A bicyclist travelled for T = 1.6 hours at a constant speed of R = 20 kilometers (km) per hour. Use the formula
D = R · T
to find the total distance traveled in kilometers.

The domain of the function is  (-∞, -2) ∪(-2, ∞) and it's range is (-∞, 1) ∪ (1, ∞). The function has vertical and horizontal asymptotes as x = -2 and y = 1

In mathematics, the domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined. The range of a function is the set of all possible output values (also known as the dependent variable) that the function can produce.

To determine the domain and range of a function, it's important to consider the nature of the function, its graph or formula, and any restrictions that may apply.

The function f(x) = - (2/ x + 2) + 1

The domain of the function is (-∞, -2) ∪(-2, ∞)

The range of the function is (-∞, 1) ∪ (1, ∞)

The vertical asymptote is x = -2

The horizontal asymptotes y =  1

The y-intercept is (0, 0)

The x - intercept is (0, 0)

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Answer: 16

Step-by-step explanation:

Since each bicycle has 2 wheels, this means 2 wheels times 8 bicycles. with comes out to 16 wheels

Answer:

16

Step-by-step explanation

If each bicycle has 2 wheels, we would multiply 2 wheels times 8 bicycles and we would get 16 wheels altogether.

Answer:

[tex]x < -3\text{ or }x > 3[/tex]

Step-by-step explanation:

[tex]|1-2x|-4 > 1\\|1-2x| > 5\\\\1-2x > 5\\-2x > 6\\x < -3\\\\1-2x < -5\\-2x < -6\\x > 3[/tex]

The coordinates of the point on the directed line segment is (- 6, 4).

A line segment is a subset of a line that has two endpoints.

We know, When a line segment is divides another line segment in the ratio of m : n at (x, y), The coordinate of the intersecting points is,

x = (nx₁ + mx₂)/(m + n) and y = (ny₁ + my₂)/2.

Therefore, The coordinates of the point directed on the line segment is,

x = (1×2 + 2×- 10)/(1 + 2).

x = (2 - 20)/3.

x = - 18/3.

x = - 6.

And,

y = (- 8×1 + 10×2)/(1 + 2).

y = 12/3.

y = 4.

So, The coordinates are (- 6, 4).

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The resulting graph should have a vertical intercept at (0, 0), a flat portion from (0, 0) to (5, 10), and a linearly increasing portion from (5, 10) to (10, 15). The slope of the second line should be $1 per kilometer.

In mathematics, a graph is a visual representation of a set of data or a mathematical function. It consists of a collection of points, called vertices, and the lines or curves, called edges, that connect them. A graph can be used to show relationships between sets of data, to model real-world situations, and to represent mathematical functions.

There are many types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more. Each type of graph is used to represent different types of data or to show different relationships between the data.

Bar graphs are used to show the frequency or quantity of discrete data items, such as the number of people who prefer a certain type of food. Line graphs are used to show the relationship between two sets of data, such as the relationship between temperature and time. Pie charts are used to show the relative proportions of different parts of a whole, such as the percentage of a budget that is allocated to different expenses. Scatter plots are used to show the relationship between two sets of numerical data, such as the relationship between height and weight.

Graphs are an important tool in mathematics and many other fields, including economics, engineering, physics, and computer science. They allow us to visualize and analyze complex sets of data and to make predictions about future trends or patterns.

We can sketch a piecewise linear graph to represent the relationship between the money collected from each sponsor and the number of kilometers walked:

For the first 5 kilometers, the sponsor donates a flat rate of $10.

After the first 5 kilometers, the sponsor donates $1 per kilometer.

To sketch this graph, we can plot two points:

(0, 0): This represents the starting point of the walkathon, where no money has been collected yet.

(5, 10): This represents the end of the first 5 kilometers, where the sponsor has donated a flat rate of $10.

Then, we can draw a line connecting these two points to represent the flat rate portion of the donation.

Next, we can plot a third point:

(10, 15): This represents the end of the next 5 kilometers (from 5 to 10 kilometers), where the sponsor has donated an additional $5 ($1 per kilometer).

Finally, we can draw a second line connecting (5, 10) to (10, 15) to represent the $1 per kilometer portion of the donation.

The resulting graph should have a vertical intercept at (0, 0), a flat portion from (0, 0) to (5, 10), and a linearly increasing portion from (5, 10) to (10, 15). The slope of the second line should be $1 per kilometer.

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The coordinates of point l are (8,9).

