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In a linear function:

The matrix for the linear transformation l₁ ◦ l₂ ◦ l₃  is:

[3   0]

[√3/2   1/2]

To obtain the matrix for the composition of linear transformations, we can multiply the individual transformation matrices from right to left. The matrix for l₁, which represents scaling along the x-axis by a factor of 3, is:

[3   0]

[0   1]

The matrix for l₂, which represents rotation counterclockwise by π/6, is:

[√3/2   -1/2]

[1/2   √3/2]

The matrix for l₃, which represents scaling along the y-axis by a factor of 1/2, is:

[1   0]

[0   1/2]

To obtain the matrix for the composition l₁ ◦ l₂ ◦ l₃ , we multiply these matrices from right to left:

[3   0]     [√3/2   -1/2]     [1   0]

[0   1]  ×  [1/2   √3/2]  ×  [0   1/2]

Performing the matrix multiplication gives us the resulting matrix:

[3   0]

[√3/2   1/2]

This matrix represents the linear transformation l₁ ◦ l₂ ◦ l₃ with respect to the standard basis for R₂.

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Answer:

-18 + x = 11

x = 29

Step-by-step explanation:

To solve this, you can use the formula of a + b = c

\(-18 + x = 11\\-18 = 18\\11 + 18 = 29\\x = 29\)

Answer:

29

Step-by-step explanation:

Your equation can be -18+x=11. Since we don't know the number, we can use x. We are trying to find out a number that when it's added to -18, the answer will be 11.

Now, we solve the equation:

-18+x=11

x=11+18

x=29. Answer

To check this answer:

we can use our equation and substitute 29 for x.

-18+x=11

-18+(29)=11

11=11.

They are equal. Therfore, the answer is correct.

In the gap between the two plates, the electric field is constant and directed from the positive plate towards the negative plate. The magnitude of the electric field between the plates is given by:E = / (2).

where σ is the charge density, and ε₀ is the permittivity of free space. The direction of the electric field is from the positive plate towards the negative plate along the negative axis, denoted as E = E b where E is a unit vector in the direction.

Part (b) Expression for the electric potential in the gap between the two plates:

The electric potential between two points is defined as the work done per unit charge in moving a positive test charge from one point to another. Since the electric field in the gap between the plates is constant and only depends on the charge density, the potential difference (V) between the two plates is given by:

V = E d

where E is the magnitude of the electric field and d is the separation between the plates. The negative sign arises because the potential decreases as we move from the positive plate to the negative plate. Thus, the expression for the electric potential in the gap between the two plates is E d. The electric potential at any point within the gap is then obtained by subtracting the potential at the negative plate (which is zero) from the potential at that point.

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Answer: (y-(-43))=-7(x-6) and y=-7x-1

Step-by-step explanation:

1) Pick two points. I'll choose (3,-22) and (6,-43)

2) Next set it up in a rise-over-run function

-43 - (-22)

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

6    -  3

3) Solve

-21/3

-7

The slope is -7

4) Find the starting value.

You can do this by substituting two points in a slope-intercept equation(y=mx+b)

y=-7x+b

-22=-7(3)+b

-22= -21+b

-1=b

The starting value is -1.

5) Slope intercept form

We can put all the info together to find that the slope-intercept is:

y=-7x-1

6) Point-slope form:

Point slope form equation is this: y-y1=m(x-x1)

y1 and x1 are one of the points while keeping x and y as variables

So our final equation is (y-(-43))=-7(x-6)

The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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A value at the center or middle of a data set is a measure of center. It  is a statistical value that represents the central or average value of a dataset.

In statistics, a measure of center refers to a value that represents the central tendency or average of a data set. It provides a single value that summarizes the central or typical value of the data. The measure of center is used to understand the central position or location of the data points.

Common measures of center include the mean, median, and mode. The mean is calculated by summing all the values in the data set and dividing by the total number of values. The median is the middle value of a sorted data set, or the average of the two middle values if there is an even number of values. The mode represents the value that occurs most frequently in the data set.

These measures of center help in understanding the central tendency of the data and provide a representative value around which the data points are distributed. They are useful for summarizing and analyzing data sets, allowing for comparisons and making inferences about the data.

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The height of the jar is 20 centimeters when the radius is 4 centimeters.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Let V be the total volume of the jar. Since the jar is one-fourth full, we know that the remaining three-fourths are empty.

