Let V be a vector space, T:V + V be a linear transformation and W be a one dimensional subspace of V. Prove that W is an invariant sub- space under T if and only if all non-zero vectors in W are eigenvectors of T.

Answer: 6.2

Step-by-step explanation:

Using the arc length formula,

[tex]x=\frac{118}{360}(2)(3)(\pi) \approx 6.2[/tex]

The composition of two functions, g(x) and h(x), is written as (g•h)(x).

Function in math is a relationship between two variables where one variable determines the behavior of the other. It is a mathematical expression that assigns each element in a set to a specific output. Functions can be used to represent things like motion, growth, and decay. They are used to create models that can be used to make predictions and analyze data. Functions are used throughout mathematics and science and can be used to solve real-world problems.

This means that the output of function g(x) is used as the input of function h(x). In this case, (g•h)(x) is equal to h(g(x)). So, (g•h)(x) = h(x-2) = (x-2)^2 - 1.

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Answer:

Step-by-step explanation:

The inequality that represents all the solutions of 10(3x + 2) > 7(2x − 4) is 10(3x + 2) > 7(2x − 4). To solve this inequality, first we must combine like terms on each side of the inequality. On the left side, 10(3x + 2) becomes 30x + 20. On the right side, 7(2x − 4) becomes 14x − 28. After combining the like terms, the inequality becomes 30x + 20 > 14x − 28. Next, we must subtract 14x from both sides of the inequality. On the left side, 30x + 20 becomes 16x + 20. On the right side, 14x − 28 becomes −28. After subtracting 14x from both sides, the inequality becomes 16x + 20 > −28. Finally, we must subtract 20 from both sides of the inequality. On the left side, 16x + 20 becomes 16x. On the right side, −28 becomes −48. After subtracting 20 from both sides, the inequality becomes 16x > −48. To solve the inequality, we must divide both sides of the inequality by 16. On the left side, 16x becomes x. On the right side, −48 becomes −3. Therefore, the solution to the inequality is x > −3.

The system of equations to describe the condition is,

22x + 74y = 10274

48x +  61y = 10261

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

Yesterday, the organization sold 22 regular tickets and 74 VIP tickets, raising $10,274

Today, 48 regular tickets and 61 VIP tickets were sold, bringing in a total of $10,261

Cost of regular ticket = ?

Cost of VIP ticket = ?

Suppose,

Cost of regular and VIP ticket are respectively,  x & y

22x + 74y = 10274

48x +  61y = 10261

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0.1728 suburban park users bike on the park trail.

A mathematical comparison of two numbers is called a proportion.

It is an equation or statement used to depict that two ratios or fractions are equal.

According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

The proportion (p) is calculated as:

p = bike the trail/number of residents

Given that,

The number of users who bike the trail = 42

The number of residents using the park trails = 243

Thus,

p = 42/243 = 0.1728

Therefore, 0.1728 suburban park users bike on the park trail.

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On solving the provided question, we can say that equation let x =amount of copies sold  = > 37,600is = .073  X x = 515,068.4932.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

let x =amount of copies sold to date.

37,600is = .073  X x

t x = 37,600 / .073

= 515,068.4932.

round to nearest 515,068.

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The perimeter of the rectangular community garden, after the size has been altered by a factor of 20, is 130 feet.

In two-dimensional shapes, a perimeter is defined to be a closed path that surrounds or outlines a shape. The perimeter of a circle or an ellipse though is called the circumference.

The perimeter P of a rectangle is equal to two times the length l plus two times the width w [P = 2(l + w)]. The length and the width of the rectangular community garden are consecutively 2,25 and 1 feet, and the scale factor is 20.

Therefore, the perimeter of the community garden is

P = 2(l + w) · 20

P = 2(2,25 + 1) · 20

P = 6.5 · 20

P = 130 feet.

This question refers to the image attached.

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Answer:

130 feet

Step-by-step explanation:

Answer: half

Step-by-step explanation:

The graph provided in the exercise must be used in this task, together with our statistical understanding, so that we can state: correct option is A

Statistics is a discipline of applied mathematics concerned with the gathering, description, analysis, and derivation of inferences from quantitative data. Calculus of differential and integrals, linear algebra, and probability theory are key mathematical concepts in statistics.

