What is the correct answer?

The function T((x, y)) = (x + y, x) is a linear transformation. Its matrix representation can be found by mapping the standard basis vectors and arranging the resulting vectors into a matrix.
The basic box representing the transformation can be drawn by considering the images of the standard unit vectors.

To show that T((x, y)) = (x + y, x) is a linear transformation, we need to demonstrate that it preserves vector addition and scalar multiplication.

Let's consider two vectors, u = (x₁, y₁) and v = (x₂, y₂), and a scalar c. The transformation of the sum of u and v is T(u + v), which is equal to (x₁ + y₁ + x₂ + y₂, x₁ + x₂). On the other hand, the sum of the individual transformations T(u) + T(v) is (x₁ + y₁, x₁) + (x₂ + y₂, x₂) = (x₁ + y₁ + x₂ + y₂, x₁ + x₂). Hence, T(u + v) = T(u) + T(v), satisfying the property of vector addition.

Similarly, the transformation of the scalar multiple of a vector c * u is T(cu), which is (cx + cy, cx). The scalar multiple of the transformation c * T(u) is c * (x + y, x) = (cx + cy, cx). Thus, T(cu) = c * T(u), demonstrating the property of scalar multiplication.

To find the matrix representation of the transformation T, we can map the standard basis vectors, i = (1, 0) and j = (0, 1), and arrange the resulting vectors into a matrix. Applying T to i and j, we have T(i) = (1, 1) and T(j) = (0, 0). Thus, the matrix representation of T is:

| 1 0 |

| 1 0 |

To draw the basic box representing the transformation, we consider the images of the standard unit vectors i and j. The image of i is (1, 1), and the image of j is (0, 0). Plotting these points on the coordinate plane, we can draw a box connecting them. This box represents the basic shape that gets transformed by the linear transformation T.

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Answer:

The next two numbers are: 70 and 70

Explanation:

Given the following series of numbers:

0.007, 0.07, 0.7, 7

We want to know the next two numbers

First, let us find the common ratio of the geometric series

The common ratio is the division of a number in the sequence by it's preceeding number.

If the sequence is: T1, T2, T3, T4, and so on, the common ratio is:

T2/T1 or T3 /T2 or T4/T3, and so on.

The common ratio of the given series is:

0.07/0.007 = 10

Note that this is the same as:

0.7/0.007, and 7/0.7

Now, to get the next number, simply multiply the last number by the common ratio, 10.

After 7, we have 7 * 10 = 70

After 70, we have 70 * 10 = 700

So, the next two numbers are: 70 and 700

We found that the height of the short wall "x" is 162.6 ft, the height of the tall wall "y" is 221.8 ft, and the distance between the canyon walls "z" is 162.6 ft.

To find the x, y, and z values we need to denote the right triangles from top to bottom as triangles 1, 2, and 3.

1. Finding the height of the short wall "x"

We can find the height of the short wall "x" (in triangle 3) with the following trigonometric function:

\( cos(\theta) = \frac{x}{H} \)

Where:

H: is the hypotenuse = 230 ft

θ: is the angle between x and H.

Knowing that the sum of θ and the angle 45° must be equal to 90°, θ is:

\( \theta = 90 - 45 = 45 \)

Hence, the height of the short wall "x" is:

\(x = cos(\theta)*H = 230cos(45) = 162.6 ft\)                

2. Finding the height of the tall wall "y"  

The height of the tall wall "y" is given by the sum of the bases of the two first right triangles (the right triangles 1 and 2):

\( y = y_{1} + y_{2} \)        

Where y₁ and y₂ can be calculated with the tangent and sine trigonometric functions.  

\(y_{1} = A*tan(20)\)        

\( y_{2} = 230sin(45) \)

Where A is the adjacent side to the angle 20°.

\( y = A*tan(20) + 230sin(45) \)      

Since the right triangles 2 and 3 form a square, with all the sides equals to x, we have:        

\( A = z = y_{2} = x = 230cos(45) \)        

We can use 230cos(45) or 230sin(45) to calculate y₂, so the height of the tall wall "y" is:      

\( y = y_{1} + y_{2} = A*tan(20) + 230cos(45) = 230cos(45)tan(20) + 230cos(45) = 221.8 ft \)                        

3. Finding the distance between the canyon walls "z"

As we said above, the "z" value is the same as "x", then:

\(z = x = 230cos(45) = 162.6 ft\)

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Risk probability is the level of probability that an investment will not produce the expected gain.

