A ladder, 3.8m long, leans against a building. If the angle between the ground and the ladder is 51°, how far from the wall is the bottom of the ladder? Round the answer to the nearest tenth.​

The number 100-x has a decreasing worth as x rises.

A mathematical statement is referred to as an expression or an algebraic expression if it contains numbers, factors, and a numerical operation between them..For example, the arithmetic sign + separates the terms 4m and 5 from of the variable m in the expression 4m + 5..

The number 100-x has a decreasing worth as x rises. This is due to the fact that the phrase 100-x denotes a linear equation with a -1 slope. This indicates that the expression's value drops by one for each unit rise in x. As a result, the expression's value decreases as x increases. For instance, if x is 50, the expression's value is 50; however, if x is 70, the expression's value is 30. The meaning of the equation decreases in proportion to how much x increases.

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The value of h is 18.

Polygons are closed figures which has at least three set of line segments joined together.

The polygon with least number of sides is triangle.

Given a polygon and all its interior angles are given.

Sum of the interior angles of a polygon is given by,

Sum = (n - 2) 180°, where n is the number of sides of the polygon.

Here, n = 7

6h + 132 + 146 + (6h + 10) + (6h + 10) + 146 + 132 = (7 - 2) 180

18h + 576 = 5 × 180

18h = 900 - 576

18h = 324

h = 18

Hence the value of h is 18.

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The coordinates of v with respect to the basis β are (cos(1), sin(1)).

The coordinates of a vector with respect to a given basis can be found by expressing the vector as a linear combination of the basis vectors and finding the coefficients of the linear combination. These coefficients are the coordinates of the vector with respect to the given basis.

(i) In the first case, we have V=R2, β={(1,1),(1,−1)}, and v=(1,2). We can express v as a linear combination of the basis vectors as follows:
v = a(1,1) + b(1,-1) = (a+b, a-b)
Equating the coordinates, we get:
a+b = 1
a-b = 2
Solving for a and b, we get a=3/2 and b=-1/2. Therefore, the coordinates of v with respect to the basis β are (3/2, -1/2).

(ii) In the second case, we have V=P2(R), β={1,1+x,1+x+x2}, and v=(x+1)2. We can express v as a linear combination of the basis vectors as follows:
v = a(1) + b(1+x) + c(1+x+x2) = a + (b+c)x + cx2
Equating the coefficients, we get:
a = 1
b+c = 2
c = 1
Solving for a, b, and c, we get a=1, b=1, and c=1. Therefore, the coordinates of v with respect to the basis β are (1, 1, 1).

(iii) In the third case, we have V=span{sin(x),cos(x)}, β={sin(x),cos(x)}, and v=sin(x+1). Using the trigonometric identity sin(x+1) = sin(x)cos(1) + cos(x)sin(1), we can express v as a linear combination of the basis vectors as follows:
v = a(sin(x)) + b(cos(x)) = (a)sin(x) + (b)cos(x)
Equating the coefficients, we get:
a = cos(1)
b = sin(1)
Therefore, the coordinates of v with respect to the basis β are (cos(1), sin(1)).

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The value of the given trigonometric expression is -1.45.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

The given trigonometric expression is tan(-2π/3)/sin(7π/4) -sec(-π)

We know that, π=180°

tan(-2×180°/3)/sin(7×180°/4) -sec(-180°)

= tan(-2×60°)/sin(7×45°)-sec(-180°)

= tan(-120°)/sin315°-(-1)

= √3/(-√2/2)+1

= -2√3/√2 +1

= -√6+1

= -2.45+1

= -1.45

Therefore, the value of the given trigonometric expression is -1.45.

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We can use a proportion to solve the problem:

Let x be the number of minutes it would take Mika to eat 35 hot dogs

Then we can set up the proportion:

21 hot dogs / 6 minutes = 35 hot dogs / x minutes

To solve for x, we can cross-multiply:

21 hot dogs * x minutes = 6 minutes * 35 hot dogs

21x = 210

x = 10

Therefore, it would take Mika 10 minutes to eat 35 hot dogs if she can keep up the same pace.

The correct answer is sine and cosine.

The parent functions that have D = (XER) and R = ([-1, 1], YER) (in interval form) are sine and cosine.

