Pls help me with this question!!!

The matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

\(\textbf{To find the matrix of } t \textbf{ relative to the basis } b', \textbf{we have to follow some steps. The steps are described below:}\)

First, we have to find the images of basis vectors under the transformation \(t\). \(t(-1,1) = (-9,7)\) and \(t(1,-5) = (-37,43)\).

Represent the image vectors of the basis in the standard basis. We use these vectors as columns in the matrix of \(t\) in the basis \(b'\).

\((-9,7) = -9(1,0) + 7(0,1) = (-9,7) = -9(-1,1) + 7(1,-5)\)

\((-37,43) = -37(1,0) + 43(0,1) = (-37,43) = -37(-1,1) + 43(1,-5)\)

Hence, we can write the following equation: \(A[x]_{b'} = [x]_S\)

Where \(A[x]_{b'}\) is the main answer in the form of a matrix, and \([x]_S\) is the coordinate of \([x]_{b'}\) with respect to the standard basis.

Now, we will write the equations with the coordinates of the basis vectors of \(b'\).

\(A[1,0] = [-9, -37]\) and \(A[0,1] = [7, 43]\)

Now we will write the matrix of \(A\) as follows:

\(A = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\)

Thus, the matrix of \(t\) relative to the basis \(b'\) is \(A' = \begin{bmatrix} -9 & 7 \\ -37 & 43 \end{bmatrix}\).

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The first polynomial can be expressed as a linear combination of the other two.

The given polynomials in V = P3(R) are 4x3 + 2x2 - 6, x3 – 2x2 + 4x+1, 3x3 – 6x2 + x +4. To determine whether the first polynomial can be expressed as a linear combination of the other two, we will use the Linear Combination Method.

The Linear Combination Method involves finding two sets of coefficients (a and b) that satisfy a certain linear equation. Specifically, the equation is:

a(4x3 + 2x2 - 6) + b(x3 – 2x2 + 4x+1) = (3x3 – 6x2 + x +4)

By comparing coefficients and solving the linear equation, we get a = -1/2 and b = 1. Therefore, the first polynomial can be expressed as a linear combination of the other two polynomials as:

-1/2(4x3 + 2x2 - 6) + 1(x3 – 2x2 + 4x+1) = (3x3 – 6x2 + x +4)

This demonstrates that the first polynomial can be expressed as a linear combination of the other two.

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The amount raised by a booster club compared with the number of  raffle tickets sold shows a constant rate of change;

A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.

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Answer:

3/4 or 0.75

Step-by-step explanation:

1. Cross multiply: (1/2) / (3/4)

2. 1 x 3 = 3 and 2 x 2 = 4

3. 3/4 or 0.75

Answer:

It's pretty simple

Step-by-step explanation:

First divide 18 and 3 = 6

then divide 30 by 6 = 5

7 multiplied by 6 = 42

Then divide 48 divided by 6 = 8

10 multiplied 6 = 60

hope this works!

Answer:

-1280

Step-by-step explanation:

10×(-2)= -20

-20×(-2)= 40

4th term: 40×(-2)= -80

5th term: -80×(-2)= 160

6th term: 160×(-2)= -320

7th term: -320×(-2)= 640

8th term: 640×(-2)= -1280

Answer:

8000

Step-by-step explanation:

8000

10^6-2*7.2/9

72000/9 = 8000

Answer:

The answer would be 49 because 72 divided by 8 would be 9 and you add 41 you get 49

Step-by-step explanation:

brainliest?

It can be deduced that the triangles are similar because the three internal angles are equal for both triangles.

It should be noted that the triangles are similar because the three internal angles are equal.

In this case, the ratio of the corresponding sides are equal and the corresponding angles are congruent.

The width of the river will be:

300/80 = AB/50

AB = (300 × 50)/80

AB = 187.50 feet.

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The distance from Jessica's school to her house is 7.48 miles.

Consider following diagram.

In right triangle ABC, vertex B is the Jessica's house vertex A be her school.

The route from her house to school consists of two straight legs.

She drives straight for 5 miles, and then she makes a right turn of 45 degrees and drives another 9 miles.

⇒ BC = 5 miles and AC = 9 miles

We need to find the distance from Jessica's school to her house in miles.

i.e., we need to find AB

Using Pythagoras theorem,

AC² = AB² + BC²

9² = AB² + 5²

AB = √(81 - 25)

AB = 7.48

Therefore, the distance from Jessica's school to her house is 7.48 miles.

