let y1 and y2 are independent random variables that are both uniformly distributed on the interval (0,1). find p(y1 <1

The radius of convergence R of the given function f(x) = (-1)^n(1 - x)² be,

R = 1/2.

Given, a function f(x)

f(x) = (-1)^n(1 - x)²

we have to find the radius of convergence R of the given function,

first will find the (n+1)th term of the given function

as, an = (-1)^n(1 - x)²

then an+1 = (-1)^(n+1)(1 - x)²

to find the radius of convergence, we will find

lim x->∞ an+1/an

lim x->∞ ((-1)^(n+1)(1 - x)²)/((-1)^n(1 - x)²)

On solving the limits, we get

lim x->∞ an+1/an = 2x

then R = 1/2

as, -1/2 < x < 1/2

so, the radius of the convergence be, 1/2

Hence, the radius of the convergence be, 1/2

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The total perimeter of the given composite figure is; 74.55 meters

The perimeter of the given figure can be calculated by dividing the figure into two parts : One is semi-circle and second is rectangle.

To find Perimeter of rectangle :

Length of the rectangle = 18 m

Width of the rectangle = 15 m

Perimeter = (2 × Length) + Width

Perimeter = (2 × 18) + 15

Perimeter = 36 + 15

Perimeter = 51 meters

To find perimeter of semi-circle :

Radius of semi-circle = 15/2 = 7.5 m

Perimeter of semi-circle = π × radius

Perimeter = 3.14 × 7.5

Perimeter = 23.55 meter

So, Total Perimeter of the figure = 51 + 23.55

= 74.55 meter

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Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.

The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).

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The correct statements regarding the comparisons of the exponential functions are given as follows:

The definition of function f(x) is given as follows:

f(x) = 4(5)^x

Meaning that it has an y-intercept and an asymptote given as follows:

From the graph of function g(x), we have that:

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1. 4

2. less than

3. increase

4. negative

Got it right on Edmentum

Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.

Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.

Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.

The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.

The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.

Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:

2/3z > 4/5 [given]

Multiply both sides by 3/2:

2/3z × 3/2 > 4/5 × 3/2

z > (4 × 3) / (5 × 2)

z > 12 / 10

Simplify further:

z > 6/5

z > 1.2

The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.

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The solution for the situation is [tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex]  Where y > 1, and the graph is attached below.

An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.

Given:

The side length x (in feet) of the base,

the height y (in feet) of the inequality y > 1/2x²+ 1 and y ≤ x,

In solving this inequality, we get,

[tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex]  where y > 1

The graph of the system is attached below.

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The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.

A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.

Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.

We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.

Degree of freedom,

df = n - 1

df = 29 - 1

df = 28.

The critical value of t calculated from the t-distribution table is,

[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]

Then, an 80% confidence interval is,

[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]

Then, the interval is written as

55.9 - 1.80 < μ < 55.9 + 1.80

54.1 < μ < 57.7

The required interval is 54.1 < μ < 57.7.

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Answer:

C. 296 R3

Step-by-step explanation:

In order to find the quotient, lets use long division:

            296 R 3

      _________

7    |    2075

        - 14

          __

            67   ==> drop 7 from 2075

          - 63

            __

              45     ==> drop 5 from 2075

            - 42

              __

                3

Therefore the value of K is -11

Answer:

  125 -v³ = (5 -v)(v² +5v +25)

Step-by-step explanation:

You want to factor the expression 125 -v³.

From your knowledge of the cubes of small integers, you recognize that 125 = 5³. That lets you see this expression is the difference of cubes, which has a factor pattern:

  a³ -b³ = (a -b)(a² +ab +b²)

Your difference factors as ...

  5³ -v³ = (5 -v)(5² +5v +v²)

  125 -v³ = (5 -v)(v² +5v +25)

Answer:

OptionB)

Step-by-step explanation:

→→When you are talking about sample proportion You are considering a Single ,set of same kind of Data,Like body weight of  Students in a class, from which you are taking out samples for Observation.

For example, A colony is being studied whether each human in that colony is healthy or not by checking their body mass index.

→→When we are investigating or considering Sampling Distribution we consider two different sets or kinds of Data set Possessing Similar Characteristics because we have to compare these two sets of Data.

