i don’t know how to solve or die this please help

I Dont Know How To Solve Or Die This Please Help

Answers

Answer 1
My friend gonna help

Related Questions

Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the presence of indicator words, the nature of the inferential link between premises and conclusion, or the character or form of argumentation).
The graphical method for solving a system of equations is an approximation, since reading the point of intersection depends on the accuracy with which the lines are drawn and on the ability to interpret the coordinates of the point.
(Karl J. Smith and Patrick J. Boyle, Intermediate Algebrafor College Students)

Answers

An argument from definition is one in which the conclusion is determined by a single word or definition. As a result, the argument is deductive and definition-based.

Deductive arguments are those that are certain, whereas inductive arguments are those that are likely.

The argument is deductive if the arguer believes that the truth of the premises absolutely establishes the truth of the conclusion. The argument is inductive if the arguer believes that the truth of the premises provides only good reasons to believe the conclusion is probably true.

Endogenous means originating from within.

The conclusion (cholesterol is manufactured within the human body) follows logically from the premises (Cholesterol is endogenous with humans).

The conclusion is claimed here on the word endogenous.

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The complete question is:

Determine whether the following arguments are best interpreted as being inductive or deductive. Also state the criteria you use in reaching your decision (i.e., the presence of indicator words, the nature of the inferential link between premises and conclusion, or the character or form of argumentation).

Cholesterol is endogenous with humans. Therefore, it is manufactured inside the human body.

Right now, Miguel is 9 kilometers into a 36-kilometer race. He is running an average of 18 kilometers every hour.

Answers

Miguel finished the 36 km in 1 hour and 30 minutes.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

18 km = 1 hour

9 km = 30 minutes

Now,

Total distance = 36 km

Distance done by Miguel = 9 kilometers

So,

The distance remaining.

= 36 - 9

= 27

Now,

Time taken to run 27 km.

18 km = 1 hour

Multiply 27/18 on both sides.

27 km = 27/18 x 1 hour

27 km = 1.5 hour

Thus,

1 hour and 30 minutes.

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Complete question.

Right now, Miguel is 9 kilometers into a 36-kilometer race. He is running an average of 18 kilometers every hour.

After how many hours Miguel will finish the 36 km.

Dr. Lawrence attended meetings from 9:00 am to 11:45 am and from 2:15 pm to 4:45 pm. How many hours did he attend meetings? ( write the minutes as a fraction of an hour)

Answers

Answer:

4 and 11/12 hour

Step-by-step explanation:

11 hour 45 min - 9 hour = 2 hour 45 minute

4 hour 45 min - 2 hour 15 = 2 hour 30 minute

Total = (2 + 2 hour) + (45 + 30 min)

= 4 hour  55 min

= 4 and (55)/60) hour

= 4 and 11/12 hour

Calculate the magnitude of the resultant of the pair of 100km/h velocity vectors that are at right angles to each other?

Answers

The magnitude of the resultant of the two velocity vectors that are at right angles to each other is approximately 141.42 km/h.

we can use the Pythagorean theorem. According to the theorem, the magnitude of the resultant is equal to the square root of the sum of the squares of the magnitudes of the two vectors. we can write:

magnitude of the resultant = sqrt ((magnitude of vector 1) ^2 + (magnitude of vector 2) ^2)

magnitude of the resultant = sqrt ((100 km/h) ^2 + (100 km/h) ^2)

magnitude of the resultant = sqrt (2(100 km/h) ^2)

magnitude of the resultant = sqrt (2) * 100 km/h

Using a calculator, we can evaluate the square root of 2 to get:

magnitude of the resultant ≈ 141.42 km/h

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Tracey paid $180 for an item that was originally priced at $410. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places. Do NOT include a % symbol with your answer.

Answers

56.10 of the original price was paid.

What is a percentage?

The percentage means the required value out of 100.

It is calculated by dividing the required value by the total value and multiplying it by 100.

The percentage change is also calculated using the same method.

In percentage change, we find the difference between the values given.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

Original price = $410

Paid price = $180

Now,

The percentage of the original price paid.

= (Original price - Paid price) / Original price x 100

= (410 - 180) / 410 x 100

= 230/410 x 100
= 56.10%

Thus,

56.10 of the original price was paid.