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9514 1404 393

Answer:

  (x, y, z) = (124, 112, 42)

Step-by-step explanation:

Opposite angles in an inscribed quadrilateral are supplementary, so ...

  y° = 180° -68° = 112°

The angle marked 71° subtends an arc twice that measure, so ...

  2(71°) = 100° +z°

  z° = 142° -100° = 42°

The angle marked y° subtends an arc twice that measure, so ...

  2y° = 100° +x°

  x° = 2(112°) -100° = 124°

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

The composite transformation that has happened is defined as follows:

From the triangle ABC to the triangle A'B'C', we have that the figure was reflected over the x-axis, as the orientation of the figure was changed.

From triangle A'B'C' to triangle A''B''C'', the figure was moved 6 units right and 2 units up, which is defined as a translation 6 units right and 2 units up.

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Answer:

6 over 1.

Step-by-step explanation:

Answer:

1/10, 3/10, 0.9

Step-by-step explanation:

Convert to decimals.

1/10 = 0.1

0.9

3/10 = 0.3

Arrange from least to greatest.

0.1, 0.3, 0.9

1/10, 3/10, 0.9

According to the given statement 16% is the probability that the person is age 48 or older.

A metric of a data set's deviation from the mean is referred to as "standard deviation" (or ""). While a high standard deviation indicates that the numbers are more spread, a smaller standard deviation suggests that the data are clustered around the mean.

After calculating the z-score, we will look up the value in the table on page (718–719).

We will employ the equation, to determine the z-score.

z= x−μ / σ

How is x=48

μ=41

σ=7 the z-score is,

z = 48 - 47 /7

z = 7 / 7

z = 1

The value for z=1 in the table is 0.84130, meaning that the region below the curve represents people who are 48 years of age and older. However, we are looking at the area that represents people who are 48 years of age and older, hence,

1−0.8413

=0.1587≈0.16

=16%

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The complete question is-

The distribution of ages of licensed drivers shopping at the Kalish County Mall is normally distributed with mean 41 and standard deviation 7. A person will be selected at random. Round your answers to the nearest hundredth. What is the probability that the person is age 48 or older?

The correct answer is: The confidence interval from the first simulation is (0. 149, 0. 195), and the confidence interval from the second simulation is (0. 180, 0. 230). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 149 and 0. 195. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0. 180 and 0. 230.

The confidence interval is a range of values that is likely to contain the true proportion of wins with the new game strategy based on the sample data.

A 95% confidence interval means that if the simulation is repeated many times, the proportion of wins with the new game strategy will fall within this range 95% of the time.

The correct interpretation of the confidence intervals is that for the first simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.149 and 0.195.

This means that if we were to repeat the simulation many times, we would expect the true proportion of wins to fall between these values in 95% of the trials.

Similarly, for the second simulation, we are 95% confident that the true proportion of wins with the new game strategy is between 0.180 and 0.230.

Therefore, the correct answer is an option (b).

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this number can be written as 3+0.242424

The two towns are distance 60 miles apart in the real world if they are 3 inches apart on a map with a scale of 1 inch to 20 miles.

60 miles

1 inch = 20 miles

3 inches = 20 miles x 3 = 60 miles

The scale of a map is a way of expressing the relationship between the distances on the map and the actual distances in the world. If the scale on a map is 1 inch to 20 miles then it means that 1 inch on the map represents 20 miles in the real world. If two towns are 3 inches apart on the map, then this means that the actual distance between them is 3 times the scale, or 3 x 20 miles = 60 miles.

The two towns are 60 miles apart in the real world if they are 3 inches apart on a map with a scale of 1 inch to 20 miles.

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The correct answer is the average speed for the entire trip is 34.5 miles per hour and The integral that represents this information is as follows: f(x)dx = ∫23 dx + ∫69 dx Where x represents the distance travelled in miles.

To find out the average speed for the entire trip, we will use the formula for average speed which is given as follows: Average speed = Total distance/Total time

Let's calculate the time taken to travel 138 miles at 23 mi/h

Speed = 23 mi/h

Distance = 138 mi

Time taken = Distance/Speed = 138/23 = 6 hours

Now, let's calculate the time taken to return back to the starting point, which is again 138 miles away but this time at 69 mi/h.

Speed = 69 mi/h

Distance = 138 mi

Time taken = Distance/Speed = 138/69 = 2 hours

Now, the total time taken for the entire trip is 6 + 2 = 8 hours.

The total distance travelled for the entire trip is 2 x 138 = 276 miles.

