Please answer these questions with no plagiarism and with your own words. ASAP
Question 1: Five-City Project. The Stanford Five-City Project is a comprehensive community health education study of five moderately sized Northern California towns. Multiple-risk factor intervention strategies were randomly applied to two of the communities. The other three cities served as controls. Outline the design of this study in schematic form.
Question 2: Employee counseling. An employer offers its employees a program that will provide up to four free psychological counseling sessions per calendar year. To evaluate satisfaction with this service, the counseling office mails questionnaires to every 10th employee who used the benefit in the prior year. There were 1000 employees who used the benefit. Therefore, 100 surveys were sent out. However, only 25 of the potential respondents completed and returned their questionnaire.
Describe the population for the study.
Describe the sample.
What concern is raised by the fact that only 25 of the 100 questionnaires were completed and returned?
Question 3: What would you report? What is an appropriate measure of central location for data that are really skewed? What is an appropriate measure of spread for data that are really skewed?

Answer:

The answer is actually 2.

C= 2cm.

Answer:

[tex]\frac{2A}{b} = h[/tex]

Step-by-step explanation:

[tex]A = \frac{1}{2}bh[/tex]

1. Multiply both sides by 2 to cancel out the 1/2 from the right side.

[tex]2A = bh[/tex]

2. Divide both sides by B so it cancels out the B on the right side.

[tex]\frac{2A}{b} = h[/tex]

The following claims cannot be verified based on the boxplots, which show that the cost of course materials for nursing majors is around the same as for non-nursing majors. Option 1 is Correct.

A college professor carried out a poll to see how much nursing majors spend on textbooks in comparison to all other majors. She chose a sample of 34 pupils at random to conduct this. Both nursing majors and non-nursing majors were assigned to each student.

The next question they were asked was how much money they had spent this semester on books and other course-related resources. A parallel boxplot depicted above summarises the replies.  As a result, we are unable to draw the conclusion that 17 students are majoring in nursing and 17 are not. Option 1 is Correct.

Learn more about boxplots visit: brainly.com/question/14277132

#SPJ4

Correct Question:

A college professor conducted a survey in order to assess how much money nursing majors spend on course material compared to all other majors. To do so, she selected a random sample of 34 students. Each student was classified as a nursing major or as a non-nursing major. They were then asked how much they spent on books and other materials required for their courses this semester. Shown above are parallel boxplots summarizing the responses. Based upon the boxplots, which of the following statements cannot be concluded?

1. The range of the distribution of the cost of course materials for nursing majors is about the same as that of non-nursing majors.

2. The maximum cost for non-nursing majors is greater than the median cost for nursing majors.

3. The variability of the cost of course materials for the middle 50% of nursing majors is greater than the variability of the middle 50% for non-nursing majors.

4. The median cost of course materials for nursing majors is over $300 more than the median cost of course materials for non-nursing majors.

5. The boxplots reveal that 17 students are nursing majors and 17 students are non-nursing majors.

The confidence interval for the proportion of left-handed golfers is (0.27, 0.31).

We have,

We will calculate the confidence interval for the proportion of left-handed golfers in a survey of 2,360 golfers.

The given information includes 29% being left-handed and a margin of error of 2%.

To calculate the confidence interval, follow these steps:

1. Convert the percentages to decimals:

0.29 for the proportion of left-handed golfers and 0.02 for the margin of error.

2. Add and subtract the margin of error from the proportion of left-handed golfers:

0.29 + 0.02 and 0.29 - 0.02.

3. Calculate the lower and upper limits of the confidence interval:

0.29 - 0.02

= 0.27 and 0.29 + 0.02

= 0.31.

Thus,
The confidence interval for the proportion of left-handed golfers is (0.27, 0.31).

Learn more about the confidence interval here:

https://brainly.com/question/24131141

#SPJ11

The correct option is NO, the line XY is not tangent to the circle Z.

The tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency

For the line XY to be tangent to the circle Z implies line XZ is perpendicular to line XY which will make the triangle XYZ a right triangle

So by Pythagoras rule, the sum of the square for the sides XZ and XY must be equal to the square of YZ, otherwise, XY is not a tangent to the circle Z

XY² = 5² = 25

XZ² + XY² = 8² + 10² = 164.

