The length and breadth of a cuboid shaped paper are 1m and 60 cm respectively. If 1920 small cubes of 5 cm each can be placed in the box, find the height of box.

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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According to the question, there are five terms in the expression 5yz^2-z-24y+77.

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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In algebra, "seven times a number" is written as 7x, which is the multiplication of seven instances of the symbol x.

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

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

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?

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Answer:56

Step-by-step explanation:

Answer:(10^4) ^2=10^4•2=10^8=100000000

The price of the car in 2020 dollars would be $31,620.

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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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

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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The two numbers that correctly complete the chart based on the proportions are

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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Formulas A and B are not compared to the original formula, which makes this study poorly structured.

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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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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]

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]

Hence, from the last bullet point, it is found that P(X = 8) is equal to zero.

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The numbers are 8 and 7.

[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{The \: difference \: between \: five \: times \: the \: first \: number \: and \: three \: times \: the \: second \ : number \: is \: 19 \: : \: } \bold{5x - 3y = 19}[/tex]

Solution 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.

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



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.

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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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.

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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The sample size was not sufficiently large is the best reason why the simulation of the sampling distribution is not approximately normal.

What happens if a sample data is not big enough?

There are different variations in population size. When a sample size taken by a person or a researcher is not big or insufficient, or inadequate for the alpha level and also analyses that one have chosen to do, it will limit the study statistical power.

Due to the above, the ability to know a statistical effect in one's sample if the effect are present in the population is greatly reduces.

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It's not possible to know how much the retailer spent based on the information provided. The information provided only tells us how the retailer selected a sample of receipts from the past week by numbering all the receipts, generating 25 random numbers, and sampling the receipts that correspond to those numbers. In order to know how much the retailer spent, you would need more information such as the total amount of money spent on all the receipts and the amount of money spent on each receipt.

Answer: V=LWH

Step-by-step explanation:

The coordinates of the intersection of the diagonals of abcd with the given vertices are (0,2).

The equation of diagonal AC is the equation of the line joining

(−4,6) and (4,−2)

Using the two point formula of a line, we have

           (y−6) / (x+4) = 6−(−2) / (−4−4)

                       x + y = 2

The equation of diagonal BD is the equation of the line joining

(5,6) and (−5,−2)

Using the two point formula of a line, we have

           (y−6) / (x−5) = 6−(−2) /  5−(−5)

                           5y = 4x+10

Multiply equation x + y = 10 by 5 to get 5x+5y=10

Replace 5y=4x+46 using 5x+5y=10

        5x + (4x+10) = 10

        5x + 4x +1 0 = 10

           9x + 10 = 10

               9x=0

                 x=0

Substitute x=0 in eqn(1), To get 0+y=2

                                                         y=2

The point of intersection of the diagonals of the given quadrilateral is (0,2)

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This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

Random Digits Used: 0.9, 0.3, 0.3

Repetition 1:

Successful Attempt (1)

Repetition 2:

Successful Attempt (1)

Repetition 3:

Successful Attempt (1)

Estimated Probability: 3/3 = 1.0

In this experiment, the probability of successfully solving a puzzle was estimated. Three repetitions of the simulation were completed, each using different random digits. The first repetition used the random digit 0.9, the second used 0.3, and the third used 0.3 again. For each repetition, the outcome was successful, meaning the puzzle was solved. This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.

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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.

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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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 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

Face value = $10,000×10/100×3/12 =$10,250

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