the sample space contains 5 as and 7 bs. what is the probability that a randomly selected set of 2 will in- clude 1 a and 1 b?

Answers

Answer 1

the probability that a randomly selected set of 2 will include 1 a and 1 b is 35/66

What is probability?

The probability is equal to the variety of possible outcomes. the total number of outcomes that could occur. For instance, there is only one way to get a head and there are a total of two possible outcomes, so the probability of flipping a coin and getting heads is 1 in 2. Writing P(heads) = 12

What are the 4 types of probability?

Classical

Empirical

Subjective.

Axiomatic

There are 66 equally likely outcomes, or C(5+7,2) =C(12,2)=66 possible outcomes. Only C(5,1)*C(7,1)=35 of these contain 1A and 1B. thus, the likelihood is 35/66.

The value of the solution is 35/66

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Related Questions

Last year, Pinwheel Industries introduced a new toy. It cost $2500 to develop the toy and S25 to manufacture each toy. Fill in the blanks below as appropriate.
A.) Give a linear equation in the form Cmn + b that gives the total cost, C, to produce n of these toys Preview
B.) The total cost to produce n 3000 toys is S
C.) With $32500, a total of toys can be produced.

Answers

Equation is C=25n + 2500 And The total cost to produce 3000 toys is $77,500 And With $32500, a total of 1200 toys can be produced

A linear equation is what, exactly?

An algebraic equation with only a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

A) Lets have linear equation y=mx+b,

C (total cost) = y and n (number of toys) =x.

The original development cost plus the production cost of each toy would equal the overall cost of creating n toys.

Because m is multiplied by n, the number of toys, the cost to produce a toy will equal m.

Due to the fact that b is a constant and its value is unaffected by the quantity of toys, it will always equal the development cost.

Therefore, C=25n + 2500

B) by above, equation put n=1750

C= 25(3000) + 2500

C= $77,500

C) Now, again by same equation, but C instead of n.

=> 32500= 25n +2500

=> 30000=25n

=> n = 1200

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How do you write as a percentage?
39
100

Answers

The percentage of 39/100 can be written as 39% as given in the question.

What is meant by percentage?

A percentage is a figure or ratio stated as a fraction of 100. The abbreviations "pct.", "pct," and "pct" are also used. A% is a dimensionless (pure) number with no unit of measurement.

The word "percent" comes from the Latin per centum, which means "hundred" or "by the hundredth." The symbol for "percent" emerged gradually from the Italian expression per cento. The "cento" symbol was developed from two circles divided by a horizontal line.

As money denominations expanded in the Middle Ages, computations with a denominator of 100 were increasingly prevalent, to the point where it became normal for mathematics texts to incorporate such computations from the late 15th to the early 16th centuries

We write 39/100 in the percentage as 39%

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a car is purchased for . each year it loses of its value. after how many years will the car be worth or less? (use the calculator provided if necessary.)

Answers

Answer: I calculated the value after 5 years to be 5,734.40 or 5,734

Step-by-step explanation:

3.9y^2+9.5y-8.2=0 solve using the quadratic formula

Answers

Solving the equation using quadratic formula the value of y in the quadratic equation is y= 0.675 or y= -3.11

Quadratic Equation

Mathematically, quadratic formula can be written as

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

from the expression, a= 3.9 , b=9.5, c= -8.2

substitute the value into the quadratic equation

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

y= [tex]\frac{-9.5^{} + or - \sqrt{9.5^{2}-4(3.9)(-8.2) } }{2(3.9)}[/tex]

y= [tex]\frac{-9.5^{} + or -\sqrt{90.25+127.92} }{7.8}[/tex]

y=  [tex]\frac{-9.5^{} + \sqrt{218.17} }{7.8}[/tex] or y= [tex]\frac{-9.5^{} - \sqrt{218.17} }{7.8}[/tex]

y =   [tex]\frac{-9.5 + {14.77} }{7.8}[/tex] or y= [tex]\frac{-9.5 - {14.77} }{7.8}[/tex]

y =   [tex]\frac{5.27}{7.8\\}[/tex] or  y= [tex]\frac{-24.27}{7.8}[/tex]

y= 0.67 or y= -3.11

Therefore the value of y in the quadratic equation is y= 0.67 or y= -3.11

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The edges of three squares are joined together to form a right triangle with legs of lengths r and s and a hypotenuse of length t . what must be true

