2 3/4− 1 2/3
Give your answer as a mixed number where appropriate.

False.

If the linear transformation T(x) = Ax is onto (also known as surjective), it means that for every vector y in the output space of T, there exists at least one vector x in the input space of T such that T(x) = y.

If the linear transformation T(x) = Ax is onto (also known as surjective), it means that for every vector y in the output space of T, there exists at least one vector x in the input space of T such that T(x) = y. However, this does not necessarily imply that T(x) is one-to-one (also known as injective).

To see why, consider a simple example where A is a 2x2 matrix such that A = [1 0; 0 0]. The linear transformation T(x) = Ax maps a 2-dimensional vector x to a 2-dimensional vector Ax, and its matrix representation is given by:

| 1 0 |
| 0 0 |

This transformation is onto, since every vector y in the output space of T can be written as y = Ax for some vector x in the input space of T. However, T(x) is not one-to-one, since T([1 1]) = T([2 0]) = [1 0], which means that two different input vectors map to the same output vector.

Therefore, the statement "if the linear transformation T(x) = Ax is onto, then it is also one-to-one" is false. In fact, a linear transformation is one-to-one if and only if its null space (also known as kernel) is trivial, which means that the only vector that maps to the zero vector is the zero vector itself.

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There are a total of 6,311,042,650 possible ways to arrange two focus groups of students, one with size 4 and the other with size 6, from a group of 30 students including John and Jane.

To calculate the total number of possible ways to arrange two focus groups of students, one with size 4 and the other with size 6, we can use the combination formula. We need to choose 4 students from 30 for the first group, which can be done in C(30,4) ways, and then choose 6 students from the remaining 26 for the second group, which can be done in C(26,6) ways.

The total number of possible arrangements is the product of these two combinations:

C(30,4) * C(26,6) = (30! / (4! * (30-4)!) ) * (26! / (6! * (26-6)!) )

= 27,405 * 230,230

= 6,311,042,650

Therefore, there are a total of 6,311,042,650 possible ways to arrange two focus groups of students, one with size 4 and the other with size 6, from a group of 30 students including John and Jane.

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Answer:

(x-2) (x+2)

Step-by-step explanation:

------------------

The amount of markup on a single rose is $2.96

Profit = Selling Price – Cost Price.

We have,

We can consider the cost price as:

Bought amount = $12.96

We can consider the selling price as:

Selling amount = $48.48

Now,

Markup price can be considered as the profit:

Profit = Sellin price - Cost price

Profit = $48.48 - $12.96

Profit = $35.52

Since in a dozen we have 12 roses the markup price for each rose is:

= $35.52 / 12

= $2.96

Thus the amount of markup on a single rose is $2.96

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Answer:

a= c/7b

Step-by-step explanation:

Divide each term by 7b and then simplify.

Hope this helps.

Answer:

i really wish i could help but i dont  know ether i'm

sry maybe some one else could help

This comparison can provide insights into potential disparities in college choices based on the type of high school attended.

The students from public high schools and private high schools are the two independent samples in this study. The goal of the study is to compare how likely these two groups are to attend public colleges.

The principal test comprises of 100 understudies haphazardly chose from public secondary schools. Out of this example, 60 understudies were intending to go to a public school. The second sample consists of 50 students who planned to attend a public college out of a total of 100 students who were selected at random from private high schools.

By contrasting the extents of understudies arranging with go to public universities in each example, the review tries to decide whether there is a tremendous distinction in the probability of going to public universities between understudies from public secondary schools and those from private secondary schools. Based on the type of high school attended, this comparison may provide insight into potential disparities in college choices.

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The length of the arc intercepted by a central angle of pi/6 radians in a circle with a radius of 5 meters is approximately 2.6 meters.

The length of the arc intercepted by a central angle, we can use the formula: s = rθ, where s is the length of the arc, r is the radius of the circle, and θ is the central angle in radians.

Given that the radius of the circle is 5 meters and the central angle is pi/6 radians, we can substitute these values into the formula:

s = (5 meters) * (pi/6 radians)

 ≈ (5 meters) * (0.5236 radians)

 ≈ 2.618 meters

Rounding to the nearest tenth, the length of the arc intercepted by a central angle of pi/6 radians in a circle with a radius of 5 meters is approximately 2.6 meters.