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9.An online news article
posted this circle graph. If a total of six million
apps were downloaded, about how many of
each kind of app was downloaded?
Apps Downloaded
Social
Media
40%
Games
25%
Music
30%
Video
5%

Answers

The social media apps are 24,00,000  , games apps are 15,00,000 , music apps are 18,00,000 and video apps are 3,00,000.

How to calculate percentage of a number?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.

Given:

Total apps : six million

Social Media : 40%

Games : 25%

Music : 30%

Video : 5%

In order to find the number of apps of each category , we need to calculate each percentages . thus,

Social Media : 40%

Therefore , Social media apps = 40% of Six million = 0.4*60,00,000

Social media apps = 24,00,000

Similarly,

Games : 25%

Games apps = 25% of 60,00,000

Games apps = 15,00,000

Music : 30%

Music apps = 18,00,000

Video : 5%

video apps = 3,00,000

Hence , the social media apps are 24,00,000  , games apps are 15,00,000 , music apps are 18,00,000 and video apps are 3,00,000.

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the critical value of f for an upper tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is

Answers

The critical value of f for an upper-tail test at a 0.05 significance level is 2.94.

The critical value of F for an upper-tail test at a 0.05 significance level with a sample size of 21 for the sample with the smaller variance and a sample size of 9 for the sample with the larger variance can be found using an F-distribution table or calculator.

Using an F-distribution table or calculator with numerator degrees of freedom (df1) of 8 and denominator degrees of freedom (df2) of 20 (since df1 is for the sample with the larger variance and df2 is for the sample with the smaller variance), the critical value of F at the 0.05 significance level is approximately 2.94.

Therefore, the answer is a. 2.94.

The complete question is:-

The critical value of F for an upper-tail test at a 0.05 significance level when there is a sample size of 21 for the sample with the smaller variance and there is a sample size of 9 for the sample with the larger sample variance is _____. a. 2.94 b. 2.45 c. 2.10 d. 2.37

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Which of the following table represents a linear function?

Answers

Answer: The first one

Step-by-step explanation:

In the first one, x is increasing by a constant rate and y is decreasing by a constant rate which means that it is linear

Look at the image below to figure out the problem

I will give brainiest to the correct answer and giving 15 points away

Answers

Answer:

54 cups

Step-by-step explanation:

2/9=12/?

12/2=6

6*9=54

Suppose that you are conducting a survey of car owners and recording the number of cars each individual has owned in their lifetime. The mean number of cars is 6, and the standard deviation is 3. Larry has owned 15 cars in his lifetime.
Which of the following statements is true?
Select the correct answer below:
A. The number of cars Larry has owned is 3 standard deviations to the right of the mean.
B. The number of cars Larry has owned is 9 standard deviations to the right of the mean.
C. The number of cars Larry has owned is 3 standard deviations to the left of the mean.
D. The number of cars Larry has owned is 9 standard deviations to the left of the mean.

Answers

Larry's car ownership is three standard deviations above the mean. As a result, option A is the correct answer.

Consider the z-score formula, which tells us how many standard deviations a person's value is from the mean:

z = (x - μ) / σ

where x is the individual's value, is the mean, and is the standard deviation.

Plugging in the values from the problem yields:

z = (15 - 6) / 3 = 3

This indicates that Larry's car ownership is three standard deviations above the mean. As a result, option A is the correct answer. Option B is incorrect because it by a factor of three overestimates the number of standard deviations. Option C is incorrect because it implies Larry has had a negative number of cars, which is illogical. Option D is incorrect because it overestimates the number of standard deviations by a factor of 3.

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What are the zeroes of the polynomial function?

Answers

Answer: The zeroes of a polynomial function are the values of x!

Step-by-step explanation:

The zeroes of a polynomial function are the values of x at which the polynomial is equal to zero. The zeroes of a polynomial can be found by setting the polynomial equal to zero and solving for x. For example, if the polynomial is f(x) = x^2 + 3x – 4, then the zeroes are -4 and 1. This is because when x = -4, f(-4) = 0 and when x = 1, f(1) = 0.

Step-by-step explanation:

zeroes of a function are the values of x that create the functional value 0.

since we have been given just 4 answer options, we could play "trial and error" to find the right one.

or we could think a little bit.

F(x) = x³ - x² - 6x = x(x² - x - 6) = x(x - 3)(x + 2)

and so the zeros are all values of x that cause that expression to be 0. and that means any value of x that sets one of the factors to 0.

x = 0 is clear.

x = 3 (3 - 3 = 0)

and

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

are the other 2 zeros.

that means D is the right answer.