In conclusion, since XZ² + XY² is not equal to XY², then XY is not tangent to the circle Z.

Read more about tangent to a circle here:https://brainly.com/question/11067500

#SPJ1

If in circle A, diameter EC is perpendicular to chord BD, and arc EB measures 62 degrees, the measure of arc ED is 208 degrees.

To solve the problem, we need to use the relationship between arcs, angles, and chords in a circle.

Since diameter EC is perpendicular to chord BD, we know that angle EBD is a right angle.

Arc EB measures 62 degrees, and we know that angle EBD is 90 degrees. Therefore, arc ED must measure:

360 degrees - arc EB - angle EBD

= 360 degrees - 62 degrees - 90 degrees

= 208 degrees

So, the measure of arc ED is 208 degrees.

To learn more about angle click on,

https://brainly.com/question/22908715

#SPJ1

The amount we will have after to be paid $13,177.97

We have,

P = $ 8100

R= 7.2%

T= 7 year

r = R/100

r = 7.2/100

r = 0.072 rate per year,

Then solve the equation for A

A = P(1 + r/n[tex])^{nt[/tex]

A = 8,100.00(1 + 0.072/1[tex])^{(1)(7)[/tex]

A = 8,100.00(1 + 0.072)⁷

A = $13,177.97

Learn more about Compound Interest here:

https://brainly.com/question/14295570

#SPJ1

Amani would need to pay $66.15 for the scooter with the discount and sales tax included.

If the regular price of the scooter is $70, and it is on sale for 10% off, the sale price would be:

Sale price = Regular price - 10% of Regular price

Sale price = $70 - 0.1*$70

Sale price = $63

So the sale price of the scooter is $63.

Next, we need to add the 5% sales tax to the sale price to get the total price of the scooter. To do this, we can calculate the amount of sales tax as:

Sales tax = 5% of the Sale price

Sales tax = 0.05*$63

Sales tax = $3.15

Therefore, the total price of the scooter, including the 10% discount and 5% sales tax, would be:

Total price = Sale price + Sales tax

Total price = $63 + $3.15

Total price = $66.15

So Amani would need to pay $66.15 for the scooter with the discount and sales tax included.

Learn more about sales tax

https://brainly.com/question/29442509

#SPJ4

The end of the stencil located at (9, 3).

We have,

The beginning of the left edge of the stencil falls at (1, −1).

She wants to align an important detail on the left edge of her stencil at

(3, 0).

Ratio = m:n = 1:3

Using section formula

3 = (x + 3)/4

x+3 = 12

x = 9

and, 0 = (y - 3)/4

y= 3

Thus, the end point are (9, 3).

Learn more about section Formula here:

https://brainly.com/question/30242630

#SPJ1

So Jordan rode his bike for a total time of approximately 6.067 hours over the five days.

The total amount of theoretical time that is open for production is known as whole Time. It serves as the foundation for the overall equipment effectiveness (OEE) availability calculation.  the length of time: The time interval between the start and end of an action is its duration. We can quickly determine the duration of any action when the beginning and ending times are provided.

To find the total time Jordan rode his bike in minutes, we can add up the times for each day:

45 + 109 + 51 + 121 + 38 = 364

Jordan rode his bike for a total of 364 minutes in the five days.

To convert this to hours, we can divide by 60:

364 ÷ 60 = 6.067

Learn more about time visit: brainly.com/question/1816510

#SPJ4

Correct Question:

The table displays the amount of time, in minutes, Jordan rode his bike for five days. How many total hours did Jordan ride his bike in the five days?

Day Time (minutes)

1 45

2 109

3 51

4 121

5 38

By using the given transformation rule and graph, the coordinates for the red triangle include the following:

Red Vertex Names                Red Triangle Vertices

A'                                                      (5, 2)

B'                                                      (3, 5)

C'                                                      (1, 4)

In Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to the coordinate of the given triangle ABC, we have the following coordinates:

(x, y)                             →                 (-x, y).