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Answer:

pipe will empty the tank in 10.5 hours, working alone.

Step-by-step explanation:

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5*3.5*x = 1;  hence   x = 1%2F%287.5%2A3.5%29.

Then  2.5x = 2.5%2F%287.5%2A3.5%29 = 1%2F%283%2A3.5%29 = 1%2F10.5.

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

The faster pipe will empty the tank in 10.5 hours, working alone.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Let x be the rate of work of the slower pipe (measured in the tank volume per hour).

Then the rate of work of the faster pipe is 2.5x of the tank volume per hour.

The combined rate of the two pipes is then  x + 2.5x = 3.5x.

We are given

7.5×3.5×x = 1

7.5×3.5 x=1

Divide both sides by 7.5×3.5

x=1/ 7.5×3.5

2.5x=2.5/ 7.5×3.5

x=1/10.5

It means that the faster pipe will empty the tank in 10.5 hours, working alone.

Hence, the faster pipe will empty the tank in 10.5 hours, working alone.

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Answer:

27, a.

Step-by-step explanation:

3 ÷ 11 = 0.27272727272727

We have the following coordinates given:

And we want to find US so we can use the following formula:

And using this formula we got:

And after solve we got:

and rounded to the nearest cent would be Us= 27.46

So to calculate 5 with an exponent of 3, you can write 5, 3 times with a multiplication symbol between them like so: 5 · 5 · 5 When we multiply them together, we get the answer to 5 with an exponent of 3.

The total weight of the two pieces together is 6 pounds.

A piece of raw silk that is 100 yards long by 1.25 yards wide weights 38lb.

Then, a piece that is 12.5 yards long (and still 1.25 yards wide) will weight:

M = (12.5/100)*38lb = 4.75 lb

And a piece of habotai silk that is 100 yards long by 1.25 yards wide weights 12lb.

Then, a piece that is 12.5 yards long will weigh:

M' = (12.5/100)*12lb = 1.5 lb

If we add these two, we get a total weight of:

M + M' = 4.5lb + 1.5lb = 6lb

The total weight of the two pieces together is 6 pounds.

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Step-by-step explanation:

A = ½ h (b₁ + b₂)

Multiply both sides by 2:

2A = h (b₁ + b₂)

Distribute the h:

2A = h b₁ + h b₂

So the second option is not correct.

Instead of distributing, divide by h:

2A/h = b₁ + b₂

Subtract b₂ from both sides:

b₁ = 2A/h − b₂

Third option is correct.

Next, use common denominator to combine.

b₁ = 2A/h − h b₂/h

b₁ = (2A − h b₂) / h

Factor out 2.

b₁ = 2 (A − ½ h b₂) / h

Fourth option is correct.

Answer:

-5/18 >4/3

Step-by-step explanation:

Make this brainliest , thank you!

Answer:

C:6

Step-by-step explanation:

Answer:  see below

Step-by-step explanation:

7) Algebraic Inequality: x ≠ 3  

   -->    -∞ < x < 3 and 3 < x < ∞

   Graph:  ←-----------o-----------→

                               3

  Interval Notation: (-∞,3) ∪ (3, ∞)

8) This is a duplicate question of #7

9) Algebraic Inequality: x ≠ 2 and x ≠ 7

    -->  -∞ < x < 2 and 2 < x < 7 and 7 < x < ∞

   Graph:  ←-------o-------o-------→

                           2        7

  Interval Notation: (-∞, 2) ∪ (2, 7) ∪ (7, ∞)

10) Algebraic Inequality: x ≠ -4 and x ≠ 0

    -->  -∞ < x < -4 and -4 < x < 0 and 0 < x < ∞

   Graph:  ←-------o-------o-------→

                          -4        0

  Interval Notation: (-∞, -4) ∪ (-4, 0) ∪ (0, ∞)

Answer:

y-intercept= 12.99      slope= 15.00x+12.99

Step-by-step explanation:

We need to determine the appropriate axis of revolution. The correct axis of revolution can be identified based on the symmetry of the region and the axis that aligns with the boundaries of R.

