The numeric value of f(x) = x - 3 at x = 7 is given as follows:
f(7) = 4.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
f(x) = x - 3.
To obtain the numeric value of the function at x = 7, we replace the lone instance of x by 7, hence:
f(7) = 7 - 3 = 4.
Missing InformationThe function for this problem is defined as follows:
f(x) = x - 3.
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The sum of 2 numbers is 15. The difference between five times the first number and three times the second number is 19. Find the two numbers.
The numbers are 8 and 7.
Step by step explanation:[tex]\textbf{2 x 2 system of equations : }[/tex]
➭Approach
Let x and y be the numbers.
[tex] \bold{The \: sum \: of \: 2 \: n \acute{u}mers \: \: is \: 15 \: : \: } \: \bold{x + y = 15}[/tex]
[tex]\bold{x+y=15}[/tex] Equation 1[tex] \bold{The \: difference \: between \: five \: times \: the \: first \: number \: and \: three \: times \: the \: second \ : number \: is \: 19 \: : \: } \bold{5x - 3y = 19}[/tex]
[tex]\bold{5x-3y=19}[/tex] Equation 2Solution by substitution method
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{cases}{ \bold{x + y= 15 \qquad \cdots(1)}}\\{ \bold{5x - 3y = 19 \qquad \cdots( 2)}} \end{cases}\end{gathered} \end{gathered} \end{gathered} [/tex]
In essence, this method of solving consists of clearing an unknown in one of the equations and then substituting the found value in the other equation.
Because it is easier, I will start solving for x in equation 1.
[tex] \bold{x = 15 - y}[/tex]
Substitute [tex]\bold{x=15-y}[/tex] into equation 2.
[tex] \bold{5 \cdot15 - y- 3y = 19}[/tex]
We are left with an equation with only one unknown, we solve to find y.
[tex] \bold{75 - 5y- 3y = 19}[/tex]
[tex] \bold{ - 5y - 3y = 19 - 75} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{-8y= -56} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{y= \dfrac{ - 56}{ - 8}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \implies{y = 7}} \: \: \: \: \: \: \: [/tex]
We have found the value of y, to find the value of x we substitute the value of y into either of the two equations.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + y = 15} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + 7 = 15 }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 15 - 7}[/tex]
[tex]\bold{\implies \: x = 8}[/tex]
『 The attached graph is just to check our results 』
[tex]\therefore[/tex] The numbers are 8 and 7.
A parabolic tunnel has a width of 20 feet and a height of 12 feet at the center. Find the cross-sectional area of the parabolic tunnel.
A. Illustrate the parabolic tunnel. Show the measurements.
A parabolic tunnel has the shape of a parabola in cross-section, with one axis being symmetric (the width) and the other axis being the height at the center. To find the cross-sectional area of the parabolic tunnel, we can use the formula for the area of a parabola:
Area = (1/2) x Width x Height
Given that the width of the parabolic tunnel is 20 feet and the height at the center is 12 feet, we can substitute these values into the formula:
Area = (1/2) x 20 x 12 = 120 square feet.
So the cross-sectional area of the parabolic tunnel is 120 square feet.
consider a small ferry that can accommodate cars and buses. the toll for cars is $3 and the toll for buses is $10. let x and y denote the number of cars and buses, respectively, carried on a single trip. suppose the x and y are independent and have the following probability distributions:
The probability of the ferry carrying x cars and y buses is given by the joint probability distribution for x and y. The expected toll for this trip is 3x + 10y.
The probability of the ferry carrying x cars and y buses can be found using the joint probability distribution for x and y. This joint probability distribution is the product of the individual probability distributions for the number of cars and buses. The expected toll for this trip is 3x + 10y, which indicates that each car carries a toll of $3 and each bus carries a toll of $10. The joint probability distribution for x and y can be used to calculate the probability of the ferry carrying x cars and y buses. For example, if the probability of the ferry carrying 3 cars and 2 buses is 0.2 then the expected toll for this trip would be
3x + 10y = 3(3) + 10(2) = $36.
Thus, the joint probability distribution for x and y can be used to calculate the probability of the ferry carrying a given number of cars and buses, as well as the expected toll for this trip.
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a farmer has 1200 ft of fencing for enclosing a trapezoidal field along a river as shown. one of the parallel sides is three times longer than the other. no fencing is needed along the river. find the largest area the farmer can enclose.
