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Axiom of Choice is also known to have some non-intuitive consequences, such as the Banach-Tarski paradox and the existence of non-measurable sets.

The Axiom of Choice is a fundamental principle in set theory that states that for any collection or family of nonempty sets, it is possible to select exactly one element from each set, creating a choice function.

In other words, given a family F of nonempty sets, the Axiom of Choice asserts the existence of a function called a choice function, which takes as input each set in the family and outputs a single element from that set. This choice function essentially "chooses" an element from each set in a consistent manner.

The Axiom of Choice is an important tool in mathematics and has significant implications in various areas, including analysis, topology and algebra.

It allows for the construction of mathematical objects that might not be easily defined without making explicit choices from infinitely many sets simultaneously.

As a result, its use is sometimes subject to scrutiny, and alternative set theories like constructive mathematics have been developed that do not rely on the Axiom of Choice.

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Answer:

To estimate the value of sec 195° using the graph of y = sec x, you would need to locate the point on the graph where x = 195°. However, since you have not provided the graph, I am unable to estimate the value of sec 195°.

Alternatively, you can calculate the value of sec 195° using the definition of the secant function. The secant function is defined as the reciprocal of the cosine function: sec x = 1 / cos x. Therefore, to find the value of sec 195°, you can calculate the cosine of 195° and take its reciprocal:

sec 195° = 1 / cos 195°

        ≈ 1 / (-0.9063)

        ≈ -1.103

Rounded to the nearest tenth, sec 195° is approximately -1.1.

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Step-by-step explanation:

20÷40

=0'5×60min

30min

80÷120

=0,6666666667×60

=40mins

john will arrive earlier

The simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

To simplify the expression (2⁵ x 5²² - 2 x 5²¹) / 25¹⁰.

we can use the properties of exponents and the fact that 25 = 5².

First, let's simplify the numerator:

(2⁵ x 5²² - 2 x 5²¹)

Using the distributive property, we can factor out 5²¹ from both terms:

= 5²¹ x (2⁵ x 5 -2)

= 5²¹ (32 x 5- 2)

= 5²¹ (160-2)

= 5²¹ x 158

Now, let's simplify the denominator: 25¹⁰

Since 25 = 5², we can rewrite it as (5²)¹⁰, which gives us:

=  (5²)¹⁰

= 5²⁰

Using the quotient rule of exponents [tex](a^m / a^n = a^{(m-n)})[/tex], we can simplify further:

=  5²¹ x 158 / 5²⁰

= 5²¹⁻²⁰ x 158

= 5 x 158

= 790

Therefore, the simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

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Answer:

The answer is point A' (3, -2).

Answer:

8

Step-by-step explanation:

total number: 128+ 154 = 282

divide by number of buses

282/36 = 7.8333...

can't split girls so need extra bus

therefore answer is 8

The slope of the line y = -3x + 9 is -3, indicating a downward (negative) slope. The y-intercept is 9, representing the point where the line intersects the y-axis.

The equation of the line is in the form y = mx + b, where m represents the slope and b represents the y-intercept.

Comparing the given equation y = -3x + 9 to the standard form, we can determine the values of the slope and y-intercept:

Slope (m): In the given equation, the coefficient of x is -3. Therefore, the slope of the line is -3.

Y-intercept (b): In the given equation, the constant term is 9. Therefore, the y-intercept of the line is 9.

So, the correct answer is:

Slope: -3

Y-intercept: 9

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A. The down payment would be $3,061.

B. The amount you would have to borrow is $27,549.

C. The monthly payment would be approximately $447.83.

A. To calculate the down payment, we need to find 10% of the sticker price.

10% of $30,610 [tex]= 0.10 \times $30,610 = $3,061[/tex]

Therefore, your down payment would be $3,061.

B. To determine the amount you would have to borrow, subtract the down payment from the sticker price.

Loan amount = Sticker price - Down payment

Loan amount [tex]= $30,610 - $3,061 = $27,549[/tex]

So, you would have to borrow $27,549.

C. To calculate the monthly payment, we need to consider the loan amount, the loan term, and the annual percentage rate (APR).

Loan term = 6 years

[tex]= 6 \times 12 = 72[/tex] months

APR = 6.24%

To calculate the monthly payment, we can use the formula for calculating the monthly payment on an installment loan:

Monthly payment = (Loan amount [tex]\times[/tex] Monthly interest rate) / (1 - (1 + Monthly interest rate)^(-Loan term))

First, let's calculate the monthly interest rate:

Monthly interest rate = (APR / 100) / 12

Monthly interest rate = (6.24 / 100) / 12 = 0.0052

Plugging in the values into the formula, we get:

Monthly payment [tex]= ($27,549 \times 0.0052) / (1 - (1 + 0.0052)^{(-72)} )[/tex]

Monthly payment ≈ $447.83

Therefore, your monthly payment would be approximately $447.83.

