The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 12521252 and standard deviation 129129 chips. ​(a) what is the probability that a randomly selected bag contains between 11001100 and 14001400 chocolate​ chips? ​(b) what is the probability that a randomly selected bag contains fewer than 10001000 chocolate​ chips? ​(c) what proportion of bags contains more than 12001200 chocolate​ chips? ​(d) what is the percentile rank of a bag that contains 10501050 chocolate​ chips?

Answers

Answer 1

Answer:

a)  P (  1100 < X < 1400 ) = 0.755

b) P (  X < 1000 ) = 0.755

c) proportion ( X > 1200 ) = 65.66%

d) 5.87% percentile

Step-by-step explanation:

Solution:-

- Denote a random variable X: The number of chocolate chip in an 18-ounce bag of chocolate chip cookies.

- The RV is normally distributed with the parameters mean ( u ) and standard deviation ( s ) given:

                               u = 1252

                               s = 129

- The RV ( X ) follows normal distribution:

                       X ~ Norm ( 1252 , 129^2 )  

a) what is the probability that a randomly selected bag contains between 1100 and 1400 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( x1 < X < x2 ) = P ( [ x1 - u ] / s < Z <  [ x2 - u ] / s )

- Taking the limits x1 = 1100 and x2 = 1400. The standard normal values are:

     P (  1100 < X < 1400 ) = P ( [ 1100 - 1252 ] / 129 < Z <  [ 1400 - 1252 ] / 129 )

                                        = P ( - 1.1783 < Z < 1.14728 )

       

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( -1.1783 < Z < 1.14728 ) = 0.755

Hence,

      P (  1100 < X < 1400 ) = 0.755   ... Answer

b) what is the probability that a randomly selected bag contains fewer than 1000 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1000. The standard normal values are:

     P (  X < 1000 ) = P ( Z <  [ 1000 - 1252 ] / 129 )

                                        = P ( Z < -1.9535 )

       

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < -1.9535 ) = 0.0254

Hence,

       P (  X < 1000 ) = 0.755   ... Answer

​(c) what proportion of bags contains more than 1200 chocolate​ chips?

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X > x1 ) = P ( Z >  [ x1 - u ] / s )

- Taking the limit x1 = 1200. The standard normal values are:

     P (  X > 1200 ) = P ( Z >  [ 1200 - 1252 ] / 129 )

                                        = P ( Z > 0.4031 )

       

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z > 0.4031 ) = 0.6566

Hence,

      proportion of X > 1200 = P (  X > 1200 )*100 = 65.66%   ... Answer

d) what is the percentile rank of a bag that contains 1050 chocolate​ chips?

- The percentile rank is defined by the proportion of chocolate less than the desired value.

- Compute the standard normal values for the limits of required probability using the following pmf for standard normal:

     P ( X < x2 ) = P ( Z <  [ x2 - u ] / s )

- Taking the limit x2 = 1050. The standard normal values are:

     P (  X < 1050 ) = P ( Z <  [ 1050 - 1252 ] / 129 )

                                        = P ( Z < 1.5659 )

       

- Use the standard normal tables to determine the required probability defined by the standard values:

       P ( Z < 1.5659 ) = 0.0587

Hence,

       Rank = proportion of X < 1050 = P (  X < 1050 )*100

                 = 0.0587*100 %  

                 = 5.87 % ... Answer


Related Questions

What is the slope of the line that passes through the points (22,-4)(−3,-9)? Write your answer in simplest form.

Answers

Answer:

1/5

Step-by-step explanation:

We can find the slope of a line passing through two points by using the following

m = (y2-y1)/(x2-x1)

    = (-9 - -4)/(-3 - 22)

    = (-9+4)/(-25)

    = -5/ -25

   = 1/5

Final answer:

The slope of the line that passes through the points (22,-4) and (−3,-9) is calculated using the formula for slope. When calculated, the slope is found to be 1/5

Explanation:

The slope of a line passing through two given points can be calculated using the formula: m = (y2 - y1) / (x2 - x1). Here, (x1, y1) and (x2, y2) are the coordinates of the two points.

In the given question, the points are (22,-4) and (−3,-9). When the values are entered into the formula, we obtain:

m = (-9 - (-4)) / (-3 - 22) = -5 / -25 = 1/5

So, the slope of the line passing through the points (22,-4) and (−3,-9) is 1/5.

