2. Rabbit Problem

When rabbits were first brought to Australia last

century, they had no natural enemies so their numbers increased

rapidly. Assume that there were 60,000 rabbits in 1865, and that by

1867 the number had increased to 2,400,000. Assume that the num-

ber of rabbits increased exponentially with the number of years that

elapsed since 1865.

Write the particular equation for this function,

b. How many rabbits would you predict in 1870?

c. According to your model, when was the first pair of rabbits in-

troduced into Australia?

Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

Adam earns $186 for 8 hours of work, so his hourly rate is $186/8 = $23.25 per hour

Kim earns $54 for 3 hours of work, so her hourly rate is $54/3 = $18.00 per hour

Kim earns $125 for 7 hours of work, so her hourly rate is $125/7 = $17.86 per hour

Kim earns $216 for 12 hours of work, so her hourly rate is $216/12 = $18.00 per hour

Adam earns $23.25 per hour and Kim earns $18.00 per hour on average.

Adam earns $23.25 - $18.00 = $5.25 more per hour than Kim.

Therefore the correct answer is A. Adam earns $5.25 more per hour than Kim.

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Answer:

A) 5

B) X-3

C) 2X+Y

step by step:

base x height = area

A Height= (5x+20) ÷ (x+4)= 5

B Base= (8x-24) ÷ 8 = x-3

C Height= (12x+6y) ÷ 6 = 2x+y

The solution is

Parallelogram A : Base = x + 4 ; Height = 5

Parallelogram B : Base = x - 3 ; Height = 8

Parallelogram C : Base = 6 ; Height = 2x + y

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the area of the parallelogram be A = Base x Height

So , Substituting the values in the equation , we get

a)

Let the parallelogram be A

Now , Area = 5x + 20

Base = x + 4

So , the height = Area / Base

Height = 5

b)

Let the parallelogram be B

Now , Area = 8x - 24

Height = 8

So , the Base = Area / Height

Height = x - 3

c)

Let the parallelogram be C

Now , Area = 12x + 6y

Base = 6

So , the height = Area / Base

Height = 2x + y

Hence , the equations are solved

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Answer: original price: £400

Step-by-step explanation:

20/100 × original price = £80

Original price = £80 ÷ 20/100

                      = £400

Answer:

55

Step-by-step explanation:

∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Given that Circle C is inscribed with 5 lines

Point C is at the center of the circle

3 lines come out of point C and make points D, A, and B on the edge of the circle.

Another line comes out of point C and goes past the edge to point E.

For ∠ABC

The geometric figure is not drawn.

For ∠BCE

The geometric figure is drawn.

For line segment CA

The geometric figure is drawn.

For Ray CA

The geometric figure is drawn.

For Circle C

The geometric figure is drawn.

For Ray BE

The geometric figure is not drawn.

For Line segment AE

The geometric figure is not drawn.

Hence,  ∠BCE is drawn, line segment CA is drawn,  Ray CA is drawn, For Circle C is drawn, Ray BE is not drawn.

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The probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes is 59.81%

How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. Look up all the related responses.

The likelihood that an event will happen is quantified by probability. An event's likelihood is determined by how frequently it will occur over the long run. Probabilities are all digits that fall between 0 and 1, inclusive—that is, all digits that fall between 0 and 1.

Let the equation of Z score be:

z = (raw score - mean) / standard deviation

Given mean of 36 minutes and a standard deviation of 3 minutes.

If x = 32:

z = (32 - 36)/3 = -1.33

and x = 37:

z = (37 - 36)/3 = 0.33

P(-1.33 < z < 0.33) = P(z < 0.33) - P(z < -1.33)

= 0.6179 - 0.0198

= 0.5981

A consumer selected at random has a 59.81% chance of having to wait between 32 and 37 minutes.

The complete question is:

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 36 minutes and a standard deviation of 3 minutes. What is the probability that a randomly selected customer will have to wait between 32 minutes and 37 minutes, to the nearest thousandth?

