-5
KERCISE 2
Calculate:
(1)
You m
5+(-2)

The number of people that live in the rural areas is 22 258 173

What is Percentage?

Percentage is a number or ratio that can be expressed as a fraction of 100.

How to determine this

44% live rural areas when there are 50 586 757 people in South Africa

i.e 44/100 * 50 586 757

= 22 258 173.08

which is approximately 22 258 173 people live in rural areas of South Africa

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The determinant of a 4x4 matrix is calculated using the Laplace Expansion method, which involves expanding the determinant along one row or column.

The formula for the determinant of a 4x4 matrix is:det(A) =[tex]a11 * a22 * a33 * a44 – a11 * a22 * a34 * a43 + a11 * a23 * a34 * a42 – a11 * a23 * a32 * a44 + a12 * a23 * a32 * a44 – a12 * a23 * a34 * a41 + a12 * a21 * a34 * a43 – a12 * a21 * a33 * a44 + a13 * a21 * a33 * a44 – a13 * a21 * a34 * a42 + a13 * a22 * a34 * a41 – a13 * a22 * a31 * a44 + a14 * a22 * a31 * a43 – a14 * a22 * a33 * a41 + a14 * a23 * a33 * a42 – a14 * a23 * a31 * a42[/tex]To calculate the determinant of a 4x4 matrix, take the sum of the products of the elements in each row/column and its corresponding minor, then multiply each product by the sign of the term (+ or -). For example, if A is a 4x4 matrix, then the determinant is: det(A) =[tex]a11 * |A11| - a12 * |A12| + a13 * |A13| - a14 *[/tex]|A14|.The minors A11, A12, A13 and A14 are the 3x3 matrices obtained by deleting the first row and first column from A. The values of the minors are calculated by applying the Laplace Expansion method to each minor.

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The expression shown on the number line is 0 - 2 + 4 which is equal to 2.

An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.

Number line contains numbers equally placed at regular intervals. Negative is shown by moving left while positive is shown by moving right

From the number line shown. It initially starts at 0. It is then moved 2 units left, to get:

0 - 2

Thereafter it is moved 4 units right to get:

0 - 2 + 4

= 2

The expression is 0 - 2 + 4

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Answer:

the coordinates of the resulting point G' are (5, 1).

Step-by-step explanation:

When a point is rotated 180° counterclockwise around the origin, it is reflected across the x-axis and y-axis. This means that the x-coordinate and y-coordinate of the point are both negated.

So, for the point G(-5, -1), the x-coordinate becomes -(-5) = 5 and the y-coordinate becomes -(-1) = 1.

Answer:

(5,1)

Step-by-step explanation:

Rotating 180 degrees about the origin means that there is a reflection against the y-axis and x-axis. Therefore, the x and y values will change their signs.

Hence, the new coordinate would be (5,1)

The experimental probability of rolling a 5 is 25/56, or 0.446.

Probability is a field of mathematics that deals with the chance of certain events happening. It is used to calculate the likelihood of different outcomes in a given situation. Probability helps to make decisions for a variety of real-world applications, such as predicting the weather, deciding whether to invest in stocks and calculating insurance rates. Probability is based on the idea that all outcomes are equally likely, and can be expressed as a number between 0 and 1, where 0 means something is impossible and 1 means something is certain.

The experimental probability is calculated by taking the total number of times a number was rolled and dividing it by the total number of rolls. In this case, the total number of times a 5 was rolled is 25, and the total number of rolls is 56. Therefore, the experimental probability of rolling a 5 is 25/56, or 0.446.

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Answer: a²+ 9² = 12² (look at the image for the solution)

Step-by-step explanation:

Step-by-step explanation:

Using the modified picture attached to this answer;

Parameters

x = Angle X

8 = x

19 = y

14 = z

Therefore,

Using Cosine rule

x² = y² + z² - 2·y·z·cos X

Masking Cos X the subject of the formula,

Cos X = (y² + z² - x²) / (2·y·z)

Cos X = (19² + 14² - 8²) / (2·19·14)

Cos X = (361 + 196 - 64) / 532

Cos X = (557 -64) / 532

Cos X = 493 / 532

Cos X = 0.92669

But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;

X = Cos-¹ [0.92669]

Since 1 / Cos = Cos-¹

Therefore,

X = 22.075

And since x, our unknown, is equal to angle X, then,

x = 22.1 (to the nearest tenth)

The characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.

A parabola is a cross-section cut out of the cone and represented by an equation.

Here,
The general form of a parabola is f(x) = ax² + bx + c, where a, b, and c are constants. In this case, the given equation is f(x) = -3x², which means that a = -3, b = 0, and c = 0.