Thus, we can write:

V = (4/3)πr²h

We can also write the volume of the baby food as:

20π = (1/4)πr²h

Simplifying this equation, we get:

80 = r²h

Now, we can substitute this value of r²h in the equation for the total volume of the jar:

V = (4/3)πr²h

V = (4/3)πr²(80/r²)

V = (4/3)π(80)

V = 320π

Therefore, the total volume of the jar is 320π cubic centimeters.

Now, we can use the formula for the volume of a cylinder to find the height of the jar:

320π = πr²h

320 = 16h

h = 20

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Answer:

5 centimeters

Step-by-step explanation:

The formula for the volume of a cylinder is:

\(\boxed{V=\pi r^2 h}\)

where:

If a cylindrical jar is one-fourth full of baby food, and the volume of the baby food is 20π cm³, then the volume of the jar is 80π cm³.

\(\begin{aligned}\textsf{Volume of the jar}& = 4 \cdot 20\pi \\&=80 \pi \; \sf cm^3 \end{aligned}\)

To calculate the height of the jar when its radius is 4 cm, substitute r = 4 and V = 80π into the formula for the volume of a cylinder, and solve for h:

\(\begin{aligned}V&=\pi r^2 h\\\implies 80\pi & = \pi (4)^2h\\80\pi & = 16\pi h\\80& = 16 h\\h&=80 \div 16\\h&=5\; \sf cm\end{aligned}\)

Therefore, the height of the jar when the radius of the jar is 4 cm is:

If you acknowledge the number of males to females in the ratio as 'parts' or 'items', then there are 6 parts in 42 students. Therefore, 1 part = 42/6 = 7 students.

Therefore, put this into the ratio, and you get 7×2 : 7×4 = 14 : 28

Therefore, there are 28 females in the class.

The Master Theorem is a mathematical tool used to analyze and solve recurrence relations that have a specific form.

It provides a framework for determining the asymptotic behavior of divide-and-conquer algorithms by classifying them into different cases.

The Master Theorem can be applied when a recurrence relation has the form:

T(n) = aT(n/b) + f(n),

where T(n) represents the time complexity of the algorithm, a is the number of recursive calls, n/b represents the size of each subproblem, and f(n) is the time complexity of the remaining work done outside the recursive calls.

The theorem provides formulas and conditions to determine the time complexity of the algorithm based on the values of a, b, and f(n). By comparing the values of a, b, and f(n) with the cases defined by the Master Theorem, we can derive the asymptotic time complexity of the algorithm.

Therefore, the Master Theorem can indeed be applied to solve recurrences that meet its specific form, making the statement "True."

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The value of the conversion is;

16, 666. 67 minutes

277.78 hours

Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.

From the information given, we have;

10⁶ seconds

But, we have to take note of;

60 seconds = 1 min

Then 10⁶ seconds = x min

cross multiply

x = 16, 666. 67 minutes

Also,

60 minutes = 1 hour

Then 16, 666. 67 minutes = x

cross multiply

x = 277.78 hours

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Answer:

134

Step-by-step explanation:

Your answer is simply 134

Answer:

True

Step-by-step explanation:

you have to move the decimal point of 0.019 to the right once, making it greater

Answer:

A&C

A. Sophia should have found the number the dimensions were multiplied by.

C. Sophia should have set up a proportion to solve for X.

Answer:

A and C

Step-by-step explanation:

Sophia was asked to find the original dimension of a reduced hexagon.

A smaller hexagon has a top side length of 1.2 inches and bottom side length of x inches. A larger hexagon has a top side length of 7.2 inches and bottom side length of 9 inches.

Sophia found that the enlarged hexagon’s dimensions were just 6 more than the original hexagon, thus x = 3. What was Sophia’s error?

Sophia should have found the number the dimensions were multiplied by.

Sophia should have divided 9 and 6 .

Sophia should have set up a proportion to solve for x.

Sophia should have multiplied 7.2 and 1.2.

Sophia is correct and did not make an error.

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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Yes, 12 refrigerators and 11 pianos overload the truck, because 12 refrigerators and 11 pianos weighs more than 7100 lb.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, a truck that can carry no more than 7100 lb is being used to transport refrigerators and upright pianos

Let the number of refrigerators be x and the number of pianos be y.

Each refrigerator weighs 250 lb and each piano weighs 425 lb.

Here, 250x+425y≤7100

Will 12 refrigerators and 11 pianos overload the truck

Now, put x=12 and y=11 in the inequality 250x+425y≤7100, we get

250×12+425×11≤7100

7675≤7100 not true

Therefore, the inequality represent the given scenario is 250x+425y≤7100.

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Answer:

m=30e

Step-by-step explanation:

30 minutes for each evening, 2 evenings, 60 minutes

Hope this helped!