A rug 4 m wide and 5 m long costs $132. How much would a 3 m by 4 m rug of the same material cost?

Answers

Answer:

4m x 5m = 20 sq/m

$132 ÷ 20 sq/m = $6.60 per sq/m

3m x 4m = 12 sq/m

12 sq/m x $6.60 = $79.20

Samir operates an orange juice stand. On Monday he used 5 bags of oranges. On Tuesday he used 7/10 as many oranges as on Monday. How many bags of oranges did Samir use on Tuesday?

Answers

Samir, Juice operator used 7/2 bags of oranges on Tuesday.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Samir operates an orange juice stand. On Monday he used 5 bags of oranges.

So, The number of bags of oranges used on Tuesday can be determined by multiplying the number of bags by the fraction.

Therefore, On Tuesday he used 5×(7/10) = 7/2 bags of oranges on Tuesday.

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Write the rule for the linear function. Remember a function rule is written using f (x) x 7 5 -1 y 2 3 6

Answers

The rule for the linear function is f(x) = (-1/2)x + 11/2

What is an equation of the line?

An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.

To write the rule for the linear function, we can start by finding the slope of the line passing through the given points (x, y):

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Slope= (6 - 2) / (-1 - 7)

Slope= 4 / (-8)

Slope= -1/2

Therefore, the slope of the line passing through these points is -1/2.

Now, we can use the point-slope form of a linear equation to find the equation that represents this relationship:

y - y₁= m(x - x₁)

Where m is the slope and (x1, y1) is any point on the line. Let's use the point (7, 2):

y - 2 = (-1/2)(x - 7)

y - 2 = (-1/2)x + 7/2

y = (-1/2)x + 11/2

Therefore, the rule for the linear function is f(x) = (-1/2)x + 11/2

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Find the number of ways of arranging the elements of [n] in such a way that even and odd numbers must alternate.

Answers

The total number of arrangements in which the elements of [n] alternate between even and odd numbers are:

(n/2)! * (n/2)! if n is odd

(n/2)! * (n/2-1)!! if n is even

The initial number in the permutation must be odd if n is odd. There are n/2 ways to organize the odd numbers and n/2 ways to arrange the even numbers because there are (n/2)! odd numbers and n/2 even numbers. There is only one way to determine the sequence in which odd and even numbers occur because they must alternate. As a result, there are (n/2)!*(n/2)! viable permutations in total.

The number of odd and even numbers is equal if n is even. There are n/2 options for the initial number since we can choose any odd number to be the first number in the permutation. The second slot thus has options for (n/2 - 1) even numbers, the third position has options for (n/2 - 1) odd numbers, and so on.

Therefore, the total number of valid permutations is (n/2) * (n/2 - 1) * (n/2 - 1) * ... * 1, which can be written as (n/2)! * (n/2-1)!!.

Thus, the total number of arrangements in which the elements of [n] alternate between even and odd numbers are:

(n/2)! * (n/2)! if n is odd

(n/2)! * (n/2-1)!! if n is even

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Fourier Transform and its Inverse
Could anyone show me how to prove the following results about Fourier Transform, please? It is stated in my book without proof. Thank you.
Let F
denote the Fourier linear operator and f
be a L1(R)
function. Then
F2(f)=f(−x).
That is, if we apply the Fourier transform twice, we get a spatially reversed version of the function.

Answers

To prove that F2(f) = f(-x), we can use the definition of the Fourier Transform.

Which is,

F{f(t)} = ∫ f(t) e^(-jwt) dt

Using this definition, we can find the Fourier Transform of F{f(t)}:

F{F{f(t)}} = ∫ F{f(t)} e^(-jwt) dt

= ∫ (∫ f(u) e^(-jvu) du) e^(-jwt) dt

= ∫ f(u) (∫ e^(-jvu) e^(-jwt) dt) du

The inner integral can be simplified as follows:

∫ e^(-jvu) e^(-jwt) dt = ∫ e^(-j(uv+w)t) dt

= δ(vw+u)

where δ is the Dirac delta function. This integral evaluates to 1 when v*w+u=0 and 0 otherwise. Thus, we can simplify the expression for F{F{f(t)}}:

F{F{f(t)}} = ∫ f(u) δ(v*w+u) du

= f(-v) (using the property of the Dirac delta function)

Note that we have substituted v for -w to make the result more readable.