Coordinate A = (-5, 2)   →  Coordinate A' = (-(-5), 2) = (5, 2).

Coordinate B = (-3, 5)   →  Coordinate B' = (-(-3), 5) = (3, 5).

Coordinate C = (-1, 4)   →  Coordinate C' = (-(-1), 4) = (1, 4).

Read more on reflection here: brainly.com/question/27912791

#SPJ1

Answer:

To find out how many faygos James can buy, we need to divide the total amount he has by the price of each Faygo.

Remember, if you don't know something you can always put an X in your equation because we're going to solve it anyways. We know that 10 Faygo's cost $22, so in order to find the price of 1 Faygo we have to divide $22/10 = $2.20.

Therefore, we can set up the equation:

$2.20x = $6.60

Simplifying (by putting x at the front of the equation), we get:

x = $6.60 / $2.20

x = 3

So James can buy 3 Faygo's for $6.60.:)

To find the simplest function f and a number a, we can begin by simplifying the expression within the limit. We can use the formula for the difference of squares to rewrite the numerator as (x^40 + x^20 + 1)(x^20 - 1). Similarly, we can use the formula for the difference of cubes to rewrite the denominator as (x - 1)(x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1).

Canceling out the common factor of x - 1 in the numerator and denominator, we are left with:

limx→1(x^20 + x^10 + 1)(x^20 - 1) / (x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1)

To find the simplest function f, we can let f(x) = x^20 + x^10 + 1. Then, f'(x) = 20x^19 + 10x^9, so f'(1) = 30.

Therefore, we can rewrite the limit as:

limx→1 [f(x) - 1] / [(x - 1)(x^2 + x + 1)(x^3 + x^2 + 1)(x^6 + x^3 + 1)]

Using L'Hopital's rule or factoring, we can simplify the denominator to (1 + 1 + 1)(1 + 1)(1 + x + x^2)(1 + x^3 + x^6), which equals 9(1 + x + x^2)(1 - x + x^2)(1 + x^3 + x^6).

Plugging in f'(1) and simplifying, we get:

limx→1 [f(x) - 1] / [(9)(1 + x + x^2)(1 - x + x^2)(1 + x^3 + x^6)]

= [f'(1)] / [9(1 + 1 + 1)(1 + 1)(1 + 1 + 1)(1 + 1 + 1 + 1 + 1 + 1)]

= 30 / 1944

Therefore, the value of the limit is 30 / 1944.
a. To find the simplest function f and the number a, we first recognize that the given limit represents the derivative of a function f at a point a:

lim(x→1) [(x^80 - 1) / (x - 1)]

We can use the definition of a derivative, which is:

f'(x) = lim(h→0) [(f(x + h) - f(x)) / h]

Comparing this with the given limit, we have:

f(x + h) = x^80
f(x) = 1

Here, x + h = x^80 and x = 1. So, f(1) = 1. Since f'(a) is given at x = 1, we have:

a = 1

The simplest function f is a power function of the form f(x) = x^n. To find n, we consider the fact that f(1) = 1:

1^n = 1

The simplest solution is when n = 1, so f(x) = x.

b. Now, we determine the value of the limit by finding f'(a). Since we found that f(x) = x, we can calculate its derivative:

f'(x) = d(x)/dx = 1

Now, we can find f'(a) by substituting a = 1:

f'(1) = 1

So, the value of the limit is 1.

Learn more about denominator at : brainly.com/question/7067665

#SPJ11

A basis for W is {[tex]x^2 - 1, x - 1[/tex]}, and the dimension of W is 2. Any polynomial in W can be written as a linear combination of the two polynomials [tex]x^2 - 1[/tex] and x - 1. Since these two polynomials are linearly independent, they form a basis for W.

a) To show that W is a subspace of P2, we need to show that it satisfies the three conditions of a subspace:

i) W contains the zero vector:

The zero polynomial p(x) = 0 satisfies p(1) = 0, so it is in W.

ii) W is closed under addition:

Let p(x) and q(x) be polynomials in W. Then:

[tex](p+q)(1) = p(1) + q(1) = 0 + 0 = 0,[/tex]

so p+q is also in W.

iii) W is closed under scalar multiplication:

Let p(x) be a polynomial in W, and let c be a scalar. Then:

[tex](cp)(1) = c(p(1)) = c(0) = 0,[/tex]

so cp is also in W.