For example , Take two colonies A and B , Check their honesty by observing how many floors they have made in their Plot.Whether they care or don't care about their Surrounding or Mother Earth by looking, if number of floors exceeds than 2 i.e ground floor and first floor , it means Dishonest , if maximum number of floor =2 ,it means honest.

The final value of company x sold price is; $22,000,500

The final value of company y sold price is; $21,999,500

Let the amount of sold out products in company x and company y be denoted by a

Now, we are told that sum of both the two companies salaries are $44,000,000.

Now, the sold price of company x is 1000 more than the other.

Thus;

Sold price of company y = y

Sold price of company x = 1000 + y

Thus;

1000 + y + y = 44000000

1000 + 2y = 44000000

2y = 44000000 - 1000

2y = 43,999,000

y = 43,999,000/2

y = $21,999,500

Thus;

Sold price of company x = $21,999,500 + $1000 = $22,000,500

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Answer: y = 5x - 4

Step-by-step explanation: The equation of a linear function can be found by using the slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (i.e., the point at which the line crosses the y-axis).

To find the equation of the linear function represented by the table, we can use the values from the table to calculate the slope. The slope is calculated as the change in y over the change in x, or (y2 - y1)/(x2 - x1). Using the values from the table, we can calculate the slope as (6 - 1)/(2 - 1) = 5/1 = 5.

Next, we can use the slope and one of the points from the table to find the y-intercept. If we use the point (1,1), we can substitute the values into the slope-intercept form to get 1 = 5*1 + b, so b = -4.

Therefore, the equation of the linear function represented by the table is y = 5x - 4.

Answer:

1.

x = 24

m = 112

z = 44

y = 72

2.

x = 35

Step-by-step explanation:

Number 1

Finding x

- Total angle in a triangle is 180.

- QVS = triangle

180 = ∠Q + ∠V + x

180 = 73 + 83 + x

x = 180 -73 - 83

x = 24

Finding m

- Total angle in a straight line is 180

- RW is a straight line

180 = m + ∠U

180 = m + 68

m = 180 - 68

m = 112

Finding z

- Total angle in a triangle is 180.

- RUS = triangle

180 = m + x + z

180 = 112 + 24 + z

z = 180 - 112 - 24

z = 44

Finding y

- Total angle in a triangle is 180.

- RWT = triangle

180 = z + y + ∠W

180 = 44 + y + 64

y = 180 - 44 - 64

y = 72

Number 2

- Total angle in a triangle is 180.

- Total angle in a straight line is 180.

180 = (180 -120) + 85 + x

180 = 60 + 85 + x

x = 180 - 60 - 85

x = 35

This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).

The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.

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The range of 90% confidence will be: (0.5305,0.5695)

What is percentage?

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Given,

Sample percentage equals 0.55

z = 1.645 for 90% confidence.

Therefore, the range of 90% confidence will be:

(0.5305,0.5695)

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A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.

Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.

Since we know the volume of the balloon, we can set up the following equation:

(4/3)πr^3 = 26*π ft^3

Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.

To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.

The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:

(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)

Plugging in the value of r that we found earlier (2.15 ft), we get:

(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min

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Answer:

3,4,5

Step-by-step explanation:

Because, it is the only pair that fulfill the pythagorean theorem/formula

Pythagorean formula: [tex]c^2 = \sqrt{a^2 + b^2}[/tex]

Where c is the longest side of the triangle, or the hypothenuse, and a and b is the two perpendicular side.

The probability of a Type I error is the probability of incorrectly rejecting the null hypothesis. When the probability of a Type I error decreases, the probability of a Type II error, It decreases the likelihood of choosing the null hypothesis wrongly.

When conducting a hypothesis test for a given sample size, a Type I error is the probability of incorrectly rejecting the null hypothesis. This means that the null hypothesis is true, but the hypothesis test incorrectly rejects it. A Type II error is the probability of incorrectly accepting the null hypothesis. This means that the null hypothesis is false, but the hypothesis test incorrectly accepts it. When the probability of a Type I error decreases, it means that the hypothesis test is more accurate in correctly rejecting the null hypothesis when it is false. This in turn means that the probability of a Type II error also decreases, as the test is more accurate in correctly accepting the null hypothesis when it is true. In other words, when the probability of a Type I error decreases, the probability of a Type II error decreases as well.

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The exact expression for the cosine function is given as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The definition of the cosine function is given as follows:

h(x) = acos(b(x - c)) + d.

