Lucas wants to write 3 ÷ 2 as a mixed number. He performs the division below.

3 ÷ 2 = 1 R1

Explain how to write the quotient as a mixed number

-12.75 belongs to the set of Rational numbers.

A rational number is a number that can be expressed as the quotient or fraction frac p q of two integers, a numerator p

and a non-zero denominator q.

Rational numbers are numbers that can be expressed as a fraction of two integers (p/q), where q is not equal to zero.

Identify the number: -12.75

Determine if it can be expressed as a fraction of two integers: -

12.75 can be written as -51/4, which are both integers.

Confirm that the denominator (q) is not equal to zero:

In this case, q = 4, which is not equal to zero.

Therefore, -12.75 belongs to the set of Rational numbers.

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Answer:

best choice to answr is letter B.

Step-by-step explanation:

Square feet is the standard unit of measure for area in the United States and is commonly used for measuring the area of rooms and other surfaces, including floors and walls. By measuring the length and width of the bathroom in feet and multiplying these two measurements, Jeffrey can determine the total square footage of the bathroom's floor and walls that need to be tiled. This will help him accurately estimate the amount of tile he needs to purchase.

The inverse function of f(x) is [tex]f^{(-1)(x)} = x/20.4[/tex], which represents a linear function with a slope of 1/20.4 and a y-intercept of 0.

In computer science and mathematics, a graph is a collection of vertices or nodes, along with a set of edges that connect them. Graphs are commonly used to model relationships between objects or entities.

In mathematics, a function is a rule that maps one set of values (the domain) to another set of values (the range), such that each element in the domain corresponds to exactly one element in the range.

According to given information:

The function f(x) = 4 * 5.1 is a constant function with a value of 20.4. The graph of f is a horizontal line passing through the point (0, 20.4) with no intercepts on the x or y axis.

The inverse function of f(x) is [tex]f^{(-1)(x)} = x/20.4[/tex], which represents a linear function with a slope of 1/20.4 and a y-intercept of 0.

To sketch the graph of [tex]f^{(-1)(x)}[/tex], plot the point (0,0) on the coordinate plane, which represents the y-intercept. Then plot another point by choosing any x-value and finding the corresponding y-value using the formula [tex]f^{(-1)(x)}[/tex] = x/20.4.

To summarize:

The graph of f(x) is a horizontal line passing through the point (0, 20.4) with no intercepts on the x or y axis.

The graph of [tex]f^{(-1)(x)[/tex] is a line passing through the origin with a slope of 1/20.4 and intercepting the x-axis at x = 20.4.

One point on the graph of f(x) is (0, 20.4).

One point on the graph of [tex]f^{(-1)(x)[/tex] is (0, 0), and another point can be found by choosing any x-value and using the formula [tex]f^{(-1)(x)[/tex] = x/20.4 to find the corresponding y-value.

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The volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

To find the volume of the solid generated by rotating ΔABC around AB, we can use the method of cylindrical shells.

First, we need to find the height of the cylinder that will be generated by the rotation. This height is simply the length of AB, which is 2.

Next, we need to find the circumference of the cylinder at any point along its height. To do this, we can use the fact that the circumference of a circle is given by 2πr, where r is the radius of the circle. In this case, the radius of the circle will be the distance from the axis of rotation (AB) to the edge of the triangle at that height.

Let x be the distance from vertex A to the point on AB directly below it. Then, at any height h, the radius of the circle will be given by:

r = BC - x

To find x, we can use the Pythagorean theorem. Let h be the height above vertex A, so that the distance from A to the base of the triangle is h/2. Then, the distance from vertex A to the point on AB directly below it is:

[tex]x = \sqrt{AB^2 - \left(\frac{h}{2}\right)^2} = \sqrt{2^2 - \left(\frac{h}{2}\right)^2}[/tex]

Now, we can find the volume of the solid generated by integrating the circumference of the cylinder at each height, multiplied by the height of the cylinder:

[tex]V = \int_0^2 2\pi\left(BC - \sqrt{2^2 - \left(\frac{h}{2}\right)^2}\right)dh[/tex]

We can simplify this integral using the substitution u = h/2, which gives:

[tex]V = 4\pi\int_0^1\left(BC - \sqrt{4 - u^2}\right)du[/tex]

Now, we need to plug in the values of BC and evaluate the integral:

[tex]V = 4\pi\int_0^1\left(5 - \sqrt{4 - u^2}\right)du[/tex]

= [tex]4\pi\left[\left(5u - \frac{u}{2}\sqrt{4 - u^2} - 2\arcsin\left(\frac{u}{2}\right)\right)\Bigg|_0^1\right][/tex]

≈ 23.39

Therefore, the volume of the solid generated by rotating ΔABC around AB is approximately 23.39 cubic units.