Statistics provide us the knowledge we need to understand how things operate. To conduct research, assess results, foster critical thinking, and make wise judgements, statistics are utilized. Almost any subject of study may benefit from the application of statistics to explore the causes, timing, and predictability of events.

The maximum points on the graph are at 21 and 31, and the sample ranges appear to be centered below 32, so we may claim so the option A is more appropriate.

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The complete question is as follows:

Answer:

0.850

Step-by-step explanation:

The first step is to write the number in standard form. Then, you place the decimal point in the quotient above the decimal point of the dividend. Then, divide and bring down the other digits such as hundredths, thousandth, and ect.

Discriminatory practises are those that have a disparate impact or treatment. When compared to differential treatment, which is deliberate discrimination, disparate impact is frequently referred to as inadvertent discrimination. Alternative words for this concept include adverse effect and adverse treatment.

Disparate treatment discrimination, put simply, is when a company treats a current employee or potential employee improperly due to that person's race, religion, colour, sex, national origin, etc. This type of discrimination is usually the most apparent and visible.

Disparate treatment and disparate impact are two different things; disparate treatment is purposeful discrimination, whereas disparate impact is accidental.

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The length of segment  is 24/√2

Given that,

Having radii of 2 and 4, respectively, and being externally tangent, are circles with centers O and P. The circle with the center at O has points A and B, while the circle with the center at P has points C and D, so that

AD and BC are frequent tangents to the outside of the circles.

To find : What is the hexagon's area?

ADPO and OPBC are congruent right trapezoids with legs 2 and 4 and with OP equal to 6. Draw an altitude from O to either DP or CP,

Creating a rectangle with width 2 and base x, and a right triangle with one leg 2, the hypotenuse 6, and the other aa Using the Pythagorean theorem,  is equal to  , and x is also equal to the height of the trapezoid. The area of the trapezoid is thus

length = 1/2 * (4+2).4√2 = 12√2

and the total length is two trapezoids, or 24/√2

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Answer:

The answer is A.

Step-by-step explanation:

Lets prove the other ones wrong.

B) It is not based on a day to day prediction, rather days with simmilar conditions before the storm.

C) The United states is too broad an area.

D) It is not based on the ammount of days it snows per month, because on say December 15 it could be 60 degrees and on December 25 it could be 2 degrees. Also you could not make any predictions on a per-day basis then.

So the only clear answer is "Historically, in this area, it has snowed 10% of the time on days with similar meteorological conditions as today."

The sine function that matches the graph is given as follows:

y = 3sin(π/5(x + 0.5))

The sine function for this problem is defined as follows:

y = Asin(B(x - C)) + D.

The parameters are described as follows:

The function has a minimum value of -3 and a maximum value of 3, for a difference of 6, hence the amplitude is obtained as follows:

2A = 6

A = 3.

The function has no vertical shift, as it oscillates between -1 x 3 = -3 and 1 x 3 = 3.

The period is of 10 units, hence the coefficient B is given as follows:

2π/B = 10

10B = 2π

B = π/5.

Due to it's midline, the function was shifted 0.5 units left, hence the coefficient C is given as follows:

C = -0.5.

Hence the function is defined as follows:

y = 3sin(π/5(x + 0.5))

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The positive and negative roots of the given quadratic graph are; -2 and 4.

We want to find the positive and negative roots of the quadratic graphs. Now, the general form of quadratic equations is expressed as;

y = ax² + bx + c

Now, for a quadratic graph, the roots are defined as the value of x where the curve crosses the x-axis.

In this given graph, we can see that the y-intercept which is the point at which the curve crosses the y-axis is at y = -8. We also see that the points at which the graph crosses the x-axis are at x = -2 and x = 4. This clearly shows that one root is positive and one root is negative.

Therefore from the two x-intercept values above as well as the y-intercept we got and when considering the type of roots that are being looked for, we can easily conclude that the positive and negative roots are as gotten above.

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Answer:C

Step-by-step explanation:

x is [tex]\sqrt{7} \\[/tex]=2.645

which means 2.645²=7

Answer:

yes because it's like multiplying my 1/2.

when you multiply a number with a fraction its the same as dividing.

Step-by-step explanation:

Example: 6/1 × 1/2 = 3

Answer:

Step-by-step explanation:

To find the annual tax withheld, you would need to calculate the amount of income tax that you owe based on your income and the state income tax rate.

