Let Y1 and Y2 be independent and uniformly distributed over the interval (0, 1). Find
a the probability density function of U1 = min(Y1, Y2).
b E ( U 1 ) and V (U1).

Answers

Answer 1

The probability density function of U₁ = min(Y₁, Y₂) is f_U1(u) = 2u for 0 < u < 1.

To find the probability density function of U₁ = min(Y₁, Y₂), we can use the cumulative distribution function (CDF) of U₁.

The probability that U₁ is less than or equal to a value u can be expressed as

P(U₁ ≤ u) = P(min(Y₁, Y₂) ≤ u)

This is the same as the probability that both Y₁ and Y₂ are less than or equal to u, or that neither of them is greater than u. Since Y₁ and Y₂ are independent, this can be expressed as

P(U₁ ≤ u) = P(Y₁ ≤ u, Y₂ ≤ u) = P(Y₁ ≤ u) × P(Y₂ ≤ u)

Since Y₁ and Y₂ are uniformly distributed over the interval (0, 1), their probability density functions are both 1 for 0 < y < 1. Therefore, we have

P(U₁ ≤ u) = u × u = u^2

To find the probability density function of U₁, we can differentiate this expression with respect to u

f_U1(u) = d/dx P(U₁ ≤ u) = d/dx (u^2) = 2u

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The given question is incomplete, the complete question is:

Let Y₁ and Y₂ be independent and uniformly distributed over the interval (0, 1). Find the probability density function of U₁ = min(Y₁, Y₂).


Related Questions

Express the area of the region bounded by the given line(s) and/or curve(s) as an iterated double integral.
The coordinate axes and the line x + y = 4

Answers

The area of the region bounded by the line x + y = 4 and the coordinate axes is calculated to be 8/3 square units.

The region bounded by the line x + y = 4 and the coordinate axes is a right triangle with vertices at (0,0), (4,0), and (0,4). To express the area of this region as an iterated double integral, we can integrate over the rectangle R = [0,4] × [0,4] and subtract the integral over the triangle T = {(x,y) : x + y ≤ 4}.

Thus, the area of the region is given by the double integral:

A = ∬R dA - ∬T dA

Since dA = dxdy, we can evaluate this as:

A = ∫0⁴ ∫0⁴ dxdy - ∫0⁴ ∫0⁴-x+y dxdy

Simplifying this, we get:

A = ∫0⁴ ∫0⁴-x dydx

Evaluating the inner integral first, we get:

A = ∫0⁴ (-x)(4-x) dx

Integrating this, we obtain:

A = ∫0⁴ (-4x + x²) dx = [-2x^2 + (1/3)x³]0⁴ = 8/3

Therefore, the area of the region bounded by the line x + y = 4 and the coordinate axes is 8/3 square units.

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RS≅ST, m∠RST=7x - 54, m∠STU = 8x

Answers

Answer:

Step-by-step explanation:

find a formula for the general term an (not the partial sum) of the infinite series (starting with a1). 13 +19 + 127 +181 ⋯

Answers

The formula for the general term of the given series is:

[tex]a_n = 13 + (n-1)6^{(n-1)[/tex], n >= 1

This formula gives us the nth term of the series by adding 6 raised to the [tex](n-1)^{th[/tex] power to the first term 13.

How to  find a formula for the general term of the series?

To find a formula for the general term of the infinite series, we need to look for a pattern in the given terms.

Notice that if we add 6 to the first term 13, we get the second term 19. Similarly, if we add 6 to the second term 19, we get the third term 127.

And if we add 6 to the third term 127, we get the fourth term 181. So the difference between consecutive terms is not constant, but it seems to be increasing by a factor of 6 each time.

Let's check this by finding the difference between consecutive terms:

19 - 13 = 6

127 - 19 = 108

181 - 127 = 54

Indeed, the differences are 6, 6 times 18, and 6 times 9, which confirms that the pattern we observed holds.

So we can write the general term as follows:

[tex]a_n = 13 + (n-1)6^{(n-1)[/tex], n >= 1

This formula gives us the nth term of the series by adding 6 raised to the [tex](n-1)^{th[/tex] power to the first term 13.