Answers

For the triangle to be true, the square of the hypothenuse is equal to sum of the square of the leg and the sum of the angles is equal to 180 degrees

Pythagoras Theorem

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC² = AB² + AC2​². Here, ​​​​AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

In this case, for the triangle to be true,

1. The sum of square of two sides (s) and (r) must be equal to the square of t

t² = s² + r²

2. The sum of angles in the right angle triangle must be equal to 180 degrees

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A final exam in Math 160 has a mean of 73 with standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is greater than 78. A) 0.0103 B) 0.0008 C) 0.8962 D) 0.0036

Answers

The correct answer is b that is the probability that the mean of their test scores is greater than 78 is 0.0008.

What is Probability?

The field of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number that lies between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty. The probability is calculated on dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas where odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

mean, μ = 73
standard deviation σ =7.8

η = 24

P (X*=78)

P( Z>3.1403)

Hence, the probability that the mean of their test scores is greater than 78 is 0.0008.

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A machine is used to fill several bags each of 20-ounces of spicey
chips. After each bag is filled, another machine weighs them. If the
bag weighs .25 less or more than the desired weight, the bag is
rejected. Write an equation to represent the maximum weight for a
bag of chips that the machine will approve.

Answers

Answer: 19.75oz < x > 20.25oz

Step-by-step explanation: let x represent the weight of the bag of chips.

This equation states that the. weight must not exceed 20.25 but it must not be below 19.75oz.

Answer: 19.75oz < x > 20.25oz

Step-by-step explanation:

What is the equation in slope-intercept form of the line that passes through the point (8, - 7) and is parallel to the line represented by y = 6x + 2

A. Y=1/6x+55
B. Y=1/6x-55
C. Y=6x+55
D. Y=6x-55

Answers

Answer:

:Equation of line is[tex]y=1.2x+3.8[/tex]To find:The equation of line that passes through the point (5, 0) and parallel to the given line.

Step-by-step explanation:

t would be appropriate to use a distribution to simulate customer arrival times at a bank or restaurant. a. exponential b. normal c. poisson d. weibull e. uniform

Answers

t-distribution in the bank or restaurant to get the customer arrival time is a b) normal distribution.

The t-distribution is defined by degrees of freedom. These are related to sample size. The t distribution is most useful when the sample size is small, the population standard deviation is unknown, or both. As the sample size increases, the t-distribution will become more normal.

The t distribution is the continuous probability distribution of z scores when the estimated standard deviation is used in the denominator instead of the true standard deviation. The purpose of the t-test is to compare a specific characteristic that describes the groups, and the means will be representative of the populations that are normally distributed.

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the franchisee estimates that customers will not wait in line more than five minutes for a car wash. a longer time will cause robot to lose the gasoline sales as well as th car wash sale. if the estimate of customer arrivals is 10 per hour, which wash unit should be selected?

Answers

Using unit I, calculate the average waiting time of customers in the wash line (μ for unit I = 12 per unit).

For unit II at 15 per hour

if waiting time is the only criterion, unit II should be purchased. But before we make the final decision, we must look at the profit differential between both units.

With unit I, some customers would balk and renege because of the 5 minute wait. And, although this greatly complicates the mathematical analysis, we can gain some estimate of lost sales with unit I by increasing Wq = 5 minutes and solving for λ. This would be the effective arrival rate of customers.

Therefore, because the original estimate of λ was 10 per hour, an estimated 2 customers per hour will be lost.

Lost profit of 2 costumers per hour × 14 hours × 1/2 ($0.70 fill-up profit + $0.40 wash profit) = $15.40 per day.