You earn $56,000 per year and the state income tax rate is 5.5%. To find the amount of tax you owe, you would multiply your income by the tax rate.

Tax Owed = Income x Tax Rate

Tax Owed = 56,000 x 0.055

Tax Owed = 3,080

So, the annual tax withheld from your salary would be $3,080.

use the 20m/70ft as the next depth and put 27 minutes for the criteria ABT. With the surface interval of 62 mins and G as the new pressure group. Use the 18m/60ft as the final depth, the final ABT will be approximately 34 mins.

If we use the general Dive Planning mode on the eRDPML and insert the option "No" for the Multilevel Dive. Furthermore, insert the option "Yes" for the First Dive. If we use 25m/80ft and click the enter button when the NDL appears. Also put 22 minutes for the criteria ABT. For the surface interval (i.e. 52 mins), E/D is the new pressure group.

i am an advanced open water diver. i plan to do three dives. the first dive is a 25-meter dive for 22 minutes followed by a 52-minute surface interval. the second dive is to 20 meters for 27 minutes followed by a surface interval of 62 minutes. my third dive is to 18 meters.

In addition, use the 20m/70ft as the next depth and put 27 minutes for the criteria ABT. With the surface interval of 62 mins and G as the new pressure group. Use the 18m/60ft as the final depth, the final ABT will be approximately 34 mins.

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A quarter-circle with a radius of 5 has the area: 25π/4, This is where the shaded area in the figure is located.

The area of a circle’s sector is calculated as /360o (r²), where r is the radius of the circle and is the angle of the sector.

The little, subtle distinctions between words are distinguished by shades of meaning. The terms “happy” and “ecstatic,” for example, both express emotion, but one is more powerful than the other. When students study shades of meaning, they learn how to effectively articulate how they feel or think. Shade is any gloomy place where sunshine or other strong light is obstructed. A shadow is a dark form that develops on a surface when an item blocks sunlight or other light.

The shaded area in the illustration is a quarter-circle with a radius equal to 10/2, or 5 units, or half the length of the square's side.

The following formula can be used to determine a circle's area:

A = πr²

If pi is present and r is the radius (approximately equal to 3.14).

A quarter-circle with a radius of 5 has the following area:

A = (π × 5²) / 4 = (π × 25) / 4 = 25π / 4

This is where the shaded area in the figure is located.

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Answer:

m(w) = $25+$20w

Step-by-step explanation:

Let m be the amount saved and w the weeks since the account was opened.  Greta starts with $25, so m(0) = $25.

She saves $20 each week, w.  m(1), the end of the first week, Greta would have $25 + $20 = $45.  This continues for future weeks.  We could write this as the follwoing:

 m(w) = $25+$20w

Week 5, for example, would end with m(5) = $25+$20*(5)

       m(5) = $125.

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x.

Part a:

The value of the integral from 0 to 6 of f(x)dx is 16. This can be calculated using the Fundamental Theorem of Calculus (FTC) which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫f(x)dx = F(6) - F(0)

The anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫f(x)dx = (62 + 2*6) - (02 + 2*0) = 36 - 0 = 16.

Part b:

The value of the integral from 4 to 9 of g(x)dx is 20. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫g(x)dx = G(9) - G(4)

The anti-derivative of g(x) is G(x) = x3 + 3x2, so the value of the integral is:

∫g(x)dx = (93 + 3*9) - (43 + 3*4) = 729 - 168 = 20.

Part c:

The value of the integral from 4 to 9 of 2*g(x) - f(x)dx is 68. This can be calculated using the FTC which states that the integral of a function is equal to the anti-derivative of that function evaluated at the upper limit minus the anti-derivative of that function evaluated at the lower limit. This can be written as:

∫(2*g(x) - f(x))dx = 2*G(9) - F(9) - [2*G(4) - F(4)]

The anti-derivative of g(x) is G(x) = x3 + 3x2 and the anti-derivative of f(x) is F(x) = x2 + 2x, so the value of the integral is:

∫(2*g(x) - f(x))dx = (2*(93 + 3*9) - (92 + 2*9)) - [2*(43 + 3*4) - (42 + 2*4)]

= (1854 - 19) - (544 - 16) = 1735 - 528 = 68.

