Starting at the origin, a bug jumps randomly along a number line. Each second, it jumps one unit to the

right or one unit to the left, either move being equally likely. Describe all the places that the bug could

be after eight seconds and tell how likely each of them is.

106. (Continuation) Describe all the places that the bug could be after nine seconds and tell how likely each

of them is.

A translation 3 units left and 2 units up best describes the graph of  f(x) = log2(x + 3) + 2 as a transformation of the graph of g(x) = log2x

How to solve this problem?

f(x) = log2(x + 3) + 2 (given)

g(x) = log2x (given)

We need to describe the best statement for the graph

The graph is shown in the image

The following steps are shown to describe the graph.

The general equation of f(x) = log2(x-h)+k

When h > 0 (positive)

The graph of the base of the function shift to the right

When  h < 0 (Negative)

The graph of the base function shifts to the left.

When k > 0 (Positive)

The graph of the base function shifts upward.

When k < 0 (Negative)

The graph of the base function shifts downward

Here h = 3 , k = 2

Hence , a translation 3 units left and 2 units up describes the graph.

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If the price of a latte is $4 and the price of a muffin is $2, then we can conclude that Julia can buy 5 lattes or 10 muffins ($20) if she chooses to buy only one of the two goods.

A price is the sum of money that one party pays or receives in exchange for another's goods or services. The cost of production may go by another name in certain circumstances. If the item is a "good" in a commercial transaction, the cost of the item will probably be referred to as its "price."

In this case, Allie receives a $20 gift card for the local coffee shop, where she only buys lattes and muffins. Here, we can conclude that Julia can buy 5 lattes. This will be 5 × $4 = $20 or 10 muffins which will be:

= 10 × $2

= $20

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The whole Python code is included below as an image, and it sets the base and height of triangles 1 and 2, then calculates the bigger area.

The code for determining the area of the triangle is:

class Triangle:

def __init__(A):

A.base = 0

A.height = 0

def set_base(A, user_base):

A.base = user_base

def set_height(A, user_height):

A.height = user_height

def get_area(A):

area = 0.5 * A.base * A.height

return area

def print_info(A):

print('Base: {:.2f}'.format(A.base))

print('Height: {:.2f}'.format(A.height))

print('Area: {:.2f}'.format(A.get_area()))

if __name__ == "__main__":

triangle1 = Triangle()

triangle2 = Triangle()

# TODO: Read and set base and height for triangle1 (use set_base() and set_height())

# TODO: Read and set base and height for triangle2 (use set_base() and set_height())

# TODO: Determine smaller triangle (use get_area())

print('Triangle with smaller area:')

# TODO: Output smaller triangle's info (use print_info())

Traingle is a type of polygon, the name itself days, tri means three, angles.

So, in a triangle, there will be three vertices, three sides and three angles.

The vertex of a triangle is a point where any two of the sides of a triangle meet.

The altitude of a triangle is the perpendicular length of the triangle, it is also called as height of the triangle. It is drawn perpendicular on the base of the triangle to the apex.

Base of a triangle is that particular side of the triangle on which an altitude is drawn.

For writing the code, we will put the input like only values, like 6.0, 7.0, 11.0 etc.

The first value will denote base of first triangle, second will denote height  of first triangle and third will denote base of second triangle and fourth value denotes height of second triangle/

Let us assume that,

Triangle with smaller area:

Base: 4.00

Height: 5.00 = [4.00*5.00]2 = 10.00

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The two inequalities that describe the total cost and no. of guests are

18a + 9c ≤ 2475 and

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Let 'a' be the no. of adults and 'c' be the no. of children.

The expense for this event must not exceed $2,475.00.

Therefore, 18a + 9c ≤ 2475...(i)

The venue can hold no more than 150 guests.