Please note that this calculation assumes a fixed interest rate throughout the loan term and does not include additional fees or taxes that may be associated with the car purchase.

It's always a good idea to consult with your credit union or financial advisor for precise calculations and information regarding loan terms.

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Answer:

Let x be the nightly rate before tax.

We know that the total cost including tax is $200.02, which is 100% of the cost before tax plus 7% sales tax:

x + 0.07x = 200.02

Combining like terms on the left-hand side:

1.07x = 200.02

Dividing both sides by 1.07:

x = 186.91

Therefore, the nightly rate before tax is $186.91, rounded to the nearest cent.

Answer:

  7

Step-by-step explanation:

You want the constant q when 4x² -8x -24 = 0 is written as (x -p)² = q.

First, we can divide by 4:

  x² -2x -6 = 0

To make the left side a perfect square, the constant there needs to be +1. Adding 7 to both sides will make it so:

  x² -2x +1 = 7

  (x -1)² = 7 . . . . . . . (p, q) = (1, 7)

The value of q is 7.

__

Additional comment

The square of a binomial is ...

  (x +b)² = x² +2bx +b²

The constant term (b²) is the square of half the coefficient of x. In the above equation, the coefficient of x is -2, so the constant needs to be ...

  (-2/2)² = 1

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To estimate the total distance traveled by the car in 36 seconds using a trapezium, we need to find the area under the curve of the graph. The trapezium can be constructed by connecting the points on the graph at the starting and ending times.

Let's break down the process into two parts:

Estimating the distance between 30 and 36 seconds:

To estimate the distance between 30 and 36 seconds, we can draw a triangle underneath that section of the curve. The base of the triangle is 6 seconds (36 - 30), and the height is the speed at 36 seconds (which is approximately 10 m/s). The area of the triangle is (base * height) / 2, so the estimated distance is (6 * 10) / 2 = 30 meters.

Estimating the distance using a trapezium:

To estimate the distance traveled in the first part of the graph (from 0 to 30 seconds), we can use a trapezium. The bases of the trapezium are the speeds at 0 and 30 seconds, which are approximately 25 m/s and 10 m/s, respectively. The height of the trapezium is the duration, which is 30 seconds. The area of the trapezium is ((base1 + base2) * height) / 2, so the estimated distance is ((25 + 10) * 30) / 2 = 525 meters.

Therefore, the estimated total distance traveled by the car in 36 seconds, using the trapezium and triangle approximation, is 30 meters + 525 meters = 555 meters.

Answer:

Step-by-step explanation:

First we need to calculate the price per kilogram of goat meat.

If 12 kg of goat meat is sold for R840, then the price per kilogram can be calculated as:

Price per kilogram = Total price ÷ Total weight

Price per kilogram = R840 ÷ 12 kg

Price per kilogram = R70

Therefore, Sam's claim that the goat meat is being sold at R60 per kilogram is incorrect. The actual price per kilogram is R70.

In conclusion, Mr Mlambo is selling the goat meat at R70 per kilogram, and Sam's claim is not valid.

The expression for the quotient of 78k and 40 without any spaces would be:

78k/40

The quotient of two numbers refers to the result obtained from dividing one number by another. In this case, you are dividing 78k by 40. In mathematical notation, division is often represented by the slash (/) symbol.

So when we say "the quotient of 78k and 40", we mean "78k divided by 40", which can be written as "78k/40".

Here, no spaces are used between the numbers, variables, and the division symbol in the expression, as per your request.

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Answer:

[tex]5x-y+7z-38=0[/tex]

or

[tex]5x-y+7z=38[/tex]

Step-by-step explanation:

Given vector equation:

[tex]\textbf{r} = \textbf{i} - 5\textbf{j} + 4\textbf{k} + \lambda(3\textbf{i} + \textbf{j} - 2\textbf{k}) + \mu(-\textbf{i} + 2\textbf{j} + \textbf{k})[/tex]

The vector 3i + j - 2k is perpendicular to n.

The vector -i + 2j + k is perpendicular to n.

[tex]\textsf{So}\;\;\textbf{n}=\left|\begin{array}{ccc}\textbf{i}&\textbf{j}&\textbf{k}\\3&1&-2\\-1&2&1\end{array}\right|[/tex]

        [tex]=\textbf{i}\left|\begin{array}{rr}1&-2\\2&1\end{array}\right|-\textbf{j}\left|\begin{array}{rr}3&-2\\-1&1\end{array}\right|+\textbf{k}\left|\begin{array}{rr}3&1\\-1&2\end{array}\right|[/tex]

        [tex]=\textbf{i}(1 \cdot 1 - (-2) \cdot 2)-\textbf{j}(3 \cdot 1-(-2) \cdot (-1))+\textbf{k}(3 \cdot 2-1 \cdot (-1))[/tex]