The largest area that can be enclosed is 720000 m²
area = lw
where
l = length
w = width
The farmer wants to enclose a rectangular plot that borders a river. He is not fencing the side along the river. Therefore,
perimeter = l + 2w
l = 1200 - 2w
Therefore,
area = (1200 - 2w)w
(1200 - 2w)w = 0
w = 0 or 1200
average = 1200 / 2 = 600 meters
Hence, the max area is at w = 600 meters
Therefore,
l = 1200 - 2(600) = 0
length = 1200 meters
width = 600 meter
Therefore,
area = 1200 × 600 = 720000 m²
Therefore, the largest area that can be enclosed is 720000 m²
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A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is:
A. $10,250
B. $10,000
C. $9,000
D. $9,750.
A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is $10,250
What is meant by face value?A digit's face value is its actual value as part of a number. We multiply the digit value by the numerical value of a number to obtain its place value. For instance, since 5 is in the tens place and is present in the number 452, its place value is (5 10) = 50. A digit's face value is the actual number.The par value is the notional value of a share, bond, or other comparable security on the date of issuance. The terms "par value" and "face value" are frequently used interchangeably. A bond's face value, or the amount of principal the issuer is required to repay at the conclusion of the bond's term, is its par value.
Face value = $10,000×10/100×3/12 =$10,250
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A car Costs $30,000 in 2015. What would its price have been in 2020 dollars?
Show all work
The price of the car in 2020 dollars would be $31,620.
What is price?Price is the monetary value of a good or service that a customer is willing to pay for it. It is the result of a complex interaction between the forces of supply and demand, and is determined by the market conditions of a good or service. Price is also an important factor for companies as it is one of the primary elements used to generate revenue and profits.
In order to calculate the price of the car in 2020 dollars, we must use the Consumer Price Index (CPI). The CPI is a measure of inflation over time and is used to calculate the value of a product in the current year from its value in the past.
The CPI for 2020 is 250.6, while the CPI for 2015 is 237.9. This gives us a ratio of 250.6/237.9 = 1.054.
We can then use this ratio to calculate the value of the car in 2020 dollars:
30,000 x 1.054 = 31,620.
Therefore, the car would cost $31,620 in 2020 dollars.
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Given the vectors A =2.00 i^ +6.00 j^ and B =3.00 i^ −2.00 j^
. (a) Draw the vector sum C = A+ B and vector difference D = A − B . (b) Calculate C and D in terms of unit vector. (c) Calculate C and D in terms of polar coordinates with angles measured with respect to the positive x axis.
The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
(a) The vector sum C = A+ B is shown in the figure below, and the vector difference D = A − B is shown below that.
(b) C = (5i^ + 4j^) and D = (-1i^ + 8j^).
(c) The polar coordinates of C = (5, 53.13°) and D = (-1, 126.87°). To calculate these, I used the formulas for converting from Cartesian to polar coordinates, where r is the magnitude of the vector and θ is the angle with respect to the x-axis. The magnitude of C is √(5^2 + 4^2) = √41 = 6.4, and the angle is arctan(4/5) = 53.13°. The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
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has a normal distribution with mean 7.5 and standard deviation 2.5. for which of the following is the probability equal to 0 ?
Using the normal probability distribution, it is found that P(X = 8) is equal to zero.
In a normal distribution with mean and standard deviation, the z-score of a measure X is given by:
[tex]Z = \frac{X-mean }{S.D.}[/tex]
It measures how many standard deviations the measure is from the mean.After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.As in any continuous distribution, the probability of an exact value, that is, P(X = x), is 0.Hence, from the last bullet point, it is found that P(X = 8) is equal to zero.
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Pls help me explain this question
Step-by-step explanation:
this means that these 4 data ranges define 4 graphing charts with the given limits per coordinate axis.
the question is, which charts are large enough to show all data points of the defined process (50 ft uncoiled rope at time 0 is then coiled up 10 ft/sec., with the function graph showing the amount of still uncoiled rope over time in minutes).
the process will take 5 minutes (50 ft with 10 ft/min, so it will be completely coiled after 5 minutes) starting at 0 minutes.
the amount of uncoiled rope will go from 50 ft down to 0 ft.
so,
0 <= x <= 5 and 0 <= y <= 75 yes
0 to 5 minutes 0 to 50 ft all covered
0 <= x <= 10 and 0 <= y <= 50 yes
0 to 5 minutes 0 to 50 ft all covered
0 <= x <= 50 and 0 <= y <= 10 no
0 to 5 minutes covered 0 to 50 ft not covered
0 <= x <= 75 and 0 <= y <= 5 no
0 to 5 minutes covered 0 to 50 ft not covered
Find the volume of the rectangular prism.