Therefore, a + c ≤ 150...(ii)

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We have evidence that this is not a symmetrical die, the standardized residuals is 9.5689

The die is tossed 1000 times

Given the observed value

x1 = 163

x2=178

x3=142

x4= 150

x5 = 183

x6 = 184

The mean = 163 + 178 + 142 + 150 + 183 + 184 / 6

= 1000 /6

= 166.67

Next we have to find the value of (observed value - Expected value)^2 / Expected value

x1 = (163-166.67)^2 / 166.67 = 0.081

x2 = (178-166.67)^2 / 166.67 = 0.7659

x3 = (142-166.67)^2 / 166.67 = 3.6598

x4 = (160 -166.67)^2 / 166.67 = 1.673

x5 = (183 - 166.67)^2 /  166.67 =  1.5938

x6 = (184-166.67)^2 / 166.67 =   1.7954

The standardized residuals = 0.081 + 0.7659 + 3.6598 +1.673 +1.5938 +1.7954 = 9.5689

Therefore, this is not a symmetrical die

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Answer:

A

Step-by-step explanation:

Blue = River Y

Red = River Z

River Y equation: y = 18

River Z equation: y = 10 + 2x

Graph A represents this system of equations.

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The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x

In mathematics, formulating an equation for a line in the form y = mx + b is known as slope intercept form. The m stands for the line's slope, and the b for the y-intercept. When you need to find a point on a line or solve for y given x, you utilize the slope intercept form.

According to the given information

Form of the slope intercept: y = mx + b

It goes through some points ( 1 , 3 )

Slope of the line given m = 3

Put x = 1 and y = 3 and m = 3 in slope intercept form equation

3 = 3( 1 ) + b

b = 0

Hence

Put the value of b = 0 in y = mx + c

y = 3x

The Slope intercept form of equation passing through points ( 1 , 3 ) and having slope 3 is y = 3x

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The total interest paid on the loan repayable over three months weekly at 2.85% per week is $3,584.96.

The total interest can be computed using an online finance calculator.

The result is then added to the late payment fees.  The default payment fee is the product of $600 and 5.

N (# of periods) = 14 weeks (3 x 4 + 2)

I/Y (Interest per year) = 2.85%

PV (Present Value) = $50,000

PMT (Periodic Payment) = $4,000

Results:

Sum of all periodic payments = $56,000.00

Total Interest = $584.96

Late payment charge = $3,000 ($600 x 5)

Total interest and late charge = $3,584.96

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Assume that the borrower repays $4,000 weekly.

The linear inequality x < - 3 is represented on the number line below

An Inequality represents the mathematical expression that shows both sides are not equal. When the relationship makes a non-equal comparison between two expressions or two numbers, then it is known as inequality. In this case, the equal sign in the expression is represented by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠).

The inequality given is;

-2x + 0.25 > 6.25

-2x > 6.25 - 0.25

-2x > 6.0

Divide both sides by coefficient of x

x < -3

Placing this on a number line, we would have;

Kindly find the attached graph below

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The point of intersection is (0, -4).

What is the point of intersection?

In a plane, intersecting lines are any two or more lines that cross one another. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.

Here, we have

Given: f(x) = -x -4, g(x) -5x -4

The lines intersect where f(x) = g(x)

f(x) = g(x)

- x - 4 = -5x - 4

-x +5x = -4 +4

4x = 0

x = 0

Now, we put the value of x in f(x) and we get

f(0) = - 0 - 4

f(0) = -4

Hence, the point of intersection is (0, -4).

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The equation of the line that has the slope of 7/3 is:  y = (7/3) x - 27/49

Finding the slope and y-intercept is necessary to express the equation of a graphed line in y-intercept (y=mx+c) form, which can then be used to get the equation of the line. The ratio of y to x is known as the slope. A slope triangle should be drawn connecting any two spots you find along the line.

Standard form, slope-intercept form, and point-slope form are the three main types of linear equations.

Given that,

slope (m) = 7/3

Putting (7,-9) into the equation: y =mx+c

or, -9 = (7/3) × (7) + c

or, -9 = 49 /3 + c

or, c = (-9) × (3/49)

or, c = -27/49

Thus, the equation becomes:

or, y = (7/3) x + -27/49

or, y = (7/3) x - 27/49

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By using the well ordering principle we can easily prove that the equation

4a³ + 2b³ = c³ does not have any solution for positive integers.

Let (a, b, c) be a positive integer solution with c the smallest possible.

Then c³ is even as the sum of a factor of 4 and factor of 2 is always even .

hence c itself is even.