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Answer:

B(t) = 125*(1.3)^t

Step-by-step explanation:

the system of inequalities that represents this situation is: x ≤ 50 , y ≤ 100 , 175 - y ≥ x Let's start by defining some variables:

Let x be the number of single reservations.

Let y be the number of reservations for two or more people.

Since there are 50 single rooms and x single reservations, there must be at least 50 - x double rooms available for reservations for two or more people. Since each of these double rooms can accommodate 2 or more people, the total number of people who can be accommodated in these double rooms is 2(50 - x) = 100 - 2x.

The total number of people who can be accommodated in the hotel is 2x + (100 - 2x) = 100. This means that y, the number of reservations for two or more people, must satisfy the inequality y ≤ 100.

Each reservation for two or more people requires a double room, so the total number of double rooms used for reservations for two or more people is y. Since there are 175 double rooms in the hotel, the number of double rooms available for single reservations is 175 - y. Each single reservation requires one room, so the total number of single rooms used for reservations is x.

Therefore, the system of inequalities that represents this situation is:

x ≤ 50

y ≤ 100

175 - y ≥ x

The first inequality represents the fact that the number of single reservations must be less than or equal to the number of single rooms available. The second inequality represents the fact that the number of reservations for two or more people must be less than or equal to the total number of people who can be accommodated in double rooms. The third inequality represents the fact that the number of double rooms available for single reservations must be greater than or equal to the number of single reservations.

These three inequalities together represent the constraints on the number of single and double rooms that can be used for reservations, and the number of people who can be accommodated in the hotel. Solving this system of inequalities will give us the feasible region of the problem, which will allow us to find the optimal solution

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from the graph we can clearly see that range along x axis is (-2π,2π) and along y axis is (4,-4)

what is range ?
In statistics, the range is a measure of the spread or dispersion of a set of data. It is the difference between the maximum and minimum values in a dataset.

In the given question,

from the graph we can clearly see that range along x axis. the range is a measure of the spread or dispersion of a set of data. It is the difference between the maximum and minimum values in a dataset.

the start point and end point of wave  is (-2π,2π) and along y axis the start point and end point of wave  is (4,-4)

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the call charges for 300 minutes on this contract are R300.

the monthly cost of talking for 300 minutes on this contract is R500.

To determine the call charges for 300 minutes on this contract, we first need to find out how many minutes are above the 50 free minutes.

300 - 50 = 250 minutes above the free minutes.

The call charges for these 250 minutes are:

250 x R1.20 = R300

Therefore, the call charges for 300 minutes on this contract are R300.

To determine the monthly cost of talking for 300 minutes on this contract, we need to add the subscription fee to the call charges:

Monthly cost = Subscription fee + Call charges

Monthly cost = R200 + R300

Monthly cost = R500

Therefore, the monthly cost of talking for 300 minutes on this contract is R500.

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Arc BEC measures 210°.

Hence, option (d) 210° is the correct answer.

The measure of arc BEC in circle D is 210°.

Given,

The figure is as follows.

The measure of arc BEC in circle D is to be found.

We see that the arc BEC is subtended by the angle BAC.

We can find the measure of this angle by using the fact that it is the average of the two arcs that it subtends (i.e. arcs BC and DE).

∠BAC = 1/2 (arc BC + arc DE)

= 1/2 (74° + 346°)

= 210°

option (d) 210° is the correct answer.

Now, the measure of arc BEC is equal to the measure of the angle BAC.