Since W satisfies all three conditions, it is a subspace of P2.

b) We can conjecture that the dimension of W is 2, because P2 is a vector space of dimension 3, and the condition p(1) = 0 imposes a single linear constraint on the coefficients of a polynomial in P2.

c) To find a basis for W, we need to find a set of linearly independent polynomials that span W. Let p(x) = [tex]ax^2 + bx + c[/tex] be a polynomial in W. Then:

p(1) = a + b + c = 0.

Solving for c, we get:

c = -a - b.

So any polynomial in W can be written as:

P(x) = [tex]ax^2 + bx - a - b = a(x^2 - 1) + b(x - 1).[/tex]

Thus, the set [tex]{x^2 - 1, x - 1[/tex]} spans W. To check linear independence, we set up the equation:

[tex]a(x^2 - 1) + b(x - 1)[/tex]= 0.

This gives us two equations:

a = 0 and b = 0.

Thus, the set[tex]{x^2 - 1, x - 1}[/tex] is linearly independent, and hence it is a basis for W.

To know more about  polynomial here

https://brainly.com/question/2833285

#SPJ4

Here are three different sequences starting with 1, 2, and 4 respectively, where the terms are generated by a simple rule:

1) Sequence starting with 1: 1, 3, 5, 7, 9...
This sequence is generated by adding 2 to the previous term.

2) Sequence starting with 2: 2, 4, 8, 16, 32...
This sequence is generated by multiplying the previous term by 2.

3) Sequence starting with 4: 4, 7, 10, 13, 16...
This sequence is generated by adding 3 to the previous term.

Now, to suggest a closed formula for the sum of these sequences, we can use the formula for the sum of an arithmetic sequence:
S_n = n/2(2a + (n-1)d)

Where:
- S_n is the sum of the first n terms of the sequence
- a is the first term of the sequence
- d is the common difference between consecutive terms of the sequence
- n is the number of terms in the sequence

For the first sequence (1, 3, 5, 7, 9...), a=1 and d=2 (since we add 2 to the previous term to get the next term). If we want to find the sum of the first 10 terms of this sequence, we can plug in these values into the formula:

S_10 = 10/2(2(1) + (10-1)2)
S_10 = 10/2(2 + 18)
S_10 = 10/2(20)
S_10 = 100

Therefore, the sum of the first 10 terms of this sequence is 100.

You can use a similar method to find the sum of the other two sequences as well.

Know more about sequences here:

https://brainly.com/question/30262438

#SPJ11

The amount of money Lily spent on peanuts and water is 2.75 dollars.

Noah spent $2.50 on 2 bags of peanuts and 1 bottle of water at a baseball game.

Emily spent $4.25 on 3 bags of peanuts and 2 bottles of water.

Using equation,

where

Therefore,

2x + y = 2.50

3x + 2y = 4.25

multiply equation(i) by 2

4x + 2y = 5

3x + 2y = 4.25

x = 0.75 dollars

y = 2.50 - 2(0.75)

y = 2.50 - 1.5

y  = 1 dollars

Therefore,

cost of Lily expenses = 2(1) + 0.75(1)

cost of Lily expenses = 2 + 0.75

cost of Lily expenses = 2.75 dollars

learn more on equation here: https://brainly.com/question/13912433

#SPJ1

[tex] \frac{ - 9}{20} [/tex]

is greater

When reporting the results of a one sample t test with 24 participants and a t-value of .92 that is not statistically significant, it is important to state that the sample did not provide sufficient evidence to reject the null hypothesis.

This means that there was not enough evidence to support the claim that the sample mean is significantly different from the population mean. Therefore, it is necessary to accept the null hypothesis. It is also important to report the level of significance used in the study, as well as the degrees of freedom. For example, if the level of significance was set at .05, and the degrees of freedom were 23, the results could be reported as follows: "The results of the one sample t test revealed that there was not a significant difference between the sample mean and the population mean (t(23) = .92, p > .05).