Because the additional cost pf unit II over unit I is only $4 per day, the loss of $15.40 profit obviously warrants installing unit II.

The original five-minute maximum wait constraint is satisfied by unit II.

Therefore, unit III is not considered unless the arrival rate is expected to increase.

Given question is incomplete.

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is it possible for two quantities to (a) have the same units but different dimensions or (b) have the same dimensions but different units? explain.

Answers

If two quantities have same units, they will be comprised of the same basic physical quantities and hence their dimensions will be same. Same dimensions do not represent the same physical quantity. For example, The kinetic energy and the potential energy are measured in the same units but they possess different physical quantities.

What is dimensions?

The minimal set of coordinates required to specify any point within a mathematical space is known as the dimension of the space in physics and mathematics. As a result, a line has a dimension of one because a point on it can be specified by a single coordinate, such as the point at 5 on a number line.

Two quantities with the same units will be made up of the same fundamental physical quantities, resulting in identical dimensions. The same physical quantity does not have the same dimensions. For instance, although having different physical properties, kinetic energy and potential energy are measured in the same units.

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help me i actually cant figure this out :(

Answers

To complete the square of the quadratic function x² + 10x + 4 we need to add 21

Completing The Square

Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. In simple words, we can say that completing the square is a process where consider a quadratic equation of the ax² + bx + c = 0 and change it to write it in the form a(x + p)² + q = 0. This method is generally used to find the roots of a quadratic equation.

Completing the square formula is a technique or method to convert a quadratic polynomial or equation into a perfect square with some additional constant. A quadratic expression in variable x: ax² + bx + c, where a, b and c are any real numbers but a ≠ 0, can be converted into a perfect square with some additional constant by using completing the square formula or technique

The equation given is

x² + 10x + 4 = 0

Take 4 to right side

x² + 10x = -4

rewrite in (x + a)² = b form

(x + 5)² = 21

x + 5 = ±√21

x = √21 - 5

x = -√21 - 5

To complete the square, we need to add 21

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14.2: Prove Pythagoras Right 15 min
Elena is playing with the equivalent ratios she wrote in the warm-up. She rewrites
=as a² = xc. Diego notices and comments, "I got b2 = yc. The a² and remind me
of the Pythagorean Theorem." Elena says, "The Pythagorean Theorem says that
a² + b² = ².1 bet we could figure out how to show that."
a
h
1. How did Elena get from = to a² = xc?
2. What equivalent ratios of side lengths did Diego use to get b² = yc?

Answers

In the following passage we have proven the Pythagoras' theorem.

What is Pythagoras' theorem?

The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC2 = AB2 + AC2 in the triangle ABC signifies this. Base AB, height AC, and hypotenuse BC are all used in this equation. The longest side of a right-angled triangle is its hypotenuse, it should be emphasized.

Here given in the question that one side of the wall 5 feet

So as it is a rectangular bedroom it can be split into 2 right-angled triangles.

So the hypotenuse of the triangle is 13 feet

Now using the Pythagoras theorem we can find out the length of the other wall

b²=h²-p²

AB² + BC² = AD × AC + CD × AC

AB² + BC² = AC (AD + CD)

Since, AD + CD = AC

Therefore, AC² = AB² + BC²

So we have p² + b² = h².

Hence, we prove the Pythagoras theorem using two triangle.

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Please help ! Need to know what the answer is solve while using the Pythagorean theorem !

Answers

Answer:

y ≈ 16.12452

Step-by-step explanation:

Pythagorean theorem = a² + b² = c²

In this example, 14 = a, 8 = b, and y = c

14² = 196, 8² = 64

196 + 64 = 260 = y²

y² = [tex]\sqrt{260}[/tex] ≈ 16.12452

If (x-2)(x-4)= (x - h)² + k, then what is the value of k?

