Simon and Luke shared a pizza. Simon ate of the pizza. Luke ate of the pizza. Which model is shaded to show the fraction of the pizza that both boys ate?

A 1/4
B 2/8
C 7/12
D 7/16​

The exponential equation that can model Heather's salary is [tex]y = 45,500(1.03)^x.[/tex]

Exponential functions are frequently used to describe processes like population expansion, radioactive decay, and compound interest that display exponential increase or decay. The beginning value of the function is the constant a, and the base b sets the rate of growth or decay. Exponential functions include a number of crucial characteristics, including a constant ratio of change across equal intervals of time and the fact that they are continuously rising or decreasing based on the value of the base. In calculus and other areas of advanced mathematics, exponential functions are also employed to simulate a variety of events.

The exponential equation that can model Heather's salary after x years can be written in the form [tex]y = a(b)^x[/tex].

Given, Heather's salary increases by 3% each year.

Substituting the value we have:

[tex]y = 45,500(1.03)^x[/tex]

Hence, the exponential equation that can model Heather's salary is [tex]y = 45,500(1.03)^x.[/tex]

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Answer:

24,968 revolutions

Step-by-step explanation:

We need to find the circumference of the wheel in order to determine how many revolutions it will take to cover a distance of 78.5 km. The formula for circumference is:

Circumference = π x diameter

Substituting the given values, we get:

Circumference = 3.14 x 1 = 3.14 meters

Now, we need to convert the distance of 78.5 km to meters, so that we can compare it with the circumference of the wheel.

1 km = 1000 meters

Therefore, 78.5 km = 78,500 meters

To find the number of revolutions taken by the wheel, we need to divide the distance traveled by the circumference of the wheel:

Number of revolutions = Distance ÷ Circumference

Number of revolutions = 78,500 ÷ 3.14

Number of revolutions = 24,968.15

Therefore, it will take approximately 24,968 revolutions for the wheel of the truck to cover a distance of 78.5 km.

Hopes this helps

We need more information, specifically the median value and the other data points, to calculate the exact number of ants in the ant farm.

To answer your question, let's first break down the given information and terms:
1. The student's ant farm is being included in the data.
2. The median is mentioned but not provided.

The number of ants in the student's ant farm:
Step 1: Determine whether the total number of data points is odd or even.
Since the median changes when the ant farm is included, we can deduce that the total number of data points must be odd.

This is because, if the number of data points was even, adding one more data point (the ant farm) would not change the median significantly.
Step 2: Identify the relationship between the median and the data points.
With an odd number of data points, the median has to be one of the data points.

This is because the median is the middle value when the data points are arranged in ascending order, and with an odd number of points, there must be a single middle value.
Step 3: Determine the number of ants in the student's ant farm.
Since we know that the median has to be one of the data points and it is not given, we cannot directly determine the number of ants in the student's ant farm.

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The given statement "The adjacency matrix representation of a graph can only represent unweighted graphs." is False because adjacency matrix can represent both unweighted and weighted graphs.

The adjacency matrix representation of a graph can represent both weighted and unweighted graphs. An adjacency matrix is a square matrix that represents the connections between the nodes of a graph.

The matrix has a size of n x n, where n is the number of nodes in the graph. The rows and columns of the matrix represent the nodes of the graph, and the values in the matrix indicate whether there is an edge between two nodes.

In an unweighted graph, the matrix entries are either 0 or 1, indicating the absence or presence of an edge, respectively. In a weighted graph, the matrix entries represent the weight of the edges connecting the nodes.

Therefore, the adjacency matrix of a weighted graph contains real numbers instead of binary values.

One disadvantage of using an adjacency matrix to represent a graph is that it can be memory-intensive. The size of the matrix is proportional to the square of the number of nodes, so it may not be practical for very large graphs.

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The given statement "if an iterative method for solving a nonlinear equation gains more than one bit of accuracy per iteration, then it is said to have a superlinear convergence rate" is true.

Explanation:

In numerical analysis, iterative methods are used to solve nonlinear equations. Iterative methods, unlike direct methods, are used to solve equations without knowing the exact solution, and they rely on an iterative process to obtain a sufficiently accurate result.