Let us consider  c = 2c₀ ;

4a³ + 2b³ = (2c₀)³

or, 4a³ + 2b³ = 8c₀³

then 2a³+b³ = 4c₀³

This time, we see that b must be even. using the same principle as above .

Put b = 2b₀ ;

2a³ + 8b₀³ = 4c₀³

then a³ + 4b₀³ = 2c₀³

thus a = 2a₀ must be even,

and 4a₀³+2b₀³=c₀³,

i.e. (a₀, b₀, c₀) is another solution. But c₀ = c/2<c.

And we have taken c to be the smallest of the solutions.

hence we get a contradiction.

Therefore our assumption is not valid.

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Answer:

Step-by-step explanation:

so a(x+4)(x-3)is total form after putting the point you will have 4(x+4)(x-3)=y

so answer is 4x^2+4x-48=y

10 inches is the scale factor from the drawing to the actual billboard

A scale factor is a ratio of change from a drawing to real life. Typically, a scale factor is unit-less; a scale factor of 48 (or 1:48) is saying that for one unit on the page, it represents 48 of the same units in real life.

A scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Scale drawings show an image either reduced or enlarged in size. The change between the original and the scaled drawing is generally represented by two numbers separated by a colon, like 10:1 (read as “ten to one”).

The difference between the ratio numbers represents the factor by which the scaled image is enlarged or reduced. So for a 10:1 scale ratio, a 1 inch (2.5 cm) drawing will be 10 inches (25 cm) in real life.

Methods are as follows :

Changing Scale Digitally-

Scan the image or snap a pic of it with your phone.

Insert the image into a suitable program or app.

Navigate to the image layout options.

Adjust the height and width under the “Scale” heading.

Save the scaled image and you’re done.

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The complete answer: A domain is a set of input data in a relationship.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

An input value and an output value are matched in a relation.

A relation is a function where each input value yields one and only one output value.

Graphs, tables, and ordered pairs can all be used to represent functions. The domain is the set of input values,

while the range is the set of output values.

The domain of a function or relation is the set of all possible independent values that it can have.

Therefore,  a domain is a set of input data in a relationship.

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The correct option is B (f-g)(y)=8 y²-y+3

What exactly are function and example?

A rule is something that produces one output from one input, such as a function. Alex Federspiel was the source of the image. As an illustration, consider the equation y=x2. For every x input, there is only one y output. The fact that x is the input value leads us to say that y is a function of x.

Which four sorts of functions are there?

The classification of various types of functions can be done using four primary categories. All functions are based on the element: one to one, many to one, onto, one to one, and into.

Given that:

f(y)=5 y²-2y+1

g(y)=-3y²-y-2

(f-g)(y) = 8y²-y+3

Option b is correct

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Answer:

Step-by-step explanation:

log base (2) of (x^2 +5) = (3) can also be described as 2^3 = x^2 + 5

simplify: 8 = x^2+5

Subtract 5 from each side: 3 = x^2

square root: x = sqrt(3)

Answer:

Step-by-step explanation:

[tex]log(2)^{(x^2+5)}=3\\[/tex]

[tex]2^3 =x^2+5\\8-5=x^2\\x^2=3\\x=\pm\sqrt{3}[/tex]

Using the given formula, we have been able to prove that; the expected value of the students' score is 18 correct responses

1) Let X denote the number of correct guesses, assuming that a student guesses randomly among the five options of all 25 questions. Then X has a binomial probability distribution with;

n = 25

p = 1/5 = 0.2

2) Let Y denote the number of correct responses on the seven questions for which the student guesses randomly from among the five options. Then Y has a binomial probability distribution with n = 7 and p = 0.20. Then the expected value of Y is;

E(Y) = np = 7(0.2) = 1.4

Using the scoring formula given, we have;

Score = (18 + Y) - 0.25(7 - Y) + 0(0)

= 16.25 + 12Y

The expected value of the students' score is;

E(16.25 + 12Y) = 16.25 + 12(1.4)

= 18 correct responses.

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Answer:

gh(b)

Step-by-step explanation:

Answer:

shifted to the right

Step-by-step explanation:

(a) There are 36 ways to select 8 apartments randomly by cluster sampling method.

(b) Throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.

