A retailer sells chemistry sets for $21 that were acquired at a cost of $15. What percentage is the mark-up?

Left and right multiplying a positive semi-definite matrix by another matrix will always result in a positive semi-definite matrix.

Positive semi-definite matrices are important in many areas of mathematics and science, including linear algebra, optimization, and physics.

Let A be a positive semi-definite matrix, and let B be an arbitrary matrix. We want to determine whether AB and BA are also positive semi-definite matrices.

First, let's consider AB. To show that AB is positive semi-definite, we need to show that for any non-zero column vector x, xT(AB)x ≥ 0. We can expand this expression as:

xT(AB)x = (xTA)Bx = yTBy

where y = Ax. Since A is positive semi-definite, we know that yTy ≥ 0 for any vector y. Therefore, we have shown that xT(AB)x ≥ 0 for any non-zero column vector x, and hence AB is positive semi-definite.

Next, let's consider BA. To show that BA is positive semi-definite, we need to show that for any non-zero column vector x, xT(BA)x ≥ 0. We can expand this expression as:

xT(BA)x = (xTB)Ax = zTAz

where z = Bx. Since A is positive semi-definite, we know that zTAz ≥ 0 for any vector z. Therefore, we have shown that xT(BA)x ≥ 0 for any non-zero column vector x, and hence BA is also positive semi-definite.

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To convert 640 L to cL, you would move the decimal point 4 places to the right. So the answer is 640 L = 64,000 cL.

Converting units is a common task in science, engineering, and everyday life. The conversion factor between liters (L) and centiliters (cL) is 1 L = 100 cL. To convert a quantity from liters to centiliters, you can multiply the number of liters by 100 or move the decimal point two places to the right. In this case, we have 640 L. To convert this to centiliters, we need to multiply 640 by 100, or move the decimal point two places to the right. Since there are two digits after the decimal point in 640, we can simply move the decimal point four places to the right to get 64,000 cL. Therefore, 640 L is equal to 64,000 cL.

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The dot product between u and v is 150.35 units²

In the problem given;

u = 10cos5

v = 16cos25

To find the dot product of two vectors, we need to find the product of the magnitude of the vectors and the cosine of the angle between them. Let's call the angle between the vectors θ.

The dot product of u and v is given by:

u•v = |u| * |v| * cos(θ)

where |u| and |v| are the magnitudes of vectors u and v. We are given the magnitudes of the vectors, which are |u| = 10 and |v| = 16.

To find cos(θ), we need to use the dot product formula with the given angle values:

cos(θ) = (u•v) / (|u| * |v|) = (|u| * |v| * cos(θ)) / (|u| * |v|)

Since u and v are both vectors in 2-dimensional space, we can use the law of cosines to find the angle between them:

cos(θ) = (u•v) / (|u| * |v|) = (u1 * v1 + u2 * v2) / (|u| * |v|)

where u1 and u2 are the components of vector u and v1 and v2 are the components of vector v.

To find the components of the vectors, we need to use the given angle values and the magnitudes of the vectors:

u1 = |u| * cos(5°) = 10 * cos(5°)

u2 = |u| * sin(5°) = 10 * sin(5°)

v1 = |v| * cos(25°) = 16 * cos(25°)

v2 = |v| * sin(25°) = 16 * sin(25°)

Substituting these values into the formula for cos(θ), we get:

cos(θ) = (u1 * v1 + u2 * v2) / (|u| * |v|) = (10 * cos(5°) * 16 * cos(25°) + 10 * sin(5°) * 16 * sin(25°)) / (10 * 16)

θ = 20°

u.v = 10 * 16 * cos 20

u.v = 150.35

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Answer:

(36 - 18x) / x√(36x^2)

Step-by-step explanation:

I assume that the expression is:

1/x - 3/6

To simplify the expression and put it in the simplest radical form, we need to find a common denominator for the two terms. In this case, the least common multiple (LCM) of the denominators is 6x. Thus, we can rewrite the expression as:

(6/x) / (6x/6) - (3/6) / (6x/6)

Simplifying the above expression gives:

(6/x) / (x/6) - (3/6) / (x/6)

(6/x) * (6/x-3) / (x/6)

Simplifying the expression further gives:

(36/x^2 - 18/x) / (x/6)

We can simplify this expression by multiplying the numerator and denominator by 6x^2, which gives:

(36 - 18x) / x√(36x^2)

Therefore, the expression in the simplest radical form is:

(36 - 18x) / x√(36x^2)

On solving the provided question, we can say that the linear equation 100(p + s) + 100(p + s)

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

salad costs s dollars per serving. he needs to order 100 lunches for seventh graders and 100 lunches for eighth graders

the linear equation

100(p + s) + 100(p + s)

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Answer: rs>4

Step-by-step explanation: The product of r and s just means rs. Then, when it says more than, you know its going to be a greater than sign: >. So your inequality would be rs>4

The rational function on the graph is the one in options B.

f(x) = 1/(x - 1)

Here we can see that the we have the graph of a rational function.