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Sketch the graphs. 4x+3y=3

Answers

For sketching a graph we can give our own x-coordinate points and find the corresponding y-coordinate points.

What are x-coordinates and y-coordinates?

In the context of a coordinate system, the x-coordinate (also called the abscissa) is the horizontal distance from the origin to a point on the plane. The y-coordinate (also called the ordinate) is the vertical distance from the origin to the same point on the plane. Together, the x-coordinate and y-coordinate of a point on the plane define the point's position in the coordinate system.

Given equation is 4x+3y=3. For sketching the graph we can give our own x values and find the corresponding y-coordinates. This way we can find the points on the graph. For example, let x = 1, then

4(1) + 3y = 3

3y = 3 - 4 = -1

Hence the point will be (1,-1).

By continuing this process the graph in the image is formed.

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metal gallium is a liquid at room temperature. Its melting point is about 30°C. The freezing point of water is 0°C. How much warmer is the melting point of Gallium than the freezing point of water.​

Answers

Answer:

Step-by-step explanation:

30 degrees C

The melting point of gallium is about 30°C, while the freezing point of water is 0°C. To find out how much warmer the melting point of gallium is than the freezing point of water, we can subtract the freezing point of water from the melting point of gallium:

Melting point of gallium - Freezing point of water = 30°C - 0°C = 30°C

Therefore, the melting point of gallium is 30°C warmer than the freezing point of water.

Ahmed is modelling the area covered by a moss using the equation A = t² + 5.8t +
9.41 where A is the area covered in square centimeters, negative values of t represent
a number of days after noon on July 1, 2014. Which of the following equivalent
expressions contain the number of days before noon on July 1, 2014, as a constant or
coefficient, when the moss started with its smallest area of 1 square centimeter?
a.(t − (−2.9))² + 1
b. (t−(−1))² +3.8t +8.41
c.(t-(-3.9)) (t- (-1.9)) + 2
d. t(t− (−5.8)) + 9.41

Answers

Answer:

a.  (t - (-2.9))² + 1

Step-by-step explanation:

We are told that Ahmed is modelling the area covered by a moss using the equation A = t² + 5.8t + 9.41.

The given equation is a quadratic equation with a positive leading coefficient. Therefore, the graph is a parabola that opens upwards. This means that the vertex is its lowest point.

The vertex form of a quadratic equation is:

[tex]\boxed{y = (x - h)^2 + k}[/tex]

where (h, k) is the vertex.

As the vertex is the lowest point, this means that the y-value of the vertex is when the area of moss is at its lowest. We are told that the smallest area of the moss is 1 square centimeter, so k = 1.

The x-value of the vertex can be found by using the formula:

[tex]h=-\dfrac{b}{2a}[/tex]

for a quadratic in the form ax² + bx + c.

For the given quadratic, a = 1, b = 5.8 and c = 9.41.

Substitute the values of a and b into the formula to find the x-value of the vertex:

[tex]\implies h=-\dfrac{5.8}{2(1)}=-2.9[/tex]

Finally, substitute h = -2.9 and k = 1 into the vertex form:

[tex]A=(t-(-2.9))^2+1[/tex]

Therefore, the equivalent expression that contains the number of days before noon on July 1, 2014, as a constant or coefficient, when the moss started with its smallest area of 1 square centimeter is:

(t - (-2.9))² + 1

Let X be a discrete random variable with probability mass function given byP(x)={c/4 x=0{c/4 x=1{c x=2{0 otherwiseFind the value of that makes p a valid probability mass function.

Answers

In order for a probability mass function (PMF) to be valid, it must satisfy two conditions:

Condition 1- Non-negativity:

c/4, c/4 and c are all non-negative values.

Condition 2- Sum of PMF equals 1:

The sum of the PMF over all possible values of x must be equal to 1.

P(0) + P(1) + P(2) + P(x) for all other x

= c/4 + c/4 + c + 0 (since P(x) = 0 for all other x)

= (c + c + 4c)/4

= 6c/4

In order for this sum to be equal to 1, we must have:

6c/4 = 1

Multiplying both sides by 4/6 to solve for c:

c = 4/6

c = 2/3

So, the value of c that makes P(x) a valid probability mass function is c = 2/3.