The rate of convergence of the iterative method determines how quickly the iterative method converges to the desired solution. The rate of convergence is one of the most critical performance metrics for iterative methods.The rate of convergence of an iterative method can be classified as linear or superlinear. An iterative method is said to converge linearly if the number of accurate digits in the solution is approximately proportional to the number of iterations. A method is said to converge superlinearly if the number of accurate digits in the solution grows faster than the number of iterations. When a nonlinear equation is solved using an iterative method, if the accuracy gained by the iterative method is greater than one bit per iteration, the method is said to have a superlinear convergence rate. Therefore, the given statement is true.

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The probability of choosing a left-handed student was determined by observing a sample of students and calculating the proportion of left-handed students in that sample.

The given probability is an empirical probability. This is because it is based on actual data obtained by observing or measuring the occurrence of an event, in this case, the proportion of left-handed students in a certain population. Empirical probabilities rely on empirical evidence and can vary from one sample to another.

In contrast, classical probability is based on theoretical probabilities calculated by assuming that all outcomes are equally likely, while subjective probability is based on personal judgments or beliefs about the likelihood of an event.

In this case, the probability of randomly choosing a left-handed student is not based on theoretical assumptions or personal judgments but rather on actual data obtained from observation, making it an empirical probability.

The probability of choosing a left-handed student was determined by observing a sample of students and calculating the proportion of left-handed students in that sample.

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Since angles, DAB and MAX are congruent (statement 1) and angles ADB and AMX are congruent (statement 2), then the two triangles are similar.  Hence,  ∆DAB ≅ ∆MAX

Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

Here, we have

1. ∠DAB ≅ ∠MAX

2. ∠ADB ≅ ∠AMX (Vertical angles are congruent)

3. ∆DAB ~ ∆MAX (Angle-Angle Similarity Postulate)

Statement 1 is given in the problem. It states that angle DAB is congruent to angle MAX.

Statement 2 follows from the fact that angles ADB and AMX are vertical angles, which means they are congruent.

Statement 3 is the conclusion of the proof, which states that triangles DAB and MAX are similar by the Angle-Angle Similarity Postulate, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Since angles, DAB and MAX are congruent (statement 1) and angles ADB and AMX are congruent (statement 2), then the two triangles are similar.

Hence,  ∆DAB ~ ∆MAX.

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To write the quadratic function in standard form, we need to expand and simplify it.

y = 9(x+2)²+8

y = 9(x+2)(x+2)+8 (square the binomial)

y = 9(x²+4x+4)+8 (distribute 9)

y = 9x²+36x+36+8 (multiply 9 by each term inside the parentheses and combine like terms)

y = 9x²+36x+44 (combine like terms)

Therefore, the quadratic function y=9(x+2)²+8 in standard form is:

y = 9x²+36x+44.

Minimum distance between A and B is 36 meters using Pythagorean Theorem.

Let's call the distance between A and O "x" and the distance between B and O "y". From the diagram, we can see that:

x = 22 - 4t (since A is moving towards O at a speed of 4m/s)

y = 14 - 3t (since B is moving towards O at a speed of 3m/s)

To find the distance between A and B, we can use the Pythagorean theorem:

[tex]distance^2 = (x-y)^2 + (22+14)^2[/tex]

Simplifying:

[tex]distance^2 = (22-4t-14+3t)^2 + 36^2\\distance^2 = (8-t)^2 + 1296[/tex]

Next, we need to find the value of t when the distance between A and B is a minimum. To do this, we can take the derivative of the distance function with respect to t, set it equal to zero, and solve for t:

[tex]d/dt(distance^2) = 2(8-t)(-1) = 0[/tex]

t = 8

Therefore, the minimum distance occurs when t = 8 seconds. Plugging this value of t back into the distance function, we get:

[tex]distance^2 = (8-8)^2 + 1296[/tex]

distance = 36

So the minimum distance between A and B is 36 meters.

In summary, particle A starts at point P, 22 meters east of fixed point O, and moves towards O at a speed of 4 m/s. Particle B starts at point Q, 14 meters south of O, at the same time as A and moves towards O at a speed of 3 m/s. The distance between A and B t seconds after the start is given by the expression:

[tex]distance = \sqrt{((8-t)^2 + 1296)}[/tex], where t: time in seconds. The minimum distance between A and B occurs at t=8 seconds, and the minimum distance is 36 meters.

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To determine the number of triangles in any given level of the pyramid, we can use the formula:

f(l) = 3(l-1)^2 + 1

where l represents the level of the pyramid.

