frac{-4}{-5}[/tex]

Cancelling the negative terms, we get,

[tex]m=\frac{4}{5}[/tex]

Thus, the slope of the line is [tex]m=\frac{4}{5}[/tex]

Therefore, Option C is the correct answer.

Answer:

Correct option is (B). 20%.

Step-by-step explanation:

The number of managers is, 1200.

The percentage of managers who identified work experience as an important characteristic to consider is, P (W) = 72%.

The percentage of managers who identified appropriate attire and behavior as an important characteristic to consider is, P (AB) = 55%.

Compute the number of managers who identified work experience as an important characteristic to consider as follows:

[tex]n(W)=1200\times P(W)\\=1200\times\frac{72}{100}\\=864[/tex]

Compute the number of managers who identified appropriate attire and behavior as an important characteristic to consider as follows:

[tex]n(AB)=1200\times P(AB)\\=1200\times\frac{55}{100}\\=660[/tex]

Compute approximately what percent greater is P (W) than P (AB) as follows:

[tex]P(W>AB)=\frac{n(W)-n(AB)}{1200}=\frac{864-660}{1200}=\frac{204}{1200}=0.17\approx0.20[/tex]

Thus, the number of managers surveyed who identified work experience as an important characteristic to consider was approximately 20% percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider.

Correct option is (B).

So in 5 acres of land produces 21,000 pounds of strawberries.

Step-by-step explanation:

Step 1:

Last year, [tex]3\frac{1}{2}[/tex] acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.

To do this we divide the total number of strawberries produced by the number of acres it was produced in.

The number of strawberries produced per acre[tex]= \frac{14,700}{3.5} = 4,200[/tex] pounds.

Step 2:

To determine the number of strawberries in 5 acres of land, we multiply the number of strawberries per acre by the number of acres.

The number of strawberries produced in 5 acres[tex]= 5(4,200) = 21,000[/tex] pounds.

So in 5 acres of land produces 21,000 pounds of strawberries.

Answer:

Step-by-step explanation:

Assuming there is a punitive removal of one point for an incorrect response.

Five undiscernable choices: 20% chance of guessing correctly -- Expectation: 0.20*(1) + 0.80*(-1) = -0.60

Four undiscernable choices: 25% chance of guessing correctly -- Expectation: 0.25*(1) + 0.75*(-1) = -0.50

I'll use 0.33 as an approzimation for 1/3

Three undiscernable choices: 33% chance of guessing correctly -- Expectation: 0.33*(1) + 0.67*(-1) = -0.33 <== The approximation is a little ugly.

Two undiscernable choices: 50% chance of guessing correctly -- Expectation: 0.50*(1) + 0.50*(-1) = 0.00

And thus we see that only if you can remove three is guessing neutral. There is no time when guessing is advantageous.

One Correct Answer: 100% chance of guessing correctly -- Expectation: 1.00*(1) + 0.00*(-1) = 1.00

The expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16. The expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.

To find the expected value of eliminating one answer and guessing among the remaining four possible answers, we need to consider the probabilities associated with each outcome.

Since there are four possible answers remaining, the probability of guessing the correct answer is 1/4. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:

Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)

Expected Value = (1/4 * 1) + (3/4 * (-1/4)) = 1/4 - 3/16 = 1/16.

So, the expected value of eliminating one answer and guessing among the remaining four possible answers is 1/16.

For eliminating three answers and guessing between the remaining two possible answers, the probabilities change.

Since there are now two possible answers remaining, the probability of guessing the correct answer is 1/2. The value of getting the correct answer is +1, and the value of getting it wrong is -1/4. Therefore, the expected value is:

Expected Value = (Probability of Correct Answer * Value of Correct Answer) + (Probability of Wrong Answer * Value of Wrong Answer)

Expected Value = (1/2 * 1) + (1/2 * (-1/4)) = 1/2 - 1/8 = 3/8.

So, the expected value of eliminating three answers and guessing between the remaining two possible answers is 3/8.

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