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The linear regression equation that gives the quantity of hoodies sold as a function of the price: y = -2.6147x + 215.34

And the number of hoodies the bookstore can sell if the price is $32. = 131

To find the linear regression equation that represents the quantity of hoodies sold as a function of the price, we will use a calculator or a spreadsheet program to perform linear regression analysis on the data.

The scatter plot with the line of linear regression of the data is shown below.

The linear regression equation that gives the quantity of hoodies sold as a function of the price is:

y = -2.6147x + 215.34

here x represents the price of hoodie and y represents the quantity of hoodies.

Now we determine the number of hoodies the bookstore can sell if the price is $32.

i.e., for x = 32 we need to find the value of y

y = -2.6147(32) + 215.34

y = 131.6696

y ≈ 131

Therefore,  the number of hoodies the bookstore can sell if the price is $32. = 131

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Find the complete question below.

Answer:

c 96%

Step-by-step explanation:

The probability that a randomly selected student likes country but not rock is 29.4%.

We know that,

P(country but not rock) = P(country) - P(country and rock)

So to calculate P(country), we know from the survey that 162 students like country and to calculate P(country and rock), we need to subtract the number of students who like all three types of music (7) from the number of students who like both country and rock (22), which gives us 22 - 7 = 15.

Therefore, P(country but not rock) = 162/500 - 15/500 = 147/500 = 0.294.

So the probability that a randomly selected student likes country but not rock is 0.294 or 29.4%.

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Answer:24 seconds

Step-by-step explanation:

Since A(t) equals the total number of pixels in the image, then to figure out when it will be zero you just need to set A(t) equal to zero. This gives you the equation

[tex]0=(256-8t)(192-8t)[/tex]

Since this equation equals zero, we know either 256-8t must equal 0 or 192-8t must since they are multiplied.

We can split this into two equations

[tex]256-8t=0[/tex]

[tex]8t=256\\t=32[/tex]

and

[tex]192-8t=0\\8t=192\\t=24[/tex]

So, after 24 and 32 seconds both the width and height equal zero. Only the height or the width need to equal zero for the total area to equal zero (A=w*h), so we go with the lesser time, 24 seconds.

By answering the presented question, we may conclude that As a result, equation the next client has a 27/41 chance of paying with something other than a debit card.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

There were 12 + 28 + 42 = 82 people in total, with 12 paying with cash and 28 using a debit card. As a result, the number of consumers who did not use a debit card is 82 - 28 = 54.

The chance that the next customer will not pay with a debit card is equivalent to the number of customers who did not pay with a debit card divided by the total number of customers. As a result, the likelihood is:

54/82

This fraction can be simplified by splitting the numerator and denominator by their largest common factor, which is 2:

54/82 = (2 × 27)/(2 × 41) = 27/41

As a result, the next client has a 27/41 chance of paying with something other than a debit card.

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The above given graph doesn't follow the property of onto-function so, it is not a onto in nature.

What about onto-function?

In mathematics, an onto function (or surjective function) is a function from one set to another in which every element in the target set is mapped to by at least one element in the domain set. In other words, an onto function maps every element in the target set to some element in the domain set.

Formally, let f: A → B be a function from set A to set B. The function f is onto if and only if for every element b in the target set B, there exists an element a in the domain set A such that f(a) = b.

An onto function is sometimes described as a function that "hits" every element in the target set. This means that the function's range is equal to its target set, or in other words, every element in the target set has a corresponding element in the range.

The concept of onto functions is important in many areas of mathematics, including analysis, algebra, and topology. It is used to study the properties of functions and to define various types of spaces and structures.

According to the given information:

x represents the input, y represent the output

According to the graph, there exists more than one x - values for at least one y - values.

So, there exists more than one input for at least one output

Hence-:  No, there exists more than one input for at least one output is correct option.

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55

The median basically means the average of the tenth and eleventh numbers as if the 20 numbers were "cut in half" to find the number in the middle. The median is all based on the order of the numbers from least to greatest. If the largest 8 numbers are increased by ten, that basically means that the tenth and eleventh numbers are unaffected and the order still stays the same from least to greatest. The median would still be 55.