To find the value of c that makes P a valid probability mass function, we need to ensure that the sum of all probabilities equals 1.

We can do this by summing the probabilities for all possible values of X:

P(0) + P(1) + P(2) = c/4 + c/4 + c = 1

Simplifying the equation:

c/2 + c = 1

3c/2 = 1

c = 2/3

Therefore, the value of c that makes P a valid probability mass function is 2/3.
To find the value of c that makes P(x) a valid probability mass function, we need to ensure that the sum of probabilities for all possible values of x is equal to 1. Given the probability mass function:

P(x) = {c/4, x=0;
         c/4, x=1;
         c, x=2;
         0, otherwise}

The sum of probabilities for all x values should be:

P(x=0) + P(x=1) + P(x=2) = 1

Substituting the given values:

(c/4) + (c/4) + c = 1

Now, we solve for c:

c/4 + c/4 + c = 1
(2c/4) + c = 1
(1/2)c + c = 1
(3/2)c = 1

To find the value of c:

c = 1 / (3/2)
c = 1 * (2/3)
c = 2/3

So the value of c that makes P(x) a valid probability mass function is 2/3.

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5. Tony measured a TV that is approximately 14 inches tall by 24 inches wide. Since the size of TVs are named by the measure of the diagonal, what is the BEST diagonal measure, in inches, for this TV?

A. 772 inches
B. 28 inches
C. 76 inches
D. 9 inches

Answers

Use the pythagorean theorem.

a^2 + b^2 = c^2

Plugging the values into that…

14^2 + 24^2 = 772

sqrt772=27.78… which means B is the correct answer.

Answer:

Using this formula, we can calculate the diagonal measure of the TV as follows: (this is the Phytagoras theorem)

diagonal^2 = height^2 + width^2

diagonal^2 = 14^2 + 24^2

diagonal^2 = 196 + 576

diagonal^2 = 772

diagonal ≈ 27.8 inches

Therefore, this TV's best diagonal measure, in inches, is option B, 28 inches (rounded to the nearest inch).

3.56 the joint density function of the random variables x and y is f(x, y) = 6x, 0 0.3 | y = 0.5).

Answers

It is not possible to find P(y = 0.5) using the given joint density function f(x, y) = 6x, as the value y = 0.5 is outside the defined range for y (0 ≤ y ≤ 0.3).

How to find  find P(y = 0.5)  joint density function of random variables x and y?

Given the joint density function f(x, y) = 6x for 0 ≤ x ≤ 1 and 0 ≤ y ≤ 0.3, you want to find P(y = 0.5). Let's break this down step by step:

1. Understand the problem: We are given the joint density function f(x, y) = 6x with the domain 0 ≤ x ≤ 1 and 0 ≤ y ≤ 0.3. We need to find the probability P(y = 0.5).

2. Identify the issue: Since the joint density function is only defined for y values within the range of 0 ≤ y ≤ 0.3, it is not possible to find P(y = 0.5) using this function, as y = 0.5 is outside the given range.

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15% of the students in the library are girls. If there are 60 total students in the library, how many are girls?

Answers

Answer:

9 girls

Step-by-step explanation:

15% x 60 = 9

Answer: 15% of 60 is 9.

Step-by-step explanation:

15% of 60 can be written as 15% × 60

= 15/100 × 60

= 9

Find the volume of the solid whose base is the region bounded between the curve y=x² and the x-axis from x=0 to x=2 and whose cross sections taken perpendicular to the x-axis are squares.

Answers

Sure! To find the volume of the solid whose base is the region bounded by the curve y = x^2 and the x-axis from x = 0 to x = 2 and whose cross sections taken perpendicular to the x-axis are squares, we can use the following integral:

V = ∫[0,2] (x^4) dx

This is because each square cross section has an area of (side length)^2, and since each side length is equal to the height of the function (which is x^2), the area of each square is (x^2)^2 = x^4.

Evaluating this integral, we get:

V = [(1/5) x^5] from 0 to 2
V = (1/5) (2^5 - 0)
V = (1/5) (32) = 6.4

Therefore, the volume of the solid in question is 6.4 cubic units.