Answer: V=LWH
Step-by-step explanation:
Please help me asap, it's missing :/
Answer: -31
Step-by-step explanation:
f(x)=x²+x-12
f(-5)=(-5)²+(-5)-12
=25-5-12
=25-17
=8
now, g(x)= -2x-15
=(-2)×(8)-15
= -16-15
= -31
(10^4)^2 in index form
Answer:(10^4) ^2=10^4•2=10^8=100000000
siete veces un número en expresión algebraica
In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.
What is the formula for algebraic expressions?An equation that includes constants, variables, and a few algebraic operations is said to be algebraic. A good example of an algebraic expression is 3x2 2xy + d. So, three different types of fundamental building blocks make up an algebraic expression: Coefficient (i.e. numbers) (i.e. numbers)
A seven-times-a-number is represented by multiplying it by seven or adding it to another integer (since this is an abbreviated successive addition ).
If x is any number, then it may be written as follows seven times: Algebraic expressions (numbers or letters) are linked by fundamental operations including addition, subtraction, multiplication, and division in mathematical language.
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Complete question -
Seven times a number in algebraic expression
N(t) = 25t + 150 for 0<=t<6, (200 + 80t)/(2 + 0.05t) for t>=8The number of fish in a pond at time t years is modeled by the function N defined above, where f is a continuous function such that f(0)=80.a) Find limt→[infinity]N(t). Explain the meaning of limt→[infinity]N(t) in the context of the problem.
a) limit→[infinity]N(t) = limit→[infinity](200 + 80t)/(2 + 0.05t) = 200.
What is a limit in plain English?
A limit in mathematics is a point at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend on limits, which are also used to determine integrals, derivatives, and continuity.
This means that as the number of years (t) approaches infinity, the number of fish in the pond (N(t)) approaches a limit of 200. In other words, as t gets larger and larger, the number of fish in the pond will get closer and closer to 200, but will never exceed 200. In the context of the problem, this means that the pond has a carrying capacity of 200 fish and that the population of fish in the pond will eventually stabilize at this level, regardless of the initial population.
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gathered a random sample of bags of potato chips from a popular company. she calculated data on different variables. for one of the variables that she collected, she constructed a
The correct option is (4) Flavor of potato chips. she uses Histogram to show the data collected from the sample of bags of Potato chips.
A histogram is a graphical representation of the distribution of a dataset, it shows how the data is spread out across different ranges of values. It is used to show the frequency of observations within each range of values, also known as a bin.
The bin is a range of values, and the height of each bar represents the number of observations within that range of values. The x-axis represents the range of values and the y-axis represents the frequency of observations.
When you construct a histogram, you will first need to decide on the number of bins to use and the range of values that each bin will cover. This is known as binning. It is important to choose the appropriate number of bins and range of values to effectively display the distribution of the data.
Question:
Anya gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one data that she collected, she constructed a circle graph. Which of the following variables did she use?
Price of bag of potato chipsNumber of chips in the bag of potato chipsWeight of bag of potato chipsFlavor of potato chipsTo know more about Histogram:
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I need help could someone figure out the two blank spots for me
The two numbers that correctly complete the chart based on the proportions are
How to calculate the new amounts of ingredients needed?This can be calculated by using the original recipe:
Batch 1:
This batch requires 1 blue paint rather than 1/2 or half, which shows you need to multiply by 2 the ingredients, based on this the correct number for the yellow paint is 1/2 as 1/4 x 2 = 1/2.
Batch 2:
This batch requires two yellow gallons rather than 1/4, which shows you should multiply the ingredients by 8. Based on this, the number for batch 2 is 4 as 0.5 or 1/2 x 8 = 4
Note: Below you can find the complete chart
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50 POINTS !!! Which are like terms in this expression?
−13n − 13 + 3/4n −1 3/4
A. − 13n and −13
B. − 13n and + 3/4n
C. − 13 and 3/4n
D. + 3/4n and − 1 3/4
Answer:B
Step-by-step explanation: They both have a variable.