(a) Given the building has 9 floors which are taken as N=9 clusters.

Each floor has 4 apartments.

It is to select 8 apartments by cluster sampling method.

That is to select a sample of size any n=2 floors(clusters) by cluster sampling method out of the population of N=9 clusters.

By simple random sampling without replacement, there are NCn = 9C2 =36 ways to select 2 clusters.

Hence, there are 36 ways to select 8 apartments randomly by cluster sampling method.

(b) The main benefit of stratified sampling over cluster sampling is that the sample obtained using this method will unquestionably include representations of both features, i.e., apartments with and without children as a full representative of the population.

In contrast, there is no guarantee that the sample of flats with and without children from the cluster sampling approach will accurately reflect both qualities. Sometimes throughout this process, we obtain floors 3, 4, 6, or 3, 6, which do not have sample flats with children, and as a result, the sample will not accurately reflect the population.

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The right question is given beow:

The probability that the first success occurs on trial number n = 3 is 0.032

Given:

probability of success on a single trial p = 0.80

trial number, n = 3

Recall the formula for the Geometric Probability Distribution

P(n) = p(1 - p)ⁿ⁻¹

where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial

P(n) = p(1 - p)ⁿ⁻¹

P(3) = 0.8(1-0.8)³⁻¹

P(3) = 0.8(0.2)²

P(3) = 0.032

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The dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

Given that:

Total surface area of the rectangular box or cuboid = 100 cm²

A rectangular box with largest volume is a cube.

The total surface area of a cube = 6 times square of one edge length.

Let the edge length = given dimensions; x, y, z

So,

x = y = z

6x^2 = 100

x^2 = 100 / 6

x = √ 100 / 6

x = 10 / √ 6 cm

x = 2.449 cm

Hence, dimensions of the rectangular box with largest volume if the total surface area is given as 100 cm2: x = y = z = 2.449 cm.

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Reason:

The horizontal width spans from 8 to 20. This is a distance of 20-8 = 12 units.

The height is some unknown, which I'll call x. We multiply the width and height to get the area. This area must be 1 to represent 100%. You can think of it like a pie chart. This applies to any probability distribution.

area = base*height

1 = 12*x

x = 1/12

Therefore, the height of this rectangle must be 1/12 so that the area of this rectangle is 1.

The solution is D = 200 feet

The diameter of the circular store is = 200 feet

What is a Circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The perimeter of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle

Given data ,

Let the diameter of the circle be represented as = D

Let the radius of the circular store be = r

D = 2r

Now , the area of the circular store be = A

The value of A = 31,415 feet²

The area of the circular store is given by the formula

Area of the circle = πr²

Substituting the values in the equation , we get

31415 = 3.1415 x r²

Divide by 3.1415 on both sides of the equation , we get

r² = 10000

Taking square roots on both sides of the equation , we get

r = 100 feet

Now , the diameter of the store = 2 x radius of the store

Diameter of the store D = 2 x 100 feet

Therefore , diameter of the store D = 200 feet

Hence , The diameter of the circular store is = 200 feet

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The maximum area of the tile to contain both grounds is 12x²y²

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

Area of ground A = 12x^2y sq. units

Area of ground B = 6xy^2sq units

Rewrite these areas properly

So, we have the following representation

Area of ground A = 12x²y sq. units

Area of ground B = 6xy² sq units

Express the areas as the products of their prime factors

This gives

Area of ground A = 2 * 2 * 3 * x * x * y

Area of ground B = 2 * 3 * x * y * y

From the above products, we have

Least common multiple = 2 * 2 * 3 * x * x *y * y

Evaluate the products

Least common multiple = 12x²y²

This represents the greatest area

Hence, the greatest area is 12x²y²

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Answer:

I cant see numbers sorry. post question again

The question is unclear.

Step-by-step explanation:

[tex]1. \: \: 3x +4 y = 8.50[/tex]

[tex]2. \: \: 5x + 8y = 14.50[/tex]

times equation 1 by 2

[tex]3. \: \: 6x + 8y = 17[/tex]

3-2 eliminates y variable

[tex]x =2.50[/tex]

[tex]y = 0.25[/tex]

The statement of the problem has already made a lot of decisions for us. We are told to use three global variables of type int[]. The variables must be static, and I have chosen to make them private, so the declarations become:

private static int[] firstNumbers;  // The first numbers in all ten questions.

private static int[] secondNumbers; // The second numbers in all ten questions.

private static int[] user answers;   // The user's answers to the ten questions.