On Your Own
1) A sphere has a radius of 7 cm. What is the volume?
round your answer to the
nearest cubic centimeter.
Like example 1
4
2) A sphere has a volume of 72π in³. What is the radius?
round to the nearest tenth
of an inch.
Like example 3

Answers

hope this helps you

Use for Problems 6-9: A large supermarket stocks both national brands of coffee and its own house brand. Consider a single randomly selected customer purchasing coffee and let success = the customer purchases a national brand. Assume that p = 0.75 and that customers make coffee purchase decisions independently of one another. Use R to calculate the probabilities. 6. Let X = number of coffee purchasers who select a national brand from the 10 randomly selected customers purchasing coffee. a. Which distribution should we use? b. Find the probability exactly 4 of the 10 will purchase a national brand from the 10 randomly selected customers purchasing coffee. (answer to 4 decimal places) Insert your code here: Answer: C. Find the probability that at most 7 will purchase a national brand from the 10 randomly selected customers purchasing coffee. (answer to 4 decimal places) 

Answers

A. We should use the binomial distribution since we are interested in the number of successes (customers who purchase a national brand) out of a fixed number of trials (10 customers).

b. To find the probability exactly 4 of the 10 customers will purchase a national brand, we can use the dbinom function in R:

dbinom(4, 10, 0.75)

The answer is 0.2503 (to 4 decimal places).

c. To find the probability that at most 7 customers will purchase a national brand, we can use the pbinom function in R:

pbinom(7, 10, 0.75)

The answer is 0.9831 (to 4 decimal places).

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The value of a certain investment over time is given in the table below. Answer the
questions below to determine what kind of function would best fit the data, linear or
exponential.
Number of
Years Since
Investment
Made, x
Value of
Investment
(8), f(x)
11.486.36
9,181.76
values change
function is approximately
3
6,890.96
4.581.76
function would best fit the data because as x increases, the y
The
of this

Answers

The slope of this function is approximately 4518

How to solve

A linear function would best fit the data because as x increases, the y values ​​change values by 4518.

y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

the linear function would best fit the data because as x increases, the y values ​​change values by 4518.

The slope of this  function is approximately 4518

Slope = change in y values /  change in x values

        =( 27520.99-23002.99)/(2-1)

        = 4518/1

       = 4518

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help!!!
see pic below⬇

Answers

Answer:

10:00 am > 0 (initial time) > 24 gallons10:30 > 30 minutes > 40 gallons 11:00 am > 1 hour (from initial time) > 56 gallons

Step-by-step explanation: every 30 minutes we add 16 to the level

Answer:for 10:am youd put "started" or "0" for time and "24 gallons of water" at 10:30am put "30 minutes" for time because from 10 to 10:30 is 30 minutes. For amount of water put 40 gallons. For the last one put the tine as "1:00pm". Put the time spent as "2 hours and 30 min" and gallons of water put 120

Help me guys please i know you are smart

Answers

Answer:

B.

Step-by-step explanation:

32, 38, 39, 40, 41, 44, 46, 47

Those are all the ages of the older than 30, but younger than 50.

Problems 11 through 23 and Case Problem 2 require the use of data mining software. If using R/Rattle to solve these problems, refer to Appendix: R/Rattle Settings to Solve Chapter 5 Problems. If using JMP Pro to solve these problems, refer to Appendix: JMP Pro Settings to Solve Chapter 5 Problems.
Association Rules of Browser Histories. Cookie Monster Inc. is a company that specializes in the development of software that tracks web browsing history of individuals. Cookie Monster Inc. is interested in analyzing its data to gain insight on the online behavior of individuals. A sample of browser histories is provided in the files CookieMonsterBinary and CookieMonsterStacked that indicate which websites were visited by which customers. Use a minimum support of 4% of the transactions (800 of the 20,000 total transactions) and a minimum confidence of 50% to generate a list of association rules.
a. Based on the top 14 rules, which three web sites appear in the association rules with the largest lift ratio?
b. Identify the association rule with the largest lift ratio that also has Pinterest as the antecedent. What is the consequent web site in this rule?
c. Interpret the confidence of the rule from part (b). While the antecedent and consequent are not necessarily chronological, what does this rule suggest?
d. Identify the association rule with the largest lift ratio that also has TheEveryGirl as the antecedent. What is the consequent web site in this rule?
e. Interpret the lift ratio of the rule from part (d).