        [tex]=\textbf{i}(1 +4)-\textbf{j}(3-2)+\textbf{k}(6+1)[/tex]

        [tex]=5\textbf{i}-\textbf{j}+7\textbf{k}[/tex]

So the equation of the plane written in Cartesian form is:

[tex]5x-y+7z+d=0[/tex]

Substituting (1, -5, 4) gives:

[tex]5(1)-(-5)+7(4)+d=0[/tex]

[tex]5+5+28+d=0[/tex]

[tex]38+d=0[/tex]

[tex]d=-38[/tex]

Therefore, the given vector equation in Cartesian form is:

[tex]5x-y+7z-38=0[/tex]

or

[tex]5x-y+7z=38[/tex]

Answer :

We know that,

where r is radius

Volume = 4/3 × 3.14 × (14)²

= 4/3 × 3.14 × 2744

= 4/3 × 8616.16

= 34464.64/3

= 11488 m³ (approx)

Surface area of sphere = 4πr²

= 4 × 31.4 × (14)²

= 4 × 3.14 × 196

= 12.56 × 196

= 2461 m² (approx)

The equation with "p" as the subject is p = [tex](a^2 - v^2) / (2k).[/tex]

To make "p" the subject of the equation "[tex]a^2 = v^2 + 2kp[/tex]," follow these steps:

Start with the given equation:

[tex]a^2 = v^2 + 2kp.[/tex]

Move the term "[tex]v^2[/tex]" to the right-hand side of the equation by subtracting [tex]v^2[/tex] from both sides:

[tex]a^2 - v^2 = 2kp.[/tex]

Divide both sides of the equation by 2k to isolate "p" on one side:

[tex](a^2 - v^2) / (2k) = p.[/tex]

Therefore, the equation with "p" as the subject is:

p = [tex](a^2 - v^2) / (2k).[/tex]

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Angle x is 110 degrees, angle y is 110 degrees, and angle z is 70 degrees.

Let's analyze the given information step by step. We are given that two lines intersect, creating four angles. One of these angles is 70 degrees. The other angles are labeled as x, y, and z.

First, we know that angles x and 70 degrees form a linear pair because they are adjacent angles and their sum is 180 degrees. Therefore, angle x must be 180 degrees minus 70 degrees, which equals 110 degrees.

Next, we are told that angles y and 70 degrees also form a linear pair. This means that angle y is also 110 degrees, as the sum of a linear pair is always 180 degrees.

Finally, angle z can be found by considering the angles around the point of intersection. The sum of the angles around a point is always 360 degrees. Since we already have angles x, y, and 70 degrees, we can find angle z by subtracting their sum from 360 degrees.

The sum of angles x, y, and 70 degrees is 110 degrees + 110 degrees + 70 degrees, which equals 290 degrees. Therefore, angle z is 360 degrees minus 290 degrees, resulting in 70 degrees.

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The percentage of students in Class X that took more than 1 hour is equal to 52%.

In Mathematics and Statistics, a percentage refers to any numerical value that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given numerical value.

Based on the information provided about the time (in hours) the students in three classes took to complete their homework, we can logically deduce that the percentage of students in Class X that took more than 1 hour can be calculated as follows;

Percentage of students in Class X = 100% - (% of between 30 minutes and 1 hour + % less than 30 minutes)

Percentage of students in Class X = 100% - (24% + 24%)

Percentage of students in Class X = 100% - 48%

Percentage of students in Class X = 52%

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

a. The equation shows that a 11-pound turkey would need to be roasted for 335 minutes.

b. A turkey that takes 300 minutes to roast would weigh 14 pounds.

a. The rule for finding the time in minutes needed to roast a turkey is:

time in minutes = 15 + (pounds of turkey * 20)

So, to find the time needed to roast a 11-pound turkey, we would use the following formula:

time in minutes = 15 + (11 pounds * 20)

= 335 minutes

b. To find the weight of a turkey that takes 300 minutes to roast, we would use the following formula:

pounds of turkey = (300 minutes - 15 minutes) / 20 minutes

= 14 pounds

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Answer:To find the original price of the sofa before the sale, we can use the formula:

sale price = original price * (1 - discount rate)

Substituting the given values, we get:

1680 = original price * (1 - 0.3)

Solving for the original price, we get:

original price = 1680 / (1 - 0.3) original price = 1680 / 0.7 original price = 2400

Therefore, the sofa cost £2400 before the sale.

Step-by-step explanation:

There are 3003 different arrangements of 5 people that can be chosen as winners out of 15 people.

The number of combinations of "n" objects taken "r" at a time is given by the formula:

C(n, r) = n! / (r! (n - r)!)

Where n! represents the factorial of "n" (the product of all positive integers up to "n").