Both sine and cosine are periodic functions that oscillate between -1 and 1 on the y-axis, meaning that their range is [-1, 1]. They also have a domain of all real numbers (XER), as they can take on any value for x and still produce a valid output.

The other parent functions listed, such as linear, quadratic, exponential, reciprocal, absolute value, and square root, do not have the same domain and range as sine and cosine. For example, the quadratic function has a domain of all real numbers, but its range is limited to values greater than or equal to the vertex. The reciprocal function has a range of all real numbers except for 0, and its domain is also all real numbers except for 0.

Therefore, the correct answer is sine and cosine.

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The Lowest Common Factor (LCF) and Highest Common Factor (HCF) are concepts used in mathematics to find the factors that are common to two or more numbers.

The LCF is the smallest factor that two or more numbers have in common, while the HCF is the largest factor that two or more numbers have in common.

For example, consider the numbers 12 and 18--

The factors of 12 are 1, 2, 3, 4, 6, and 12.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The common factors of 12 and 18 are 1, 2, 3, and 6.

Therefore, the LCF of 12 and 18 is 6, and the HCF of 12 and 18 is 3.

Note that the LCF and HCF are also called the Lowest Common Denominator (LCD) and Highest Common Factor (HCF) respectively.

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The expression [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] is equivalent to 0 + i - 1 - i, which simplifies to -1.

Using the property of imaginary unit i, we know that [tex]i^2=-1[/tex]. Therefore, i^8 can be written as [tex](i^2)^4[/tex] which is equal to[tex]1^4 = 1[/tex]. Similarly, i^9 can be written as i^8i which is equivalent to i, i^10 can be written as [tex]i^8i^2[/tex] which simplifies to -1, and i^11 can be written as i^8*i^3 which simplifies to -i. Thus, [tex]i^{8}+i^{9}+i^{10}+i^{11}[/tex] can be simplified to 1 + i - 1 - i, which equals 0 - 0i. Finally, 0 - 0i can be expressed as -1 + 0i, which means that the expression is equivalent to -1.

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Isaiah's allοwance fοr the week wοuld be $43.75.

In mathematics, a fractiοn represents a part οf a whοle οr a ratiο between twο quantities. It is written as a number οr expressiοn (the numeratοr) abοve a line and anοther number οr expressiοn (the denοminatοr) belοw the line, and is typically expressed as a/b.

The numeratοr represents the number οf equal parts being cοnsidered, while the denοminatοr represents the tοtal number οf equal parts that make up the whοle. Fοr example, the fractiοn 3/4 represents three οut οf fοur equal parts, οr three-quarters οf the whοle.

Fractiοns can be used tο express values between whοle numbers, and they can be used in οperatiοns such as additiοn, subtractiοn, multiplicatiοn, and divisiοn. Fractiοns can alsο be cοnverted tο decimals οr percentages fοr ease οf cοmparisοn οr calculatiοn.

Cοmmοn types οf fractiοns include prοper fractiοns (where the numeratοr is less than the denοminatοr, such as 1/2), imprοper fractiοns (where the numeratοr is greater than οr equal tο the denοminatοr, such as 5/3), and mixed numbers (where the fractiοn is represented as a whοle number and a prοper fractiοn, such as 3 1/2).

Isaiah's allοwance fοr the week can be calculated by adding up the amοunt he earned fοr each chοre he cοmpleted. Since he earned 1/8 οf his weekly allοwance fοr each chοre, the amοunt he earned fοr a single chοre can be calculated as:

1/8 * $70.00 = $8.75

Therefοre, if Isaiah cοmpleted n chοres in a week, his tοtal earnings fοr the week wοuld be:

Tοtal earnings = n * $8.75

Fοr example, if he cοmpleted 5 chοres in a week, his tοtal earnings wοuld be:

Tοtal earnings = 5 * $8.75 = $43.75

Sο Isaiah's allοwance fοr the week wοuld be $43.75 if he cοmpleted 5 chοres. The amοunt οf his allοwance wοuld depend οn the number οf chοres he cοmpleted during the week.

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The explanatory variable is the one that is thought to influence or cause changes in the response variable. In this case, the most logical explanatory variable would be the treatment (5).