Learn more about Slope of a Line here:

https://brainly.com/question/34207674

#SPJ3

You roll a number cube one time
What is the probability of not rolling a number more than 62 Write your
answer as a fraction.​

Answers

Answer:

6/6 or 1/1

Step-by-step explanation:

A standard number cube has 6 sides to it. Therefore there are 6 possibilities, as you can roll either a 1, 2, 3, 4, 5, or 6.

The question is asking what the probability is for not rolling a number more than 62. To reword the question to get rid of the confusing 'not', "What is the probability of rolling a number less than 62?"

All the possibilities on the dice are less than 62, therefore it is guaranteed you will not roll a number more than 62. The probability is 1, or written as a fraction 1/1, or 6/6, since 6 sides of the 6 sided cube are less than 62.

a web music store offers two versions of a popular song. the size of the standard version is 2.9 megabytes (MB). the size of the high-quality version is 4.8 MB. yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 6188 MB. How many downloads of the standard version were there?​

Answers

Answer:

280 downloads

Step-by-step explanation:

-let x denote the number of standard version downloads.

-Given that the high-quality version was downloaded four times as often as the standard version it is denoted as 4x

-This can then be expressed as:

[tex]x(2.9)+4x(4.8)=6188\\\\2.9x+19.2x=6188\\\\22.10x=6188\\\\x=280[/tex]

Hence, the number of standard version downloads is 280

The side lengths of a triangle are 12, 15, and 10 square root 3. Classify the triangle.

Answers

Answer: Scaline?

Step-by-step explanation:

The triangle having sides 12, 15 and 10√3 is a Scalene type triangle.

Properties Scalene Triangle:It has no equal sides.It has no equal angle.There is no line of symmetry.

How to classify the given triangle?Given length of sides AB = 12 , BC =  15 & AC = 10√3As all the sides are not equal to each other, hence their angles are also not equal.Thus, it can be classified as a scalene triangle.

Thus, the triangle having sides 12, 15, and 10√3 is a Scalene type triangle.

Learn more about Scalene Triangles here:

https://brainly.com/question/16589630

#SPJ2

To divide 14 2/3 divide by 2 3/4, Erik multiplied 14 2/3 times 4/3. Explain Erik's error.

Answers

Answer:

Erik should have divided 14 2/3 by 2 3/4, but instead he multiplied causing him to have a greater answer than 5 and 1/3

(give brainliest please)

After the outbreak of a mysterious disease the average wait time at a hospital increased by 70% before the outbreak the average wait time at the hospital was m minutes

Answers

Answer:

1.7m

Step-by-step explanation:

Given that 'm' was the waiting time before the outbreak

After the outbreak, waiting time increased by 70%.

This implies that :

70% of m increase

m + 70% of m

m + 70/100 of m

m + ( 70÷100 ) × m

m + 0.7m

= 1.7m

A right triangle has legs with lengths equal to 10inches and 9x inches. It’s hypotenuse measures (x+10) inches.
What is the approximate value of the hypotenuse?

Answers

Answer:

the answer is 10.25

Step-by-step explanation:

Answer:

the approximate value of the hypotenuse is 10.25 seconds

Step-by-step explanation:

Multiply (x−3)(x+2)

Answers

We FOIL, multiply firsts, outers, inners and lasts, and add them all up.

(x-3)(x+2) = x·x + 2x - 3x + (-3)(2) = x² - x - 6

Answer: x² - x - 6

Answer:

x^2 - x - 6

Step-by-step explanation:

(x - 3) (x + 2)

you can use the distributive property and multiplyfirst, you multiply the first x by the second x.that would be x^2.then, you multiply the first x by 2.which is 2x. by now you should have x^2 + 2x.now, you multiply -3 by the second x. this equals -3x.now, you have x^2 + 2x - 3x.next, you multiply -3 by +2.this would result in -6.now combine all of the solutions you got and you should have:x^2 + 2x - 3x - 6the last step is to combine like terms.x^2 is an only term, so leave that alone.+2x and -3x are like terms. so, you want to add these.that would remain as x^2 - xnow, -6 is an only term as well. so, just leave that in the end.in conclusion, your answer is x^2 - x - 6

HELP ME ASAP PLEASE!!!WILL MARK BRAINLIEST!!!

What’s x?

#3 only. But if u wanna do #5 then go ahead lol

Answers

Answer:

x=10.85

Step-by-step explanation:

you add 85 and 31 equaling 116.