We have 15 people entering the contest, and we want to choose 5 winners. Thus, we have:

C(15, 5) = 15! / (5! × (15 - 5)!)

15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

5! = 5 × 4 × 3 × 2 × 1

(15 - 5)! = 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Plugging these values into the formula:

C(15, 5) = (15×14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)

C(15, 5) = 3003

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The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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The year that they will next be seen together is 2219.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

The least common factor is obtained factoring 8 and 54 by prime factors as follows:

8 - 54|2

4 - 27|2

2 - 27|2

1 - 27|3

1 - 9|3

1 - 3|3

1 - 1.

Hence:

lcf(8, 54) = 2³ x 3³ = 216.

Then the next year is of:

2003 + 216 = 2219.

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The percent decrease in the calculator price is approximately 83.14%.

To calculate the percent decrease, you can use the following formula:

To calculate the percent decrease, you need to know the initial value and the final value.

The formula for percent decrease is:

Percent Decrease = [(Original Value - New Value) / Original Value] * 100

In this case, the original value is $59, and the new value is $9.95. Substituting these values into the formula:

Percent Decrease = [($59 - $9.95) / $59] * 100

Percent Decrease = [$49.05 / $59] * 100

Percent Decrease ≈ 83.14%

Therefore, the percent decrease in the calculator price is approximately 83.14%.

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The lengths of the sides of the Triangle are 3 units, 10 units, and 12 units.

The length of the sides of a triangle are in the extended ratio 3:10:12. This means that the ratio of the lengths of the sides can be written as 3x:10x:12x, where x is a common factor.To determine the actual lengths of the sides, we need to assign a specific value to x. Let's assume x = 1 for simplicity.

Then, the lengths of the sides of the triangle become:

Side 1: 3(1) = 3 units

Side 2: 10(1) = 10 units

Side 3: 12(1) = 12 units

So, the lengths of the sides of the triangle are 3 units, 10 units, and 12 units.the extended ratio of the sides, 3:10:12, indicates the proportional relationship between the lengths. However, it doesn't provide information about the specific size or shape of the triangle.

For example, we can determine whether it is a right triangle or an equilateral triangle by comparing the ratios of its sides. However, additional information would be required to make further conclusions about angles, area, or other geometric properties of the triangle.

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The value of x for the given value of y in the equation y = x + 2 - 1 is 1

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

y = x + 2 - 1

Also, we have the value of y to be

y = 0

When the equation is evaluated, we have

y = x - 1

substitute the known values in the above equation, so, we have the following representation

x - 1 = 0

Add 1 to both sides

x = 1

Hence, the value of x for the given value of y is 1

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The vertices of the image triangle N'M'O' are N'(-1, 2), M(-4, 1), and O'(-3, 3).

We may use the idea of reflection to get the vertices of the picture N'M'O' created when triangle NMO is reflected over the line x = -3.

The distance between each of the x-coordinates of the original positions and x = -3 must be calculated.

The distance (from -3 to -5) is 2 units for N(-5, 2).

The distance (from -3 to -2) is 1 unit for M(-2, 1).

Since the point is already on the line, the distance for O(-3, 3) is 0 units.

Then, maintaining the same vertical coordinate, we move each point the same distance to the opposite side of the line.

We move 2 units to the right of N(-5, 2) to obtain N'(-1, 2).

We move one unit to the left from M(-2, 1) to obtain M(-4, 1).

We don't need to move at all for O(-3, 3), as the point is already on the line. Thus, O'(-3, 3).

Hence the vertices of the image triangle N'M'O' are N'(-1, 2), M(-4, 1), and O'(-3, 3).

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1.  The velocity of the object is 1.25 m/s.

2. This indicates that the object is moving in the positive direction.

3. The total distance traveled by the object is 10 m.

4.  The displacement of the object is 10 m.

1.The velocity of an object can be determined by calculating the slope of the graph. Since velocity is the rate of change of position, it is equal to the change position- in position divided by the change in time.

By examining the graph, we can see that the change in position between the initial and final points is 14 m - 4 m = 10 m. The corresponding change in time is 10 s - 2 s = 8 s.

Therefore, the velocity of the object is:

Velocity = Change in position / Change in time = 10 m / 8 s = 1.25 m/s

2. Based on the position-time graph, we observe that the object's position is increasing with time. This indicates that the object is moving in the positive direction.

3. To find the total distance traveled, we need to consider the absolute values of the changes in position. In this case, the object moves from 4 m to 14 m, which results in a change of 10 m. Since the direction is not specified, we consider the magnitude of the change.

Therefore, the total distance traveled by the object is 10 m.

4.Displacement is the change in position of an object, taking into account both magnitude and direction. In this case, the object starts at a position of 4 m and ends at a position of 14 m.

Therefore, the displacement of the object is:

Displacement = Final position - Initial position = 14 m - 4 m = 10 m.

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