Now we can use the formula for average speed to calculate the average speed of the entire trip.

Average speed = Total distance/Total time = 276/8 = 34.5 miles per hour

Therefore, the average speed for the entire trip is 34.5 miles per hour.

The integral that represents this information is as follows: f(x)dx = ∫23 dx + ∫69 dx Where x represents the distance travelled in miles.

The limits of integration are from 0 to 138 for both integrals, representing the forward and backward journeys.

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Answer:

A. R: -1 < y < 3

Answer:

\(\sf y =\dfrac{-1}{5}x-\dfrac{1}{4}\)

Step-by-step explanation:

Here, m is the slope and b is the y-intercept.

Substitute the values of m and b in the above equation.

  \(\sf m = \dfrac{-1}{5} \\\\b = \dfrac{-1}{4}\)

       Slope y-intercept form:

              \(\sf \boxed{y=\dfrac{-1}{5}x - \dfrac{1}{4}}\)

Answer:

5/27 ft²

Step-by-step explanation:

a = 1/3

b = 1/3 × 5/3 = 5/9, as 1 2/3 = 5/3

the area of the rectangle is a×b

Ar = 1/3 × 5/9 = 5/27 ft²

Answer:

-10

Step-by-step explanation:

h(-4) = 2(-4)+7 which equals -1

g(h(-4)) = -1²-9 which equals -10

Both of Nick's bags weigh 41 kilograms combined.

In mathematical terms, if we let W1 be the weight of the first bag and W2 be the weight of the second bag, then the total weight of both bags can be expressed as W1 + W2.

Substituting the given values, we get:

Total weight of both bags = 24 + 17 = 41 kilograms.

This is a simple addition problem that involves adding the weights of two bags to find the total weight.

The complete question is:

Nick is going on vacation. one of his bags weighs 24 kilograms. the other bag weighs 17 kilograms. how much do both of nick's bags weigh combined?

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ABCD area =

AB = 4√2

AX= 3 ft = Height

then Area is

AREA= AB• AD • Sin 30°

THEN ANSWER IS

AREA= 4√2• 3 = 12√2 ft2

. = 17 square foots

Answer:

The correct answer is - 17.

Step-by-step explanation:

Given:

total students = 219

in chemistry = 112

in physics = 45

not enrolled in either of these = 79

solution:

The number of students in both classes can be calculated by

P ( A or B) = P (A) + P (B) - P (A and B)

then putting and solving the given vaues in formula

=> (219-79) = 112+45-x

=> 140 = 157 -x

=> 17 = x

The calculated values are as follows:

(1101011)2 is equal to (107)10.

(0.11111)2 is equal to (0.96875)10.

(110.11100)2 is equal to (6.875)10.

a. (1101011)2 = (107)10

To convert a binary number to base 10, you need to multiply each digit of the binary number by the corresponding power of 2 and sum up the results.

(1101011)2 = (1 × 2^6) + (1 × 2^5) + (0 × 2^4) + (1 × 2^3) + (0 × 2^2) + (1 × 2^1) + (1 × 2^0)

= (64) + (32) + (0) + (8) + (0) + (2) + (1)

= (107)10

Therefore, (1101011)2 is equal to (107)10.

b. (0.11111)2 = (0.96875)10

To convert a binary fraction to base 10, you need to multiply each digit of the binary fraction by the corresponding negative power of 2 and sum up the results.

(0.11111)2 = (1 × 2^-1) + (1 × 2^-2) + (1 × 2^-3) + (1 × 2^-4) + (1 × 2^-5)

= (0.5) + (0.25) + (0.125) + (0.0625) + (0.03125)

= (0.96875)10

Therefore, (0.11111)2 is equal to (0.96875)10.

c. (110.11100)2 = (6.875)10

To convert a binary number with fractional part to base 10, you need to split the number into its integer and fractional parts. Then, convert each part separately using the same method as in previous examples.

For the integer part:

(110)2 = (1 × 2^2) + (1 × 2^1) + (0 × 2^0)

= (4) + (2) + (0)

= (6)10

For the fractional part:

(0.11100)2 = (1 × 2^-1) + (1 × 2^-2) + (1 × 2^-3) + (0 × 2^-4) + (0 × 2^-5)

= (0.5) + (0.25) + (0.125) + (0) + (0)

= (0.875)10

Combining the integer and fractional parts:

(110.11100)2 = (6) + (0.875)

= (6.875)10

Therefore, (110.11100)2 is equal to (6.875)10.

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