Let (V, ∥ · ∥) be a complete normed vector space and its induced metric d(x, y) = ∥x − y∥ for x, y ∈ V . Suppose f : V → V is a linear function, i.e., f(x + y) = f(x) + f(y), ∀ x, y ∈ V and f(αx) = αf(x) for all x ∈ V and α ∈ R. You may use the following facts without proof: f(0) = 0 and f(x − y) = f(x) − f(y), ∀ x, y ∈ V .
(1) Show that f is a (strict) contraction if and only if there exists a constant C with 0 < C < 1 such that ∥f(x)∥ ≤ C∥x∥ for all x ∈

Given the word problem, we can deduce the following information:

1. The ratio of the two complementary angles is 3:7.

To determine the measures of both angles, we must note first that complementary angles are two angles whose measures add up to 90°. So our equation would be:

We simplify the equation above:

We plug in x=9 into 3x to get the first angle:

Angle 1 = 3x = 3(9) = 27

Then, we plug in x=9 into 7x to get Angle 2:

Angle 2= 7x=7(9)=63

Therefore, the measures of both angles are 27° and 63°.

Answer:

61 miles

Step-by-step explanation:

The two triangles are congruent so GF is congruent to PN.

PN = 61

All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

Learn more about variable quantities on

https://brainly.com/question/14257045?referrer=searchResults

#SPJ4

Answer:

To find the perimeter of a polygon, you just have to add the values of each side.

For example, if a rectangle has a length of 10 inches and a width of 5 inches, you would add, 10 + 10 + 5 + 5, which is equal to 30. This is found because the length of one side is 10, the other is also 10, and the width is 5, and the other is also 5.

Answer:

270 9764

359

548

69

80

554

331

594

850

667

216

8674

213

253

5

3

64

7

45

692

213

649

8574

6646

549

837

849

The correct interpretation of a 95% confidence interval for the proportion of young adults who skip breakfast being .20 to .27 is that there is a 95% chance that the true proportion of young adults who skip breakfast lies between .20 and .27.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. In this case, we are 95% confident that the true proportion of young adults who skip breakfast lies between .20 and .27. This means that if we were to repeat this study many times, 95% of the resulting confidence intervals would contain the true proportion of young adults who skip breakfast. It is important to note that this does not mean that there is a 95% chance that the true proportion of young adults who skip breakfast is between .20 and .27, but rather that we are 95% confident that it is.

To learn more about confidence interval : brainly.com/question/29680703

#SPJ11

$21.00

Step-by-step explanation:

if 1 yard equal 6 dollars

do 6 times 3 = 18

and half of 6 is 3

add 18+3=21 dollars

Answer:

y=1/6x+2

Step-by-step explanation:

To start, you know what m is; it's just the slope, which you said was 1/6. So you can right away fill in the equation for a line somewhat to read:

y=1/6x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(12,4). When x of the line is 12, y of the line must be 4.

Because you said the line passes through this point, right?

Now, look at our line's equation so far: . b is what we want, the 1/6 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (12,4).

So, why not plug in for x the number 12 and for y the number 4? This will allow us to solve for b for the particular line that passes through the point you gave!.

(12,4). y=mx+b or 4=1/6 × 12+b, or solving for b: b=4-(1/6)(12). b=2.

Answer:

52°

Step-by-step explanation:

it should always add up to 180°

The speed of the car traveling at 45 miles per hour can be converted to feet per second.The car's speed of 45 miles per hour can be converted to feet per second by multiplying it by the conversion factor of 1.46667.

Therefore, the car's speed is approximately 66.0 feet per second.To convert the speed from miles per hour to feet per second, we need to consider the conversion factors. One mile is equal to 5,280 feet, and there are 3,600 seconds in an hour. To convert miles per hour to feet per second, we can multiply the speed in miles per hour by the following conversion factor: 5280 feet/1 mile × 1 hour/3600 seconds. Simplifying this expression, we get 1.46667 feet/second. Multiplying this conversion factor by the car's speed of 45 miles per hour, we find that the car is traveling at approximately 66.0 feet per second.

To learn more about car click here: brainly.com/question/31448756

#SPJ11

Based on the given side lengths (a=16 mm, b=63 mm, c=65 mm), the triangle is a(n) right triangle. This is because it satisfies the Pythagorean theorem: a² + b² = c² (16² + 63² = 65²).

A right triangle is a triangle with two perpendicular sides and one angle that is a right angle (i.e., a 90-degree angle). The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

The hypotenuse, or side c in the illustration, is the side that is opposite the right angle. Legs are the sides that meet at the correct angle. Side a may be thought of as the side that is opposite angle A and next to angle B, whereas side b is the side that is next to angle A and next to angle B.

A right triangle is considered to be a Pythagorean triangle and its three sides are referred to as a Pythagorean triple if the lengths of all three of its sides are integers.

Visit here to learn more about  trigonometry : brainly.com/question/26719838

#SPJ11

Answer:

9.8

Step-by-step explanation:

=5.9 . tan 59° = 5.9 × 1.66 = 9.8

The IH states that the sum of the angles in convex polygon C(which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A.

Using induction all convex polygons with n vertices have angles that add to (n - 2)·π, therefore let P(n) be that. We will demonstrate that P(n), where n≥3, holds for every n ∈ N. We demonstrate P(3), which states that any convex polygon with three vertices has an angle total of 180 degrees. Any triangle formed by such a polygon has angles that add up to 180°.

Assume that P(n) holds for some n ≥ 3 and that all convex polygons with n vertices have angles that add to (n-2) 180° for the inductive step. We demonstrate P(n+1), which states that each convex polygon with n+1 vertices has an angle sum of (n-1)·π. Let A represent any n+1-vertex convex polygon.