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Answer: Kaitlyn can run the triangular route represented by HEDF. This route is the same distance as Lucy's route, ABDF, because it is composed of three sides of the same length. H is the starting point, E is the midpoint, and F is the endpoint. The route starts at point H, travels to point E, then to point D, and finally to point F, completing the triangle.



Yara's mother was 32n-5 years old 5 years ago in terms of n.

Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:

Mother's age = 4n * 8 years

We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:

Mother's age 5 years ago = 4n * 8 years - 5 years

Now we can simplify this equation:

Mother's age 5 years ago = 32n - 5 years

Now we can substitute the value of n to find the mother's age in terms of n.

To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.

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The Binomial Expression is defined as the type of algebraic expression that consists of exactly two terms .

What is Binomial Expression ?

The algebraic expression which contains exactly only two terms is termed as  binomial expression . It is called a two term polynomial.

the binomial is also called a sum or a difference between two or more monomials. Binomial is the simplest form of a polynomial.

Some Examples of Binomial Expression are ⇒ [tex]4x^{2} +6y^{2}[/tex] , [tex]xy^{3} +xy[/tex] ;

Various Mathematical Operations can be performed on Binomial Expression such as Addition , Subtraction , Multiplication and Division .

and The  Equation that contains one or more binomial expression is called as a Binomial Equation.

The given question is incomplete , the complete question is

What is a Binomial Expression ?

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Given the function p(x)=6x+2, p(-2) is -10 while p(4) is 26, this shows that value of p(-2) is smaller than the value of p(4). The correct option is B.

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). It is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.

p(x)=6x+2

for p(-2)

p(-2) = 6(-2) + 2

p(-2) = -12 + 2

p(-2) = -10

for p(4)

p(4) = 6(4) + 2

p(4) = 24 + 2

p(4) = 26

p(-2) < p(4)

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Answer:

(B) "The value of p(-2) is smaller then the value of p(4)" is True

Step-by-step explanation:

p(x)=6x+2

p(-2) = 6*(-2)+2

p(-2) = -12+2

p(-2) = -10

p(4) = 6*(4)+2

p(4) = 26

====

p(-2) = -10

p(4) = 26

===

(A) The value of p(-2) is larger then the value of p(4).   False

(B) The value of p(-2) is smaller then the value of p(4).  True

(C) The value of p(-2) is the same as the value of p(4).  False

(D) The values of p(-2) and p(4) cannot be compared.   False

The probability that a sequence will contain exactly one 0 as calculated from the data given is found to be 3/8.

Taking into consideration the sequences where the digit 0 occurs , we will get the possibilities of getting 0 and 1 as 2 .

The number of sample points in the  sample space will be ,

2 x 2 x 2 = 8 sample points.

These sample space are, S = {111, 110, 101, 011, 100, 010, 001, 000},

Now , the sequence having all three 0 as seen from the sample space is found to be 3.

So the  probability becomes , P(0) = no of favorable outcomes / total number of outcomes =3/8.

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The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

A number can be obtained by multiplying the square root by itself. Square root is represented by the symbol sqrt, which stands for square root of, end square root. The reverse of squaring an integer is finding its square root. The result of multiplying a number by itself yields its square value, whereas the square root of a number can be found by looking for a number that, when squared, yields the original value. If 'a' is the square root of 'b,' then a a = b.

given

Use the average rate of change formula to substitute.

(√1)−(√−4) / (1)−(−4)

Condense the phrase.

1/5−2i/5

The rate of change, y=−√x−4 +5 , is expressed as 1/5−2i/5 .The square root of a number is the number itself.

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The Pythagorean theorem rounding of 16 and 18 would be = 24 (approximately)

Pythagorean theorem is defined as the theorem that expresses the relationship that exists between the three side of a right angle triangle.

The relationship states that the square of the longest side is equal to the sum of the square of the other two sides.

That is, c² = a² + b²

Where, a = 16

b = 18

c² = 16²+18²

c² = 256 + 324

c² = 580

C =√580

C = 24.1

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The only difference is a -2 in x in 1 transformation in 2 transformation. The function is shifted up by b units with f (x) + b.