Looking at region R, we observe that it is symmetric about the y-axis. The curve y = 3x^4 is reflected across the y-axis, and the lines x = 1 and x = -1 are equidistant from the y-axis. Therefore, the axis of revolution should be the y-axis (Option B). Revolving region R about the y-axis will generate a solid with rotational symmetry. To set up the integral for finding the volume, we will use the method of cylindrical shells. The integral will involve integrating the product of the circumference of each cylindrical shell, the height of the shell (corresponding to the differential element dx), and the function that represents the radius of each shell (in terms of x). While the integral setup is not explicitly required in the question, understanding the appropriate axis of revolution is crucial for correctly setting up the integral and finding the volume of the solid generated by revolving region R.

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The equation illustrated shows that the value of x will be x = -3 1/2.

It should be noted that an equation simply shows the relationship that exists between the variables.

The equation will be:

3 + x = -1/2

Collect the like terms.

x = -1/2 - 3

x = - 3 1/2

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Answer:

no

Step-by-step explanation:

The equation of 2 quantities varying directly is

y = kx ← k is the constant of variation

y = 23x + 1 is not in this form so does not represent direct variation.

Answer:

y=-x+11

Step-by-step explanation:

Answer:

290.761

Step-by-step explanation:

The sum of three circles could be equal to 9

We know that a triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

We are given that All triangles have the same value, and all circles have the same value.

WE can see that the triangle = 5

And there are number of circle= 3

Therefore, the sum of three circles =  9

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The friend has to save for 5 and 2/3 of a month to in order to make up the remaining 85 to get the 125 headphone.

An inequality that consists of two or more parts is called a compound inequality. Either "or" or "and" may be used in these components. A number between 5 and 10 could be used as x in an inequality, for instance, if it states that "x is larger than 5 and less than 10". Any time one of the two inequalities is true when the two inequalities are united by the word or, the compound inequality is solved. The two separate solutions have been combined to form the final answer. Inequalities that are separated by "and" or "or" form a compound inequality. The intersection of the inequality graphs is shown by the graph of a compound inequality with a "and."

Cost of the headphone 125.

What the friend have: 40.

What need to save: 125-40 = 85

Let x = amount to be saved per month

Months to save up the 85 is 15

The equation would be 15 x = 85

Therefore x = 85/15

Which is 5 2/3 months.

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The simplification form of the expression "(z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12)" is = "1/(z+6)".

To add the two fractions, we need to have a common denominator. Since both fractions already have the same denominator of z^(2)+8z+12, we can simply add the numerators together and keep the same denominator.

So, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = (z+2)/(z^(2)+8z+12)

Now, we need to simplify the fraction as much as possible. We can do this by factoring the denominator and seeing if there are any common factors that can be canceled out.

The denominator can be factored as (z+6)(z+2).

So, (z+2)/(z^(2)+8z+12) = (z+2)/(z+6)(z+2)

Now, we can see that there is a common factor of (z+2) in both the numerator and denominator, so we can cancel them out.

So, the final simplified answer is 1/(z+6).

Therefore, (z)/(z^(2)+8z+12)+(2)/(z^(2)+8z+12) = 1/(z+6).

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The maximum value of the objective function will be:50(100) + 50(20) = 5000 + 1000 = 6000

The given linear programming is:Max 50A + 50Bs.t.10A ≤ 100010B ≤ 80020A + 40B ≤ 4000A, B ≥ 0 To solve the linear programming using the solver follow these steps:Step 1: Open the Excel spreadsheet and go to Data, choose the solver and enable it.

Step 2: A Solver Parameters dialog box will appear. Input the necessary details as follows:Set Objective: 50A + 50BTo: Max Subject to constraints:

10A ≤ 100010B ≤ 80020A + 40B ≤ 4000

Select variables to change: A, BStep 3: Click Solve and the optimal value of A and B will be found.In this case, the optimal value of A is 100 and that of B is 20.

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Proportional ratio to the ratio 1/8 = 2/16 or 4/32 or 3/24 and so on.

What is proportional ?

A proportionality is a ratio which thus examines two numbers. 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. Proportions are denoted by the symbols "::" or "=".

According to Question

As long as you multiply or divide by the same number to both the numerator and denominator you will get a proportional ratio

Therefore:

When we Multiple 2 to numerator and denominator

we get 2/16.

When we Multiple 3 to numerator and denominator

we get 3/24.

When we Multiple 4 to numerator and denominator

we get 4/64/.

AND So on

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