13x-21=116

    +21 =+21

13x=137

13x= 13x

x=10.85

PLZ HELP RIGHT NOW PLZ I WILL MARK BRAINLIEST I BEG NO SILLY ANWSER =(
anwser plz

1. 7(3-3x)=84 what is x

2. -7(-4-3m)=112 what is m

3.-182=7(2b-8)+7b what is b

4. -101 = -5(8x-5) -6 what is x

Answers

Answer:

1. x=-3

2. m=4

3. -6=b

4. x=3

Step-by-step explanation:

1. 7(3-3x)=84 what is x

- Distribute the 7 using distributive property, which will give you 21-21x=84.

- Add 21 to both sides to aim to isolate the x variable, which will give you -23x=63.

- Divide both sides by the coefficient of x, -23, to finally get x by itself: x=-3

2. -7(-4-3m)=112 what is m

- Distribute the -7 using distributive property, which will give you 28+21m=112. Be wary of negatives.

- Subtract 28 to both sides, which will give you 21m=84.

- Divide both sides by 21 (the coefficient of m) to get m by itself: m=4

3.-182=7(2b-8)+7b what is b

- Distribute the 7 using distributive property, which will give you -182=14b-56+7b

- Add like terms to get -182=21b-56.

- Add both sides by 56, which will get you -126=21b.

- Divide both sides by the coefficient of b, 21, to get b by itself: -6=b

4. -101 = -5(8x-5) -6 what is x

- Distribute the -5 using distributive property, which will give you -101=-40x+25-6. Beware of negatives.

- Add like terms to get -101=-40x+19.

- Subtract both sides by 19 to get -120=-40x.

- Divide both sides by 40 (the coefficient of x) to get 3=x.

Hope this helps!

A target survey found that 4 out of 5 customers who entered the store made a purchase. If this store recorded 22,853 purchased last week, estimate the number of customers who entered the store

Answers

Answer:

28,566.25

Explanation:

22,853 is 4/5 of the customers, so we set up an equation where 22,853 over x is equal to 4 over 5. Cross multiply to get x * 4 = 22,853 * 5. Divide both sides by 4 to get 28,566.25.

In simplest terms what is the answer to 1/8added to 1/6

Answers

Answer:

7/24

Step-by-step explanation:

1/8  added to 1/6

means  1/8  plus  1/6

1/8  = 3/24,

1/6= 4/24

3/24 + 4/24 = 7/24

Answer:

7/24

Step-by-step explanation:

1/8+1/6

=(1*6)+(1*8)

------------------divide

      8*6

=14/48

14/2

--------

48/2

=7/24

im sorry the math is weird my key board is small on this computer and i can only do so much but i hope that this helps you and you can do good in online school and happy quarantine stay home if you can to stop the spread of corona and help open the world again:)

A group of students is timed while sprinting 100 meters. Each student’s speed can be found by dividing 100 m by their time. Is each statement true or false? Explain your reasoning.
Speed is a function of time.
Time is a function of distance.
Speed is a function of number of students racing.
Time is a function of speed.


Answers

Answer:

True

Step-by-step explanation:

since, S= D/T the distance traveled would only be 100m, it is a consatnt variable dividing it with the time it takes to reach that distance would be its speed. Unless there is an acceleration happening in that process the speed would change depending on the situation.

Final answer:

Speed is a function of time and time is a function of speed, with these relationships demonstrated through the equations speed = distance/time and time = distance/speed. The number of students racing does not affect an individual's speed.

Explanation:

A student asked several questions related to speed, distance, and time while analyzing a 100-meter sprint. To address these questions, we will look at the relationships between these quantities.

Speed is a function of time: True. Speed can be calculated as the distance traveled divided by the time it took, so if you know the time, you can calculate the speed using the equation speed = distance/time.

Time is a function of distance: False. Time can be a function of speed and distance (time = distance/speed), but this question does not provide information indicating that time is directly dependent on distance alone.

Speed is a function of the number of students racing: False. The speed of a student is independent of the number of students racing; it is determined by the individual's performance (distance/time).

Time is a function of speed: True. Given a constant distance, time can be calculated by dividing the distance by the speed (time = distance/speed).

The graph of the function f(x) = –(x + 6)(x + 2) is shown below.
Which statement about the function is true?
a) The function is increasing for all real values of x where
x < –4.
b) The function is increasing for all real values of x where
–6 < x < –2.
c) The function is decreasing for all real values of x where
x < –6 and where x > –2.
d) The function is decreasing for all real values of x where
x < –4.