The sign of "a" determines the direction of the parabola. When "a" is negative, the parabola opens downward, and when "a" is positive, the parabola opens upward. In this case, a = -3, which means the parabola opens downward.

If a parabola is reflected over the x-axis, the sign of "a" remains the same. If it is reflected over the y-axis, the sign of "a" changes. In this case, the parabola is reflected over the x-axis, which means the sign of "a" remains negative.

Therefore, the characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.

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Operationalization of variables in research involves defining a concept in a way that it can be measured or observed.

It is the process of taking abstract concepts, such as attitudes, beliefs, or behaviors, and defining them in a way that they can be measured using empirical methods. This is done by creating a set of specific and concrete indicators or measures that represent the concept being studied. The operationalization of variables is a critical step in the research process, as it ensures that the data collected is both reliable and valid, and can be used to draw meaningful conclusions and make predictions.

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Answer:

-1/30

Step-by-step explanation:

-1/6 divided by 2/3(9 - 3/4) - 1/2

2/3(9 - 3/4) - 1/2

= 18/3 - 6/12 - 1/2

= 72/12 - 6/12 - 6/12

= 60/12

= 5

We have

-1/6 ÷ 5

= -1/6 x 1/5

= -1/30

The rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

From the given table the rate of change or slope is m=8-5/2-1

m=3

The ride cost $3 per mile.

The equation which show the total cost to travel x miles is y=3x.

Hence, the rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.

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Answer:

x=1,y=4

Step-by-step explanation:

5x+y=9

5x=9-y

x=(9-y)/5

put it in 10x-7y=-18

10x((9-y)/5)-7y=-18

18-2y-7y=-18

-9y=-36

y=4

x=(9-4)/5=1

Answer:

x = 1

y = 4

Step-by-step explanation:

5x + y = 9

10x - 7y = -18

Time the first equation by -2

-10x - 2y = -18

10x - 7y = -18

-9y = -36

y = 4

Now put 4 in for y and solve for x

5x + y = 9

5x + 4 = 9

5x = 5

x = 1

Let's check

5(1) + 4 = 9

5 + 4 = 9

9 = 9

So, x = 1 and y = 4 is the correct answer.

Answer:

[tex]\huge\boxed{\sf f(5) = 11}[/tex]

Step-by-step explanation:

f(x) = 2x + 1

Put x = 5

So,

f(5) = 2(5) + 1

f(5) = 10 + 1

[tex]\rule[225]{225}{2}[/tex]

A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

In Math's, an intercept is a point on the y-axis, through which the slope of the line passes. It is y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept. There are basically two intercepts, x-intercept and y-intercept.

Rewrite the function as an equation:

→ y = 2x + 1

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is y = mx + b where m is the slope of b is the y-intercept:

→ y = mx + b

Find the values of m and b using the form y = mx + b:

→ m = 2

→ b = 1

Therefore, A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:

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Answer: I Don't Know.

Step-by-step explanation: Add a picture.

The length is 30 unit and width is 10 unit.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

length of a rectangle is three times its width.

Perimeter of the rectangle = 80

let the width be x then length = 3x

So, Perimeter of the rectangle = 80

2( x+ 3x) = 80

4x= 40

x= 10

Thus, the length is 30 unit and width is 10 unit.

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The first four terms of the arithmetic sequence are -3, 4, 11, 18.

If the first term of an arithmetic sequence is -3 and the common difference is 7, then we can use this formula to find the nth term of the sequence:

Un = a + (n - 1)d

Where

Un is the nth term

a is the first term

d is the common difference, and

n is the position of the term in the sequence.

To find the first four terms of the sequence, we can substitute n = 1, 2, 3, 4 into the formula and solve for Un:

n = 1:

U1 = -3 + (1 - 1)7 = -3

n = 2

U2 = -3 + (2 - 1)7 = 4

n = 3

U3 = -3 + (3 - 1)7 = 11

n = 4

U4 = -3 + (4 - 1)7 = 18

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Answer:

3. d

4.b

5.a

6. is 15

Step-by-step explanation:

mn=5

no=5

op=10

pq=10

The expression that represents how much more Elena spent is $3.2 + p

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

The variable p represents the price, in dollars, per pound of cherries.

Elena buys a watermelon for $ 6.35 and 5 pounds of cherries.