Numbers used to identify the position of a point in a plane or in space. It is mostly used in mathematics, science, and engineering. Coordinates are used to define locations on maps, to plot graphs, and to identify points on a two-dimensional plane. By knowing the coordinates of two points, one can calculate the distance between them.


To find this point, we must first calculate the midpoint between j and k. The midpoint can be found by taking the average of the x-coordinates and y-coordinates. The midpoint between j and k is (8,10). Since the ratio of jl:kl is 5:1, we can determine that l is 5 units away from j and 1 unit away from k. This means that l must be 5 units up and 1 unit to the right from the midpoint. Thus, the coordinates of l are (8,9).

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Answer:

$610.25

Step-by-step explanation:

The simple  interest  at a higher FICO score over the lower FICO score
= 8.9% - 4.2% = 4.7%

4.7% = 4.7/100 = 0.047 in decimal

Therefore at simple interest the amount of money saved for 1 year on a loan of $12,984

= $12,984 x 0.047 = $610.25

Answer:

$611.63

Step-by-step explanation:

To Calculate the amount of interest saved with a higher credit score, we need to find the difference in the amount of interest paid over the course of one year on a loan of $12,984 at each interest rate.

First, we'll calculate the interest paid at 4.2% interest with a FICO score of 776:

Interest rate = 4.2%

Loan amount = $12,984

Simple interest = Interest rate x Loan amount

Simple interest = 4.2% x $12,984

Simple interest = $545.45

Next, we'll calculate the interest paid at 8.9% interest with a FICO score of 495:

Interest rate = 8.9%

Loan amount = $12,984

Simple interest = Interest rate x Loan amount

Simple interest = 8.9% x $12,984

Simple interest = $1,157.08

The difference in interest paid is the amount saved by having the higher credit score:

Interest saved = Interest paid at 8.9% - Interest paid at 4.2%

Interest saved = $1,157.08 - $545.45

Interest saved = $611.63

Therefore, having a higher credit score of 776 would save you $611.63 in simple interest over the course of one year on a loan of $12,984.

Answer:

what is this -by-step explanation:

Answer:

large

Step-by-step explanation:

divide the price by the grams, to find how much each is worth than, figure out that the large is worth 0.1, medium, 0.2, and small, 0.3, so they large you get more for less.

From density, the probability that X>1.6 or X<0.36 is 1 - (0.36 + 0.64) = 0.00.

Density in mathematics is a measure of how much of a certain quantity is contained within a given area or volume. It is defined as the ratio of the mass of the object to the volume of the object.

For example, the density of water is 1 gram per cubic centimeter (1 g/cm3). Density can be used to measure the concentration of a substance in a given area, such as the amount of salt in a given volume of water. Density can also help to identify different substances, such as air, oil, and water. It is an important concept in physics, chemistry, and engineering.

The probability that X>1.6 or X<0.36 is 0.00 because the density function is 0 for values outside the range from 0.36 to 1.6. The density function is a measure of how likely it is for a value of X to be within a certain range, and since the density of X is 0 for values outside the range, the probability of X being outside that range is also 0.

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Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes.

Yes, in ggplot2, mapping refers to the process of connecting variables in a data set to visual elements of a plot, such as points, lines, or other shapes. This is done by mapping variables to aesthetic properties of the plot, such as the x and y coordinates, the size, color, or shape of the points, or other visual properties that can be customized.

For example, if we have a data set with two variables, x and y, we can create a scatterplot of the data by mapping the x variable to the x-axis and the y variable to the y-axis, using the aes() function in ggplot2. We can also customize the appearance of the points by mapping other variables to the size, color, or shape of the points, as well as adding other elements to the plot, such as a title or legend.

The mapping process is an important part of data visualization in ggplot2, as it allows us to explore the relationship between different variables and to communicate our findings in a clear and effective way. By mapping variables to visual elements of a plot, we can create informative and visually appealing graphics that can help us understand and communicate complex data sets.

In programming, a variable is a named storage location that can hold a value or a reference to a value. Variables are used to store and manipulate data in a program, and they can take on different values at different times during the execution of the program.

In most programming languages, variables are defined by specifying a name and a data type. The data type determines the kind of data that can be stored in the variable, such as numbers, strings, or Boolean values, and also affects the size and behavior of the variable.

Variables can be assigned a value using the assignment operator, which stores the value in the variable's memory location. Once a value has been assigned to a variable, it can be accessed and manipulated using its name.

In addition to simple data types, programming languages also support more complex types of variables, such as arrays, objects, and pointers, which can store collections of values or references to other variables.