The IH states that the sum of the angles in convex polygon C (which, by the IH, is (n - 2)·π) and the sum of the angles in triangle B (180°) is the same as the sum of the angles in A. As a result, the total angle in A is (n-1) 180°. Thus, the induction is complete and P(n + 1) holds.

To learn more about angles in convex polygon link is here

brainly.com/question/13585442

#SPJ4

Answer:

7 cm

Step-by-step explanation:

An equilateral triangle has all sides equal.

To find the measure of the side, simply divide the perimeter by 3. This is because a triangle has 3 sides.

21 ÷ 3 = 7

Answer:

7

Step-by-step explanation:

a number: x

3 times a number: 3x

twenty-two more than 3 times a number: 3x + 22

difference between 64 and 3 times the number: 64 - 3x

3x + 22 = 64 - 3x

6x = 42

x = 7

Answer: 7

The fill up for the missing steps are:

Note that we are given:

Based on the definition of perpendicular lines, ΔFHG ~ ΔKJG  are known to be right angles.

So: Δ FHG ≅  ΔKJG due to the fact that all the right angles are congruent.

ΔFHG  and  ΔKGJ are vertical angles and as such, the angle are congruent to angle  ΔKGJ

Based on AA similarity theorem, ΔFHG ~ ΔKJG

Due to the above, the fill up for the missing steps are:

Learn more about congruent angles from

https://brainly.com/question/7724930

#SPJ1

Answer:

D) The ratification of a constitutional amendment establishing term limits for presidents.

Step-by-step explanation:

If a president were to exceed his limits of power over the people, he would consider them as slaves, and him the king.

Answer:

D

Step-by-step explanation:

Answer: \(17.33ft\)

Step-by-step explanation:

We need to go from area to radius to circumference.

Formula for the area:

\(A=\pi r^2\)

Solve for r;

Divide by pi

\(r^2=\frac{A}{\pi}\)

Extract the square root.

\(r=\sqrt{\frac{A}{\pi} }\)

Plug in the value of the area.

\(r=\sqrt{\frac{24ft^2}{3.14} } \\r=2.76ft\)

Now that you've found the radius, use the circumference formula to calculate it.

\(C=2\pi r\\C=2(3.14)(2.76ft)\\C=17.33ft\)

Answer:

the 1st one

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i got it right

The exponential form of given number 121200 is 1.212 × \(10^5\)

And the earth sun distance in kilometers in powers of 10 notation is 1.5 × \(10^8\)

For given question,

We need to express 121,200 in exponential (powers of 10) notation.

To use scientific notation, pick a value between 1 and 10, then multiply it by 10ˣ.

The number between 1 and 10 in 121200 is 1.212 with 5 decimal points.

So, the exponential notation of given number would be,

121,200 = 1.212 × \(10^5\)

Earth's average distance from the Sun is around 93 million miles (150 million kilometers). That's one AU.

So the number between 1 and 10 in 150,000,000 is 1.5, with 8 decimal points.

So, the distance between he Earth and the Sun is:

150,000,000 = 1.5 × 10⁸

Therefore, the exponential form of given number 121200 is 1.212 × \(10^5\)

And the earth sun distance in kilometers in powers of 10 notation is 1.5 × \(10^8\)

Learn more about the powers of 10 here:

https://brainly.com/question/13303295

#SPJ4

Answer:

-8 < x < -2

start number line at -10 and end it at 0

draw an open circle* over the dash indicating -8 and -2

connect the open circles

*open circle because it is less than and greater than, not less than or equal to and greater than or equal to

Answer:

-8<x<-2

Step-by-step explanation:

yw luv :D

The actual time is 6:30.

Since Sri's car clock is not accurate, it is gaining time at a constant rate. By knowing that at 12:00 noon the car clock and the watch were in sync, we can estimate that the car clock is gaining 5 minutes per hour.

Therefore, when Sri looks at his car clock at 7:00 and his watch is missing, we can calculate that the actual time is 6:30. This is done by subtracting the 5-minute difference in time between the car clock and the watch at 12:30 (12:35 car clock, 12:30 watch) from the 7:00 car clock. The result is 6:30.

To learn more about subtracting, visit:

brainly.com/question/2346316

#SPJ4

Answer:

Variability (also called spread or dispersion) refers to how spread out a set of data is. Variability gives you a way to describe how much data sets vary and allows you to use statistics to compare your data to other sets of data. The four main ways to describe variability in a data set are: range. Interquartile range.

Step-by-step explanation:

Answer:

The total weight in tons the cars on the truck= 18 tons.

Step-by-step explanation:

The statement "the first step in the sampling design process is to determine the sample size" is false because according to the text, the first step in the sampling design process is to clearly define the target population.

The first step in the sampling design process is typically to define the target population and the research objectives.

This involves specifying the characteristics of the population under study and identifying the specific research questions or objectives that the sampling will address.

Once the target population and research objectives are established, the next steps in the sampling design process typically involve determining the appropriate sampling method (such as random sampling, stratified sampling, or cluster sampling) and selecting the sampling frame (the list or source from which the sample will be drawn).

After these initial steps, researchers can then consider factors such as the desired level of precision, confidence level, and variability in the population to determine the appropriate sample size.

The determination of the sample size usually comes after clarifying the research objectives and selecting the appropriate sampling method.

To know more about sampling design refer here:

https://brainly.com/question/32283666#

#SPJ11

Answer:

Here's for you...........

Answer:

D and A

Step-by-step explanation:

1. 610:488 simplify

5:4

2.360:(488+551+610+360+391)

360:2400

3:20

Answer:

yo you know you can use the brainly scan &solve

Answer:

240 cm^2

find the scale factor of the length

k=20/6=3.33...

multiply the area of triangle ABC by the scale factor so 72 x 3.333..=240