Reason: Both involve the variable n.
Something like choice A is eliminated since -13n has n, but -13 does not. Choices C and D are eliminated for similar reasoning.
what is the z* critical value for constructing a 94% confidence interval for one proportion? this value is not listed on the t distribution table, so you will need to use this z-table to determine the value. round to 2 decimal places.
z-score for 94% confidence interval = 1.88
Confidence Interval:
The confidence interval indicates the level of confidence that the true parameter lies in the proposed range.
(a) What z-score is used for a 99% confidence interval to estimate a population proportion? Use 3 decimal places in your answer.
z-score for 99% confidence interval = 2.575
(b) What z-score is used for a 94% confidence interval? Round your answer to 2 decimal places.
z-score for 94% confidence interval = 1.88
(c) What z-score is used for a 93% confidence interval? Round your answer to 2 decimal places.
z-score for 93% confidence interval = 1.81
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Answer: 1.88
Step-by-step explanation:
e dg e 23
A teacher has a goal of displaying the names of 2 students selected at random from a group of 30 students in a classroom. Any possible pair of students should be equally likely to be selected. Which of the following algorithms can be used to accomplish the teacher's goal?
Answer:
Step-by-step explanation:
The teacher can use a random sample size number generator to select two numbers between 1 and 30. The numbers generated correspond to the indices of the list of student names, thus selecting two students at random. This ensures that any possible pair of students is equally likely to be selected.
1. Create a list of 30 student names.
2. Create a random number generator that generates two numbers between 1 and 30.
3. Use the random number generator to generate two numbers.
4. Use the two numbers generated to select two student names from the list using the numbers as indices.
5. Display the two student names selected.
The teacher's goal of randomly selecting two students from a group of 30 can be accomplished by using a random number generator. This generator can be used to generate two numbers between 1 and 30, which correspond to the indices of the list of student names. By selecting two numbers at random, the teacher is able to ensure that any possible pair of students is equally likely to be selected. This can be done by first creating a list of 30 student names and then using the random number generator to generate two numbers. The numbers generated can then be used to select two student names from the list using the numbers as indices. Finally, the two student names selected can be displayed.
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Use the table below to answer the question. True or false:
y
y is a function of
x
The given statement is False.
What is Function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is defined as a set of ordered pairs in which for each value of x there is only one corresponding value of y.
However, in this case, we have multiple x-values that correspond to the same y-value.
For example, x = 12 and x = 22 both correspond to y = 12. and y=22 Therefore, y is not a function of x.
Therefore, The given statement is False.
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1. (05.01 LC) Which data set could be represented by the boxplot shown? (1 point) boxplot with the minimum of 6, lower quartile value of 7, median of 9, upper quartile of 13, and maximum of 14. {6, 6, 8, 8, 9, 12, 13, 13, 14} {6, 6, 7, 9, 9, 12, 13, 14, 16} {6, 7, 8, 9, 10, 11, 12, 13, 14} {6, 7, 9, 9, 9, 12, 13, 14, 14}
A data set which could be represented by the boxplot shown include the following: A. {6, 6, 8, 8, 9, 12, 13, 13, 14}.
What is a box-and-whisker plot?In Mathematics, a boxplot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:
Minimum = 6.First quartile = 7.Median = 9.Third quartile = 13.Maximum = 14.By critically observing the box-and-whisker plots or boxplot (see attachment), we can logically deduce that it correctly represents this data set {6, 6, 8, 8, 9, 12, 13, 13, 14}.
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A sports reporter records the number of touchdowns scored each week during the football season. What statistical question could the reporter ask about the data?
Answer:
There are a lot of questions the reporter could ask.
Step-by-step explanation:
There are several statistical questions that a sports reporter could ask about the data on the number of touchdowns scored each week during the football season, depending on their focus and the information they want to gather. Some examples could be:
What is the mean number of touchdowns scored per week?
What is the median number of touchdowns scored per week?
What is the mode of number of touchdowns scored per week?
What is the range of the number of touchdowns scored per week?
What is the standard deviation of the number of touchdowns scored per week?
Is there a trend or pattern to the number of touchdowns scored per week?
Is there a difference in the number of touchdowns scored per week between home and away games?
What factors are associated with the number of touchdowns scored per week?