Variables are a fundamental concept in programming, and they are used extensively in all kinds of software applications, from simple scripts to complex systems. Understanding how to use variables effectively is an essential skill for any programmer.

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We have shown that when the input value increases from x to x + 1 the output values h(x + 1) and h(x) have a quotient of 4

To show that when the input value increases from x to x+1, the output values h(x+1) and h(x) have a quotient of 4, we need to show that:

{h(x+1) - h(x)}/{1} = 4

Which simplifies to:

h(x+1) - h(x) = 4

If we assume that h is a differentiable function, we can use the mean value theorem to prove this.

By the mean value theorem, there exists a number c between x and x+1 such that:

h(x+1) - h(x) = h'(c)

Where h'(c) is the derivative of h evaluated at c.

Since h'(x) is the rate of change of h with respect to x, we can interpret the equation h(x+1) - h(x) = h'(c) as saying that the change in h over the interval from x to x+1 is equal to the instantaneous rate of change of h at some point c in that interval.

If we assume that h'(x) = 4 for all x, then we have:

h'(c) = 4

For any c between x and x+1. Substituting this into the equation above, we get:

h(x+1) - h(x) = 4

which is what we wanted to show.

Hence, if h is a differentiable function and h'(x) = 4 for all x, then when the input value increases from x to x+1, the output values h(x+1) and h(x) have a quotient of 4

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Answer:

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

Step-by-step explanation:

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

 = 10 * 0.0676 * 0.4052

 = 0.211

The solution is, 0.211 is the probability assignments for the x distribution.

Here, we have,

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

now, we have,

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

= 10 * 0.0676 * 0.4052

= 0.211

So, 0.211 is the probability assignments for the x distribution.

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Answer: D

Step-by-step explanation:

This is a valid example of stringing arguments together using conditional statements.

The first statement establishes a conditional relationship between Martin shooting the sheriff and Martin shooting first.

The second statement also establishes a conditional relationship, but this time between Martin using his best pistol and Martin shooting first.

By combining the two conditional statements, we can conclude that if Martin didn't use his best pistol, then he didn't shoot first.

This follows from the fact that not using his best pistol would mean Martin didn't shoot first (according to statement 2), and if he didn't shoot first, then he couldn't have shot the sheriff (according to statement 1).

Therefore, the conclusion of the argument, which is that if Martin didn't use his best pistol, then he didn't shoot the sheriff, follows logically from the two conditional statements.

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Answer:

Step-by-step explanation:

To find the 90% confidence interval for the difference in proportions, we can use the following formula:

CI = (p1 - p2) ± zα/2 * √( (p1 * (1-p1) / n1) + (p2 * (1-p2) / n2) )

where:

p1 and p2 are the sample proportions from the city and rural area, respectively

n1 and n2 are the sample sizes from the city and rural area, respectively

zα/2 is the critical value from the standard normal distribution for a 90% confidence level, which is 1.645

First, we need to calculate the sample proportions:

p1 = 112 / 272 = 0.4118

p2 = 53 / 105 = 0.5048

Next, we can plug in the values and calculate the confidence interval:

CI = (0.4118 - 0.5048) ± 1.645 * √( (0.4118 * (1-0.4118) / 272) + (0.5048 * (1-0.5048) / 105) )

CI = (-0.146, -0.031)

Therefore, the 90% confidence interval for the difference in proportions is (-0.146, -0.031). This means we are 90% confident that the true difference in proportions of religious people between the city and rural areas lies between -0.146 and -0.031. Since this interval does not include zero, we can conclude that the proportion of religious people is significantly different between the two areas.

The total distance from Bethany’s house to her parents’ house would be = 524.8 miles

The first distance covered by Bethany towards the parents house = 127.56 miles.

The distance remaining for her to arrive to ab destination = 397.24 miles

The total distance covered

= 127.56 miles + 397.24 miles

= 524.8 miles.

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The total distance, in miles, from Bethany's house to her parents' house is 524.8 miles.

The total distance is determined using the mathematical operation of addition.

Addition is one of the four mathematical operations, including subtraction, division, and multiplication.

The distance already covered after driving from her house = 127.56 miles

The distance remaining = 397.24 miles

The total distance from Bethany's house to her parents' = 524.8 miles (127.56 + 397.24)

Thus, the total distance is 524.8 miles.

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The required generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Therefore, option B is the correct.

The Interquartile Range (IQR) formula is a measure of the middle 50% of a data set. The smallest of all the measures of dispersion in statistics is called the Interquartile Range. The difference between the upper and lower quartile is known as the interquartile range.

