12. Vreni took part in a charity walk.
She walked a distance of 20 kilometres.
a) She raised money at a rate of $12.50 for each kilometre.
i. How much money did she raise by walking the 20 kilometres?
(1 mark)
ii. The money she raised in part (a)(i) was 5
52
of the total money raised.
Work out the total money raised.
(2 marks)
iii. In the previous year the total money raised was $2450.
Calculate the percentage increase on the previous year’s total.
(2 marks)

11b) Part of the 20 kilometres was on a road and the rest was on a footpath.
The ratio road distance : footpath distance was 3 : 2.
i. Work out the road distance.
(2 marks)
ii. Vreni walked along the road at 3km/h and along the footpath at 2.5km/h.
How long, in hours and minutes, did Vreni take to walk the 20 kilometres?
(2 marks)
iii. Work out Vreni’s average speed.
(1 mark)
iv. Vreni started at 08 55. At what time did she finish?
(1 mark)

12
c) On a map, the distance of 20 kilometres was represented by a length of 80 centimetres.
The scale of the map was 1 ∶ .
Calculate the value of .

The required, relation shown in graphs A and D is functions.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
The curves shown in graphs B and C are not functional, as both graphs consist of only one variable.

While curve shown in graph A and D are function because it shows the relationship between two variables x and y.

Graph A shows, Absolute value function,
Graph D shows the quadratic function.

Thus, the Relation shown in graphs A and D is functions.

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Answer:

37 and -18

Step-by-step explanation:

Answer:

let x and y be two numbers

Answer:

Step-by-step explanation:

2.73 (rounded)

The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

Let a, b, c, and d are the zeroes of the polynomial.

Then the polynomial is given as,

⇒ (x - a)(x - b)(x - c)(x - d)

The degree of the polynomial will be greater than or equal to the number of zeroes.

Form a polynomial whose real zeros and degree are given.

Zeros: -1, 0, 6 and Degree: 3

Then the polynomial is given as,

⇒ (x + 1)(x + 0)(x - 6)

⇒ x(x + 1)(x - 6)

Information is given about a polynomial​ f(x) whose coefficients are real numbers.

Degree​ 4; ​ zeros: 7i, 2, -2

The last root will be opposite to the 7i and will be - 7i.

The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.

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Answer:

The answer is B -2x +24

Step-by-step explanation:

I will show you how I got this answer step by step

-3(2x-8) + 4x

step 1

distribute the -3 through the parentheses

step 2

collect like terms

so -6x+4x = -2x

ANSWER: -2x+24

The expression is equivalent to the given expression is -2x +24

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

Given that, is an expression -3(2x-8)+4x, we need to find an expression equal to the given,

Simplifying the expression,

= -3(2x-8) + 4x

= -6x + 24 + 4x

= -6x+4x = -2x

Hence, the expression is equivalent to the given expression is -2x +24

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The supplied statement states that the iterated integral after being converted to interpolation is 32/3.

In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."

Therefore, the area is,

[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]

So,

[tex]y=\sqrt{2 x-x^2}[/tex]

y² = 2x - x²

x² - 2x + y² = 0

x² - 2x + 1 + y² = 1

(x-1)² + y² = 1

In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).

Region R's polar coordinates are

x = r cos∅, y = r sin∅

So,

[tex]y=\sqrt{2 x-x^2}[/tex]

y² = 2x - x²

x² + y² = 2x

r² = 2r cos∅

r = 2 cos∅

The polar coordinates of the sphere of integration as,

[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]

The provided integral then becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]

[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]

Let u = sin∅ then du = cos ∅ d∅

If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.

The above integral thus becomes,

[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]

= 32/3

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If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.

This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.

here,

In a situation whereby an individual is blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.

This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.

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Zach is trying to find out the hypotenuse value of the right-angle triangle.

What is the right triangle?

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".

Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.

In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.

Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.

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The required graph has been attached below which represents the cube root function f(x) = ³√x.

The cube root function is given in the question, as follows:

f(x) = ³√x

We have to determine the graph of the given function.