Notice that we have an asymptote  at x = 1.

That means that the denominator becomes zero when we evaluate the function in x = 1.

Then the denominator is something like:

x + a

And when x = 1 we get:

1 + a = 0

a = -1

Then the denominator is:

x - 1

And the rational function is:

f(x) = 1/(x - 1)

The correct option is B.

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The solution to the given problem is 25/88. The solution has been obtained by applying BODMAS rule.

What is the BODMAS rule?

The letters BODMAS stand for Bracket, Of, Division, Multiplication, Addition, and Subtraction. An explanation of a mathematical expression's execution sequence is provided by the BODMAS. According to the BODMAS rule, brackets must be answered first, then powers or roots (i.e. of), Division, Multiplication, Addition, and finally Subtraction.

We are given an expression as (3/11 + 2/11) * 5/8

Now, as per the BODMAS rule, we will first solve the brackets.

On solving the brackets, we get

5/11 * 5/8

Now, on solving it further, we get

5/11 * 5/8 = 25/88

Hence, the solution to the given problem is 25/88.

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120% is equivalent to the fraction 11/5.

Fractions are defined as part of a whole. A whole can be an object or a group of objects. In real life, if you cut a pie out of the whole pie, that piece becomes part of the pie. Fractions are words of Latin origin. "Fractus" means "broken" in Latin.  

If 1/5 = 20%, then we can convert 120% to a fraction by first dividing by 100 to get the decimal equivalent, and then adding 1 to get the fractional equivalent:

120% = 120/100 = 1.2

1.2 + 1 = 2.2

Therefore, 120% is equivalent to the fraction 11/5.

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The equation of line p is y = (3/4)x + 13/2.

The equation of line q is y = (3/5)x + 23/5.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

Line p passes through points (-2, 5) and (3, 8).
This means,

Slope = (8 - 5) / (3 + 2) = 3/4

m = 3/4

And,

Consider (-2, 5) = (x, y)

5 = (3/4) x -2 + c

5 = -3/2 + c

c = 5 + 3/2

c = 13/2

So,

y = (3/4)x + 13/2

Line q passes through the points (-1, 4) and (4, 7).

Slope = (7 - 4) / (4 + 1) = 3/5

m = 3/5

And,

Consider (-1, 4) = (x, y)

4 = (3/5) x (-1) + c

4 = -3/5 + c

c = 4 + 3/5

c = 23/5

So,

y = (3/5)x + 23/5

Thus,

The equation of line p is y = (3/4)x + 13/2.

The equation of line q is y = (3/5)x + 23/5.

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The complete question:

Find the equation of the Line p passes that passes through points (-2, 5) and (3, 8) and Line q that passes through points (-1, 4) and (4, 7).

The number of chairs from number 27 to 66 in a row at an auditorium is calculated by using subtraction is 40.

To calculate the number of chairs in the row, we need to subtract the chair number of the first chair from the chair number of the last chair and add 1.

Number of chairs = (last chair number - first chair number) + 1

The first chair number is given as 27, and the last chair number is given as 66.

Substituting these values in the formula, we get:

Number of chairs = (66 - 27) + 1

Number of chairs = 40

Therefore, there are 40 chairs in the row, and the correct answer is option (3) 40.

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____ The given question is incorrect, the correct question is given below:

There are chairs from no, 27 to 66 in a row at an Auditorium. Then

how many chairs are there in the row ?

(1) 38

(2) 39

(3) 40

(4) 48

Were using the following formula to determine a line's equation using two points: Assuming (x1, y1) & (x2, y2) represent two important points on the line, y2 - y1 Equals m(x2 - x1).

A point in mathematics is symbolized by such a dot (.) and utilized to indicate an accurate location in space. It lacks all three dimensions—length, breadth, and height. It has no size, in other terms. A point's name is often written in all caps.

A straight line is mathematically represented by the equation y=mx+b. The y-intercept, or point at which line crosses the y-axis, is denoted by the letters "b," whereas the letters "m" denote the slope of the line.

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Answers: Each twin is 11 years old. Barb is 33 years old

Work Shown:

x = age of each twin

3x = Barb's age

x+x+3x = 5x = total of their ages = 55

5x = 55

x = 55/5

x = 11

Each twin is 11 years old. Barb is 3x = 3*11 = 33 years old.

Check: twin1+twin2+barb = 11+11+33 = 55

The answers are confirmed.

Percentage decrease is the difference between starting and ending values. It shows a loss of value from the original expressed as a percentage regardless of units. The amount of decrease is the original amount minus the final amount.