The formula can be derived by noticing that each level of the pyramid consists of a square with sides of length l-1, and four triangles attached to each side of the square. Each of these triangles has a base of length l-1 and a height of l-2. Therefore, the area of each triangle is (1/2)(l-1)(l-2), and the total area of the four triangles on each level is 2(l-1)(l-2). Adding this to the area of the square, which is (l-1)^2, gives the total number of toothpicks in the level: 3(l-1)^2. Finally, we add 1 to account for the top toothpick.

Thus, the function is:

f(l) = 3(l-1)^2 + 1

To find out how far Jacky walks every day, we need to divide the total distance he walks every week (220 1/2 m) by the number of days he walks.

Assuming he walks every day, there are 7 days in a week. So,

220 1/2 m ÷ 7 = 31 1/2 m

Therefore, Jacky walks 31 1/2 meters every day.

A residence assistant (ra) at a local university devises a plan to spot check the dorm for illegal drinking, the technique they using is Systematic Sampling.

Systematic sampling is a form of probability sampling technique in which sample members are chosen from a wider population using a defined, periodic interval but a random beginning point. By dividing the population size by the required sample size, this interval, also known as the sampling interval, is computed.

If the periodic interval is predetermined and the beginning point is random, systematic sampling is still regarded as random even though the sample population has been chosen in advance.

Systematic sampling, when done effectively on a big population of a defined size, can assist researchers, particularly those in marketing and sales, in obtaining representative results on a sizable group of individuals without having to contact every single one of them.

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Let's first find the area of the window:

Area of window = 4 * m * 4 * m = 16 * m^2

Now, let's find the area of the curtain:

Area of curtain = 3 * m * 2.5 * m = 7.5 * m^2

We're given that the area of the window is 2 square meters less than the area of the curtain, so we can set up the following equation:

16 * m^2 = 7.5 * m^2 - 2

Simplifying this equation, we get:

8.5 * m^2 = 2

m^2 = 2 / 8.5

m^2 = 0.2353

Taking the square root of both sides, we get:

m = 0.4851

Therefore, the possible areas of the window are:

16 * m^2 = 16 * (0.4851)^2 = 3.7 square meters (rounded to one decimal place).

Answer:

new height of the figure will be 175% of the original height.

Step-by-step explanation:

To calculate the new height of the figure after using a vertical scale factor of 175%, we can use the following formula:

New height = Original height x Scale factor

Let's say the original height of the figure is h. Then, using a vertical scale factor of 175% means multiplying the original height by 1.75. Therefore:

New height = h x 1.75

Simplifying:

New height = 1.75h

So the new height of the figure will be 175% of the original height.

The correct answer to the given question is "it is inverse."

One of the most essential characteristics of the normal distribution is that it is bell-shaped.

This implies that it is symmetrical, with the highest point at the mean or center and the curve declining on either side of the mean.

Normal distribution is a crucial concept in statistics and is widely utilized in research and decision-making processes.

It is a probability distribution that is commonly used to describe the distribution of a set of data.

The normal distribution has several characteristics that distinguish it from other probability distributions.

The normal distribution is not inverse, meaning that the tails do not approach the x-axis as they extend.

Rather,

The normal distribution has a gradual decline, with the tails diminishing in size but never reaching zero.

It is also asymptotic, which means that the tails of the distribution continue indefinitely without ever touching the x-axis, although they become increasingly small as they move away from the mean.

Normal distribution is not skewed, which means that it is symmetrical around the mean.

A skewed distribution is one in which the mean, median, and mode are not equal, indicating that one side of the curve is longer than the other.

The normal distribution's symmetry is one of its most important features since it indicates that the mean, median, and mode are all equivalent, and the data is uniformly distributed on either side of the mean. Therefore, the correct answer to the given question is "it is inverse."

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The Taylor series for f(x) = x³ centered at a = -1 is: f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

To find the Taylor series for f(x) = x^3 centered at a = -1,

Determine the function's derivatives:
  f(x) = x³
  f'(x) = 3x²
  f''(x) = 6x
  f'''(x) = 6

Evaluate each derivative at the center point, a = -1:
  f(-1) = (-1)³ = -1
  f'(-1) = 3(-1)² = 3
  f''(-1) = 6(-1) = -6
  f'''(-1) = 6

Write the Taylor series expansion formula:
  f(x) ≈ f(a) + f'(a)(x-a) + (f''(a)(x-a)²)/2! + (f'''(a)(x-a)³)/3! + ...