The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.

Thus, the required graph has been attached below which illustrates the cube root function f(x) = ³√x.

Hence, the correct answer would be an option (B).

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Isolate the absolute value on one side of the equation, Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.

Piecewise Definition: with respect to a number of discrete intervals, sets, or pieces.

[tex]|a|=\left \{ {{a if a > =0} \atop {-aifa < =0}} \right.[/tex]

Square root definition:

|a|=√a²

There are a few Rules to define absolute value:

1.  |–a| = |a|

2.  |a| ≥ 0

3.  Products: |ab| = |a|*|b|

4.  Quotients: |a / b| = |a| / |b|

5.  Powers: |an| = |a|n

6.  Triangle Inequality: |a + b| ≤ |a| + |b|

7.  Alternate Triangle Inequality: |a – b| ≥ |a| – |b|

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Answer:

4) is the least with 14.111°

1) is next with 17.9°

2) is next with 30.22°

5) is next with 65.84°

3) is the greatest with 86.82°

Step-by-step explanation:

1) csc θ = 3.2547

1/sinθ = 3.2547

sinθ = 1/3.2547

θ = [tex]sin^{-1}[/tex] 1/3.2547 or 17.9 ° ( I checked using a calculator here)

[tex]sin^{-1}[/tex]x is also known as arcsin.

Now, i will do the rest the same way.

2) θ = arccos(0.8641) = 30.22°

3) θ = arctan(17.9926) = 86.82°

4) θ = arcsin(0.2438) = 14.111°

5) θ = arctan(1/0.4485) = 65.844°

So, now u can tell the orders.

Pls mark as brainliest. This took a while. Cheers.

answer: none it is  -3

Answer: 3 more days

Step-by-step explanation:

8.75mi(has to run)-3.5mi(already ran)=5.25mi(left to run)

5.25mi(left to run)/1.75mi(how many she runs in a day)=3 more days (until she runs 8.75 mi)

Answer:

Step-by-step explanation:

An isosceles triangle with sides of 3/6, 3/6 and an unknown length, and a circle tangent to the two sides with a given radius can be solved using the Pythagorean theorem, trigonometry and the circle area formula.

We know that the triangle is isosceles, so the angle at point B is congruent to angle at point C, and let's call it x. Now we know that angle BAC = 90- x. Since the circle is tangent to the side AB and AC at B and C respectively, we can use the property of tangents that says that the radius of a circle that is tangent to a line is perpendicular to that line, and we can use the triangle formed by the radius, the side and the angle at that point to apply the Pythagorean theorem.

3/6^2 + r^2 = (3/6/sin(x))^2

r^2 = (3/6)^2 (1/sin^2(x) -1)

Now we can use the area of the circle formula A = πr^2, to find the area of the circle that passes through the vertices A, B, and C:

A = π r^2 = π(3/6)^2 (1/sin^2(x) -1)

Using the values of the problem we get

A = π(3/6)^2 (1/sin^2(90- x) -1) = π(3/6)^2 (1/cos^2(x) -1) = π(52^2) = 2701π = 27.01 (D)

Therefore the area of the circle that passes through vertices A, B, and C is 27.01.

By distributive property for real numbers, the expression (- 4 + v + 4 · x) · (- 6) is equivalent to the expression 24 - 6 · v - 24 · x.

In real algebra, distributive property is an algebraic property where a real number is "distributed" on every term of a sum of real numbers. This property is described below:

c · (a + b) = a · c + b · c

Where a, b, c are real numbers.

Now we proceed to use distributive property in the following case. First, write the entire expression:

(- 4 + v + 4 · x) · (- 6)

Second, apply distributive property:

(- 6) · (- 4) + (- 6) · v + (- 6) · (4 · x)

Third, use associative property:

(- 6) · (- 4) + (- 6) · v + [(- 6) · (4)] · x

Fourth, use sign laws and multiply on each term:

24 - 6 · v - 24 · x

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The nonstop trip from Stein to Constance will take 48 minutes.

Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Let us suppose the distance between Stein to Constance as d:

Then according to the distance formula, we have:

Distance = Speed * Time

Now, let the velocity of boat be v, and the velocity of water be x.

To go from Stein to Schaffhausen it takes 40 minutes. This is represented as:

d = (v + x) (40) equation 1

To go from Schaffhausen to Stein it takes 60 minutes, this is represeted as:

d = (v - x)(60) equation 2.

Divide the equation 1 and equation 2 wegwt thw following:

3v - 3x = 2v + 2x

v = 5x

Substitute this value in the distance formula:

d = (5x + x) (40)

d = 240x

d/ x = 240

X can be written as v/5, substitute this value in the above equation we have:

d/ v = 48 minutes.

Hence, nonstop trip from Stein to Constance will take 48 minutes.

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No, the absolute value of equations does not always have two answers

Understanding the absolute value is crucial for mathematicians. We place vertical bars on either side of a number to show its absolute value. On a number line, absolute value refers to distance from zero. A negative number's absolute value is a positive number. A positive number has the same absolute value as another positive number.

There are not always two solutions to an equation's absolute value. An equation involving fundamental values may have one or more solutions, depending on the equation's overall structure and the values that are being entered. For example, whereas the equation |x| = 2x has no solutions, but the equation |x| = 1 has two solutions (x = 1 and x = -1).

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Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.

The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.

Such data may come from a larger population, or from a data-generating process.

1 The correct option is B.

As the hypothesis testing helps to predict when certain certainty within which range the stock value will fluctuate.

The sampling is used to gather data from the population.

The sampling can be either random or systematic. The correct option is B.

2 The correct option is C

as the null hypothesis represents the current and present claim or knowledge.

The Alternate hypothesis is the assumption about the parameter need to be checked against the null hypothesis that is it is a new assumption to be proven. So the correct option is B.

3  The correct option is A.

As either there can be sufficient evidence to reject the null hypothesis or insufficient evidence to reject the null hypothesis.

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The surface area per unit volume is increased by a factor of 1000.

1000

The surface area of a cube is 6 times the square of its side length, (A = 6s^2). Since the volume of a cube is the cube of its side length, (V = s^3), the surface area per unit volume is 6/s.

If the volume is increased by a factor of 10, the side length is increased by a factor of 10^(1/3), which is about 3.162. The surface area per unit volume is therefore increased by a factor of 6/3.162, which is about 1,000.

The surface area per unit volume is increased by a factor of 1000.

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The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.

Let x be the number of square feet of carpet and y be the number of square feet of hardwood.

The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:

x + y <= 2000

The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:

4.50x + 8.25y <= 10000

So the system of inequalities is:

x + y <= 2000

4.50x + 8.25y <= 10000

This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.

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The difference in the amount of interest paid the first month between the average and worst score is given as follows:

$94.58.

The average interest rate would allow you to do so while paying the least amount of money, due to the lower rate compared to the poor.

The equation to model the interest accrued after t years is given as follows:

I(t) = Prt

.

In which the parameters of the equation are explained as follows:

For the average score, the parameters are given as follows:

P = 25000, r = 0.0535, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0535 x 1/12

I = 111.46.

For the poor score, the parameters are given as follows:

P = 25000, r = 0,0989, t = 1/12. (as one month = 1/12 of a year).

Hence the interest accrued is of:

I = 25000 x 0.0989 x 1/12

I = 206.04.

Hence the difference is of:

206.04 - 111.46 = $94.58.

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Answer:$

94.58

Step-by-step explanation:

Answer:

A [tex]180^{\circ}[/tex] rotation about the origin, then a dilation by a scale factor of [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The preimage is larger than the image.

Also, the orientiation of the triangle didn't change.

When x=22 minutes, Amira was 9 blocks away from the house.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

From the given distance time graph,

At time x=22,

Corresponding y value is 9

Therefore, when x=22 minutes, Amira was 9 blocks away from the house.

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Answer:

  a ≠ 0

Step-by-step explanation:

You want to know the restriction applicable to 2(y+a)/a(x-3).