The formula for Percent Decrease is: Decreased Value = (Original Value – New Value)/Original Value.

The computation of our Percent Decrease:

= (64 - 21)/61 * 100

= 70.49%

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Answer:

[tex]\huge\boxed{\sf S=\frac{20}{6} \pi \ mm}[/tex]

Step-by-step explanation:

Radius = r = 10 mm

Degree = θ = 60°

Arc length = S = ?

[tex]\displaystyle S=\frac{\theta}{360} \times 2 \pi r[/tex]

Insert the values in formula.

[tex]\displaystyle S = \frac{60}{360} \times 2 \pi (10)\\\\S=\frac{1}{6} \times 20 \pi\\\\S=\frac{20}{6} \pi \ mm\\\\\rule[225]{225}{2}[/tex]

After solving the expression from the given data we get that the cost of the book is £5.90.

Let's assume the cost of the book is "b" in pounds. From the information given, we can set up the following system of equations:

6x = 12.30 (Andy pays £12.30 for 6 sketch pads)

2x + b = 10 (Jo pays £10 for 2 sketch pads and 1 book). where x is the cost of one sketch pad in pounds. Solving the first equation for x, we get: x = 12.30/6 = 2.05

Substituting this value of x into the second equation, we get: 2(2.05) + b = 10

Simplifying this equation, we get: 4.10 + b = 10

Solving for b, we get: b = 5.90

Therefore, the cost of the book is £5.90.

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The probability that the player takes exactly 5 shots before missing one is approximately 0.0539, or 5.39%.

The probability of missing a free throw shot is 0.12, and the probability of making a free throw shot is 0.88 (which is 1 - 0.12).

To find the probability that the player takes exactly 5 shots before missing one, we can use the geometric distribution, which models the number of independent and identical Bernoulli trials needed to get a success.

In this case, a "success" is missing a free throw shot, and the "trials" are the number of shots the player takes before missing one. The probability of success (missing a shot) is p = 0.12, and the probability of failure (making a shot) is q = 0.88. The probability of taking exactly 5 shots before missing one is:

P(X = 5) = q^4 * p

where X is the random variable representing the number of shots the player takes before missing one.

Plugging in the values, we get:

P(X = 5) = (0.88)^4 * 0.12

= 0.0539

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The height of the triangle is the distance that is found between the tip of the triangle at the top to the base of the triangle.

A triangle's height is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.

The length of a perpendicular segment from the base to the vertex directly across from it determines the height that corresponds to it. The vertex that is not an endpoint of the base is the one on the opposite side.

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Answer:

he inequality to determine the years in which more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher is:

0.48t + 18 > 40

Subtracting 18 from both sides:

0.48t > 22

Dividing both sides by 0.48:

t > 45.83

So, for years t greater than 45.83, more than 40% of women ages 25 and older in the United States will hold a bachelor's degree or higher.

Step-by-step explanation:

Answer:

  height = 2/5h

Step-by-step explanation:

You want the height of a frustum if the volume of the frustum is 98/125 times the volume of the original cone, which was of height h.

Let h' represent the height of the part of the cone that is removed to leave the frustum. Then its volume (v') is ...

  v' = (volume of large cone)(1 - 98/125) = v·(27/125)

The scale factor between h' and h is ...

  (h'/h)³ = v'/v = 27/125

  h'/h = ∛(27/125) = 3/5

The height of the frustum in terms of the height of the original cone is ...

  frustum height = (height of large cone) - (height of small cone)

  frustum height = h - (3/5)h

  frustum height = 2/5h

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The area of the rectangular piece to be painted after cutting will be 1200 cm².

What is the definition of a rectangle?

Rectangles are four-sided polygons with 90-degree internal angles. Two sides meet at right angles at each corner or vertex. The rectangle is distinguished from the square by the fact that its opposite sides are of equal length.

If one side of a rectangle is 20 cm long, the opposite side is also 20 cm long.

A rectangle has two intersecting diagonals. The length of both diagonals is the same.

The perimeter is defined as P = 2 (Length + Width).

Area of a Rectangle=Length*Breadth

Now,

Length of cardboard=42cm

breadth=32 cm

Area of cardboard=42*32=1344cm²

Area of square to be cut=6*6=36cm²

and total 4 squares are cut

Then the area of the box that is made to be painted is =1344*4*36

=1200 cm²

hence,

          The area of the rectangular piece to be painted after cutting will be 1200 cm².

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The lemon are limiting ingredient  in lemonade recipe.

Here the limiting ingredient is lemon because here for 1 cup of sugar we have 1 lemon it's clearly seems that the juice of 1 lemon never melt the 1 cup of sugar that's why here limiting ingredient   is lemon.

A limiting reagent is a substance that is completely consumed upon completion of a chemical reaction. They are also called limiting agents or limiting reactants. According to the stoichiometry of a chemical reaction, a certain amount of reactants is required for the reaction to go to completion. Consider the following reactions involving the formation of ammonia.