Transformations can be divided into four categories: translation, reflection, rotation, and dilation. Rotate, reflect, or translate the geometric figures on a coordinate plane. The label given to a function, f, that maps to itself is the transformation, or f: X X. The pre-image X is transformed into the picture X after the transformation. It is possible to utilize any operation, or a combination of operations, in this transformation, including translation, rotation, reflection, and dilation.

given

J(2, 2), (3, 4), H(4,3), G(3,0) to J'(-1,2), I'(0, 4), H'(1, 3), G'(0, 0)

in 2 transformation as the only change is that -2 in x in 1 transformation

The function is shifted up by b units with f (x) + b.

The function is shifted downward by b units when f (x) b.

The function is moved left by b units when f (x + b) is used.

The function is moved right b units by the expression f (x b).

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The time taken by Wendy after she learned flying is m/4 minutes or 0.25m minutes.

We will solve this problem with the help of Percentages.

In the concept of percentages, we know that:

100% = 100/100 = 1

75% = 75/100 = 3/4

50% = 50/100 = 1/2

25% = 25/100 = 1/4

In our question, it is given that previously wendy took ‘m’ minutes to commute.

Now she reduced her daily commute by 75% after learning how to fly.

So, our new time = (100-75)% of previous time

= 25% of m minutes

= 25/100 of m minutes = ¼ of m minutes = m/4

So our final answer will be m/4 minutes or 0.25m minutes taken by wendy to commute now.

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As per the given points in the question, the slope in the simplest form will be equal to 0

Using two of the points on the line you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise and the horizontal change is called the run. The slope equals the rise divided by the run.

Here the given points are (−5,8) and (−11,8)

Hence the required slope of the line is

=   8     -       8

     11 -  [ - 5 ]

=      0      

 - 11 + 5

=        0    

        - 6

= 0

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The paper is folded into 5 folds before the area is less than 1 square inches.

What is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Here the area of the folded paper after n folds is,

A = 90[tex](\frac{1}{3})^n[/tex]

Now put n=0 into given formula,

A = 90[tex](\frac{1}{3})^0[/tex]=90×1 = 90 square inches.

Here Area of the paper before being fold is 90 square inches.

Now area is less than 1 square inches then

=> 90[tex](\frac{1}{3}) ^n[/tex] < 1

=> [tex](\frac{1}{3}) ^n < \frac{1}{90}[/tex]

Here if n= 4 then  [tex](\frac{1}{3}) ^4 > \frac{1}{90} = \frac{1}{81} > \frac{1}{90}[/tex] then n=5.

Hence the paper is folded into 5 folds before the area is less than 1 square inches.

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The exponential function to model the predicted value of Bruce's investment account is

y = 6225 * 2^x.

The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

here, we have,

we know that,

An exponential function is written in the form - y=a*(b)^x

Here, y is the function, a is the base value b is the rate and x is time period.

now, we have,

from the given information, we get,

This equation uses the initial value of the account (6225)

and the base of the exponent (2) representing the account will double in value every decade.

if, we have,

the predicted value of Bruce's investment account is y.

time period is, x decades after starting the account.

So, the exponential equation will be -

y = 6225 * 2^x.

Therefore, the exponential equation is .

y = 6225 * 2^x.

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When a polynomial has four or more terms, the easiest way to factor it is to use grouping.

Grouping can be understand more better with an example:

for eg:  factor x^3 + x^2 – x – 1 by using grouping. Just follow these steps:

However, x^2 – 1 is a difference of squares and factors again as (x+1)(x-1). This gives you a final factorization of: (x + 1)(x + 1)(x – 1), or (x + 1)2(x – 1).

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The description of a solution to the problem modeled by the function y = 2x + 8 is given as follows:

The time needed to complete 40 parts  is of 16 minutes.

The function for this problem is defined as follows:

y = 2x + 8.

In which the variables are defined as follows:

Hence, solving the function for x, we are going to obtain the time needed to produce y parts, giving the description of a solution for this problem.