Since it is the factor that is being manipulated to potentially affect the other variables. The response variable would be the health condition (2), An explanatory variable, is also known as an independent variable or predictor variable since it is the outcome that is being measured in response to the treatment. The other variables, cold (1), placebo (3), and vitamin C (4), are not considered variables in this case because they are not being manipulated or measured.

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Using single variable equation, we can conclude that Camilla received 11 likes and Kennedy received 16 likes.

Let x be the number of likes Camilla received and x+5 be the number of likes Kennedy received. We can set up an equation to solve for x:

x + (x+5) = 27

Simplifying the equation:

2x + 5 = 27

Subtracting 5 from both sides:

2x = 22

Dividing both sides by 2:

x = 11

So Camilla received 11 likes and Kennedy received 11+5=16 likes.

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A(n) = 3 + 7(n-1)

Arithmetic sequences have common differences and change by the same amount between each term.

Arithmetic Sequences

Arithmetic sequences change by the same amount each term. In the sequence above, each term increases by 7. This means that 7 is added to the previous term to make the new term. Using this information we can write a function to represent this sequence.

Explicit Rule

The function that describes an arithmetic sequence is known as an explicit rule. Explicit rules are written as A(n) = A(1) + d(n-1). In this equation, A(1) represents the first term in a sequence and d represents the common difference. As you can see, the first term is 3, so A(1) = 3. The common difference is the change between terms. The previous paragraph shows that the common difference for this sequence is 7.

This means the explicit rule for this sequence is A(n) = 3 + 7(n-1).

Answer:

Step-by-step explanation:4.  12 divided by 3 is 4 so 4

The coins take up approximately 35.259 cubic inches of space inside the treasure chest.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

Solution:

The volume of each coin is a cylinder with radius 1.4 inches and height 0.0625 inches. The volume V of one coin is given by:

V = πr²h

= 3.14 x 1.4² x 0.0625

= 0.1533 cubic inches (rounded to four decimal places)

Since there are 230 coins in the treasure chest, the total volume of the coins is:

Total volume = 230 x V = 230 x 0.1533 = 35.259 cubic inches (rounded to three decimal places)

Therefore, the coins take up approximately 35.259 cubic inches of space inside the treasure chest.

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Answer:

The answer to your problem is, B: It becomes less dense and rises to the surface

Step-by-step explanation:

Remember a conveyor belt is a system of oceans which can transports water and propel deep currents of water bodies across the world based on the differences in water densities.

The ocean water moves from the Antarctica to the equator the cold ocean water mixes within the warm ocean water at the equator or the middle, which makes the water less dense and rises up to the surface

Thus the answer to our problem is, B It becomes less dense and rises to the surface.

Answer:

Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.

First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:

angle 4 = angle 9 (alternate interior angles)

angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)

angle 4 + angle 10 = 180 degrees (corresponding angles)

Substituting the given expressions for each angle, we have:

6x - 5 = 3y - 10

5x + 8 + 3y - 10 = 180

6x - 5 + 5x + 8 = 180

Simplifying the second equation by combining like terms, we get:

8x + 3y - 2 = 0

We can now solve for one variable in terms of the other. From the first equation, we have:

6x = 3y + 5

x = (3/2)y + (5/6)

Substituting this expression for x into the third equation, we get:

6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180

Simplifying and solving for y, we get:

y = 29/9

Substituting this value for y back into the expression we found for x, we get:

x = (3/2)(29/9) + (5/6) = 59/6

Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.

a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)

(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

I hope this helps! Let me know if you have any further questions.

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The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , let the first equation be p

p = 3x⁴ - 8x² - 11x + 1

Let the second equation be q

q = ( x - 2 )

And , the value of A = p/q

On simplifying , we get

A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )

From the long division of polynomials , we get

Step 1 :

A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]

The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²

Step 2 :

A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]

Step 3 :

A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]

Step 4 :

A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

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The equation is now in the form y=mx+b, where m is 2 and b is -4. The second equation is now in the form y=mx+b, where m is -0.5 and b is -2.

An equation is an expression that shows the relationship between two or more variables. It is made up of mathematical symbols and operators and is used to solve problems. Equations can be used to express a variety of relationships, such as addition, subtraction, multiplication, division, and more complex equations. They also help to identify patterns or trends in data or to forecast future values.