A rational expression is undefined when its denominator is zero. The restrictions are applied so that no denominator is zero.

Here, the expression is ...

  [tex]\dfrac{2(y+a)}{a}(x-3)[/tex]

The only denominator is 'a'. It cannot be zero.

The restriction is a ≠ 0.

__

Additional comment

If we assume this is a relation in which x- and y- are the only variables, there is no restriction on the relation as written.

Perhaps you intend that (x-3) be a denominator factor. Then the relation would have the restriction x≠3. Such an expression would need to be written as ...

  2(y+a)/(a(x-3)) . . . . . . using parentheses around the denominator

<95141404393>

The probability that the entire batch will be accepted will be 9339

4000-90 = 3910 (non-defective) (non-defective)

If P(first not defective) = 3910/4000 and it is not changed (1 less to choose from and 1 less not defective)

P(second is not flawed if first is flawed) = 3909/3999 If the item is also not replaced (a total of 2 less to choose from and 2 less not defective)

P

(1st and 2nd are not defective, so the third is also not defective)) = 3908/3998

Simply multiply these three fractions to get the answer: 3910(3909>)(3908)) / (4000(3999)(3998)).

=9339

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The length and breadth of the rectangle are 10m and 6m respectively

The shorter side of a rectangle is called its breadth (width) and the longer side is the length.

The area of a rectangle = L×B

and the perimeter = 2(L+B)

where L is the length and B is the breadth

therefore 60 = LB, and B = 60/L

and 32 = 2(L+B)

substitute 60/L for B

32 = 2(L+60/L)

divide both sides by 2

16 = L+60/L

16 =( L²+60)/L

therefore L² +60 = 16L

L² -16L +60= 0

L²-10L-6L +60 = 0

L(L-10)-6(L-10) = 0

L-10 = 0 or L-6 = 0

therefore L = 10 or 6

when L is 10m then B = 60/10 = 6m

when L is 6m then B = 60/6 = 10m

Since the longer side is length then L = 10m and B = 6m

therefore the length and breadth of the rectangle are 10m and 6m respectively.

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Step-by-step explanation:

(e) = number of erasers she had originally.

now she has 38.

so,

A

38 = (e) + 10

B

38 - 10 = (e) + 10 - 10

28 = (e)

she had originally 28 erasers.

Answer:

The ratio of boys to girls is 4:5, which can be simplified to 4/5.

The fraction of the class that is boys is 4/5 (or 0.8), and the fraction of the class that is girls is 5/9 (or 0.5555).

So, 4/9 of the class is boys.

The number of hot cocoas the Ai Mi would be expected to sell with a high temperature of 64 ºF is given as follows:

60.

As the graph of the linear function is given, the most practical way to define the function is using the slope-intercept format, as follows:

y = mx + b.

In which the coefficients are given as follows:

From the graph, when x = 0, y = 111, hence the intercept b is given as follows:

b = 111.

When x increases by 5, from 0 to 5, y decays by four, from 111 to 107, hence the slope m is obtained as follows:

m = -4/5

m = -0.8.

Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:

y = -0.8x + 111.

The prediction for a high temperature of x = 64 is given as follows:

y = -0.8(64) + 111

y = 60 hot cocoas, rounded.

The graph is given by the image presented at the end of the answer.

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To complete the given statement, we have;

i. SM > DM

ii. <PQS < <RQS

iii. AS > RM

iv. m<1 = m<2

Any given shape which is bounded by straight side is referred to as a plane shape. Examples include: triangles, rectangle, trapezium, parallelogram etc.

It can be observed in the given question that the shapes have different properties regarding their length of sides and measure of internal angles. Each of the statement can be completed as thus;

1. From triangle SJD,

m<SJM > m<DJM

Then, it can be deduced that;

SM > DM

2. From quadrilateral PQRS,

RS > PS

It can be deduced that;

<PQS < <RQS

3. From triangle AMS, it can be deduced that AS > RM.

4. From quadrilateral ABCD,

AD II BC

Then,

m<1 = m<2             (by alternate angle property)

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