What is the probability of scoring a certain number of touchdowns per week?
Are the number of touchdowns scored per week follow a normal distribution?
These are just a few examples of the questions that a sports reporter could ask about the data. The specific question will depend on the goals of the analysis and what the reporter wants to convey to their audience.
Please really need help on these
Answer:
2. True
3. Maximum
4. [tex]2(m-9)^2[/tex]
Step-by-step explanation:
Question 2:
Yes, it is the vertex formula used to calculate the vertex of a quadratic funtion.
Question 3:
Since the first term of the equation has a negative coefficient, the parabola turns upside down, which opens down. Therefore the equation has a maximum.
Question 4:
[tex]2m^2-36m+162\\[/tex]
Find the GCF:
[tex]2(m^2-18m+81)[/tex]
Find the perfect square binomial:
[tex]81*1=81\\\\(-9*-9)\\\\-9*-9=81\\\\-9-9=-18[/tex]
Therefore this equation can be written as a perfect square binomial.
[tex]2(m-9)^2[/tex]
What length of 2-in. by 4-in. material will be required to make six bench legs each 28 1/4 in. long?
Material will be required to make six bench legs each 28 1/4 inch is 169.5 inches.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is Decimal?
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.
The simple solution is to convert 28 1/4 to a decimal and be cautious about converting it back to a fraction if necessary.
28 1/4=28.25
You need Six of them.
1 leg measures28.25 inches.
6 legs = x
Cross multiply 1/6 = 28.25 / x
x = 6* 28.25
x equals 169.5 inches
How many feet is that exactly? To calculate the amount of feet, divide by 169.5 /6=28.25 feet.
2 by 4s are typically 6 feet long. Unfortunately, you will need two of these for two more for 6 feet.
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Which input in this table is incorrect?
Which of the following is a correct interpretation of the expression
−
4
−
(
−
7
)
−4−(−7)minus, 4, minus, left parenthesis, minus, 7, right parenthesis?
A correct interpretation of the expression -4 - (-7) include the following: D. the number that is 7 to the right of -4 on the number line.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this context, the expression -4 - (-7) equals to 3 and it simply means that you would start at -4 on the number line and move 7 places to the right;
x = -4 - (-7)
x = -4 + 7
x = 3.
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help would be appreciated!
Complete the equation describing how
x and y are related.
0 1 2 3
4 5
y 0 1 2 3 4 5
y = [? ]x
Enter the answer that belongs in [?].
Answer:56
Step-by-step explanation:
How many terms does the following expression contain?
5yz^2-z-24y+77
According to the question, there are five terms in the expression 5yz^2-z-24y+77.
What is expression?Expression is the representation of an idea or feeling in a creative way. It is the manifestation of someone's thoughts, emotions, and desires through an artistic form. Expression can take on many forms including writing, music, painting, sculpting, and dancing. Expression allows us to communicate our innermost feelings and beliefs to the outside world. It can be used to reach out to those who may be feeling isolated, to inspire and empower others, or to simply bring joy to those who experience it. Expression is a unique way of conveying our ideas and is an important part of the human experience.
The first term is 5yz^2, the second term is -z, the third term is -24y, the fourth term is +77, and the fifth term is the constant 77.
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by evaluating first and second derivatives using differential calculus (and not a purely graphical solution), show that the molar entropy of mixing is maximized for a specific value for nne and determine this value as well as the corresponding maximized change in molar entropy upon mixing (in j/mol-k).
The molar entropy of mixing is given by the equation S_mix = R(x1lnx1+x2lnx2).
To maximize the molar entropy of mixing, we need to find the value of x1 and x2 that will produce the maximum value of S_mix. Differentiating S_mix with respect to x1 and x2 and setting the derivatives equal to 0 will yield the critical points. The critical points can then be tested to see which one produces the maximum value of S_mix. After differentiating, we get x1 = x2 = 1/2. This implies that the molar entropy of mixing is maximized when the mole fraction of each component is 0.5. The corresponding maximized change in molar entropy upon mixing is Rln2 which is equal to 2.30258509299405 j/mol-k.
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Question 7
Find the measure of each angle indicated
Answer:
<Q = 93
Step-by-step explanation:
The sum of the angles of a triangle is 180
<Q + <P + < R = 180
<Q + 51+36 = 180
<Q+87=180
<Q = 180-87
<Q = 93