Answer: coin

Step-by-step explanation: because the dice has to many outcomes

Answer:

Step-by-step explanation:

Hey Love:

here's the answer,

2/9(9a-44)

Burger Quick has a smaller IQR (Interquartile Range) than Super Fast Food, indicating that the middle 50% of the data is more tightly clustered around the median.

Super Fast Food is able to estimate their wait time more consistently because it has a smaller range, which means the wait times reported by the 20 people are more closely clustered around the median wait time of 12 minutes.

Burger Quick may predict wait times more reliably than Super Fast Food due to a reduced IQR (Interquartile Range).

The IQR is a measure of the spread of the middle 50% of data, defined as the difference between the third (Q3) and first (Q1) quartiles. A lower IQR shows that the middle 50% of the data is more closely grouped around the median, implying that the data is more consistent.

Burger Quick has an IQR of 14.5 (Q3=24, Q1=9.5) in this situation, while Super Fast Food has an IQR of 7 (Q3=15.5, Q1=8.5). As a result, Burger Quick has a lower IQR and can predict their wait time more reliably than Super Fast Food.

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Answer:

The shape formed is rectangle.

20 trials may not be enough to get a reliable estimate of the probability, especially if the true probability is close to 0.5.

Based on Zoe's results,

The probability that she will make it to the finals of the Royal Arena Chess Tournament is 96.2%.  

Here's how to solve the problem:  

Zoe must win at least 5 matches out of 8 to make it to the finals.  

There are different ways to solve the problem, but one way is to use the binomial probability formula:  

P(X = k) = (n choose k) * [tex]P^{k}[/tex] * [tex]q^{n-k}[/tex]

where:

P(X = k) is the probability of getting exactly k successes out of n trialsn is the number of trialsp is the probability of success in one trialq is the probability of failure in one trial is the probability of getting k successes q^(n-k) is the probability of getting n-k failures(n choose k) is the binomial coefficient, which represents the number of ways to choose k objects out of n distinct objects without regard to order (n choose k) = n! / (k! * (n-k)!)

The binomial probability formula is used to calculate the probability of getting a specific number of successes in a fixed number of independent trials, each with the same probability of success.

It is a discrete probability distribution that describes the probability of X successes in n trials.For this problem:P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)where:P(X >= 5) is the probability of getting at least 5 successes out of 8 trialsP(X = 5) is the probability of getting exactly 5 successes out of 8 trialsP(X = 6) is the probability of getting exactly 6 successes out of 8 trialsP(X = 7) is the probability of getting exactly 7 successes out of 8 trialsP(X = 8) is the probability of getting exactly 8 successes out of 8 trials

T[tex]0.5^{5}[/tex]he probabilities can be calculated using the binomial probability formula with n = 8 and p = 0.5  

Since Zoe estimates she has a 50% chance of winning each match

P(X = 5) = (8 choose 5) * [tex](0.5)^5[/tex]* [tex](0.5)^{(8-5)[/tex] = 56 * 0.03125 * [tex]0.5^3[/tex]

= 0.21875P(X = 6)

= (8 choose 6) * [tex](0.5)^6[/tex] * [tex](0.5)^{(8-6)[/tex]

= 28 * 0.015625 * [tex]0.5^2[/tex]

= 0.109375P(X = 7)

= (8 choose 7) * [tex](0.5)^7[/tex] * [tex](0.5)^{(8-7)[/tex]

= 8 * 0.0078125 *[tex]0.5^1[/tex]

= 0.03125P(X = 8)

= (8 choose 8) * [tex](0.5)^8[/tex] * [tex](0.5)^{(8-8)[/tex]

= 1 * 0.00390625 * [tex]0.5^0[/tex]

= 0.00390625P(X >= 5)

= 0.21875 + 0.109375 + 0.03125 + 0.00390625

= 0.36328125

Therefore, the probability that Zoe will make it to the finals of the Royal Arena Chess Tournament is approximately 36.3%.

However, Zoe simulates the situation by rolling a six-sided die 8 times.  

The simulation gives an estimate of the probability, which may be different from the exact probability calculated using the binomial probability formula.  

The simulation results may also depend on the sample size (i.e., the number of trials).  

In this case, 200 trials may not be enough to get a reliable estimate of the probability, especially if the true probability is close to 0.5.  

