An individual is presented with three different glasses of cola, labeled C, D, and P. He is asked to taste all three and then list them in order of preference. Suppose the same cola has actually been put into all three glasses. What are the simple events in this ranking experiment? (Enter your answers as a comma-separated list.What probability would you assign to each one?A. It is impossible to determine the probability of the simple events with the given information.B. The probability of an individual event where D is ranked first is 1/12. The probability of another individual event is1/4.C. The probability of an individual event where D is ranked first is 1/5.The probability of another individual event is 1/15.D. All of the simple events have the same probability, 1/6.E. All of the simple events have the same probability, 1/3.

The statements that are true on the graph include:

At the point where the line hits x = 4, the y coordinates would be 0. This means that the point ( 4, 0 ) lies on the line. The point where the line crosses x = 0, y is the value of 4 which means that ( 0,  4 ) lies on the line.

The point ( - 8, 9 ) also lies on the line because as the line extends upwards, it would intersect the point ( - 8, 9 ).

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Shannon planted 6 - t trees.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

Shannon planted t fewer trees than toby.

Toby planted 6 trees.

Shannon planted.

= t - 6 trees.

Therefore, the result is 6 -t.

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Therefore , the solution of the given problem of linear equation comes out to be total amount collected is $4956.

The foundation for a linear regression curve is the equation y=mx+b. B is the slope, and m is the y-intercept. The previous sentence is sometimes referred as a "mathematical equation involving two variables," even though that y or y are separate components. Two variables make up bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b is the equation for a single set of equations.

Here,

Given :

Pupil : price per ticket is $8

teacher :  price per ticket is $20

Thus ,

Let the x be the total amount of teacher is :

So,

Pupil collected 416$ more than teachers total amount is :

Pupil total amount = 416 + x

So,

Total tickets sold is 1/4 of the ticket sold :

=> 1/4y * 20 = x

=> 5  = x/y

=>x = 5y

So,

=> 416 + 5y = 3/4 * 8 y

=> 416 + 5y = 6y

=> y = 516 tickets were sold

Thus ,

=> 1/4 * 516 =  129

=> 129 * 20 = 2580

For pupil is :

=> (516 -219) * 8

=> 2376

Total amount collected is => 2580 + 2376 = 4956

Therefore , the solution of the given problem of linear equation comes out to be total amount collected is $4956.

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To calculate the probability of arrival of ten customer in one hour at a service station then use of option a. Poisson probability distribution is more applicable.

Therefore, the required probability for the given situation is Poisson probability distribution .

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The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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Answer:

Area is 438 Square Feet

Perimeter is 298

Step-by-step explanation:

Area is 438 Square Feet

Area= L x W

438 = L x 3

438 divided by 3 = 146

L=146

Perimeter is 2 (L x W)

2 (146x3)

Perimeter is 298

On average Carmen earned $38.8 per week of profit and for 12 weeks the profit earned is $465.6.

What is average?

In everyday terms, an average is one number chosen to represent a list of numbers; it is often the sum of the numbers divided by the number of numbers in the list (the arithmetic mean).

The profit earned by Carmen in her first week = -$44.50

The profit earned by Carmen in her second week = -$26.25

The profit earned by Carmen in her third week = $80.50

The profit earned by Carmen in her fourth week = $88.75

The profit earned by Carmen in her fifth week = $95.50

The average profit earned by Carmen is = sum of profit earned / number of weeks profit earned

Substitute the values into the equation -

Average = [(-44.50) + (-26.25) + 80.50 + 88.75 + 95.50] / 5

Average = 194/5

Average = 38.8

The avearge profit per week is $38.8

To find the profit Earned by Carmen in 12 weeks use the arithmetic operation of multiplication -

Profit Earned = 12 × Average profit per week

Substitute the values in the equation -

Profit Earned = 12 × 38.8

Profit Earned = 465.6

Therefore, the profit earned is $465.6.

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Answer:465.6

Step-by-step explanation:

The number of days you will need to work in order to earn R3500,00 given the ratio of amount earned in 5 days is 20 days

If in 5 working days, you earn R87,500

Then, you will earn R350,000 in x working days

The task content can be solved using the concept of equivalent ratio;

Number of days : amount earned

5 : 87,500 = x : 350,000

5/87500 = x / 350,000

cross product

5 × 350,000 = x × 87500

1,750,000 = 87,500x

divide both sides by 87,500

x = 1,750,000 / 87,500

x = 20

Hence, you need to work for 20 days in order to earn R350,000

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Income normally uses a ratio scale of measurement.

Hence, option (a) is correct choice.

A ratio scale is a numerical scale with a genuine zero and equal gaps between adjacent points. A zero on a ratio scale, unlike an interval scale, indicates the complete absence of the variable being measured. Ratio scales include length, area, and population.

A ratio scale may be used to label variables, arrange them in order, and calculate the equal distance between variables. The ratio Scale enables unit conversion. British thermal units, such as Joules, kilograms, and grams, are ratio scale units.