Therefore, the null hypothesis is accepted." Overall, it is important to be transparent in reporting the results of any statistical test and to provide enough information to allow others to replicate the study or understand the results.

Know more about sample here:

https://brainly.com/question/13287171

#SPJ11

The graph is  a coordinate grid with one line that passes through the points 0 comma 1 and 3 comma negative 1 and another line that passes through the points 0 comma negative 1 and 2 comma negative 5.

The system of linear equations is:

y = -2/3x + 1

y = -2x - 1

To determine which graph shows the solution to the system, we need to graph the two equations on the same coordinate grid and find their intersection point, which represents the solution to the system.

For the first equation, y = -2/3x + 1, the y-intercept is 1 and the slope is -2/3. We can use this to find one more point, say by setting x = 3:

y = -2/3(3) + 1 = -1

So one point on the line is (3, -1), and we can plot it on the coordinate grid.

For the second equation, y = -2x - 1, the y-intercept is -1 and the slope is -2. We can use this to find another point, say by setting x = 0:

y = -2(0) - 1 = -1

So another point on the line is (0, -1).

Thus, the answer is a coordinate grid with one line connecting points 0 comma 1 and 3 comma negative 1 and another line connecting points 0 comma negative 1 and 2 comma negative 5.

For more details regarding graph, visit:

https://brainly.com/question/17267403

#SPJ1

Account A has a principal of  $15,000

Account B has a principal of $6250

Hence, account A will earn the highest interest in the first month.

When we talk about the simple interest, we mean the kind of interest that is charged only on the principal sum and not on the interest of the former year. Given that 18 months is 1.5 years and 15 months is 1.4 years we can now have that;

I= PRT/100

A = P + I

P = principal

I = interest

R = rate

T =time

Thus;

For account A

8.1 = P * 0.036 * 1.5/100

8.1 = 0.054P

P = $15,000

For account B;

19.25 = P * 0.022 * 1.4/100

P = 1925/0.308

P = $6250

Learn more about simple interest:https://brainly.com/question/25845758

#SPJ1

Answer: So greatest to least would be 0.4,    0.34,   1/4   21%,  and 3/100 for the least

Step-by-step explanation:

1/4=0.25

0.4=0.40

21%=0.21

0.34=0.34

3/100=0.03

The slope of any line parallel to the given line is also 9.

The slope of any line perpendicular to the given line is -1/9.

We have,

The given line is y = 9x - 6

This is in the form of y = mx + c.

So,

The slope of the line is 9.

Now,

Parallel lines have the same slope,

So the slope of any line parallel to the given line is also 9.

Perpendicular lines have negative reciprocal slopes,

So the slope of any line perpendicular to the given line is -1/9.

Thus,

The slope of any line parallel to the given line is also 9.

The slope of any line perpendicular to the given line is -1/9.

Learn more about the equation of a line here:

https://brainly.com/question/23087740

#SPJ1

To find dx/dt and dy/dt for the given curve with parametric equations y = Int and x = 4ts, we can use the chain rule of differentiation.

First, let's find dx/dt:

dx/dt = d/dt (4ts)

Using the product rule of differentiation, we get:

dx/dt = 4s + 4t(ds/dt)

However, we don't know what ds/dt is. But we do know that s = x/4t, so we can use the quotient rule of differentiation to find ds/dt:

ds/dt = d/dt (x/4t)

ds/dt = (4t(dx/dt) - x(4(dt/dt))) / (4t)^2

Simplifying this expression, we get:

ds/dt = (dx/dt)/t - x/(4t^2)

Substituting this back into the expression for dx/dt, we get:

dx/dt = 4s + 4t[(dx/dt)/t - x/(4t^2)]

Simplifying this expression, we get:

dx/dt = 4s - (x/t)

Next, let's find dy/dt:

dy/dt = d/dt(Int)

Since Int is a constant, its derivative with respect to t is 0. Therefore,

dy/dt = 0

In summary, we have found that:

dx/dt = 4s - (x/t)

dy/dt = 0

This means that the slope of the curve at any point is given by dx/dt, and that the curve is horizontal (i.e. dy/dt = 0) at every point.