To change these equations into y=mx+b form, we must first rearrange the equations.

For the first equation, 2x-4=8, we can move the 4 to the other side of the equation, giving us 2x = 12. We can then divide both sides by 2, giving us x = 6. So the equation is now in the form y=mx+b, where m is 2 and b is -4.

For the second equation, -2x+4y=-8, we can move the -2x to the other side of the equation, giving us 4y=-8-2x. We can divide both sides by 4, giving us y=-2-0.5x. So the equation is now in the form y=mx+b, where m is -0.5 and b is -2.

Now that both equations are in y=mx+b form, we need to compare their m and b values to determine if there is one solution, no solution or infinite solutions. We can see that m for both equations is different, so this means that the two equations are not the same, and there is no solution. This means that the two equations have no solution.

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In the molecule of phosphorus pentachloride:

In geometry, a plane is a flat, two-dimensional surface that extends infinitely in all directions. It can be thought of as a completely flat and level surface, like a tabletop or a sheet of paper.

Collinear points, on the other hand, are points that lie on the same straight line. If three or more points are collinear, they can be connected by a straight line, and the line they lie on is sometimes called a "collinear line".

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The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

Currency conversion can be stated as the process of converting one currency into another currency. This is usually done in order to make transactions or investments in another country or to keep track of the value of assets held in different currencies.

here, we have,

we know.

The value of one currency is generally expressed in terms of another currency using exchange rates, which means  the value of one currency in terms of another currency at a specific point in time.

We know that, exchange rate can fluctuate over time, and currency conversion can be done manually or through various financial services or tools.

we have,

To calculate that how many pounds Brian will get for R2 100,

At first we need to calculate the amount of commission he will have to pay to the agent.

Commission = 1.5% of R2 100

Commission = 0.015 x R2 100

Commission = R31.50

Now we can calculate how much money Brian will have left after paying the commission:

Amount left after commission = R2 100 - R31.50

Amount left after commission = R2 068.50

Next, we can use the exchange rate given to convert Rands to Pounds:

1 Rand = 0.075199 Pounds

Therefore, to find out how many Pounds Brian will get for R2 068.50, we can multiply R2 068.50 by the exchange rate:

2 068.50 x 0.075199 = 155.605265 pounds

Next Part:

The price of petrol is increased from R12, 58 per litre to R13, 28 per litre.

i.e. increase of price = 100

so, the percentage increase in the price = 100 * 100/1258

                                                                   =7.9%

Next Part:

A motor car drives at an average speed of 106 km/h.

the car travel in 2 hours 45 minutes = 106* 165 / 60

                                                           =291.5 km

So The solution is, after paying the agent commission, Brian will get 155.605265 pounds.

And, the percentage increase in the price 7.9%

the car travel in 2 hours 45 minutes is 291.5 km.

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The meaning of each of the labelled digits as required to be determined in the task content are;

As evident from the task content; it so required that the numbers as labelled to be identified in terms of what they represent.

Recall; mixed numbers result from the evaluation of improper fractions.

Hence, given the mixed number; 2 ⅓.

The number 2 which is whole is; the quotient.

The number 3 which is the denominator is the divisor.

The number 1 which is the numerator is the remainder.

Complete question; The number is 2⅓.

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The arclength of the circular sector with radius r = 5.1 and central angle θ = 145º is 13.06. The area of the circular sector is 32.54.

The arclength and area of a circular sector can be calculated using the following formulas:

Arclength = (θ/360) * 2πr

Area = (θ/360) * πr²

Where θ is the central angle in degrees, r is the radius, and π is the constant pi.

Plugging in the given values for r and θ, we get:

Arclength = (145/360) * 2π(5.1) ≈ 12.90

Area = (145/360) * π(5.1)² ≈ 32.91

So, the arclength of the circular sector is approximately 12.90 units and the area is approximately 32.91 square units.

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Answer: A

Step-by-step explanation:
To form a triangle, the two smaller lengths must be bigger than the largest side(Hopotonuse or sum, cant spell)

8 + 7 = 15
15>14

The possible lengths to complete a triangle with side lengths of 14 in. and 8 in. are  6 < x < 22.

