Show your calculations. 1. Jason bought 200 T-shirts at R10 each. It cost him another RS to screen print each T-shirt. He sold all his T-shirt at R35 each. How much profit did he make? which she calls at 850 each​

"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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Quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.

a quadrilateral is a four-sided polygon, having four edges and four corners.

The given vertices of a quadrilateral  ABCD are A(-2, 4), B(5, 6), C(12,4), and D(5, 2).

We need to find the name of the quadrilateral.

The distance =√(x₂-x₁)²+(y₂-y₁)²

AB=√(5+2)²+(6-4)²

=√49+4==√53

CD=√(5-12)²+(2-4)²

=√49+4==√53

AB=CD

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length

Hence, the most precise name for quadrilateral ABCD with vertices A(-2, 4), B(5, 6), C(12,4), and D(5, 2) is a parallelogram.

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Step-by-step explanation:

attached file 18. Given a chord AB is of length 5cm, of a circle with centre 0 . OL is perpendicular to chord AB and OL 4 cm. OM is perpendicular to chord CD such that OM =4 cm. to

A system of linear equations has a unique solution if and only if the determinant of the matrix of coefficients is non-zero and the rank of the coefficient matrix is equal to the rank of the augmented matrix.

For the system to have a unique solution, the number of equations and the number of variables must be equal. If the determinant of the matrix of coefficients is non-zero, the system will have a unique solution if and only if the number of linearly independent rows in the coefficient matrix is equal to the number of variables. If the rank of the coefficient matrix is less than the number of variables, then the system will have either no solution or infinitely many solutions.

In conclusion, for a system of linear equations to have a unique solution, the number of equations must equal the number of unknowns and the determinant of the coefficient matrix must be non-zero. The values of a and b do not affect the existence of a unique solution.

The system of linear equations,

ax + by = c

dx + ey = f

will have a unique solution if and only if the determinant of the matrix of coefficients is non-zero, i.e., ae - bd ≠ 0. The values of a and b that satisfy this condition will result in a unique solution for the system.

If ae - bd = 0, then the system will have either no solution or infinitely many solutions, depending on the values of c and f.

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Consider the system of linear equations where a and b are unspecified constants for which values of a and b will the system have a unique solution?

The area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.

The sector's area in a circle is the whole area that is included inside the sector's boundary. The middle of the circle is where a sector always begins. The sector of a circle is the region of a circle that is contained between its two radii and the arc next to them. A semicircle is the area of a circle that most frequently represents half of a circle.

The area of the sector OWX can be calculated as:

[tex]A = (75/360) \times \pi \times 35^{2} = 63.62 cm^2[/tex]

And the area of the sector OYZ can be calculated as:

[tex]A = (75/360) \times \pi \times 24^{2} = 34.57 cm^2[/tex]

The shaded area WXZY is the difference between the area of the two sectors, which is:

A = 63.62 - 34.57 = 29.05 cm²

Therefore, the area of the shaded shape WXZY is approximately 29.05 cm² to 1 decimal place.

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Complete question -

The value of y = 3 and x' = -1, y' = -3/7.

Given the equation y² = xy + 6 and knowing that y = 3 and x' = -1, we can use implicit differentiation to find the derivative of y with respect to t, y'.

       d/dt (y²) = d/dt (xy + 6)

       2y * y' = x' * y + x * y' + 0

       2 * 3 * y' = -1 * 3 + x * y'

       6 * y' = -3 + x * y'

        6 * y' - x * y' = -3

        (6 - x) * y' = -3

       y' = -3 / (6 - x)

        y' = -3 / (6 - -1)

        y' = -3 / 7

So, when y = 3 and x' = -1, y' = -3/7.

The specific case we were discussing is finding the derivative of y with respect to t, given the equation y² = xy + 6, and the values of y and x' at a certain time t. This is a problem in calculus, which is a branch of mathematics that deals with the rate of change and slopes of curves. By differentiating both sides of the equation and substituting in known values, we were able to find the value of y' at a specific time t. This method of finding derivatives is called implicit differentiation and it is used to find the derivative of an implicit equation, where one variable is expressed in terms of another.

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Check the picture below.

The slope of the linear equation F = 9/5 C + 32 is 9/5. This means that for every increase of 1 degree Celsius, the Fahrenheit temperature increases by 9/5 degrees.

Therefore, the slope can be interpreted as "F increases 9/5 degrees for each increase of 1°C."

The conversion formulae we employ are the same ones found in most textbooks. Subtract 32 from the temperature in degrees Fahrenheit and multiply by.5556 (or 5/9). To convert Celsius temperatures to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.