Explaining this in 200 words:

To find the derivative of a curve with parametric equations, we use the chain rule of differentiation. By differentiating x and y with respect to t, we can express dx/dt and dy/dt in terms of s and t. In this particular example, we first found dx/dt using the product rule of differentiation. We then used the quotient rule to find ds/dt, which allowed us to substitute back into the expression for dx/dt. Finally, we found dy/dt by differentiating the constant Int with respect to t.

The resulting expressions for dx/dt and dy/dt tell us important information about the curve. The slope of the curve at any point is given by dx/dt, which we found to be 4s - (x/t). This means that the slope of the curve varies depending on the values of s and t. The curve is horizontal (i.e. dy/dt = 0) at every point, which means that it does not rise or fall as t changes. Overall, finding the derivatives of parametric curves allows us to better understand their behavior and properties.

More on parametric equation: https://brainly.com/question/30451972

#SPJ11

The equation x² + 2x + __ = (__)² should be completed by the following:

D. 1; x + 1.

x² + 2x + 1 = (x + 1)²

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:

x² + 2x + (2/2)² = (2/2)²

x² + 2x + (1)² = (1)²

x² + 2x + 1 = (x + 1)²

Read more on quadratic functions here: brainly.com/question/29499209

#SPJ1

Answer:

We need at least 42 particles to estimate the population mean within 3.2 micrometers with 99% confidence.

Step-by-step explanation:

The problem is not related to the definition of N99 masks, but it involves statistical inference.

To solve this problem, we need to use the central limit theorem, which states that the sample mean of a large sample will be approximately normally distributed, regardless of the underlying distribution of the population.

We can use the formula for the margin of error to find the sample size needed to estimate the population mean within a certain margin of error with a certain level of confidence.

Assuming a normal distribution with a standard deviation of (21-5)/2 = 8 micrometers, we can use the following formula:

Margin of error = z * (standard deviation / sqrt(sample size))

where z is the z-score corresponding to the desired level of confidence. For a 99% confidence level, the z-score is 2.576.

We want the margin of error to be 3.2 micrometers, so we can solve for the sample size:

3.2 = 2.576 * (8 / sqrt(sample size))

sqrt(sample size) = 2.576 * 8 / 3.2

sqrt(sample size) = 6.44

sample size = 6.44^2 = 41.5

Therefore, we need at least 42 particles to estimate the population mean within 3.2 micrometers with 99% confidence.

Two norms on a linear space X are equivalent if they define the same topology, meaning they have the same open sets. To show ||x||p and ||x||[infinity] are equivalent in Rⁿ, use the inequalities max |xi| ≤ (Σ [tex]|xi|p)^{1/p}[/tex] ≤ [tex]n^{1/p}[/tex] max |xi|.

To show that two norms on a linear space X are equivalent if and only if they have the same open sets,

If two norms on X are equivalent, then they have the same open sets.

Let ||·|| and ||·||' be two equivalent norms on X, meaning that there exist positive constants c1 and c2 such that for any x in X,

c1||x|| <= ||x||' <= c2||x||

To show that ||·|| and ||·||' have the same open sets, we need to prove that a set U is open with respect to ||·|| if and only if it is open with respect to ||·||'.

Suppose U is open with respect to ||·||. Let x be any point in U, and let r be a positive real number such that the open ball B(x, r) = {y in X : ||y - x|| < r} is contained in U. We want to show that there exists a positive real number r' such that the open ball B'(x, r') = {y in X : ||y - x||' < r'} is also contained in U.

Let c = c2/c1, and choose r' = r/c2. Then, for any y in B'(x, r'), we have

||y - x||' <= c2||y - x||/c2 = ||y - x||

Therefore, y is also in B(x, r), which implies that y is in U. Hence, U is open with respect to ||·||'.