Plug in the derivatives and center point from steps 2 and 3:
  f(x) ≈ -1 + 3(x+1) + (-6(x+1)²/2! + (6(x+1)³)/3! + ...

Simplify the expression:
  f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

So, the Taylor series for f(x) = x³ centered at a = -1 is: f(x) ≈ -1 + 3(x+1) - 3(x+1)² + (x+1)³

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To determine the number of trees that are less than 8 feet tall, we need to look at the stem values that are less than 8. From the given stem-and-leaf plot, we can see that the stem values less than 8 are 5, 6, and 7.

For the stem value of 5, there are two leaves, indicating that there are two trees that are 5 feet tall. For the stem value of 6, there are four leaves (2, 6, 8, 10), indicating that there are four trees that are 6 feet tall. For the stem value of 7, there are three leaves (5, 6, 9), indicating that there are three trees that are 7 feet tall.

Therefore, the total number of trees that are less than 8 feet tall is:

2 + 4 + 3 = 9

So there are 9 trees that are less than 8 feet tall.

In the pattern of this nineteenth-century quilt from Baltimore, Maryland, there are 0 matching groups of similar motifs.

It could be because each motif in the quilt is unique, without any exact replicas. This is a common characteristic of handmade quilts, where the maker often creates each design element with subtle variations in color or stitching.

Additionally, if the quilt was made using traditional piecing methods, the use of templates or free-hand cutting techniques could result in slight differences in each motif. Overall, it is important to closely examine the quilt to determine the number of matching sets of identical motifs.

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Answer:

The height of a stack of  glasses is . The correct option is (D)

Step-by-step explanation:

Step-1:

We are given the height, when  glasses are stacked together, the height is .

We are given the height, when  glasses are stacked together, the height is .

We have to find the height when  glasses are stacked together.

Step-2:

The height of  glasses can be considered as the  term of an A.P.

The height of  glasses can be considered as the  term of an A.P.

The height of  glasses can be considered as the  term of an A.P.

Step-3:

From  we can calculate the value of  in terms of .

Substitute this value in

Substitute this value back in :

Step-4:

The value of the  term is

Therefore, the height of  glasses is . Hence the correct option (D).

Answer:

Jaime is correct, -1 x n is always equal to n ÷ (-1) for all values of n.

Thus, we can see that -1 x n and n ÷ (-1) both simplify to -n. Therefore, Jaime is correct, the value of -1 x n is always equal to the value of n ÷ (-1) for all values of n.

Ben must read at least 20 pages per day to reach his goal of reading at least 140 pages over the next 7 days. The inequality that would represent the number of pages Ben must read each day to reach his goal is:

x ≥ 20

Where x represents the number of pages Ben must read each day to reach his goal of at least 140 pages over the next 7 days.

To arrive at this inequality, we can use the fact that Ben must read at least 140 pages in 7 days. If we assume that he reads the same number of pages each day, we can represent the total number of pages he reads as 7x, where x is the number of pages he reads each day. Therefore, the inequality we need is:

7x ≥ 140

We can simplify this inequality by dividing both sides by 7:

x ≥ 20

Any value of x greater than or equal to 20 will satisfy the inequality and allow Ben to reach his goal.

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Answer:

Could you please provide more information so I can help you with your problem?

Answer:

you must pls pls post full question

Answer:

a) 60 villagers

b) 5%

Step-by-step explanation:

The probability of having every bin filled with at least one ball if n balls are distributed randomly into m bins is given by the formula 1 - (m-1/m)^n.

Let's break it down step-by-step:

Step 1: Probability of a ball being put into a specific Bin Since there are m bins, the probability of a ball being put into a specific bin is 1/m. Therefore, the probability of a ball not being put into that bin is (m-1)/m.

Step 2: Probability of a ball not being put into a specific Bin Since there are m bins, the probability of a ball not being put into a specific bin is (m-1)/m. Therefore, the probability of a ball being put into that bin is 1/m.

Step 3: Probability of every bin being filled with at least one ball Using the above two probabilities, the probability of a specific bin not being filled with a ball is (m-1)/m. Therefore, the probability of all m bins not being filled with a ball is (m-1/m)^n. Finally, the probability of every bin being filled with at least one ball is 1 - (m-1/m)^n.