So, the price of the cherries bought by Elena will be = 5*p

Then the total amount spent by Elena during her purchase of fresh fruits is:

$6.35 + 5*p

On the other hand, Tania buys a pineapple for $ 3.15 and 4 pounds of cherries. So, the price of the cherries bought by Tania will be 4*p

Therefore, the total amount spent by Tania during her purchase of fresh fruits is:

$3.15 + 4*p

You want to determine an expression to represent how much more Elena spent. That is, you want to determine the difference between the money spent by Elena and the money spent by Tania, which represents how much more Elena spent:

Total amount spent by Elena on fresh fruits - Total amount spent by Tania on fresh fruits

$6.35 + 5*p - ($3.15 + 4*p)

Solving:

$6.35 + 5*p - $3.15 - 4*p

($6.35 - $3.15) + (5*p - 4*p)

$3.2 + p

The expression that represents how much more Elena spent is $3.2 + p

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Answer:

One daylily costs $9, and one pot of ivy costs $9.

Step-by-step explanation:

Step 1: Write a System of Algebraic Equations

We are given 2 different variables, or "unknowns", that we need to find the value of here - the cost of one daylily, and the cost of one pot of ivy. We know that the cost of each plant remains constant (doesn't change), and we are given the following information:

We can see that we have a system of equations in the making. The first thing to do when writing a system is assign letters to variables. Let's let the cost of one daylily be denoted as [tex]d[/tex], and the cost of one pot of ivy be denoted as [tex]i[/tex] (in dollars for each). From the above information, we can write the system:

[tex]d+8i=81 \hspace{0.8cm} (1)\\10d+11i=189 \hspace{0.1cm} (2)[/tex]

Step 2: Solve the System (with Substitution)

Now that we have a solution, let's use it to solve for the value of each variable. There are many ways to do this (addition, subtraction, etc), but it seems that the quickest way to solve this particular system is using the substitution method. This is where you write one variable in terms of the others by manipulating one equation, and then substituting that expression in for the isolated variable in the other equation. It's easy to do this here because we already have a [tex]d[/tex] in (1).

Isolating [tex]d[/tex] in (1) by subtracting [tex]8i[/tex] from both sides, we get:

[tex]d+8i=81\\d=81-8i\hspace{0.5cm} (3)[/tex]

Substituting (3) into (2) and solving for i, we get:

[tex]10d+11i=189\\10(81-8i)+11i=189\\810-80i+11i=189\\810-69i=189\\-69i=-621\\\bf i=9[/tex]

Substituting this value into (3), we get:

[tex]d=81-8i\\=81-8*9\\=81-72\\=\bf9[/tex]

Therefore, one daylily costs $9, and one pot of ivy costs $9.

1) The value of P(A∩B) = 0.

2) The value of P(A|B) = 0.

3) P(A|B) is not equal to P(A). A and B are independent events.

4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.

5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.

1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.

2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.

3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.

However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).

4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.

If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.

5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.

Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.

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Note that the probability that a combined sample tests positive is 0.67232 or 67.232%.

Let P(pos) be the probability that an individual sample tests positive.

We know P(pos) = 0.2,

so the probability that an individual sample tests negative is:

P(neg) = 1 - P(pos) = 0.8.

Let P(combined_neg) be the probability that a combined sample tests negative (i.e., all five component samples are negative).

Since the component samples are independent, we can calculate

P(combined_neg) as the product of their individual probabilities:

P(combined_neg) = P(neg) x P(neg) x P(neg) x P(neg) x P(neg)

= 0.8⁵
= 0.32768

Therefore, the probability that a combined sample tests positive (i.e., at least one of the five component samples tests positive) is:

P(combined_pos) = 1 - P(combined_neg)

= 1 - 0.32768

P(combined_pos) = 0.67232

Thus, the probability that a combined sample tests positive is 0.67232 or 67.232%.

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1 kilogram is equal 2.2046 pounds.

Therefore, 150 kilograms is equal to 330.693 pound.

Pound:

A pound (commonly abbreviated lb, plural lbs) is a unit used to measure the mass of something. It is used in the imperial system and the US trade system. There are various definitions. The most commonly used group of definitions today is the International Pound Sterling. This is equal to 0.45359237 kilograms, divided into 16 avoirdupois ounces.

Kilogram:

The kilogram is the unit of mass in the International System of Units (SI), expressed as kg. A unit of measurement widely used worldwide in science, technology and commerce, colloquially referred to simply as the kilogram. It means "a thousand grams."

Kilograms are defined in seconds and meters based on basic physical constants. This allows suitably equipped metrology laboratories to calibrate mass measuring instruments such as Kibble balances as a basic standard for determining accurate mass in kilograms.

Converting 150 kg to US pounds. We'll convert the formula in two different versions.