The parameters of the function are given as follows:

The difference between the maximum value and the minimum value is of 6 - (-9) = 15, hence the amplitude is obtained as follows:

a = 15/2 = 7.5.

From the graph given at the end of the answer, the period is of 7 units, hence:

2π/b = 7

7b = 2π

b = 2π/7.

The minimum value should be at x = 0, however it is at x = -0.5, hence the phase shift is given as follows:

c = -0.5.

Considering the amplitude of 7.5, without vertical shift the function would oscillate between -7.5 and 7.5, however is oscillates between -9 and 6, hence the vertical shift is given as follows:

d = -1.5.

Thus the function is defined as follows:

h(x) = 7.5cos(2π/7(x + 0.5)) - 1.5.

The graph of the function is given by the image shown at the end of the answer.

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C. H2 1,96

To establish whether there is a significant difference between treatments using the Kruskal-Wallis test, the calculated value of H should be compared to the critical values ​​in the table of H values. The critical value of H to use depends on the significance level chosen for the test (0.05 in this case).

Using a significance level of 0.05, the critical value of H for a sample size of n-8 for each treatment is approximately H2 1.96. That is, if the calculated H value is greater than 1.96, we can conclude that there is a significant difference between the treatments.

Hence, the correct answer in this case is c. H2 1,96

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The most likely statement about the comparison of standard deviation of Test A and Test B is (a) The standard deviations found in Test A and Test B will be about the same  .

What is Standard Deviation ?

The term standard deviation is defined as a measure which shows the  variation (such as dispersion) from the mean .

it is given that in Test A 100 experimental measurements is taken , and

in Test B 400 experimental measurements is taken .

we know that standard deviation is just  square root of average of the square distance of measurements from the mean.

So , it is not affected by the number of experimental measurements .

thus , the standard deviation remain same for both the tests .

Therefore , the correct option is (a) .

The given question is incomplete , the complete question is

In test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again .

Which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?

(a) The standard deviations found in Test A and Test B will be about the same

(b) The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.

(c) The standard deviation found in Test will about be four times as big as the standard deviation found in Test B

(d) The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A .

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To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.

Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.

Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.

Answer:

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Step-by-step explanation:

The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].

This would mean [tex]y=\frac{x}{3}-2[/tex].

Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.

[tex]x = \frac{y}{3} -2[/tex]

Then rearrange for [tex]y[/tex]:

[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]

This new equation of [tex]y[/tex] is the inverse function.

f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]

Answer:

x = 75

y = 15

Step-by-step explanation:

What you need to know to solve this question:

1. Angles in a triangle sum up to 180

2. Angles on a straight line add up to 180

3. A right-angle is 90

4. The triangle illustrated is a right-angle triangle

Solving for x:

According to principle 2:

x + 105 = 180

x = 180 - 105

x = 75

Solving for y:

According to principles 1 and 3:

x + y + 90 = 180

(75) + y + 90 = 180

y = 180 - 90 - 75

y = 15

By using the properties of angle, it can be concluded that

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

What is angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

[tex]\angle QPS[/tex] and [tex]\angle TSU[/tex] are not consecutive interior angle as [tex]\angle PST[/tex] falls in between

[tex]\angle QPS[/tex] and [tex]\angle RSU[/tex] are not consecutive interior angle as [tex]\angle RSU[/tex] is an exterior angle

[tex]\angle QPS[/tex] and [tex]\angle TSP[/tex] are consecutive interior angle

[tex]\angle QPS[/tex] and [tex]\angle OPN[/tex] are not consecutive interior angle as [tex]\angle OPN[/tex] is an exterior angle

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Answer:

HA:A hypotenuse and an acute angle define congruence

HL:A hypotenuse and a leg define congruence

LL: Two legs define congruence

LA:A leg and an acute angle define congruence

Step-by-step explanation:

HA theorem:

                     When hypotenuse and one acute angle of a triangle is congruent to hypotenuse and one acute angle of a other triangle, then the triangles are congruent

HL theorem:

                     When hypotenuse and one leg of a triangle is congruent to hypotenuse and one leg of other triangle, then the triangles are congruent

LL theorem:

                    When two legs of a triangle is congruent to the two legs of other triangle, then the triangles are congruent

LA theorem:

                    When one leg and one acute angle of a triangle is congruent to one leg and one acute angle of other triangle, then the triangle are congruent

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