Answers

Answer:

its A

Step-by-step explanation:

i got i right

What type of transformation maps AQRS to AQ'R'S'?
O
O
dilation
reflection
O
O
rotation
translation

Answers

The answer would be rotation

The  type of transformation maps AQRS to AQ'R'S' is rotation.

The following information should be considered;

A rotation is a type of transformation that takes each point in a figure and rotates it a specific number of degrees. The result of a rotation represent a new figure, called the image. The image is congruent to the original figure.

Learn more: https://brainly.com/question/4626564?referrer=searchResults

The City Zoo has different admission prices for adults and children. When three adults and two children went to the zoo, the bill was $77.50. If two adults and three children got in for $70.00 then what is the price of an adult's ticket and what is the price of a child's ticket?

Answers

Answer:

The price of an adult's ticket is $18.5 and price of a child's ticket is $11.

Step-by-step explanation:

We are given the following in the question:

Let x dollars be the cost of an adult's ticket and y dollars be the cost of a child's ticket.

The cost of three adults and two children tickets is $77.50

Thus, we can write the equation:

[tex]3x + 2y = 77.50[/tex]

The cost of two adults and three children tickets is $70.00

Thus, we can write the equation:

[tex]2x+3y = 70[/tex]

Solving the two equations, we get

[tex]6x+4y-(6x+9y) = 155-210\\\Rightarrow -5y = -55\\\Rightarrow y = 11\\\Rightarrow 2x + 33 = 70\\\Rightarrow x = 18.5[/tex]

Thus, the price of an adult's ticket is $18.5 and price of a child's ticket is $11.

In AABC, the measure of A is 108° and the
measure of B is 38° . What is the measure of
C?

Answers

Answer:

Should be 34

Step-by-step explanation:

Answer:

∠C=34

Step-by-step explanation:

The interior angles of a triangle add to 180 degrees, so

∠A +∠B+ ∠C=180

We know that ∠A is 108, and ∠B is 38, so we can substitute them in

108+38+∠C=180

Combine like terms by adding 108 and 38

146+∠C=180

Subtract 146 from both sides

∠C=34

What 4 out 100 in percent

Answers

Answer:

4%

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

How much is 4 out of 100 written as a percentage? Convert fraction (ratio) 4 / 100

Colin rolls a fair dice and flips a fair coin.
What is the probability of obtaining a 3 and a tail?
Give your answer in its simplest form.

Answers

Final answer:

The probability of Colin getting a 3 on a die and a tail on a coin simultaneously is 1/12, obtained by multiplying the individual probabilities (1/6 for the die and 1/2 for the coin).

Explanation:

The probability of obtaining a 3 when rolling a fair dice is 1/6, since a dice has 6 sides and only one of them is a 3. Similarly, the probability of obtaining a tail when flipping a fair coin is 1/2, because a coin has 2 sides, heads and tails.

The probability of both events happening (rolling a 3 and flipping a tail) is the multiplication of their individual probabilities. Hence, the probability is 1/6 times 1/2 equals 1/12.

So, the final simplified form of the probability of Colin rolling a 3 on a die and flipping a tail on a coin, according to the rules of probability, is 1/12.

To find the probability of rolling a 3 and flipping a tail, we need to determine the probability of rolling a 3 on the dice and the probability of flipping a tail on the coin, and then multiply these probabilities together. A fair dice has 6 equally likely outcomes, so the probability of rolling a 3 is 1/6. Similarly, a fair coin has 2 equally likely outcomes, so the probability of flipping a tail is 1/2. Multiplying these probabilities gives us (1/6) * (1/2) = 1/12. Therefore, the probability of obtaining a 3 and a tail is 1/12 in its simplest form.

Learn more about Probability here:

https://brainly.com/question/32117953

#SPJ12

how do u solve quadratic equations

Answers

Answer:

[tex]\frac{ -b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Step-by-step explanation:

1) the equation listed above is the quadratic formula! you can solve ANY quadratic equation with it

quadratic equations in the form of:

ax^2+bx+c

just substitute a,b,and c for the numbers in the quadratic equation!

2)factoring:

my 2nd favorite method:

your equation will be in the form of:

ax^2+bx+c

where you need to find:

what*what=c

and

what+what=b

once you find those two things out then substitute those numbers in place of "b"

for example:

x^2+7x+10

factors of 10:  5,2  10,1   -2,-5   -10,-1

factors of 10 that=7

5,2

so

x^2+5x+2x+10

now group this equation:

group a) x^2+5x

group b) 2x+10

gcf of group a)  x

so

x(x+5)

group b) gcf:2

so

2(x+5)

combine the numbers outside the parantheses:

(x+2)(x+5)=0

x+2=0

x=-2

x+5=0

x=-5

hence x=-2,-5

hope this helps!