Answers

k = x^2 -6x + 8 - (x - h)^2

find the value of m n (4x-33) (3x+30)

Answers

Answer: 4(x + y) = 4x + 4y 2(3x + 4) = 2(3x) + 2(4) = 6x + 8

Step-by-step explanation:

x + 6 + 3x = 5x - 4

I need help because I don’t really know how to do this. This is for geometry

Answers

Answer: x = 10

Step-by-step explanation:

x + 6 + 3x = 5x - 4

First you want to group your like values together

6 +4 = 5x - 3x - x

Note that when any value crosses the = sign, The sign in front of it (+/-) changes. (e.g. -4 changes to +4 after it crosses the = sign)

Then work out your values

10 = x

Also note that x is the same as 1x. So you minus 3x from 5x to get 2x and 2x minus 1x is equal to 1x which is the same as x.

Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire house receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are between 4 and 6 minutes?
37.7%
44.3%
55.7%
62.3%

Answers

Step-by-step explanation:

55.7% of fire station response times are between 4 and 6 minutes. This can be calculated using the z-score formula, which is (x-μ)/σ, where x is the value of interest (in this case, 4 and 6 minutes), μ is the mean (4.5 minutes), and σ is the standard deviation (1.2 minutes). The z-score for 4 minutes is -0.42 and the z-score for 6 minutes is 0.42. Using a standard

Kadita counted 30 pigs and chickens on the farm. Jack counted a total of 68 legs for the animals. How many pigs were there on the farm?.

Answers

Kadita has 4 pigs and 26 chickens in on his farm.

Given, Kadita counted 30 pigs and chickens on the farm. Jack counted a total of 68 legs for the animals.

Let the number of pigs be, x

and the number of chickens be, y

x + y = 30

4x + 2y = 68

Now, we have to two equations,

x + y = 30

2x + y = 34

On subtracting both the equations, we get

x = 4

and y = 30 - 4

y = 26

So, Kadita has 4 pigs and 26 chickens in on his farm.

Hence, Kadita has 4 pigs and 26 chickens in on his farm.

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Which of these relations is a function?

Answers

By using the vertical line test we will see that the relation that is a function is the one in the top left graph.

Which of these relations is a function?

Here we ave the graphs of some relations, and we want to see which one of these represents a function.

To check that, we need to do the vertical line test.

The test says that if we draw a vertical line on the coordinate axis, and that line intercepts the graph of the relation more than one time, then the relation is not a function.

With that test we can see that the only relation that is a function is the one in the top left graph, is the only one that passes the vertical line test.

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The angles of a triangle add up to 180 degrees. The second angle is 6 degrees larger than the smallest angle. The third angle is 4 times as big as the smallest angle. Find the measure of the smallest angle (in degrees) degrees

Answers

Let the first angle be y
y+(y+6)+(yx4)=180
y+y+4y+6=180
6y+6=180
6y=174
y=29

The first angle is 29
The second angle is 35
The third angle is 116

Hope this helps

Use the slope formula to determine the slope of a line that passes through the points (-5,-3) and (9,-10)

Answers

Answer:

-1/2

Step-by-step explanation:

y2-y1/x2-x1

-10-(-3)/9-(-5)=-7/14=-1/2

In cell I5, insert the AVERAGEIFS function to calculate the average SAT score that meets two conditions: Scores in the range I11:I67 are greater than or equal to 3500 and Final Decisions in the range J11:J67 are Early Admissions (cell E3). Use mixed references appropriately.

Answers

The term in cell I5 will be for the AVERAGEIFS function:

AVERAGEIF( I11:I67 ,"<3500",J11:J67 ,"E3")

For the given question the termed   AVERAGEIFS  is the function formula in excel which returns the average of all the cells available in the sheet in a range that meets a given condition.the syntax for the term is  AVERAGEIF(range, criteria, [average_range]),  where the range is  Required like  One or more cells to get the average. Criteria os the basically the form of an expression, number, or cell reference, and at last the average range is optional it is just the set of cells to average.