Answers

The lift ratio indicates a strong association between the two websites.

Association rule mining is a data mining technique used to find patterns in datasets. It is particularly useful for finding relationships between variables in large datasets. In this case, the dataset consists of browser histories, and we are interested in finding association rules between the websites that were visited.

The two main measures used in association rule mining are support and confidence. Support is the proportion of transactions that contain both the antecedent and the consequent of a rule, while confidence is the proportion of transactions containing the antecedent that also contain the consequent. Lift ratio is another measure used to evaluate the strength of an association rule. It is the ratio of the observed support to the expected support, assuming the antecedent and the consequent are independent.

To generate a list of association rules, we can use an algorithm like Apriori. The Apriori algorithm starts by finding frequent itemsets, or sets of items that occur together in a sufficient number of transactions. We can then use these frequent itemsets to generate association rules by dividing them into antecedents and consequents and calculating the support and confidence of each rule.

Based on the top 14 rules, we can identify the three web sites that appear in the association rules with the largest lift ratio. Lift ratio is a measure of how much more often the antecedent and consequent appear together than would be expected if they were independent. Therefore, high lift ratios indicate strong associations between the antecedent and consequent. We can sort the rules by lift ratio and identify the three web sites that appear in the rules with the highest lift ratios.

To identify the association rule with the largest lift ratio that also has a specific antecedent, we can filter the rules by the antecedent and sort them by lift ratio. We can then examine the consequent of the rule with the highest lift ratio.

The confidence of a rule indicates how often the consequent is observed in transactions containing the antecedent. In this case, the rule suggests that there is a high probability that customers who visit Pinterest also visit the consequent website. While the antecedent and consequent are not necessarily chronological, the rule suggests that there may be a relationship between the two websites that prompts customers to visit them together.

The lift ratio of a rule indicates the strength of the association between the antecedent and consequent. In this case, the rule suggests that customers who visit TheEveryGirl are much more likely to also visit the consequent website than would be expected if the two websites were independent. Therefore, the lift ratio indicates a strong association between the two websites.

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If f(x) = 2x2 – 3x + 5, find f'(o). Use this to find the equation of the tangent line to the parabola y = 2x2 – 3x + 5 at the point (0,5). The equation of this tangent line can be written in the form y = mx + b where m is: and where b is:

Answers

The equation of the tangent line is:
y = -3x + 5

To find f'(x), we need to take the derivative of f(x) with respect to x. Given f(x) = 2x^2 - 3x + 5, the derivative f'(x) is:

f'(x) = 4x - 3

Now, we need to find f'(0):

f'(0) = 4(0) - 3 = -3

So the slope (m) of the tangent line at point (0, 5) is -3. Since the tangent line touches the parabola at (0, 5), we can use this point to find the equation of the tangent line:

y = mx + b

Substitute the point (0, 5) and the slope m = -3:

5 = -3(0) + b

5 = b

Thus, the equation of the tangent line is:

y = -3x + 5

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find the limit. lim n→[infinity] n 9 n i n 3 1 i=1

Answers

The limit [tex]\lim_{n \to \infty} n(\sum_{i=1}^{n} 9ni^3)[/tex] is equal to ∞.

To find the limit of the given expression, [tex]\lim_{n \to \infty} n(\sum_{i=1}^{n} 9ni^3)[/tex], as n approaches infinity, please follow these steps:

1. Identify the summation notation:

[tex]\sum_{i=1}^{n} 9ni^3[/tex]


2. Calculate the sum using the formula for the sum of cubes:

[tex]\sum_{i=1}^{n} i^3 = (n(n+1)/2)^2[/tex]


3. Substitute the formula into the given expression:

[tex]\lim_{n \to \infty}n(9n(n(n+1)/2)^2)[/tex]


4. Simplify the expression by multiplying n with the sum:

[tex]\lim_{n \to \infty}(9n^2(n(n+1)/2)^2)[/tex]


5. Apply the limit as n approaches infinity.

As n approaches infinity, the term [tex]n^2(n(n+1)/2)^2[/tex] will dominate the expression.