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Based on Zoe's 200 trials in the simulation the probability that she will make it to the finals means 22% chance.

The probability of her making it to the finals can be calculated by looking at the number of trials where she won at least 5 matches.

According to the table, she won 5, 6, 7, or 8 matches in 14, 21, 8, and 1 trials, respectively.
To find the probability,
1. Add up the number of trials where Zoe won at least 5 matches: 14 + 21 + 8 + 1 = 44 trials
2. Divide this sum by the total number of trials (200): 44/200

In the simulation,

Each even number represents a win for Zoe.

Therefore, we can calculate the probability of Zoe winning at least 5 matches by adding up the probabilities of getting 5, 6, 7, or 8 even numbers in 8 rolls of a six-sided die.

Using the table provided, we can see that there are 218 trials out of 200 where Zoe gets 5 or more even numbers. Therefore, the probability of Zoe winning at least 5 matches is:

218/200 = 1.09 or 109%

This means that based on the simulation, Zoe is more likely than not to make it to the finals.

However,

It is important to note that the simulation assumes that each match has a 50% chance of being won by Zoe, which may not be accurate in real life.

The actual probability of Zoe making it to the finals may be different from the simulation results.
So, based on Zoe's results, the probability that she will make it to the finals is 44/200 or 0.22, which means a 22% chance.

This is based on her simulation using a six-sided die, not her actual 50% chance of winning each match.

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Answer & step-by-step explanation:

To rotate a point (x, y) 270° counterclockwise about the origin, we can swap the x and y coordinates and negate the new x coordinate. So the new coordinates for L(1, 6) would be:

x' = -6

y' = 1

Therefore, the new vertex for L would be (-6, 1). Similarly, the new vertices for M(8, 7) and N(5, 2) would be:

M': (-7, 8)

N': (2, 5)

So the rotated triangle would have vertices L'(-6, 1), M'(-7, 8), and N'(2, 5).

Answer:

M': (-7, 8)

N': (2, 5)

Step-by-step explanation:

I did the test

Hope this helps :)

Answer:

36 cm

Step-by-step explanation:

a = 1/2 h(b1+b2)

So 10 + 8 = 18 18x4= 72/2  = 36 cm

The correct option is B, that the reason that justifies that the lines are parallel.

We know that l and m are parallel, and we know that angles 1 and 3 have the same measure.

Notice that angles 1 and 3 are in opposite quadrants (second and fourth). If these where in the same intersection, these would be vertical angles, and thus have the same measure.

In this case we know that the angles have the same measure, then the lines a and b can only be parallel, this is proven by the alternate exterior angles converse (exterior because the angles are exterior to the square formed by the intersections).

So the correct option is B.

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Answer:

96

Step-by-step explanation:

Answer: B. y = -x + 5

Step-by-step explanation:

Given the table, lets pick two consecutive points to find the slope.

(-4, 9) (-1, 6) are the first points that show in the table.

Lets plug it in the (y2-y1)/(x2-x1) expression

(6 - 9)/(-1 - -4)

=(-3)/(3)

=-1

The slope is -1

Now lets look at the answer choices and see if any of the equations with the format y= mx + b has -1 as its slope. We can eliminated a and c.

Now lets use the data in the table, and plug in a given point to see if which of the equations left are correct.

Lets use the point: (-4, 9)

For b.

y = -x + 5

9 = -(-4) + 5

9 = 4 + 5

9 = 9

B is the correct answer.

For d.

9 = -(-4) - 5

9 = 4 - 5

9 = -1

this equation is incorrect, so D is incorrect.

When we solve for train speed we get: -190 mph

It is clear that this is impossible because speed cannot be negative. Thus, the problem statement must contain a mistake.

The rate at which an object travels a distance is called speed.

This is a well-known algebraic puzzle. Let's use "x" for the other train's speed. The first train travels 1012 miles in 4 hours, or 253 miles multiplied by 4.

The second train travels 4 hours' worth of distance, or x * 4 miles. They will have travelled a total of 252 miles when they cross paths. Thus, we can create the following equation:

1012 + 4x = 252

When we solve for x, we get:

x = (252 - 1012) / 4 = -190 mph

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