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can someone help me really quick

(please Explain how you know this is correct)

Answers

If Mark’s package was 25 pounds, it would cost about $15 to ship. This is because there is a proportional relationship between cost and weight. As we know the weight, you can look at the line, look to the left where the cost is and see it would be between $10 and $20. As it is in the middle of those two options, your answer is $15

Answer:

$12.50

Step-by-step explanation:

Look at the graph down below \/

U can also mark where the pounds is so right at 25 pounds it would be about $12~

please solve this quadratic inequality:
x^2+10x+16>-5

Answers

Answer: x<-7 or x>-3

Step-by-step explanation: Tell me if its wrong ill fix it

answer:

x>-7, x>-3

step-by-step explanation:

- the first step would to be to add five to both sides: x^2+10x+21>0

- then you can solve be grouping which results in: (x+7)(x+3)>0

- the final answer will be: x>-7, x>-3

hope that helps!

What’s y=-3(x-1)2 squared +3 in factored form

Answers

Answer: y=−16.309691adqrsux+16.309691adqrsu+3

Let's solve for y.

y=((((((((−3(x−1))(2))(s))(q))(u))(a))(r))(2.718282))(d)+3

This is the best I could come up with


Amira is solving the equation x2 - 6x - 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

Answers

The answer is 9. You would use the equation b/2 squared. Hope this helped. Sorry if i am wrong

in 2006, 68.1 million people subscribed to cable television. in 2013, that number had decreased to 57.1 million. find the percent decrease in the number of cable tv subscribers from 2006 to 2013.

Answers

The percent decrease in the number of cable TV subscribers from 2006 to 2013 is 17.92%.

In the given question, in 2006, 68.1 million people subscribed to cable television. in 2013, that number had decreased to 57.1 million.

We have to find the percent decrease in the number of cable TV subscribers from 2006 to 2013.

The number of subscriber in 2006 is 68.1 million.

The number of subscriber in 2013 is 57.1 million.

Then the percent decrease in the number of cable tv subscribers from 2006 to 2013 is

Percent decrease in the number of cable TV subscribers = (subscriber in 2006 - subscriber in 2006)/subscriber in 2006 *100

Percent decrease in the number of cable TV subscribers = (61.4-50.4)/61.4 *100

Percent decrease in the number of cable TV subscribers = 11/61.4 *100

Percent decrease in the number of cable TV subscribers = 0.1792*100

Percent decrease in the number of cable TV subscribers = 17.92%

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A computer chess game and a human chess champion are evenly matched. They play fourteen games. Find probabilities for the following events.
(Round all answers to four decimal places.)
(a) They each win seven games. P =
(b) The human chess champion wins eleven games. P =
(c) The computer wins at least eleven games. P =

Answers

The probability that they each win six games is 0.225.  

Given : A computer chess game and a human chess champion are evenly matched. They play twelve games.

To find : The probability that they each win six games?

Applying binomial distribution,

Here n=12 and p=0.5

(a) They each win seven games. P =

[tex]P(X=k)=\frac{n !}{k !(n-k) !} \times p^k \times(1-p)^{n-k}[/tex]

The probability that they each win six games is k=6.

(b) The human chess champion wins eleven games. P =

[tex]\begin{aligned}& P(X=6)=\frac{12 !}{6 !(12-6) !} \times 0.5^6 \times(1-0.5)^{12-6} \\& P(X=6)=\frac{12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 !}{6 \times 5 \times 4 \times 3 \times 2 \times 6 !} \times 0.015625 \times 0.015625 \\& P(X=6)=11 \times 2 \times 3 \times 2 \times 7 \times 0.015625 \times 0.015625 \\& P(X=6)=0.225\end{aligned}[/tex]

(c) The computer wins at least eleven games. P =

Therefore, The probability that they each win six games is 0.225.

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5. A retail store selling soaps, lotions, and candles must ship products to each of their locations. Each shipping box must contain 40 items and weigh exactly 25 pounds (400 ounces) Each body spray weighs 8 ounces and each shower gel weighs 12 ounces. The graph shows a system of equations for this scenario where z is the number of body sprays and is the number of shower gels in one shipping package In parts a-d determine which point(s) best match each description

Answers

The solution of the system of equations is given as follows:

x = 20 -> 20 body sprays.y = 20 -> 20 shower gels.