As several elements of a given unit, interval scale may quantify size and magnitude. A ratio scale can be used to quantify size and magnitude by dividing one designated unit by another.

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Answer:

Q 1 : Solution:

Let the height of the building be h.

We know that tan(60) = h/9 (angle of elevation formula)

h = 9tan(60) = 9sqrt(3)/3 = 3*sqrt(3) = 3.464101615 m (approx)

Q 2 : Solution:

Let the height of the pole be h.

Let the shorter segment be x, and the longer segment be 9x.

We know that tan(theta) = x/(20) = 9x/(20+h) (angle subtended formula)

By cross multiplying and simplifying, we get:

x = (20h)/(h+180)

The ratio of the segments is x:9x = 1:9, so x = (20h)/(h+180) = 1/10 * h

h = 10x = (20h)/(h+180)

h^2 + 180h - 20h^2 = 0

h(20-h) = 0

h = 0 or h = 20

Since the pole has a height, h = 20m is not possible, so the height of the pole is h = 178.8m

Answer: y-int = (0,7)

x-int= (-7,0)

Step-by-step explanation:

-x+2y=7

2y=x+7

y-int = (0,7)

x-int= (-7,0)

on the graph, (1,4) (2, 4.5) (3, 5) etc

Are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python

It is a branch of mathematics that deals with the occurrence of a random event.

Given that In a large IT company,

75% of programmers are male while 36% know Python.

27% of the programmers are male and know Python.

We need to find the probability that he knows Python

P(M)=0.75

P(P)=0.36

P(MUP)=0.27

The probability that he knows Python is 0.36-0.27=0.09

Independent events are those events whose occurrence is not dependent on any other event.

Hence, are "being male" and "knowing Python" are independent events and 0.09 is the probability that he knows Python

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Answer: The shape of the distribution of the age of first heart attack in the US population who have had at least one heart attack is likely to be positively skewed, with the majority of cases occurring in older age groups and a relatively small number of cases occurring in younger age groups. The frequency of heart attacks generally increases with age, reaching a peak in the older age groups.

Step-by-step explanation:

Step-by-step explanation:

To find the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007, we need to add the two given polynomials.

The polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 would be:

negative -19x^2+ 181x + 14,420 + 866x^2 – 78x + 10,190

Simplifying, we get:

847x^2 + 103x + 24,610

So the polynomial for the total electricity generated by both geothermal and wind power during 2002-2007 is 847x^2 + 103x + 24,610.

The type of sampling used to judge the appeal of the television sitcom is a b) stratified sample.

A stratified sample is a type of sampling where the population is divided into subgroups or strata based on certain characteristics, and then a random sample is taken from each of these strata. In this case, the population is divided into three age categories and a random sample of 10 people is selected from each category.

Stratified sampling is useful when the characteristics of each stratum are different and you want to make sure that the sample accurately reflects the entire population. By dividing the population into age categories, this method ensures that the sample is representative of the different age groups and their opinions on the pilot show.

Overall, stratified sampling is a useful method for accurately estimating the characteristics of a population by taking into account any relevant differences within it.

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Answer:

B.80

Step-by-step explanation:

use of pythagoras theorem.

a^2 + b^2 = c^2

where c is hypotenuse

Answer:

D

Step-by-step explanation:

first we can see from question is finding perimeter which means first step we need is  

                       24+24=48

second , we can know it from picture

ABD=[tex]\frac{1}{2}[/tex] times 60= 30, which means it is 1/2 marks

P=DB/BA

which we see DB=BE

so 2 time DB( or BE)=18 which is 18

so we just need use 24+24+18=66

The farthest point from P is point U with a distance of 6.4 units

From the question, we have the following parameters that can be used in our computation:

P = (-1, 3)

To determine the farthest point, we make use of the distance formula represented as

distance = √[(y₂ - y₁)² + (x₂ - x₁)²]

So, we have

PR = √[(4 - 3)² + (2 + 1)²] = 3.2

PS = √[(1 - 3)² + (-4 + 1)²] = 3.6

PT = √[(5 - 3)² + (0 + 1)²] = 2.2

PU = √[(-2 - 3)² + (3 + 1)²] = 6.4

This means that the fartherst point is point U

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Answer:

below

Step-by-step explanation:

6x -6  = 8 x

-6 = 2x

x = -3

Answer:

X = -3

Step-by-step explanation:

Let's slowly create an equation

Six less than six times a number = eight times the number

if x = that number...

Six less than six times of x = eight times of x

6 less than 6 times of x is 6x-6

8 times x is simply 8x

So 6x - 6 = 8x

We can rearrange this equation by adding 6 to one side and subtracting 8x from the other

6x - 8x = 6

Combining like terms makes it -2x = 6

Last step is dividing by -2, giving us x = -3

The range includes all numbers from 0 to 12.5. So correct option is D.

Probability is a branch of mathematics that deals with the likelihood or chance of an event happening. It is a number between 0 and 1 that indicates the likelihood of an event occurring, with 0 meaning that an event is impossible and 1 meaning that an event is certain to occur.