First one:

kilograms * 2.20462262 = 330.69339300 pounds.

The first version of the formula gives the most accurate result.

Sometimes even the smallest differences can matter. So, if you need accurate results, this formula will be the best option for figuring out how many pounds are in 150 kg.

Now,

we can also go to the second version of the formula and calculate how many pounds is 150 kg.

For the second version of the formula below:

This may be the best option if you want to quickly convert 150 kg to pounds, for example while shopping. It is important to remember that the results are imprecise.

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The area of the kite is 40 square meters, calculated by using the area of a kite formula.

To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:

Area = (d1 x d2) / 2

where d1 and d2 are the lengths of the diagonals.

Here is an example of how to use this formula:

Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:

Area = (8 x 10) / 2

Area = 40 square meters

So the area of the kite is 40 square meters.

There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.

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The amount of interest after 2 years and 3 months to repay the loan will be $587.25.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The formula for interest is written as,

I = (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

Jamal's parents borrow $2900.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year.

The amount of interest after 2 years and 3 months is given as,

I = [$2,900 x 9 x (2 + 3 / 12)] / 100

I = $2,900 x 0.09 x 2.25

I = $587.25

The amount of interest after 2 years and 3 months to repay the loan will be $587.25.

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Answer:

5

Step-by-step explanation:

5(5) - 7(3) + 1 = 5

Answer:

Step-by-step explanation:

The minimum interior angle possible for a regular polygon is given by the formula:

interior angle = (180° * (n-2)) / n

where n is the number of sides in the polygon. The formula is based on the fact that the sum of the interior angles of a polygon with n sides is equal to (n-2) * 180°.

As n increases, the value of the interior angle decreases and approaches the minimum value of 180°. However, for a regular polygon, all interior angles must be equal, so the minimum possible value is given by the formula above.

For example, consider a regular hexagon (n=6). The minimum interior angle is given by:

interior angle = (180° * (6-2)) / 6 = 120°

So, the minimum interior angle possible for a regular polygon is 120°.

Each point on the least-squares regression line represents a predicted y-value at a given x-value, based on the relationship between the two variables determined through regression analysis.

Regression is a statistical method used to analyze and understand the relationship between two variables. The least-squares regression line is a line of best fit that helps predict the value of one variable based on the value of another.

The correct answer is C, each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.

The line is created by minimizing the sum of the squared differences between the actual y-values and the predicted y-values.

In other words, the line is chosen such that the average difference between the actual and predicted y-values is as small as possible.

Mathematically, the regression line is represented by an equation of the form

=> y = b0 + b1x,

where b0 and b1 are coefficients determined by minimizing the sum of squared residuals.

The predicted y-value for a given x can then be found by plugging in the x-value into the equation.

Complete Question:

Explain what each point on the​ least-squares regression line represents.\

Choose the correct answer below.

A. Each point on the​ least-squares regression line represents the​ y-value of the data set at that corresponding value of x.

B. Each point on the​ least-squares regression line represents one of the points in the data set.

C. Each point on the​ least-squares regression line represents the predicted​ y-value at the corresponding value of x.

D. Each point on the​ least-squares regression line represents the​ y-values that would be considered ideal at that corresponding value of x.

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Answer:

A = 80ft^2

Step-by-step explanation:

Area of trapezoid = (a + b/2) x h

A = ((6 + 10)/2) x 10

A = (16/2) x 10

A = 8 x 10

A = 80ft^2

Answer:

Area is 80 square feet

Step-by-step explanation:

The shape of the bedroom is a trapezoid

h = perpendicular height of trapezoid

Area of a trapezoid:

                      [tex]\frac{1}{2}[/tex]×(Sum of parallel sides)× h

                 = [tex]\frac{1}{2}[/tex] × [(10 + 6) feet] × (10 feet)

                 = [tex]\frac{1}{2}[/tex] × (16 feet) × (10 feet)

∴ Area of Skylar’s Bedroom    = 80 square feet

                                                   = [tex]80 ft^{2}[/tex]

The equations of the functions are C(x) = 2.5x + 60, R(x) = 10x and P(x) = 7.5x - 60

Defining the variables, we have

For the equation of the money they spend:

So, the equation for the total money spent can be written as:

C(x) = 2.5x + 60

For the equation of the money they collect:

So, the equation for the total money collected can be written as:

R(x) = 10x

To calculate the profit from selling, we subtract the cost from the revenue

So, we have

P(x) = 10x - 2.5x - 60

Simplifying this equation, we get:

P(x) = 7.5x - 60

Hence, the profit equation is P(x) = 7.5x - 60

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We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

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