How to obtain the amounts with the system of equations?


The variables of the system of equations are given as follows:

Variable x: number of body sprays in the box.Variable y: number of shower gels in the box.

Each shipping box must contain 40 items, hence:

x + y = 40.

The box weighs 400 ounces, hence, considering the weight of each item, we have that:

8x + 12y = 400.

From the first equation, we have that:

x = 40 - y.

Then the number of shower gels is obtained as follows:

8(40 - y) + 12y = 400

4y = 80

y = 80/4

y = 20.

The number of body sprays is of:

x = 40 - 20 = 20.

Missing Information

The problem is incomplete, hence we build and solve the equations, which will help you obtain the other information.

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when we maximize or minimize the value of a decision variable by running several simulations simultaneously, we have found an optimal solution to the problem and attitude toward risk becomes irrelevant. how does the description of benji's face in paragraph 81 help build tension? quiet town by jason gurley Which strategy is most helpful for drawing connections between ideas in an informational text? A. identifying the key idea in each paragraph B. researching the persons mentioned in the text C. verifying evidence used by the author D. making a prediction about the author which of the following can reduce the incentive of business partners to hold up a company when the company has made relationship-specific investments? a long-term relationship based on trust exists between the partners and the company. a high level of market power is held by the business partners. the greater the level of relationship-specific investments, the lower the incentive for the partners to hold-up. the more the company relies on the business partner, the lower the incentive for the partners to hold-up. Research shows that ____________ is positively linked with self-esteem and life satisfaction. r. davis, capital at the beginning of the year was $2,050. rob davis also withdrew $800 from the company during the year. what is the amount of total assets reported on the balance sheet? in 1978 californians passed proposition 13 that cut property taxes. this led to a severe drop in a major funding sources for k-12 public schools. what did proposition 98 (1988) mandate the state to do for securing money for k-12 schools and community colleges? how large is the states community college system Compare antibacterial spectrum of amoxicillin (Amoxil) to amoxicillin/clavulanate (Augmentin). Adding a beta-lactamase inhibitor, like clavulanate, increases coverage against:A. Gram negative and anaerobic pathogensB. Gram positive pathogensC. MRSA What is the circumference in terms of pi for a circle with a area 81? Louis Philippe was called the "Citizen King" because he:was born to a common family.dressed and acted like a middle class citizen.expanded voting rights.gave up his throne to marry for love. is it possible for a heat engine to operate without rejecting any waste heat to a low-temperature reservoir? explain. how many ways are there for eight men and five women to stand in a line so that no tow women stand right next to each other a nurse needs to administer a continuous medication drip to a client. the nurse knows that, for a continuous infusion, she will likely need to add medication to which volume of iv solution? Apply the ditributive property to factor out the greatet common factor. 60 40 y = The first time they exercised this was when they heard Marbury v. Madison, and the practice continues today. For this assignment, you will look at the Supreme Court's decision in Brown v. Board of Education.1) Research Brown v. Board of Education to find the arguments presented on both sides and the opinion on the Court.2) Do you believe the justices in this case were practicing judicial activism or judicial restraint? What evidence tells you this?3) Do you believe the justices in this case were mostly strict constructionists or broad constructionists? What evidence tells you this?4) If this case were heard today, would the current Supreme Court make the same decision? This is not an opinion question. Please make sure to find out information about our current Supreme Court justices when answering this question. in preparation, you identify all possible outcomes and the probability of each outcome. which approach to negotiation are you using? game theory individual differences cognitive approach situational characteristics Solve each inequality. Use the number line provided to test intervals.Thank you!! :) supplementary information (si) not necessary for the audited financial statements to be fairly presented is presented with those statements. an auditor engaged to report on the si has what responsibility for subsequent events related to si? what was the kaphars motivation in painting over the figures in the painting? group of answer choices to shift the audiences gaze to privilege the black experience to rewrite the constitution to erase history what is included in the role that commercial printing services play for contemporary artists when reproducing their work?