Therefore, we have shown that F{F{f(t)}} = f(-v). Since F2(f) = F{F{f(t)}}, we can conclude that F2(f) = f(-x), as required.

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2. A minor league baseball park has 7000 seats. Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2. When all seats are sold, the revenue is $26,400. If the number of box seats is one-third the number of bleacher seats, how many seats of each type are there? Give a complete sentence explaining what your answers mean.

a. Clearly define the variables in this problem:
x =
y=
z =

b. Write the equations for this problem.


c. Solve using the Gauss-Jordan method.

Answers

If a minor league baseball park has 7000 seats. Box seats cost $6, grandstand seats cost $4, and bleacher seats cost $2.  x = 400, y = 5400, z = 1200.

What is the equation?

The two equations are

x + y + z = 7000

6x + 4y +2z = 26400

Hence,

1/3z + y + z= 7000

4/3z+ y= 7000

y= 7000 - 4/3z

Substitution

6×1/3z + 4×(7000 - 4/3z) + 2z= 26400

Solving for z

2z + 4×7000 - 4×4/3z + 2 z= 26400

2z + 28000 - 16/3z + 2 z= 26400

2z - 16/3z + 2z= 26400 - 28000

-4/3z= -1600

z= (-1600)÷ (-4/3)

z= 1200

So,

x= 1/3z

x= 1/3×1200

x = 400

y= 7000 - 4/3z

y= 7000 - 4/3×1200

y= 5400

Therefore x = 400, y = 5400, z = 1200.

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uestion
Estimate √283 between two consecutive whole numbers.

Answers

Answer: The square root of 283 lies between the square roots of 256 and 324, which are 16 and 18, respectively. Therefore, an estimate for the square root of 283 is between 16 and 18, and we can round to the nearest whole number, which is 16.

Step-by-step explanation:

A
D
In parallelogram
m (2x +12)
5x°
B
C
ABCD, m Find the value of X
and of

Answers

Answer:

the value of x will be 24degree and angle D will be 120degree

The line plot shows the amount of time that Melissa spent last week exercising. What is the difference between the longest time and the shortest time Melissa spent exercising?

Please tell me how you got the answer thank you
i need a quick response

Answers

The difference between the longest time and the shortest time Melissa spent exercising (Range) is; 3/4 hours.

What is the range of the given set of data?

As evident from the task content; the difference between the longest time and the shortest time Melissa spent exercising, otherwise termed the range is to be determined.

By observation, the longest time = 1 hour while the shortest time = 1/4 hour.

Hence, the difference is; 1 - 1/4 = 3/4 hours.

On this note, the difference as required is; 3/4 hours.

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a coin that comes up heads with probability p is continually flipped until the pattern t, t, h appears. (that is, you stop flipping when the most recent flip lands heads, and the two immediately preceding it lands tails.) let x denote the number of flips made, and find e[x].

Answers

A coin that comes up heads with probability p is continually flipped until the pattern t, t, h appears, the expected number of flips needed to obtain the pattern "t, t, h" is 6/p.

We can approach this problem by using the concept of geometric distribution, which models the number of independent and identical Bernoulli trials (coin flips) needed to obtain the first success (in this case, the pattern "t, t, h").

Let X be the random variable representing the number of flips needed to obtain the pattern "t, t, h". The probability of obtaining "t, t, h" on any given three flips is (1-p)(1-p)p, and the probability of not obtaining this pattern on any given three flips is 1 - (1-p)(1-p)p.

Thus, X follows a geometric distribution with parameter p, and its probability mass function is given by:

P(X=k) = (1-p)(1-p)p^(k-3), for k=3, 4, 5, ...

The expected value of a geometric distribution with parameter p is given by 1/p. Therefore, the expected number of flips needed to obtain the pattern "t, t, h" is:

E[X] = 1/p + 2/p + 3/p = (1+2+3)/p = 6/p.

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Suppose the newspaper states that the probability of rain today is 25%. What is the probability of the complement? (Enter your answer to two decimal places.) Enter a number.​

Answers

Answer:

The probability of the complement (no rain) is 0.75 or 75%.

Step-by-step explanation:

The complement of an event A is the probability of A not occurring, which is equal to 1 - P(A).

Given that the probability of rain today is 25%, the probability of no rain (the complement of rain) is:

P(no rain) = 1 - P(rain)

P(no rain) = 1 - 0.25

P(no rain) = 0.75

Therefore, the probability of the complement (no rain) is 0.75 or 75%.

Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a graphing utility to confirm your results. an= 8n/ n +6 monotonic and not bounded not monotonic and not bounded O monotonic and bounded O not monotonic and bounded

Answers

To determine whether the sequence with the given nth term is monotonic and bounded, we can look at the first derivative of the function.

The nth term an = 8n/(n+6) can be rewritten as an = 8 - 48/(n+6).

Taking the first derivative, we get a'(n) = 48/(n+6)^2, which is always positive for n>0.

This means that the sequence is monotonic increasing.

To determine whether the sequence is bounded, we can take the limit as n approaches infinity.

lim n→∞ an = lim n→∞ 8n/(n+6) = 8

This means that the sequence is bounded above by 8, and since it is increasing, it is also bounded below by its first term a1 = 8/7.

Therefore, the sequence with the nth term an = 8n/(n+6) is monotonic and bounded.

To confirm our results, we can graph the function and see that it is indeed increasing and approaches 8 as n increases.

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What is the difference between sample statistics and population parameters called?

Answers

The difference between sample statistics and population parameter is called sampling error .

Sample statistics is the description in number or representation in number of the data measured by samples . The examples include mean , median , mode , average , percentiles etc .

Population parameter is also the description in number or representation in number of data about an entire population . The examples include population mean , population variance etc.

The sample statistics is calculated over data by say 100 regular customers whereas the population parameter is calculated by data over the specific target market . So , you can say that people of sample statistics are a subset of people of population parameter .

To understand better look at this example ,

By sample statistics , the mean Vitamin D level in sample of 100 men is 63nmol/L

Now by population parameter , the true mean Vitamin D level in all middle aged and older European men is 63nmol/L

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Wendy will have new carpet installed on her rectangular bedroom floor. The floor is 15 feet in length and 12 feet in width. The carpet costs $27.50 per square yard, and installation costs $4.15 per square yard. Which statement about the total cost of the carpet and installation is true?
a. The total cost is $379.80 since $31.65×12 = $379.80.

b. The total cost is $633.00 since $31.65×20 = $633.00.

c. The total cost is $474.75 since $31.65×15 = $474.75.

d. The total cost is $4,950.00 since $27.50×180 = $4,950.00

Answers

Since $31.65 x 20 = $633, the carpet's total cost includes both installation and delivery.

Describe a yard.

In both the British Imperial and US Customary Systems of Measurement, a yard is a unit of length. It corresponds to 3 feet or 36 inches. Yd is its emblem. Medium-sized object length is frequently measured using it.

How do you convert square yards to area feet?

To get the area value, multiply it by 9. To change the area from square feet to square yards, all you need to do is that. For instance, you must multiply 27 by 9 to convert 27 square feet to square yards.

Floor space is 15 x 12 ft², or 180 ft².

We know that 9ft² is 1 yard

So 180ft2 = 1/9*180 square yard

               = 20 square yard

Cost of 1 square yard = carpet cost + installation cost

                                  = $27.50 + $4.15

                                  = $31.65

Cost of 20 square yard = 20 * 31.65

                                    = $633

As a result, Wendy's room's carpet costs $633.

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Order angles from smallest to largest then the sides from smallest to largest in the triangle
SSS _,_,_
AAA _,_,_

Answers

The angles from smallest to largest are ∠A, ∠C, ∠B and the order of sides from smallest to largest is BC, AB, AC.

What is Triangle?

A triangle is a two dimensional figure which consist of three vertices, three edges and three angles.

Sum of the interior angles of a triangle is 180 degrees.

Given a triangle ABC.

The two angles of a triangle is given as 21° and 96°.

∠A = 21° and ∠B = 96°.

We have the fact that, the sum of the interior angles of a triangle is 180 degrees.

So, ∠A + ∠B + ∠C = 180°

21° + 96° + ∠C = 180°

∠C = 63°

The side opposite the smallest angle will be the smallest side.

So, the side opposite ∠A = 21° is BC, which is the smallest side.

The side opposite ∠C = 63° is AB , which is the second largest side.

The side opposite ∠B = 96° is AC, which is the largest side.

Hence the order of angles and side are ∠A, ∠C, ∠B and BC, AB, AC respectively.

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PLEASE HELP ASAP! Due soon !

Answers

The value of f(x) when x = -1 is 6.

The value of f(x) when x = 0 is 7.