Risk probability refers to the likelihood that an investment will not generate the expected returns. It is an important concept in investment analysis and decision-making.  When making investment decisions, it is crucial to assess the potential risks involved. Risk probability helps us evaluate the likelihood of an investment not meeting our expectations. It provides an estimate of the chances of experiencing a loss or not achieving the desired level of gain.

For example, let's say you are considering investing in stocks. Before making a decision, you would analyze various factors such as market trends, company performance, and economic indicators. By assessing the risk probability, you can determine the likelihood of the investment not producing the expected returns. Also understanding the risk probability, investors can better manage their investment portfolios and make more informed decisions.

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Answer:

2^(7/2)

Step-by-step explanation:

Here, we want to write 2√32 as a power with a rational exponent.

That would be 2 * √32

= 2 * 32^1/2

= 2 * 2^5(1/2)

= 2 * 2^5/2

According to law of indices, this becomes the following;

2^(1 + 5/2)

= 2^(7/2)

The correct option is :

A package that weighs 7 pounds will cost $17 for both options.

The declaration that shows that the provided variables exist is a mathematical equation. When describing the scenario in this circumstance, two or more factors are taken into account.

The equation can be used to symbolize the price, y: Y is equal to 3 plus 2 times the weight of the package, x.

Another choice is for the buyer to pay a one-time price of $17, which is represented by the equation y = 17, in order to send the package.

We'll compare the equation as a whole.

In this case,

3 + 2x = 17

Compile similar terms

2x = 17 - 3

2x = 14

x = 14 divided by 2x = 7

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Answer:

m = 0.1

b = 5

Step-by-step explanation:

The slope-intercept formula is mx + b.

m = slope

b = y-intercept.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Answer:

m = 0.1

b = 5

Step-by-step explanation:

The equation is set up in point-slope form (y = mx + b).

y = mx + b

y = 0.1x + 5

Answer:

C the 3 one is the answer

Answer:

x=-4, y=-1

Step-by-step explanation:

Given the following system of equations, solve the system using elimination.

\(\left \{ {{-2x-y=9} \atop {2x-9y=1}} \right.\)

(1) - Add the equations together

\(\left\begin{array}{ccc}&-2x-y=9\\+&2x-9y=1\end{array}\right\\\\\Longrightarrow -10y=10\\\\\therefore \boxed{y=-1}\)

Notice how the x term was eliminated, hence the name for this method is "elimination."

(2) - Take the value we just found for y and plug it into either of the two equations and solve for x

\(2x-9y=1\\\\\Longrightarrow 2x-9(-1)=1\\\\\Longrightarrow 2x+9=1\\\\\Longrightarrow 2x=-8\\\\\therefore \boxed{x=-4}\)

(3) - Thus, the system is solved. When x=-4, y=-1.

Answer:

The missing angle to this triangle is 55 degrees, x is 14.65, and the other missing length is 8.4.

Step-by-step explanation:

In a triangle, all of the angles sum up to 180 degrees. We are given it is a right triangle with another given angle of 35 degrees. 180 degrees - 90 degrees - 35 degress is 55 degrees. Now, we can use law of sines to find x. x / sin 90 degrees = 12 / sin 55 degrees. sin 90 degrees can be simplified to 1. x = 12 / sin 55 degrees. x = 14.65. By using the pythagorean theorem, we can find the last missing side, which is 8.4.

The answer is option (C), that is, the events of rolling a fair die two times are independent. The events are neither disjoint nor exclusive.

When rolling a fair die two times, one can get any one of the 36 possible outcomes equally likely. Let A be the event of obtaining an even number on the first roll and let B be the event of getting a number greater than 3 on the second roll. Let’s see how the outcomes of A and B are related:

There are three even numbers on the die, i.e. A={2, 4, 6}. There are four numbers greater than 3 on the die, i.e. B={4, 5, 6}. So the intersection of A and B is the set {4, 6}, which is not empty. Thus, the events A and B are not disjoint. So option (A) is incorrect.

There is only one outcome that belongs to both A and B, i.e. the outcome of 6. Since there are 36 equally likely outcomes, the probability of the outcome 6 is 1/36. Now, if we know that the outcome of the first roll is an even number, does it affect the probability of getting a number greater than 3 on the second roll? Clearly not, since A∩B = {4, 6} and P(B|A) = P(A∩B)/P(A) = (2/36)/(18/36) = 1/9 = P(B). So the events A and B are independent. Thus, option (C) is correct. Neither option (A) nor option (C) can be correct, so we can eliminate options (D) and (E).

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Since they polled 22 people and this is a very small sample size to represent the entire population,

So it would have large chances to get inaccurate results.