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The surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.

The surface area of a box with a height of 8 inches, a length of 12 inches, and a width of 6 inches can be calculated using the formula SA = 2lw + 2lh + 2wh. In this case, SA stands for surface area, l stands for length, w stands for width and h stands for height.

To calculate the surface area of the box, substitute the given values for l, w and h into the formula and solve:

SA = 2(12)(6) + 2(12)(8) + 2(6)(8)

SA = 144 + 192 + 96

SA = 432 square inches

Therefore, the surface area of the box with a height of 8 inches, a length of 12 inches, and a width of 6 inches is 432 square inches.

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The probability of getting a difference of 3 when two fair dice are thrown together is 1/9.

Probability is the measure of how likely it is that a certain event will occur. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that an event is certain. Probability can also be expressed as a percentage or fraction. Probability is used to describe the likelihood of an event occurring, and its calculation is based on the number of possible outcomes of the event.

This is due to the fact that there are 6 possible outcomes for each dice, and 36 possible outcomes when both dice are thrown. The only way to get a difference of 3 is for the first dice to show a 4 (1/6 probability) and the second dice to show a 1 (also 1/6 probability). This gives a combined probability of 1/6 x 1/6 = 1/36, which is 1/9.

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The radius of the circle will be [tex]\sqrt{22}[/tex].

In our question, we shall first extend QRS to the circle's point T.

According to the power of a point.

[tex]QP^{2}[/tex]  =  QR*QT

[tex]6^{2}[/tex]  =  3*QT

QT = 12

Since QR = 3, RT = 9.

Since RS = 3, ST = 6.

Draw OT and OR, creating a triangle(TSO) and triangle(RSO).

OT and OR are radii, Let the radius be r.

Use the Law of Cosines on these two triangles.

OT2  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

OR2  =  r2  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

Since these are equal:

[tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)  =  [tex]3^{2}[/tex] + [tex]2^{2}[/tex] - 2*3*2*cos(RSO)

40 - 24*cos(TSO)  =  13 - 12*cos(RSO)

Since angle(RSO) is supplementary to angle(TSO),  cos(RSO) = - cos(TSO)

40 - 24*cos(TSO)  =  13 + 12*cos(TSO)

27  =  36*cos(TSO)

0.75  =  cos(TSO)

Since  [tex]OT^{2}[/tex]  =  [tex]r^{2}[/tex]  =  [tex]6^{2}[/tex] + [tex]2^{2}[/tex] - 2*6*2*cos(TSO)

[tex]r^{2}[/tex]  =  40 - 24*0.75  

[tex]r^{2}[/tex]  =  22

r  =  [tex]\sqrt{22}[/tex]

Hence the radius of the given circle will be [tex]\sqrt{22}[/tex].

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The probability that the quarterback completes his first pass on his 4th attempt is 0.44

The term probability in math is defined as the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes

Here we have given that assume a quarterback completes 44% of his passes.

Here we have to convert the percentage into decimal form, then we get,

=> 44/100

When we divide it, then we get the probability that the quarterback completes his first pass on his 4th attempt is written as,

=> 0.44

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24 different seatings are possible when five people are to be seated around a circular table such that two seatings are considered the same if one is a rotation of the other.

What is fundamental counting principle?

A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle. It asserts that if there are n ways to do something and then m ways to do something else, then there are nm methods to do both of these acts. The Fundamental Principle of Counting assists in determining how selection is made based on available options. The Fundamental Principle of Counting streamlines the method to choosing by taking into account all of the available options and their combinations in order to calculate the Probability.

Here,

Since there are 5 peoples,

let us fix the first person and remaining will be set according to that.

this can be arranged in,

(5-1)!=4!

=24 ways

When five persons are sitting around a circular table, 24 distinct seatings are available, with two seatings regarded the same if one is a rotation of the other.

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Answer:

Step-by-step explanation:

width = 3x + 1

height = (24x^3 - 58x^2 + 23x + 15) / (12x^2 - 11x - 5)

Answer:

2.56% or 2.6% (to nearest 10th of a %)

Step-by-step explanation:

Percent error is determined by the expression

    [(Measured - Actual)/Actual]*100%

 [16" - 15.6"]/(15.6")*100% = 2.56%

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