Note that these declarations are not in any subroutine. These statements only create variables, not arrays. We still need to create three arrays of length 10. The arrays can be created using the new operator. This initialization could in fact be combined with the declaration of the variables:

private static int[] firstNumbers = new int[10];

private static int[] secondNumbers = new int[10];

private static int[] userAnswers = new int[10];

Another possibility would be to create the three arrays at the beginning of the main() routine. In fact, I chose to create them in the subroutines where they are first used.

The program has three stages -- create the problems, administer the quiz, and grade the quiz -- and we are told to write a subroutine to do each stage. The main program simply has to call the subroutines:

public static void main(String[] args) {

   createQuiz();

   administerQuiz();

   gradeQuiz();

}

This is an example of using subroutines to break up a large task into several simpler subtasks, so that programming each subtask becomes a separate problem. The subroutines are short and not too hard to write. Looking at administerQuiz() as an example, note that the user's answers have to be stored in the array, the user answers so that they can be used when grading the quiz. I create the array itself before asking any questions and then store the user's responses in the array as they are read by the user. On the other hand, the arrays that hold the numbers that occur in the questions have already been created and filled before administerQuiz() is called. Here's the subroutine:

private static void administerQuiz() {

   userAnswers = new int[10];

   for (int i = 0; i < 10; i++) {

       int questionNum = i + 1;

       System.out.printf("Question %2d:  What is %2d + %2d  ? ",

                     questionNum, firstNumbers[i], secondNumbers[i]);

       userAnswers[i] = TextIO.getlnInt();

   }

}

A couple notes about the output: I wanted to number the questions 1, 2, ..., 10, but the elements of the arrays are numbered 0, 1, ..., 9. This means that the question number that I output has to be one more than the array index. Also, all the numbers that occur in my program are either one or two digits. By allowing exactly two digits for each number in the output, I can get everything to line up neatly. Here's the I/O for a sample run of the program:

Welcome to the addition quiz!

Question  1:  What is 40 + 14  ? 54

Question  2:  What is 18 + 38  ? 46

Question  3:  What is 21 + 31  ? 52

Question  4:  What is 18 + 36  ? 54

Question  5:  What is 43 + 12  ? 55

Question  6:  What is 21 + 17  ? 38

Question  7:  What is 33 + 25  ? 58

Question  8:  What is 39 + 21  ? 70

Question  9:  What is  1 + 25  ? 26

Question 10:  What is 39 + 26  ? 65

Here are the correct answers:

  Question  1:  40 + 14  =  54.  You were CORRECT.

  Question  2:  18 + 38  =  56.  You said 46, which is INCORRECT.

  Question  3:  21 + 31  =  52.  You were CORRECT.

  Question  4:  18 + 36  =  54.  You were CORRECT.

  Question  5:  43 + 12  =  55.  You were CORRECT.

  Question  6:  21 + 17  =  38.  You were CORRECT.

  Question  7:  33 + 25  =  58.  You were CORRECT.

  Question  8:  39 + 21  =  60.  You said 70, which is INCORRECT.

  Question  9:   1 + 25  =  26.  You were CORRECT.

  Question 10:  39 + 26  =  65.  You were CORRECT.

You got 8 questions correct.

Your grade on the quiz is 80.

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Answer:

[tex]2x^2+7x+C[/tex]

Step-by-step explanation:

Find the antiderivative of f'(x)=4x+7

[tex]\frac{4x^{1+1} }{1+1}+7x+C\\\frac{4x^2}{2}+7x+C\\ 2x^2+7x+C\\[/tex]

Answer:

To find the difference between the elevations of City A and City B, we need to subtract the elevation of City A from the elevation of City B. Since City A is located 15 meters below sea level, and City B is located 43 meters above sea level, the difference between their elevations is $43 - (-15) = 43 + 15 = 58 meters. Therefore, the difference between the elevations of City A and City B is 58 meters.