2.plz answer question with explanation

Answers

The answer is 4 because 2x10 = 20 so 5x4 = 20

The population of a town is increasing at a rate of 2.8% per year. In 2001 the town had a population of 34,229. Find the population of the town in 2013

Answers

Answer:

The population of the town in 2013 is 47,677. (to the nearest whole number)

Step-by-step explanation:

To calculate this, we will compare the increase to the increase of the present value of an amount of money invested in 2001, increasing at an annual percentage rate of 2.8%, to yield the future value worth a certain amount in 2013. To calculate, the formula below is used:

FV = [tex]PV ( 1 + \frac{i}{n}) ^{n*t}[/tex]

where:

FV = Future Value = ???

PV = present value = 34,229

i = interest in decimal = 2.8% = 0.028

n = frequency of compounding period per year = 1

t = number of compounding years = 2001 to 2013 = 12 years.

FV = [tex]34,229(1+\frac{0.028}{1} )^{(1*12)}[/tex]

FV = 34,229 × (1.028)¹²

FV = 47,677.29 = 47,677 (to the nearest whole number)

Please Help Me!! I can’t figure this out!!

Answers

Answer:

a=12 ft, b=12 ft

Step-by-step explanation:

-Length A and length B are equal since the right angle triangle is also an isosceles triangle.

-We use the Law of sines to calculate the two lengths:

[tex]\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{12\sqrt{2}}{Sin\ 90\textdegree}\\\\a=b=12\sqrt{2} \ Sin \ 45\textdegree\\\\a=b=12\ ft[/tex]

Hence, length a is equal to length b which is equal to 12 ft

What is the range of y = sin θ

A. [-1, 1]

B. [0, infinite]

C. all real numbers

D. 2pi

Answers

Answer:

A

Step-by-step explanation:

range is the possible y values

sin x and cos x parent graphs all have range from [-1, 1].

factors a, b, c, d affect the graph of asin(bx+c)+d

since a and b = 1 and c and d = 0, the range is default [-1,1]

What nationality were the terrorists that blew up the Alfred P. Murrah Federal
Building in Oklahoma City?
A.Sudanese
B.Saudi Arabian
C.Syrian
D.American

Answers

The answer is American

which number doesn't belong?
9 16 25
43

Answers

Answer:

43

Step-by-step explanation:

Square root of 9 is 3

Square root of 16 is 4

Square root of 25 is 5

Square root of 43 is not a whole number.

Answer:

43

Step-by-step explanation:

The first three numbers are perfect squares:

9 = 3²

16 = 4²

25 = 5²

43 is not a perfect square.

Find the unknown side length, x. Write your answer in simplest radical form.
A. 24
B. 4 √ 37
C. 2 √ 154
D. 5 √ 117
PLEASE HELP!!

Answers

Answer:

b

Step-by-step explanation: i just took the test and B. is the correct answer

Answer:

(B) 4/37 is correct

Step-by-step explanation:

I got it correct on edge

Fred sold half of his comic books and then bought 7 more. He now has
11. How many did he begin with ?

Answers

Answer:

8

Step-by-step explanation:

11-7=4

4x2=8

answer=8

He has 8 comic books before he sold any of his comic books.

Barbara has a bag that contains 8 blue coins and 2 red coins. She removes one coin at random, records the color, then places it back in the bag. She does this 50 times. She finds that P(blue) = 37/50. If Barbara does 100 trials of this experiment, how many blue coins could she expect to get?

Answers

Answer:

74

Step-by-step explanation:

37/50 * 100 = 74

Answer:

Step-by-step explanation:

Help due today pleas

Answers

Answer:

Cylinder A: 603.508

Cylinder B: 602.88

Step-by-step explanation:

Cylinder A:

V=[tex]\pi[/tex][tex]r^{2}[/tex]h

v=[tex]6.2^{2}[/tex]*5*3.14

V=38.44*5*3.14

V=192.2*3.14

V=603.508

Cylinder B:

V=[tex]\pi[/tex][tex]r^{2}[/tex]h

V=[tex]4^{2}[/tex]*12*3.14

V=16*12*3.14

V=192*3.14

V=602.88

Other Questions
Which shows one way to determine the factors of x + 11x2 3x 33 by grouping?O x2(x + 11) + 3(x 11)O x(x 11) 3(x 11)O x2(x + 11) + 3(x + 11)O x2(x + 11) 3(x + 11) Find the quotient.158152A)1516B)1510C)156D)154 What are the capitals of the two states that contain the word "north?" A Raleigh, Columbia B Pierre, Columbia C Raleigh, Bismarck D Bismarck, Pierre 9+___=101+____=10200+500+2000-3000 Vonda and Aleiyah are shopping together at the mall for new jeans. Vonda is willing to pay $90 and Aleiyah is willing to pay $50 for a pair of jeans. What is the gain in total consumer surplus when the price decreases from $59 to $40?a. $60b. $10c. $31d. $29 If you are writing a summary of a historical text about the Civil War, whichinformation should probably not be included?A. Your opinion about which side was rightB. The dates when the war began and endedC. The causes of the warD. The names of important generals Why are freshwater ecosystems such important resources? Mark all that apply Alison bought some shirts for herclothing store for $15 each. She received$50 off her entire purchase and spent a total of $440. How many shirts did Alison purchase for her store? How many population can make up a community How did cities address the problems caused by urban living? Technological innovations improved crowding. Residents organized neighborhood watch programs. Governments began to offer services such as mass transit and sanitation. City planners increased land dedicated to public use. THE TABLE SHOWS THE AGES OF THE SWIMMERS ON DION'S SWIM TEAM.THE MEAN AGE OF THE SWIMMERS IS 10.WHAT DOES THE MEAN REPRESENT Whats the answer for this ? Question 6In a box of 11 parts, 4 of the parts are defective. Two parts are selected at random without replacement.Find the probability that both parts are defective. Pre-Test: Chemical BondingWhich type of solid is likely to be the best conductor of electric current?O ionic compoundO covalent compoundO metal elementO nonmetal element FULL POINTS AND BRAINLIEST2.Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. 3.What does the slope of the line represent within the context of your graph? What does the y-intercept represent? What is the random mixing of gas molecules called?OA. DiffusionO B. VolumeO.C. TemperatureOD. Pressure As a result of complaints by the staff about noise, the coffee and recreation area for student interns at OHaganBooks will now be in a 512 square foot rectangular area in the headquarter's basement against the southern wall. (The specified area was arrived at in complex negotiations between the student intern representative and management.) The construction of the partition will cost $16 per foot for the north wall and $4 per foot for the east and west walls. What are the dimensions of the cheapest recreation area that can be made? In 1806, the antislavery forces brought a new bill before Parliament that would limit British involvement in the slave trade. Some of the most powerful testimony in favor of the bill came from former army officers who had been to the Caribbean and had seen the courage of the former slaves and the horrors of slavery. The slaves spoke through the testimony of the very men who had gone to fight them. One member of Parliament told his colleagues of the tortures he had seen in the islands. Slavery was not an abstraction, an economic force, a counter in the game of world politicsit was the suffering of men and women. Members of Parliament were being confronted with the reality of slavery, just as audiences at Clarkson's lectures were when he showed shackles and whips. While Parliament debated the new bill, Clarkson and his allies went on lecturing, talking, changing minds all across England. They succeeded. Newspapers reported that even in Bristol, a port city with a harbor filled with slave ships, "the popular sentiment has been very strongly expressed against the continuance of that traffick in human flesh." Sugar Changed the World, Marc Aronson and Marina Budhos How does this passage support the claim that the sugar trade led to the end of slavery in some parts of the world? It emphasizes that Parliament was biased toward plantation owners and wrongfully supported them. It shows that the French followed the example of the English in overthrowing the crown to free enslaved people. It describes how testimony on the brutal practices on sugar plantations convinced Parliament to end the slave trade. It demonstrates that neither Britain nor France wanted to make changes in the practice of slavery until America did. While performing online research on bacteria, Emilie found that some bacteria survive even in hydrothermal vents that can be traced back to early common ancestors. Which bacteria are these?A. hydrophilic bacteriaB. hydrophobic bacteriaC. thermophilic bacteriaD. thermophobic bacteriaE. lipolytic bacteria At December 31, 2020, Sager Co. had 1,200,000 shares of common stock outstanding. In addition, Sager had 450,000 shares of preferred stock which were convertible into 750,000 shares of common stock. During 2021, Sager paid$1,200,000 cash dividends on the common stock and $800,000 cash dividends on the preferred stock. Net income for 2021 was $6,800,000 and the income tax rate was 40%. The diluted earnings per share for 2021 is (rounded to the nearest penny) _______.