The most suitable equation that would express the time Duarte spends to play chess with his dad is m= 30e

Number of minutes each evening= 30 mins=m

They played together every evening= e.

Therefore, the equation that would express the time Duarte spends to play chess with his dad is m = 30e.

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The best measure of variability for the data is the standard deviation the player that more consistent is Option B: Player B.

What is standard deviation?

The standard deviation is a metric that reveals how much variance from the mean there is, including spread, dispersion, and spread. A "typical" variation from the mean is shown by the standard deviation. Because it uses the data set's original units of measurement, it is a well-liked measure of variability.

The best measure of variability for this data would be the standard deviation.

To determine which player was more consistent, we need to calculate the standard deviation for each player's data set.

For Player A, the mean is 3 and the standard deviation is 2.

For Player B, the mean is 2.44 and the standard deviation is 1.41.

Since Player B has a lower standard deviation, they are more consistent than Player A.

Therefore, the correct answer is -

Option B: Standard deviation; Player B was more consistent.

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The expression you provided is the limit as n approaches infinity of (1+1/n)ⁿ. This is a well-known limit in calculus and it has a value of e, which is approximately 2.71828.

This limit is often used to define the number e, which is a mathematical constant that appears in many areas of mathematics and science. The proof of this limit involves using the properties of exponential and logarithmic functions, as well as the concept of limits and infinite series.  The expression you provided is the limit as "n" approaches infinity of (1+1/n)ⁿ.  Mathematically, we can express the limit as: lim (n → ∞) (1+1/n)ⁿ = e

This means that as "n" approaches infinity, the expression (1+1/n)ⁿ approaches the value of "e." The number "e" is a fundamental constant that appears in many areas of mathematics, including calculus, logarithms, and exponential functions. It has important applications in various fields, such as finance, physics, and engineering.

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Answer:

slope(m)=6

Step-by-step explanation:

(2 , -1)=(x1 , y1)

(3 , 5)=(x2 , y2)

use formula : y2 - y1/x2 - x1

=5-(-1)/3-2

=5+1/1

=6/1

=6

therefore slope of a line is 6.

To find the cat's final position, we need to add up all the vectors representing the cat's movements.

The cat first travels along the vector −1, 2.

Next, the cat chases the ball along the vector 2, 6 − , which we can write as (2, 6) − (0, 1) = (2, 5).

Then, the cat darts after the ball 1.5 times along the vector 4, 3, which we can write as 1.5(4, 3) = (6, 4.5).

Finally, the cat's position after catching the ball is the sum of all these vectors:

(-1, 2) + (2, 5) + (6, 4.5) = (7, 11.5)

Therefore, the vector describing the cat's final position is (7, 11.5).

Answer:

The correct answer to this question is 2x = 45

Step-by-step explanation:

If you take 5 and multiply it by 9 you get 45. Therefore, 2x = 45 is the correct answer. (Also I know its right because I did the assignment and got this one right) Hope this helps :-)

Answer:

y equals 3x plus 4 is the answer

Step-by-step explanation:

hope it helps

The correct equation is p - 53 = 118.

⇒ p - 53 = 118

Therefore, the correct equation is p - 53 = 118.

A histogram is a univariate display of quantitative data that organizes data into bins and shows the frequency of observations within each bin.


A histogram is a graphical representation that displays the distribution of quantitative data. It consists of a series of contiguous bars, where each bar represents a specific range or bin of values, and the height of the bar corresponds to the frequency or count of observations falling within that range.

Histograms are commonly used to visualize the shape, central tendency, and spread of a dataset. By examining the heights of the bars, one can determine the frequency of values within each bin and identify patterns such as peaks or clusters. This makes histograms an effective tool for exploring the distribution and characteristics of a single variable in a dataset.

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Answer:

Decimal form: 2.07

Step-by-step explanation:

Answer:

\(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}\)

Step-by-step explanation:

\(\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4\)

Answer:

The answer is actually not an option here. The answer is y=-1/3x+16

The probability of a chance event is a number between 0 and 1 that expresses the likelihood that an event can occur.

The probability of a chance event is a numerical representation ranging from 0 to 1 which denotes the degree of possibility that a specific event may transpire. The likelihood of the occurrence of an event can be quantified using the concept of probability. In particular, a probability of 0 denotes the impossibility of the event, while a probability of 1 indicates that the event is certain to occur.

The concept of probability has proven to be a valuable resource in supporting informed decision-making amidst conditions of unpredictability.

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Answer:

the answer is b you have it right

Step-by-step explanation:

your welcome