Probability is used to model and make predictions about real-world situations such as the outcome of a coin flip, the results of a survey, or the success of a marketing campaign. It is also used in many fields including statistics, finance, engineering, and sciences to make decisions based on uncertain data.

Probabilities can be calculated using various methods, such as counting, Bayes' theorem, and simulation. In general, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

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The length of PX is 1.56.

The Pythagorean Theorem is a mathematical principle that relates the lengths of the sides of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

c² = a² + b²

The Pythagorean Theorem is one of the most famous and widely-used theorems in mathematics, and is a fundamental principle in geometry. It is used to find the length of one side of a right triangle when the lengths of the other two sides are known, and is also used to test whether a triangle is a right triangle.

Since YP is perpendicular to AB, we have right triangle APY with AP as hypotenuse and PY as the height.

Using the Pythagorean theorem, we can find the length of AP:

AP² = AY² + PY²

AP² = 4.7² + 1.4²

AP² = 22.09

AP = 4.7

Similarly, since ZP is perpendicular to BC, we have right triangle CPZ with CP as hypotenuse and PZ as the height.

Using the Pythagorean theorem, we can find the length of CP:

CP² = CZ² + PZ²

CP² = 3.2² + PZ²

CP² = 10.24

CP = 3.2

Since PX is perpendicular to AB, we have right triangle BPX with BP as hypotenuse and PX as the height.

Using the Pythagorean theorem, we can find the length of BP:

BP^2 = AP^2 + CP^2

BP^2 = 4.7^2 + 3.2^2

BP^2 = 26.69

BP = 5.15

Finally, using the Pythagorean theorem, we can find the length of PX:

PX^2 = BP^2 - PY^2

PX^2 = 5.15^2 - 1.4^2

PX^2 = 2.46

PX = 1.56

Therefore, the length of PX is 1.56.

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a) The Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b) The total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

a. Nash Equilibrium: A Nash Equilibrium is a set of strategies such that each player's strategy is a best response to the strategies of the other players.

In this game, each person i chooses their effort level x i to maximize their own payoff, which is the worth of the project divided by 2. Their individual payoff is given by:

pi = (2x1x2) / 2 = x1x2

By taking the derivative of pi with respect to xi and setting it to zero, we get the following first-order condition:

dpi/dx i = x2 - xi = 0

Since xi is in the range [0,1], we have xi = x2.

Thus, the Nash Equilibrium is when both players put in the same effort level x1 = x2 = x.

b. Total Payoff: The total payoff of the project is given by:

pt = x1x2 + x1x2 = 2x1x2

By factoring the total payoff function, we get:

pt = 2x1x2 = 2x1x1 = 2x12

So, the total payoff is a convex function of x1, which means that increasing x1 will always increase the total payoff.

Since the Nash Equilibrium is when both players put in the same effort level, there is no effort level that yields a higher total payoff than the Nash Equilibrium.

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(a) New value = 0.81 * Old value

(b) New value = 0.81 * $388,000 = $313,480.

Answer:30, 22, 44

Step-by-step explanation: 2x+x+(x+8) represents how many calls for each  evening. you simplify,

2x+x+(x+8)=4x+8

you know the total is equal to 96, so you do 4x+8=96.

x=22 calls for the SECOND evening. Next, you double and add 8 to get each evening.

Answer: A line parallel to the x-axis and at a distance of 7 units above the x-axis.

Answer:

66

Step-by-step explanation:

the difference of 54 and 32 is 54 - 32 = 22

the difference of 8 and 5 is 8 - 5 = 3

then

22 × 3 = 66

Max saves £5.50, which is 550p.

For every 50p Max saves, his mum gives him 20p, so for 550p, he gets 550/50 * 20p = 440p from his mum.

Altogether, Max has 550p + 440p = 990p, which is equivalent to £9.90.

The profit function is P ( x ) = 2x² + 5x - 12 and the number of months during which the company is not making a profit is x = 1.5 years = 18 months

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the profit function be represented as P ( x )

Let the cost function of the company be C ( x ) = 17 - 8x - 2x²

Let the revenue function of the company be R ( x ) = 5 - 3x

Now , Profit = Revenue - Costs

Substituting the values in the equation , we get

P ( x ) = R ( x ) = C ( x )

P ( x ) = 5 - 3x - ( 17 - 8x - 2x² )

On simplifying the equation , we get

P ( x ) = 2x² + 5x - 12

Now , when the profit of the company is 0

2x² + 5x - 12 = 0

On factorizing the equation , we get

2x² + 8x - 3x - 12 = 0

2x ( x + 4 ) - 3 ( x + 4 ) = 0

Taking the common factors of the equation , we get

( 2x - 3 ) ( x + 4 ) = 0

The value of x cannot be negative , so

2x - 3 = 0

Adding 3 on both sides of the equation , we get

2x = 3

Divide by 2 on both sides of the equation , we get

x = 3/2 years

Therefore , the number of months x = 18 months

Hence , the equation is solved

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