[tex]3H_{2} +N_{2} - > 2NH_{3}[/tex]

In the above reaction, 3 moles of hydrogen gas are required to react with 1 mole of nitrogen gas to produce 2 moles of ammonia. But what if only 2 moles of hydrogen gas and 1 mole of nitrogen were available during the reaction? Not all nitrogen can be used in this case (because 3 moles of hydrogen gas are required to react all the nitrogen). Hydrogen gas is therefore called the limiting reagent for this reaction as it limits the reaction.

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The area of the composite figure is 24m², which is option C.

What is a composite figure?

A two-dimensional figure built up of fundamental two-dimensional shapes like triangles, rectangles, circles, semicircles, etc. is known as a composite shape or composite figure. To get the area of a composite shape, first determine the individual areas of every component. The total of the individual regions will then represent the area of the composite shape.

From the figure, we can see that from a big rectangle, 4 small identical squares of side 1m are cut from each corner.

We are asked to find the area of the rest of the rectangle which makes the composite figure.

W first find the area of the original rectangle.

Its length  = 5 + 1 + 1 = 7 m

Its breadth = 2 + 1 + 1 = 4 m

So the area of the rectangle = length * breadth = 7*4 = 28 m²

Now the side length of the square = 1 m

Area of one square = 1*1 = 1m²

So are of four identical squares = 4 * 1 = 4 m²

Therefore area of the composite figure = area of big rectangle - area of 4 squares = 28 - 4 = 24m²

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Answer:

24m^2 is ur answer

Step-by-step explanation:

Hope this helps

The initial amount A is 1 and the growth factor B is 1.4 in the Exponential function f(t)=14^x.

Given,

f(x) = 1.4^x

It is an exponential function.

y = a.b^x

where a is the initial quantity and b is the growth/ decay component.

Now we are able to examine the given feature with

A = 1

B = 1.4

An exponential function is a mathematical function that has the form f(x) = a^x, where a is a constant greater than zero and not equal to one, and x is a variable. This function is widely used in a variety of fields, such as finance, physics, and biology, due to its ability to model growth, decay, and change over time.

Exponential functions are essential in understanding various natural phenomena, from population growth to radioactive decay, and they play a crucial role in the advancement of scientific research.The exponential function has several unique properties, such as exponential growth, where the function grows at an increasing rate as x increases. Additionally, the function has an asymptotic relationship with the x-axis, meaning it never actually touches the x-axis but gets infinitely close to it.

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Answer:

6 students must play both piano and guitar

The probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.

To create a Venn diagram for this situation, you would need two circles that overlap in the middle. One circle would represent the 48% of teenagers who read the book, and the other circle would represent the 58% of teenagers who saw the movie. The overlap between the two circles would represent the 22% of teenagers who both read the book and saw the movie.

            +-----------------------------------------+

            |                                                 |

            |                    Read                    |

            |                   48% (R)                 |

            |                                                 |

            +--------------------+-------------------+

            |                         |                       |

            |                         |                       |

            |                         |                       |

            |    Both (B∩R)   |   Movie (M)   |

            |     22% (B)        |   58% (M)      |

            |                          |                      |

            |                          |                      |

            |                          |                      |

            +---------------------+------------------+

                              Not Read

                            30% (N∩M)

Here, R represents the event of reading the book, M represents the event of watching the movie, and B represents the event of both reading the book and watching the movie. The numbers in parentheses represent the percentage of US teenagers in each event. The area of each circle represents the total number of US teenagers.

To find the probability that a randomly selected US teenager has either read the book or seen the movie, you need to find the total area of the two circles (the 48% who read the book plus the 58% who saw the movie) and subtract the overlap (the 22% who both read the book and saw the movie). This gives you:

P(read or saw) = 48% + 58% - 22% = 84%

So the probability that a randomly selected US teenager has either read Harry Potter and the Half Blood Prince or seen the movie is 84%.

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The value of the given ratio 3/4 : 1/2 is 3/2.

To get the value of a ratio, we just need to take the quotient between the first and second values.

For example, the value of a:b is a/b.

In this case we have the ratio:

3/4 : 1/2

Taking the quotient we will get:

(3/4)÷(1/2) = (3/4)*(2/1) = 6/4

                                    = 3/2

That is the value of the ratio.

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The value of x in the polygon is 30

from the question, we have the following parameters that can be used in our computation:

Exterior angles = x, 2x, 4x, 5x, 8x, and 10x.

The sum of exterior angles of a polygon is 360

Using the above as a guide, we have the following:

x + 2x + 4x + 5x + 8x + 10x = 360

Evaluate the like terms

30x = 360

So, we have

x = 12

Hence, the value of x is 12

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