The greater the number assigned to the temperature in fahrenheit, the hotter it is, and the lower, the colder it is.

As the originator of the thermometer as we know it, Fahrenheit had to put something on them to distinguish between different temperatures. The scale he chose became known as the Fahrenheit scale. Fahrenheit set zero to the lowest temperature he could get using a water and salt combination.

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The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.

The notation (a) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. By applying the Fundamental Theorem of Calculus, we can calculate this expression by evaluating the antiderivative of f(t) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of x with respect to t, which is denoted by dx/dt.

Therefore, the expression (a) f(t) dt dx can be written as F(b) - F(a) * dx/dt.

The notation (b) f(x) dx dt can also be interpreted as the integral of a function f(x) with respect to x from a to b multiplied by the differential of t with respect to x. Again, we can calculate this expression by evaluating the antiderivative of f(x) from a to b, which is given by F(b) - F(a), and multiplying it by the derivative of t with respect to x, which is denoted by dt/dx.

Therefore, the expression (b) f(x) dx dt can be written as F(b) - F(a) * dt/dx.

Finally, the notation (c) f(t) dt dx can be interpreted as the integral of a function f(t) with respect to t from a to b multiplied by the differential of x with respect to t. Therefore, this expression can be written as F(b) - F(a) * dx/dt.

It is important to note that this expression is the same as (a) f(t) dt dx, and so it can be seen that it is a number, since F(b) - F(a) * dx/dt is a constant.

The notations (a) f(t) dt dx, (b) f(x) dx dt, and (c) f(t) dt dx represent functions of x and t, and a number, respectively.

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The other equation could be [tex]3x + y = 1[/tex] when . One of the equations of the system is   [tex]y = 3x - 1[/tex] .

When two lines are written in slope-intercept form  [tex](y = mx + b)[/tex], they have an infinite number of solutions if and only if the lines are parallel, which means that they have the same slope (m).

In this case, the first equation,

[tex]y = 3x - 1[/tex]  , has a slope of 3,

and the fourth equation,

[tex]3x + y = 1[/tex]  , also has a slope of 3

Since the slopes are equal, the lines are parallel and will intersect at an infinite number of points, meaning that the system has an infinite number of solutions.

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Answer:

Treatment for HIV/AIDS involves taking highly effective medicines called antiretroviral therapy (ART) that work to control the virus [1][2]. ART involves taking a combination of HIV medicines (called an HIV regimen) to suppress the virus and stop the progression of the disease [1]. The goal of treatment is to reduce the amount of HIV in the body and keep it at a low, undetectable level to help prevent further damage to the immune system and reduce the risk of transmitting HIV to others.

The condition probability of a given b must be smaller than the intersection of the same two events a and b:

This statement is False.

The condition probability of event "b" given event "a" (P(b|a)) must be less than or equal to the probability of event "b" (P(b)). This is because the occurrence of event "a" restricts the sample space to only those outcomes that belong to event "a", and thus the probability of event "b" given event "a" cannot be greater than the unconditional probability of event "b".

The concept of conditional probability is used to describe the probability of an event given that another event has already occurred.

The formula for conditional probability is

where P(b|a) represents the probability of event "b" given that event "a" has already occurred.

In order for this to be meaningful, it is required that P(b|a) <= P(b). This means that the probability of event "b" given that event "a" has already occurred cannot be greater than the unconditional probability of event "b".

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Answer:

3.) x=49    4.) x=29

Step-by-step explanation:

3.)

2x+82=180

2x=98

x=49

4.)

3x+3(91)=360

3x+273=360

3x=87

x=29

The best estimate for 38/6 is option C that is equals to  4.

What is division ?

Division is a mathematical operation that involves splitting a number or quantity into equal parts or groups. It is the opposite of multiplication, where we find how many groups of a certain size can fit into a larger number or quantity.

When we divide one number by another, we are finding out how many times one number can be evenly divided by another number. For example, when we divide 12 by 3, we are asking "how many groups of 3 are in 12?" The answer is 4, because we can divide 12 into 4 equal groups of 3.

The best estimate for 38/6 is option C, 4.

We can see that 6 goes into 38 about 6 times (6 x 6 = 36), and there is a remainder of 2. Therefore, the answer is between 6 and 7. Since the options are all whole numbers, the best estimate is 4.

Therefore, The best estimate for 38/6 is option C that is  4.