Conversely, suppose U is open with respect to ||·||'. Let x be any point in U, and let r' be a positive real number such that the open ball B'(x, r') = {y in X : ||y - x||' < r'} is contained in U. We want to show that there exists a positive real number r such that the open ball B(x, r) = {y in X : ||y - x|| < r} is also contained in U.

Let c = c2/c1, and choose r = c1r'. Then, for any y in B(x, r), we have

||y - x||' <= c2||y - x||/c1 <= c2r/c1 = r'

Therefore, y is also in B'(x, r'), which implies that y is in U. Hence, U is open with respect to ||·||.

In Rⁿ, show that the following norms are equivalent

||x||p = (Σ[tex]|xi|^p)^{1/p}[/tex] and ||x||[infinity]: = max |xi|

i=1 1≤i≤n

To show that the two norms are equivalent, we need to show that there exist positive constants c1 and c2 such that c1||x||[infinity] ≤ ||x||p ≤ c2||x||[infinity] for all x in Rⁿ.

First, we will show that c1||x||[infinity] ≤ ||x||p. Let x be any element in Rⁿ. Then,

||x||[infinity] = max{|x1|, |x2|, ..., |xn|} ≤[tex]|x1|^p + |x2|^p + ... + |xn|^p[/tex] = Σ[tex]|xi|^p[/tex]

Since p > 0, we can take the p-th root of both sides to get

||x||[infinity] ≤ (Σ[tex]|xi|^ \infty)^{1/p}[/tex] = ||x||p

Therefore, c1 = 1 is a valid constant.

Next, we will show that ||x||p ≤ c2||x||[infinity]. Let x be any element in R^n. Then,

||x||p = (Σ[tex]|xi|^p)^{1/p}[/tex] ≤ (Σ[tex]|xi|^ \infty)^{1/p}[/tex]=[tex]n^{1/p}[/tex] ||x||[infinity]

Therefore, c2 = [tex]n^{1/p}[/tex] is a valid constant.

Since we have found positive constants c1 and c2 such that c1||x||[infinity] ≤ ||x||p ≤ c2||x||[infinity], we have shown that the two norms are equivalent.

To know more about linear space:

https://brainly.com/question/31644229

#SPJ4

The probability that a randomly selected golf ball will be purple is 1/6

From the question, we have the following parameters that can be used in our computation:

The probability that a randomly selected golf ball will be purple is calculated as

Probability = Purple/Number of golf balls

Substitute the known values in the above equation, so, we have the following representation

Probbaility = 2/12

Simplify

Probbaility = 1/6

Hence, the value of the probability is 1/6

Read more about probability at

https://brainly.com/question/251701

#SPJ1

Answer:

The 18 oz jar is the better buy.

Step-by-step explanation:

Q1 = 44000 + (-0.6745) * 12166 = 36753 (rounded to the nearest whole number)

a. The distribution of X is normal with mean 44,000 and standard deviation 12,166.

b. Let Z be the standard normal variable. Then,

Z = (57239 - 44000) / 12166 = 1.0933

Using a standard normal table or calculator, we find that P(Z < 1.0933) = 0.8628. Therefore, the probability that a randomly selected acre in the forest has fewer than 57,239 ants is 0.8628.

c. Let Z1 and Z2 be the standard normal variables corresponding to 44,753 and 59,087, respectively. Then,

Z1 = (44753 - 44000) / 12166 = 0.0611

Z2 = (59087 - 44000) / 12166 = 1.2463

Using a standard normal table or calculator, we find that P(0.0611 < Z < 1.2463) = 0.3653. Therefore, the probability that a randomly selected acre has between 44,753 and 59,087 ants is 0.3653.

d. The first quartile corresponds to the cumulative probability of 0.25 in a standard normal distribution. Using a standard normal table or calculator, we find that the Z-score corresponding to a cumulative probability of 0.25 is approximately -0.6745. Therefore, the first quartile of the distribution of ants per acre in the forest is:

Q1 = 44000 + (-0.6745) * 12166 = 36753 (rounded to the nearest whole number)

To learn more about corresponding visit:

https://brainly.com/question/1597341

#SPJ11