When y = 40, the solution for x is given as follows:

40 = 2x + 8

2x = 32

x = 32/2

x = 16 minutes.

The interpretation of this solution is that a time of 16 minutes is needed to obtain a production of 40 parts.

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simplest form of  equation V= 60

Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1.

A 'Simplest Form Calculator' is a free online tool that reduces a fraction to its simplest form. In this calculator, you can enter value and find its simplest form within a few seconds.

V=S3

S = 20

Give your answer in simplest form.

V = S3

V = S× 3

S = 20

Therefor

V = 20 × 3

V= 60

simplest form V= 60

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Answer: No, -0.0022 is not less that -0.022

Step-by-step explanation:

1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.

The process to solve 3 equations with 3 unknown  is explained below.

The term equation is known as a mathematical statement that is made up of two expressions connected by an equal sign.

The process of 3 equation with 3 unknown variable is explained step by step as follows:

First of all we have to write all the equations in standard form cleared of decimals or fractions.

And then we have to choose a variable to eliminate them then we have to choose any two of the three equations and eliminate the chosen variable.

After that we have to select a different set of two equations and eliminate the same variable as in Step 2.

Now, we have to solve the two equations from steps 2 and 3 for the two variables they contain.

And then we have to substitute the answers from Step 4 into any equation involving the remaining variable.

And then finally we have to check the solution with all three original equations.

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Polya's 4 step method is a process designed to help problem solvers become better at tackling difficult problems.

It was developed by the mathematician George Polya in 1945 and consists of four basic steps:

1. Understand the problem: The first step is to read and understand the problem. This means understanding the problem and identifying what information is given and what is required.

2. Devise a plan: The second step is to identify a strategy or plan of attack. This involves breaking the problem down into smaller parts, identifying the key elements, and using logical reasoning to identify a solution.

3. Carry out the plan: The third step is to execute the plan. This involves following the steps of the plan in order to solve the problem.

4. Look back: The fourth and final step is to take a look back at the solution and evaluate it. This involves checking to make sure the solution is correct and making any necessary adjustments.

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Answer:

[tex] \sf \: 6 + 3b + 8 = 32[/tex]

Step-by-step explanation:

Given expression,

→ 6 + 3b + 8

Now we have to use,

→ b = 6

Let's solve the expression,

→ 6 + 3b + 8

→ 6 + 3(6) + 8

→ 6 + 18 + 8

→ 24 + 8

→ 32 => final value

Hence, the answer is 32.

We can use the Z-score formula to determine what percent of patients have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

The Z-score formula is:

Z = (X - M) / SD

Where:

X = Patient's score (45)

M = Mean score (52)

SD = Standard deviation (5)

Plugging in the given values:

Z = (45 - 52) / 5

Z = -7 / 5

Z = -1.4

This Z-score of -1.4 corresponds to a percentage of approximately 9.1% of patients who have a score equal to or lower than the patient's score of 45 on the cognitive abilities test.

It is important to note that this percentage is approximate, as it's calculated based on the standard normal distribution table which provides approximate values, and it assumes the scores of the test are normally distributed, in case this assumption is not met the result may not be accurate.

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Answer:

FALSE

Step-by-step explanation:

It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.

Answer:

The restaurant owns 225 forks

Step-by-step explanation:

We can get our answer by displaying as an equality

9 to 4/100

x to 100/100

You can multiply 4 by 25 to get 100 so to get the amount of forks, multiply 9 by 25

9 * 25 = 225

Answer:

225 forks

Step-by-step explanation:

9 to 4/100

x to 100/100

Multiply 4 by 25 to get 100 so to get the number of forks, multiply 9 by 25!

9 * 25 = 225

Hope this helps.

Answer:

x = -4 or x = -1

Step-by-step explanation:

Let's check

x = -4

(-4 + 4)(-4 + 1) = 0

(0)(-3) = 0

0 = 0

Let's check x = -1

(-1 + 4)(-1 + 1) = 0

(-3)(0) = 0

0 = 0

So, x = -4 or x = -1 is correct answer!