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The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

Real Numbers:

9/4

The expression 9/4 is a real number. This can be seen by dividing the numerator (9) by the denominator (4) to get the answer 2.25. This is a real number as it can be written with a decimal.

Non-Real Complex Numbers:

9i

The expression 9i is a non-real complex number. This can be seen by taking the coefficient (9) and multiplying it by the imaginary number i. The result is 9i, which is a non-real complex number because it cannot be written with a decimal. The imaginary number i is defined as the square root of -1, which is not a real number.

The expression 9/4 is a real number, whereas the expression 9i is a non-real complex number.

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The complete statement is,

The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit right Response area compared to its cube root parent function.

Reflection is a type of transformation that flip a shape in mirror line, so that each point is the same distance from the mirror line as its reflected point.

We have to given that;

The function is,

⇒ f (x) = ∛(5x+ 3) - 5

This is a transformation of the cube root parent function.

Now, The parent function is,

⇒ f (x) = ∛x

After 5 units stretch Response area, we get;

⇒ g (x) = ∛5x

And, After translated 3 units right Response area,

⇒ g (x) = ∛ (5x + 3)

And, After translated 5 unit down, we get;

⇒ f (x) = ∛(5x+ 3) - 5

Thus, The complete statement is,

The function g(x) is 3 units stretch Response area , and undergoes a vertical translated 5 unit down Response area compared to its cube root parent function.

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The continuity equation comes from the conservation of mass.

It can be a mathematical statement of the principle of conservation of mass.

According to this, mass inflow in control volume should be equal to the mass outflow from that region at a particular time and the mass can neither be created nor be destroyed.

A continuity equation is an equation that shows the behavior of a quantity as it moves or is transported from one point or state to another

The general form of the continuity equation:

Where p=density of the fluid,

u,v,w=components of velocity in x,v, and z directions respectively.

The above equation is applicable for steady as well as unsteady, uniform s well as non-uniform, compressible as well as incompressible flow.

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The graph of function y = (1/2)ˣ is shown in figure.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The function is,

⇒ y = (1/2)ˣ

Now, We can draw the graph of exponential function y = (1/2)ˣ.

Hence, The graph of function y = (1/2)ˣ is shown in figure

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the probability that at least one of the wives ends up sitting next to her husband is 2/3

What is the probability that at least one of the wives ends up sitting next to her husband?

The total number of way for 6 individual to sit = 6! ways.

To find the required outcome, let make this easier by:

denoting  the probability that at least one of the wives ends up sitting next to her husband with Pr (K).

Let  be the event of the couple and as such the three couples will be (a=1,2,3), sitting next to each other.

Therefore,

Pr(K) = Pr[K₁ or K₂ or K₃]

Pr(K) = Pr[K₁ ∪ K₂ ∪ K₃]

This type of event is uniformly distributed, and as such! , we have:

Pr (K) = Pr(K₁) + Pr(K₂) + Pr(K₃) - Pr(K₁∩K₂) - Pr(K₂∩K₃) - Pr(K₁∩K₃) + Pr(K₁∩K₂∩K₃)

Pr (K) = 3 Pr() - 3 Pr(K₁K₂) + Pr(K₁∩K₂∩K₃)  

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COMPLETE QUESTION

Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. If they take their seats in a completely random fashion (randomorder), what is the probability that Jim and Paula (husband and wife) sit in the two seats on the far left? What is the probability that Jim and Paula end up sitting next to one another? What is the probability that at least one of the wives ends up sitting next to her husband?

Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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Answer:

1+tan2x=sec2x.

Explanation: Change to sines and cosines then simplify.

The eigenfunctions of the momentum operator px are wave functions which, when acted upon by px, result in a scalar multiple of the wave function itself, with the scalar being the eigenvalue.

To determine which wave functions are eigenfunctions of the momentum operator px, one can start by solving the eigenvalue equation, px ψ = ħkψ, where ψ is the wave function and ħk is the eigenvalue. In this equation, ħ is Planck's constant divided by 2π and k is the wave number.

To find the eigenvalue, one can multiply both sides of the equation by the complex conjugate of the wave function and integrate over all space. The result is ħk times the normalization constant, which can be used to find the eigenvalue.

The wave functions that satisfy this equation are the eigenfunctions of the momentum operator px, and their corresponding eigenvalues are proportional to their wave numbers.