The value of f(x) when x =9 is 10

The value of f(x) when x = 81 is 16

How to explain the function

A function simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The value of f(x) when x = 0 is:

= ✓0 + 7

= 7

.

The value of f(x) when x =9 is:

= ✓9 + 7

= 10

The value of f(x) when x = 81 is:

= ✓81 + 7

= 16

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6 Lola buys 2.5 meters of red fabric for $6.55 per meter. She buys 3.2 meters of
blue fabric for $5.25 per meter. How much money does she spend in all? 21
Round your answer to the nearest cent.

Show your work.

Answers

The total money she spent in all is $34.00(nearest cent)

What is word problem?

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math. If you've ever taken a math class, you've probably solved a word problem.

This word problem are interpreted into mathematical equation.

Lola bought 2.5 meters red for 6.55$ per yard

total for red = 2.5 × 6.55 = $16.4

She bought blue 3.2 meters for 5.25$

total for blue = 3.2 × 5.5 = $17.6

The total money spent = $17.6 + $16.4

= $34.00(nearest cent)

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Suppose a certain home improvements outlet knows that the monthly demand for framing studs is 2300 when the price is $0.99 each but that the demand is 3900 when the price is $0.67 each. Assuming that the demand function is linear, write its equation. Use p for price and q for quantity

Answers

Assuming that the demand function is linear, the equation will be

p + 0.0001q = 5.

Here are the steps to get to the final equation:

p = price and q = quantity,

Information is given in the question that,

When the price is $4.77, the demand is 2,300, and the price is 3,300, and the demand is also 3,300.

The generic equation for a line is now stated, using the points mentioned above as the line's points:

We get, 2,300 - q = -10,000(4.77 - p)

or

= 2,300 - q = -47700 + 10,000p

or

= 10,000p + q = 2300 + 47700

or

= 10,000p + q = 50000

or

= p + 0.0001q = 5

Thus the equation will be p + 0.0001q = 5.

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A total of N balls are put in two urns, so that initially urn A has i balls and urn B has N - i balls. At each step, one ball is chosen at random from the N balls If it is from urn A, it is moved to urn B, and vice versa. Let Xn be the number of balls in urn A after n steps. Show that {Xn, n > 0) is a DTMC, assuming that the successive random drawings of the balls are independent. Display the transition probability matrix of the DTMC.

Answers

We have shown that {Xn, n > 0) is a DTMC, assuming that the successive random drawings of the balls are independent by using the Memoryless property and Time-independent transition probabilities.

(1) Memoryless property:

Suppose we are at time n and know that Xn = i.

To determine the probability of moving to state j at time n+1, we only need to know the number of balls in urn A at time n and the number of balls that are drawn at time n+1.

The past history of the chain before time n is irrelevant. Therefore, the Markov chain has a memoryless property.

(2) Time-independent transition probabilities:

To calculate the transition probability from state i to state j, we need to consider the possible ways in which the number of balls in urn A can change from i to j. The transition probability from state i to state j is given by:

P(i,j) = P(Xn+1 = j | Xn = i) = P(Xn+1 = j | Xn = i, ball drawn from urn A) * P(ball drawn from urn A) + P(Xn+1 = j | Xn = i, ball drawn from urn B) * P(ball drawn from urn B)

= P(Xn+1 = j-1 | Xn = i, ball drawn from urn A) * (i/N) + P(Xn+1 = j+1 | Xn = i, ball drawn from urn B) * ((N-i)/N)

= (i-1)/(N-1) * (i/N) + (N-i-1)/(N-1) * ((N-i)/N)

= (i-1)(N-i)/N(N-1) + (N-i-1)i/N(N-1)

Therefore, the transition probability matrix is given by:

P = [P(i,j)] =

[(N-2)/N(N-1) 2/N(N-1) 0 0 ... 0]

[(N-3)/(N-1)(N-2) (N-1)/(N-1)(N-2) 2/N(N-2) 0 ... 0]

[0 (N-4)/(N-2)(N-3) (N-2)/(N-2)(N-3) 3/N(N-3) ... 0]

[0 0 (N-5)/(N-3)(N-4) (N-3)/(N-3)(N-4) ... 0]

[ ........................................... ]

[ 0 0 ... 0 2/N(N-1) (N-2)/N(N-1)]

Therefore, we have shown that {Xn, n > 0} is a DTMC with the transition probability matrix given by P.

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