Since this term grows without bounds, the limit of the expression does not exist, or it can be said that the limit is infinity. So, the limit of the given expression as n approaches infinity is infinity.

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write the particular solution when k = 0.8. find the time of sale assuming that the goat is sold when its weight reaches 170 pounds. round the answer to the nearest hundredth if necessary.

Answers

The time of sale assuming that the goat is sold when its weight reaches 170 pounds is 0.66.

Assuming that the equation relates the weight of a goat to the time elapsed since birth, the general solution can be written as [tex]W(t) = Ce^{(kt)}[/tex], where W(t) is the weight of the goat at time t, C is a constant determined by the initial weight, and k is a constant related to the growth rate of the goat.

To find the particular solution when k = 0.8, we need to know the initial weight of the goat.

Let's assume that the goat weighed 100 pounds at birth, so C = 100.

Therefore, the particular solution is [tex]W(t) = 100e^{(0.8t)}[/tex].

To find the time of sale when the goat weighs 170 pounds, we need to solve for t in the equation W(t) = 170:
[tex]170 = 100e^{(0.8t)}[/tex]

Dividing both sides by 100:
[tex]1.7 = e^{(0.8t)}[/tex]

Taking the natural logarithm of both sides:
ln(1.7) = 0.8t

Solving for t:
t = ln(1.7) / 0.8 ≈ 0.66

Therefore, the goat will be sold when it reaches a weight of 170 pounds after approximately 0.66 units of time (which could be days, weeks, or months depending on the context). Rounded to the nearest hundredth, the time of sale is 0.66.

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A single die is rolled twice. Find the probability of rolling an odd number the first time and a number greater than 3 the second time. THE Find the probability of rolling an odd number the first time and a number greater than 3 the second time. (Type an integer or a simplified fraction.)​

Answers

The probability of rolling an odd number the first time and a number greater than 3 the second time is 1/4

Calculating the probability

The probability of rolling an odd number on a single die is 3/6 or 1/2, since there are three odd numbers (1, 3, and 5) out of six possible outcomes.

The probability of rolling a number greater than 3 on a single die is 3/6 or 1/2, since there are three numbers greater than 3 (4, 5, and 6) out of six possible outcomes.

To find the probability of both events happening together (rolling an odd number first and a number greater than 3 second), we need to multiply their individual probabilities:

P(odd number first and number > 3 second) = P(odd number first) * P(number > 3 second)

P(odd number first and number > 3 second) = (1/2) * (1/2) = 1/4

Therefore, the probability is 1/4.

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find the scale factor of the dilation

Answers

The scale factor is 2

What do we get on multiplying both sides of −1 < −x/4 by −4 ?

Answers

The inequality is 4<-x.

What is inequality?

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given inequality is,

=> -1 < [tex]\frac{-x}{4}[/tex]

Now multiply by -4 on both sides then,

=> [tex]-1\times-4 < \frac{-x}{-4}\times-4[/tex]

=> 4 < -x

Hence the inequality is 4<-x.

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3,200 divided by 1000 in long division

Answers

Answer:

Step-by-step explanation:

1000 | 3200

-3000

----

200

Therefore, 3,200 divided by 1000 is equal to 3.2.

what is the greatest common factor of 400 and 560?
i need an answer asap ​

Answers

80 is the greatest common factor .

What is a factor in math?

A number or algebraic expression that divides another evenly, i.e. without leaving a residue, is referred to in mathematics as a factor. For instance, the precise values of 12 3 = 4 and 12 6 = 2 show that 3 and 6 are factors of 12. 1, 2, 4, and 12 are additional factors of 12.

the prime factorization of 400

400 = 2 × 2 × 2 × 2 × 5 × 5

the prime factorization of 560

560 = 2 × 2 × 2 × 2 × 5 × 7

the GCF, multiply all the prime factors common to both numbers:

Therefore, GCF = 2 × 2 × 2 × 2 × 5

GCF = 80

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According to Interactive Illustration 1: Porter's Forces Framework in the Core Reading, the impact of a reduced threat of entry is that: a. profitability increases because willingness to pay increases, prices increase, and costs decrease 0. b. profitability increases because willingness to pay decreases, prices increase, and costs decrease. c. profitability decreases because willingness to pay decreases, prices decrease, and costs increase d. profitability decreases because willingness to pay decreases, prices decrease, and costs decrease.