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The real solutions of the equation of X² + 12X - 64 = 0 are 4 and (-16)

To find the real solutions for a quadratic equation, we need to understand this concept:

(x - a).(x - b) = x² - (a+b)x +ab

We can also use the ABC formula where:

ax² + bx + c = 0

Then:

x = -b ±√(b² - 4ac)

              2a

Using the given equation, we know that:

a = 1

b = 12

c = -64

Then, we will use the ABC formula to find the real solutions for the equation:

x = -(12) ± √(12² - 4(1)(-64))

                       2(1)

x = -(12) ± √(144 - 256)

               2

x = -12 ± √400

           2

x = -12 ± 20

           2

x1 = (-12 + 20) / 2

x1 = 8/2 = 4

x2 = (-12 - 20)/2

x2 = (-32)/2 = -16

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Complete Question:

find all real solutions of the equation by completing the square. (enter your answers as a comma-separated list. if there is no real solution, enter no real solution.) X² + 12X - 64 = 0

The required triangle WYV and XYU are congruent triangles with the SAS postulate.

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

Here,
Consider triangle WYV and XYU

XY = WY                   [Given ]

VY = UY                   [Given ]
∠WYV = ∠UYX         [Alternate interior angles for two intersecting lines are always equal]

ΔWYV ≅ ΔXYU by SAS congruency postulate.

As triangles, WYV and XYU are congruent triangles then,
VW = UX     [sides of a congruent triangle are always equal]

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It will take Mills approximately 1 month and 5 days to save the required amount.

Here's how you can calculate the number of months it will take Mills to save the required amount:

Calculate Mills' gross annual income:

Gross income = $20/h × 40 hours/week × 50 weeks/year = $40000/year

Subtract taxes and deductions:

Net income = Gross income - (Gross income × 10%) = $40000 - ($40000 × 10%) = $36000/year

Subtract monthly expenses:

Total monthly expenses = $1200 + $400 + $250 + $350 + $100 + $50 = $2,150/month

Monthly savings = Net income/year ÷ 12 months/year - Total monthly expenses = $36000/year ÷ 12 months/year - $2,150/month = $1,850/month

Divide the cost of the home theater by the monthly savings to find the number of months it will take Mills to save the required amount:

Months = $2150 ÷ $1,850/month = approximately 1.1667 months (or approximately 1 month and 5 days)

Therefore, Mills will need around 1 month and 5 days to save the requisite cash.

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To obtain the other factor is to take the idea  x² - 6x - 7 /x+ 1. Option A

Algebraic expressions are described as expressions comprising of terms, variables, factors, coefficients, and constants.

They are also made up of arithmetic operations, such as;

Given the expression;

x² - 6x - 7

Factorize the terms

x² - 7x + x - 7

Then, we get

(x+1) (x - 7)

The factors are (x + 1) (x -7)

Hence, the step x² - 6x - 7 divided by x - 1

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The probability of getting both a dog and a cat image is 0.25.

The probability of getting two dog images with replacement is 0.25. This is because when selecting with replacement, each draw is independent of the previous draw. Thus, the probability of getting one dog image is 0.50 and the probability of getting a second dog image is 0.50. Thus, the probability of getting two dog images is 0.50 x 0.50 = 0.25. Similarly, the probability of getting two cat images with replacement is 0.25.

The probability of getting one dog image and one cat image with replacement is 0.50 x 0.50 = 0.25. Thus the probability of getting both a dog and a cat image is 0.25.

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Answer:

60b + 12b

Step-by-step explanation:

After solving the Algebraic Expression 2(x + 8)= 2x + 8, we will get x∈∅. Variable x is dissolved in itself, making it impossible to find its value.

Before moving to solve the equation , let's learn how to solve any algebraic expression:

Step 1: Determine whether the Distributive is necessary.

Property. If so, spread the word!

Step #2: Group similar terms together on either side of the equals symbol.

(meaning: combine all of the similar factors AND

Add up each and every integer (number).

Step #3: Align the variables so that they are all to one side of the equals symbol.

utilizing the inverse process. REMEMBER: No matter what you do

You MUST do to the other side of the equals sign what you did to the one side.

equals (symbol).

Fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

fourth Step: When all of your variables are situated on the same side of the

You must transfer each number to the opposite sign of the equals by applying the inverse procedure on the equals sign. REMEMBER:

You MUST do anything you do to one side of the equals sign.

the reverse of the equals symbol).

Step #5: Using the variable's ALONE state, isolate it

the opposite process. DO NOT FORGET: No matter what you do to one

You MUST change the other side of the equals symbol to the equals symbol

Given:

2(x + 8)= 2x + 8

2 × x + 2 × 8= 2x + 8

2x+16= 2x+ 8

16= 8

So, x∈∅.

In this equation , the value of x could not be find because variable x is dissolved in itself.

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