Then, the wrong with this poll is

"The conclusion is based on a small sample."

Answer:

1/2x^3

Step-by-step explanation:

The formula for the volume of a rectangular prism is v = b x w x h (volume is base times width times height).

Just plug the numbers (or in this case variables) into the formula:

v = x times x times 1/2x

v = 1/2 times x^3

v = 1/2x^3

Volume

Option A

Viktor is in the 60th percentile, which is 85, while the percentile for 71 is 26.666.

Percentile is defined as the value below which a given percentage falls under. Ben, for instance, is the fourth tallest child in a group of 20, and eighty percent of the kids are shorter than you. As a result, Ben is in the 80th percentile.

We have the data

Sort the data as follows: 58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

employing the percentile formula,

Percentile is calculated as follows: 71 Percentile

(4 / 15)*100 Percentile

26.666 Percentile = (Number of Values Below "x" / Total Number of Values) 100

Consequently, 71's percentile is equal to 26.666.

Identifying the rank

Thus, the ranking is 0.6.

To find the rank for viktor

Find the percentile using the formula,

Percentile = Rank × Total number of the data set

Percentile = 0.6 × 15

Percentile = 9

Now, counting 9 values from left to right we reach 85, and we can say that all the values below 85 will come under the 60th percentile. In other words, 60% of the values are below 85.

The 60th percentile is 85

Thus viktor is in 60th percentile is 85

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Answer:

a. 452.4 cm³ to the nearest tenth b. 113.1 cm³ to the nearest tenth

c. 5.0 cm to the nearest tenth

Step-by-step explanation:

a. The volume of the water V₁ = πr²h since it is in a cylindrical container. r = 6 cm and h = 10 cm - 6 cm = 4 cm (since it is filled to a depth of 6 cm measuring from the top, so we have a height from the bottom of 10 cm - 6 cm = 4 cm).

So, V₁ = πr²h

= π × (6 cm)² × 4 cm

= 452.39 cm³

= 452.4 cm³ to the nearest tenth

b. The volume of the sphere V₂ = 4πr³/3 where r = radius of sphere = 3 cm.

V₂ = 4πr³/3

= 4π(3 cm)³/3

= 113.1 cm³ to the nearest tenth

c. When the sphere is placed in the container, the new volume of water in the container would be V = V₁ + V₂

So V = 452.4 cm³ + 113.1 cm³ = 565.5 cm³

Since the volume of water is still the volume of a cylinder, its height h is

h = V/πr²

= 565.5 cm³/π(6 cm)²

= 5.0 cm to the nearest tenth

Answer:

90 degrees

Step-by-step explanation:

A triangle's degrees add up to 180. You are already given 2 of the. Let x be the 3rd angle. Here is the equation: 29+61+x=18. x=90.

Hope this helped!

Answer:

A.90°

Step-by-step explanation:

A triangle's interior angles are equal to 180°.

So since two angles are given all you need to do is add the given angles and subtract the sum from 180°.

61°+29°=90°

180°-90°=90°

The missing angle m<R is equal to 90°

Your answer is: A.90°

Hope this helps! :)

Answer:

4.8

Step-by-step explanation:

12/5=2.4

2 times 2.4=4.8

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

10.

Step-by-step explanation:

Lets define a square root.  A square root is a number multiplied by itself.        10 x 10 = 100, this is the closest we can get to 105, therefore 10 is the answer.

Answer:

  2.76×10^-3 m/s²

Step-by-step explanation:

You want to know the acceleration of the moon toward the Earth, given its distance is 3.8×10^8 meters, Earth's mass is 5.98×10^24 kg, and the gravitational constant is 6.673×10^-11 N·m²/kg².

The acceleration of one body by another is ...

  a = GM/r²

where G is the gravitational constant, M is the body creating the gravitational field, and r is the distance between the masses.

  a = (6.673×10^-11)(5.98×10^24)/(3.8×10^8)² N/kg

  a = (6.673·5.98/3.8²)×10^(-11+24-16) m/s² ≈ 2.76×10^-3 m/s²

The amount she earned this week is £325

Shirley earns £52 for an 8 hour shift at a call centre.

Therefore,

8 hours = £52

1 hour = ?

cross multiply

1 hour earning = 52 / 8

1 hour earning = £6.5

Therefore,  In one week, Shirley works fifty hours at the call centre. The amount she earns during the week is as follows:

Hence,

amount she earns this week = 6.5 × 50

amount she earns this week = £325

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A logarithm is inverse of the power. The logarithm of the number cancels the exponents of the number. The statement A is true for the given equation which is,

\(x+1&=3^2\\\)

Given information-

The given logarithm expression is,

\(\log_3(x+1)=2\)

A logarithm is inverse of the power. The logarithm of the number cancels the exponents of the number.