Therefore, the probability of having every bin filled with at least one ball if n balls are distributed randomly in to m bins is given by the formula 1 - (m-1/m)^n.

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Answer:

The population of Tokyo is 50 times larger than that of Detroit.

Step-by-step explanation:

The population of Tokyo in 2011 was 3.5 x 10^7 (35,000,000) and the population of Detroit was 7 x 10^5 (700,000).

To calculate how many times larger the population of Tokyo is than that of Detroit, we can divide the population of Tokyo by the population of Detroit:

Population of Tokyo / Population of Detroit = (3.5 x 10^7) / (7 x 10^5)

Simplifying this expression, we get:

Population of Tokyo / Population of Detroit = 50

Therefore, the population of Tokyo is 50 times larger than that of Detroit.

The weight of the cable Dustin is using would be 58.67 pounds.

As per the given statement, Dustin is using a cable to lift heavy equipment.

His company has a table of the weights of various lengths of cable.

If Dustin needs to use 88 feet of cable, Pounds will this cable weigh:

Let us find the solution to the problem given in the question.

The length of the cable Dustin is using is 88 feet.

Using the table given by his company, the weight of the 88 feet long cable can be determined.

Using the terms given in the question, the solution is as follows:

Dustin needs to use 88 feet of cable, and the weight of this cable can be found from the table given by the company.

If we look at the table, it is evident that there is a weight of 2 pounds for every 3 feet of cable, so the weight of the 88 feet of cable Dustin is using would be:

Pounds of 3 feet of cable = 2 pounds of 3 feet of cable.

Pounds of 1 foot of cable = (2/3) pounds of 1 foot of cable

So, the weight of 88 feet of cable = (2/3) × 88 = 58.67 pounds.

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Question: Dustin is using cable to lift heavy equipment. his company has a table of the weights of various lengths of cable. if dustin needs to use 88 feet of cable, how many pounds will this cable weigh?

Length of cable in feet: 5 15 25 35

Weight of cable in pounds: 24.4 73.2 122.0 170.0

Step-by-step explanation:

2x + 2y = 108   and    x*y = 720   so  y = 720 /x    sub into first equation

2x + 2 * 720/x  = 108     multiply through by 'x'

2x^2 - 108x  + 1440 = 0   Use quadratic formula to find  x= 24,30

so the dimensions of the field are 24m  x 30m    

  to make a square by reducing a dimension means reducing 30 to 24 :

       a reduction of 6 out of 30

              6/30   * 100% = 20 %   reduction

The minimum number of possible successes of the experiment which can be expected, is calculated out to be 6.

Since the probability of success is the same for men as it is for women, we know that the probability of success for a man in this trial is also 0.60.

This defines a random binomial variable with n=10 trials and p=0.60 probability of success.

The minimum number of possible successes is zero. It is possible for none of the 10 men to respond positively to the treatment, although the probability of this occurring is relatively low (0.4¹⁰ = 0.0001048576 or about 0.01%).

The maximum number of possible successes is 10. It is possible for all 10 men to respond positively to the treatment, although the probability of this occurring is also relatively low (0.60¹⁰ = 0.0060466176 or about 0.60%).

To find the expected number of successes, we can use the formula for the expected value of a binomial random variable:

E(X) = n x p

E(X) = 10 x 0.60

E(X) = 6.0

So the expected number of successes is 6.0.

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The statement "As x --> ∞ in the expression  [tex](1+1/x)^{x}[/tex], the output approaches е" is true.

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

As x apprοaches infinity, the term with the highest pοwer dοminates the expressiοn. In this case, the highest pοwer is x in the expοnent. Therefοre, we can write:

[tex]\lim_{x \to \infty}[/tex] [tex](1+1/x)^{x}[/tex]= [tex]e^ \lim_{x \to \infty} (1/x)(x)[/tex]

Since the (1/x) × x term simplifies to 1 as x approaches infinity, we have:

[tex]\lim_{x \to \infty}[/tex] [tex](1+1/x)^{x}[/tex] = [tex]e ^ \lim_{x \to \infty}1[/tex] = e

So, the limit of the expression as x approaches infinity is e.

Therefore, the statement "As x --> ∞ in the expression  [tex](1+1/x)^{x}[/tex], the output approaches е" is true.

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