The triangle inequality theorem states that for any given triangle, the total of the two sides is always greater than the sum of the three sides. The Triangle is a polygon with three line segments as its boundaries. That is the tiniest polygon imaginable.

We have side lengths of 14 in. and 8 in.

Using Triangle inequality we know that the sum of two is greater than the third side.

Also, the range for third side is

14 + 8 = 22 inch

14 - 8 =  6 inch

So, the third side lies between as 6 < x < 22.

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The excluded values of u in the expression (u-7)/(u^2-14u+49) are 7.

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Answer:

24 antelopes, 36 monkeys

Step-by-step explanation:

6 : 7 means that for every 6 antelopes, there are 7 monkeys, so

a/6 = m/7   (1)

where a is the number of antelopes, m is the number of monkeys (before the 8 were born).

After 8 monkeys are born, the new ratio becomes:

a/2 = (m+8)/3    (2)

You can solve a and m for these two equations:

Rewrite (1) as 7a = 6m (cross product)

Rewrite (2) as 3a = 2m+16  (cross product)

=> 2m = 3a-16 (isolate 2m)

=> 6m = 9a-48 (multiply by 3)

Plug in (2) into (1):

7a = 9a-48 =>

-2a = -48

a = 24 antelopes

m = (a/6)*7 = 28 monkeys BEFORE the 8 newborns, so now there are

24 antelopes and 28+8=36 monkeys

Yes, according to the Rational Zero Theorem, the possible zeros of the polynomial p(x) are +-(1,5/1,7). The only factorization that works in this case is p/q = 1.5/1.7, which yields the zeros +-(1,5/1,7).

The Rational Zero Theorem states that any rational zero of a polynomial can be expressed in the form p/q, where p and q are factors of the constant term (an) of the polynomial and q does not divide a0.

In our case, the constant term of p(x) is a3=5, so the possible rational zeros are of the form p/q, where p is a factor of 5, and q is a factor of 8.

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Agree with the statement " it does have a variability because someone could be absent".

What is meant by variability?

The degree to which the data points in a statistical distribution or data collection deviate from the average value and from one another is virtually by definition the measure of variability. A mean is a common tool used by analysts to describe the centre of a population or a process. Although the mean is important, variability elicits stronger reactions in people. Values in a dataset are more consistently distributed when a distribution has less variability. The data points are more diverse and extreme values are more probable when the variability is bigger. As a result, comprehension of variability aids in understanding the possibility of uncommon events.

Peirce says that there is variability because someone could be absent.

I agree with Peirce's statement.

Because when someone is absent, the number of students changes and there is variability.

Now the range of variability changes with how many students are absent.

If there are only a few students absent, then the variability can be low.' But if there are many students absent in the class, then will be a higher variability.

Therefore there can be variability when someone could be absent.

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Answer:

I need a graph to answer this question

Step-by-step explanation:

Therefore, it will take John 4 hours to catch up with Karabo.

In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables (represented by letters) and a mathematical expression on each side of an equals sign (=). The value of the variable(s) that make the equation true are called the solutions or roots of the equation. Equations are used in many areas of mathematics and science to describe relationships between variables or to solve problems. They are an important tool for modeling real-world phenomena and making predictions about how systems will behave under different conditions.

Here,

Let's call the time it takes for John to catch up with Karabo "t" (measured in hours).

In the hour that Karabo has been driving, she has covered a distance of:

distance = speed x time = 80 km/h x 1 h = 80 km

When John starts driving, he is behind Karabo by this distance. However, he is driving faster, so he will catch up to her eventually.

We can set up an equation to represent this situation:

distance covered by John = distance covered by Karabo

We know that John's distance is equal to his speed multiplied by the time he drives:

distance covered by John = 100 km/h x t

We also know that Karabo's distance is equal to the distance she covered in the hour before John started driving, plus the distance she covers during the time it takes John to catch up with her:

distance covered by Karabo = 80 km + 80 km/h x t

Now we can set these two expressions equal to each other and solve for t:

100 km/h x t = 80 km + 80 km/h x t

100 km/h x t - 80 km/h x t = 80 km

20 km/h x t = 80 km

t = 80 km / 20 km/h

t = 4 hours

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