The exponential rule of the logarithm is,

If,

\(log_a(b)=c\)

Then,

\(b=a^c\)

Use this logarithm law in the given equation,

\(\begin{aligned}\\ \log_3(x+1)&=2\\ x+1&=3^2\\ \end\)

The above equation is the equation of statement A.

Thus the statement A is true for the given equation which is,

\(x+1&=3^2\\\)

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Answer:

Option A:  is the correct statement

Step-by-step explanation:

Answer:

MSN < LSO

Step-by-step explanation:

Identical Shapes which makes them linear pairs because they pair with each other.

Thanks Please Mark Brainliest, (Trying to rank to genius)

Therefore, the explicit formula for the given geometric sequence is: B. an = 0.5 * (-0.2)^(n-1).

The given sequence is a geometric sequence, where each term is obtained by multiplying the previous term by a constant ratio. To find the explicit formula for this sequence, we need to determine the common ratio.

Looking at the given sequence, we can see that each term is obtained by multiplying the previous term by -0.2. Therefore, the common ratio is -0.2.

The explicit formula for a geometric sequence is given by:

aₙ = a₁ * rⁿ⁻¹

Where:

aⁿ represents the nth term of the sequence,

a₁ represents the first term of the sequence,

r represents the common ratio of the sequence,

n represents the position of the term.

Using the known values from the sequence, we have:

a₁ = 0.5 (the first term)

r = -0.2 (the common ratio)

Plugging these values into the formula, we get:

\(aₙ = 0.5 * (-0.2)^(n-1)\)

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The explicit formula for the given geometric sequence is an = 0.5(-0.2)^(n-1). The correct answer is B.

To find the explicit formula for the given geometric sequence, we observe that each term is obtained by multiplying the previous term by -0.2.

The general form of a geometric sequence is given by an = a1 * r^(n-1), where a1 is the first term and r is the common ratio.

In this case, the first term (a1) is 0.5, and the common ratio (r) is -0.2.

Plugging these values into the general formula, we get:

an = 0.5 * (-0.2)^(n-1).

Therefore, the explicit formula for the given geometric sequence is option B. an = 0.5 * (-0.2)^(n-1).

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Answer:320

Step-by-step explanation:PEMDAS. So first you would do the exponent 2^5= 32 (2x2=4 4x2=8 8x2=16 16x2=32)

Then you multiply 10x32 which equals 320

a. The value of the annuity is $326,450 and b. the interest is $99,451.

Periodic Deposit = $2000

Rate = 5.25% compounded quarterly

Time = 8 years

Since the deposits are made at the end of every three months, there are 8 * 4 / 3 = 10.6667 compounding periods.

Applying the formula to calculate the future value of an annuity:

FV = PMT x [((1 + r / n)^(n*t) - 1) / (r/n)]

where FV = Future Value of Annuity, PMT = Periodic Deposit, r = Interest Rate per compounding period, t = Time in years and n = Number of compounding periods

Therefore, the Future Value of Annuity is:

FV = $2000 x [((1 + 0.0525 / 4)^(4*10.6667) - 1) / (0.0525/4)] ≈ $326,449.56

Rounded to the nearest dollar, the future value is $326,450.

To find the interest, we subtract the sum of all deposits from the Future Value of Annuity, which is:

Interest = $326,449.56 - ($2000 x 4 x 8)≈ $99,450.56

Rounded to the nearest dollar, the interest is $99,451.

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The z - test static is, z = (0.38 -p₀) / 0.02, Where p₀ is the specific sample proportion.

To calculate the z-test statistic for this hypothesis test, we need to follow a few steps.

Determine the null and alternative hypotheses.

Let's assume our null hypothesis is H0: p = p₀,

Where p0 is the hypothesized proportion. And our alternative hypothesis is Ha: p ≠ p₀ (two-tailed test).

Calculate the standard error (SE) using the formula:

SE = √((p₀ * (1 - p₀)) / n)

Given that the sample proportion is 0.38 and the sample size is 801,

We can substitute these values into the formula:

SE = √((0.38 * (1 - 0.38)) / 801)

     ≈ 0.02

Calculate the z-test statistic using the formula:

z = (p - p₀) / SE

Substituting the values, we have:

z = (0.38 - p₀) / 0.02

Here the specific value of p₀ is not given.

Hence,

The z - test static is, z = (0.38 -p₀) / 0.02

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Answer:

first give options it is very hard to do