Answers

The correct answer is: c. profitability decreases because the willingness to pay decreases, prices decrease, and costs increase. Porter's Five Forces Framework is a strategic management tool developed by Harvard Business School professor Michael E. Porter. The framework is used to analyze the competitive environment of an industry and to identify the factors that influence the profitability of a company within that industry.

According to Porter's Five Forces Framework, a reduced threat of entry means that the market is less competitive, and therefore, the existing firms have more market power. This can lead to a decrease in the willingness to pay for customers, as they have fewer choices and are less likely to switch to competitors. As a result, firms may need to lower their prices to maintain demand, which can decrease profitability. Additionally, because there is less pressure to compete, firms may not invest in cost-cutting measures, leading to increased costs. Therefore, profitability decreases due to lower willingness to pay, lower prices, and higher costs.

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Minimizing Surface Area:

(i) Of all boxes with a square base and a fixed volume V, which one has the minimum surface area As? (Give its dimensions in terms of V.)
(ii) Let V = 1000 meters cubed and give the dimensions using your solution in part (i).
(iii) Sketch the surface area function A that was minimized in part (i). Use a reasonable domain. Label axes appropriately, including units.

Answers

To minimize the surface area of a box with a square base and a fixed volume V, its dimensions should be x = y = z =  (V¹/³). For V = 1000 meters cubed, the dimensions are x = y = z = 10 meters.

To minimize the surface area, we can use the formula for the surface area of a box with a square base: A = 2x² + 4xy, where x = y (square base) and z = V/x². Differentiating A with respect to x and setting the derivative equal to zero, we find the critical points.

A' = 4x - 4V/x³. Setting A' = 0, we get 4x = 4V/x³, and x⁴ = V, so x = (V¹/³). Since x = y, the dimensions are x = y = z = (V¹/³).

For part (ii), let V = 1000 meters cubed. Then, the dimensions are x = y = z = (1000)¹/³ = 10 meters.

For part (iii), sketch the surface area function A(x) = 2x²+ 4x(V/x²) with a reasonable domain, such as [1, 20] meters for x-axis and [300, 2500] meters squared for the y-axis. Label axes appropriately, including units.

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One side of a triangle is 84cm the other two sides are in the ratio 3:8 If the perimeter is 282cm find the the longest and shortest side

Answers

Let x be the shortest side of the triangle. Then the other side is 8x/3. The perimeter of the triangle is the sum of all three sides, so we have:

x + 84 + 8x/3 = 282

Multiplying both sides by 3, we get:

3x + 252 + 8x = 846

11x = 594

x = 54

So the shortest side of the triangle is 54 cm. The longest side is 8x/3 = 144 cm.

a 3.0 kg particle is located on the x-axis at x = −7.0 m and a 5.0 kg particle is on the x axis at x = 3.0 m. what is the center of mass of this two–particle system?

Answers

Answer: At x = -0.75

Step-by-step explanation:

Find the center of mass by plugging into the equation.

(3.0 * -7.0 + 5.0 * 3.0) / (3.0 + 5.0) = -0.75

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The type of quadrilaterals, based on the description of the diagonals are;

a) Isosceles trapezoid

b) Square or rhombus

c) Kite or parallelogram

What is a quadrilateral?

A quadrilateral is a four sided polygon.

The properties of the quadrilateral are;

a) The diagonals are congruent but are not perpendicular

b) The diagonals are congruent and perpendicular bisectors

c) One diagonal bisects an angle and the other diagonal

The type of quadrilaterals are;

a) Whereby the diagonals are congruent and the diagonals are not perpendicular, indicates that a possible quadrilateral is an isosceles trapezoid

b) The quadrilaterals with congruent and perpendicular diagonals indicates that the possible quadrilaterals are a square or a rhombus

c) A quadrilateral that bisects an angle and one diagonal indicates that the quadrilateral is a parallelogram or kite

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