Given that, a wildlife biologist captured and released 34 trout's from two different lakes and measured them to the nearest inch.

Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.

In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.

Therefore, option B is the correct.

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Answer:

[tex]\sf{The\;Marginal\;Revenue\;} $MR(8) = \boxed{288} \;dollars per unit$}[/tex]

Step-by-step explanation:

What is Marginal Revenue?
Marginal Revenue is the revenue that is gained from the sale of an additional unit. It is the revenue that a company can generate for each additional unit sold

Given the equation for revenue function
[tex]R(q) = -7q^2+400q[/tex]

the Marginal Revenue [tex]MR(q)[/tex] is the first derivative of this function wrt [tex]q[/tex]

[tex]MR(q) = \dfrac{d}{dq}\left(R(q)\right)\\= \dfrac{d}{dq}(-7q^2 + 400q)\\\\= \dfrac{d}{dq}(-7q^2) + \dfrac{d}{dq}(400q)\\\\= -14q + 400\\\\[/tex]

For [tex]q = 8,[/tex] this works out to:

[tex]MR(8) = -14(8) + 400\\\\= -112 + 400\\\\= 288[/tex]

And that is the answer

Step-by-step explanation:

is given above in the pdf

The True Statement are:

20/21 of students in Manuel Class either walk or take bus to school.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

We have 2/7 of the students walk to school

and, 2/3 take the bus to school.

So, if both choices are considered

= 2/7 + 2/3

= 6/21 + 14/ 21

= 20/ 21

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The units for the amount of time that the plane descends are minutes, and the units for the plane's altitude are feet. Let's define a variable t for the amount of time that the plane descends. Then we can write an expression for the plane's altitude in terms of t as:

Altitude = 34,000 - (1,000 * t)

This expression represents the plane's initial altitude of 34,000 feet, minus the rate of descent (1,000 feet per minute) times the amount of time that the plane descends.

To find when the plane will be at an altitude of 3,000 feet, we can set the expression equal to 3,000 and solve for t:

3,000 = 34,000 - (1,000 * t)
31,000 = 1,000 * t
t = 31

So the plane will be at an altitude of 3,000 feet after 31 minutes of descent.

To find how long before the plane touches down on the runway, we can set the expression equal to 0 and solve for t:

0 = 34,000 - (1,000 * t)
34,000 = 1,000 * t
t = 34

So the plane will touch down on the runway after 34 minutes of descent.

Here is the completed worksheet:

Quantity Name | Time | Altitude
--- | --- | ---
Unit | minutes | feet
Given Value 1 | 10 | 34,000
Given Value 2 | | 24,000
Slope | | -1,000
Intercept | | 34,000
Expression | t | 34,000 - (1,000 * t)
Question 1 | 31 | 3,000
Question 2 | 34 | 0

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The total number of students in the vans and buses is 484

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols to solve equations and understand the relationships between variables. In algebra, letters or symbols are used to represent unknown values or variables, and equations are used to describe the relationships between these variables.

Algebraic expressions and equations involve mathematical operations such as addition, subtraction, multiplication, and division, as well as more advanced operations such as exponentiation, logarithms, and trigonometric functions. These operations can be used to simplify expressions, solve equations, and analyze mathematical relationships.

Elementary algebra, which is concerned with the basic concepts and techniques of algebra, such as simplifying expressions, solving equations, and graphing functions.

Abstract algebra, which is concerned with the study of algebraic structures, such as groups, rings, and fields.

Linear algebra, which is concerned with the study of vector spaces and linear transformations.

Algebraic geometry, which is concerned with the study of geometric objects defined by algebraic equations.

Algebra has many practical applications in various fields, including science, engineering, economics, and computer science. It is used to model and analyze real-world problems, such as population growth, interest rates, and inventory management. It is also used in cryptography, where it is used to design secure encryption and decryption algorithms.

Let's start by using algebra to represent the information given in the problem.

Let x be the number of students in each van and each bus. Since every van had the same number of students as every bus, we can say that the total number of students in the vans and buses is:

10(x) + 12(x) = 256

Simplifying, we get:

22x = 256

Dividing both sides by 22, we get:

x = 11.6363636...

Since we can't have a fraction of a student, we need to round x to the nearest whole number. We have two options: rounding up to 12 or rounding down to 11.

If we round x up to 12, then each van and each bus had 12 students. The total number of students in the vans and buses is:

10(12) + 12(12) = 240

This is not equal to the given total of 256, so rounding up to 12 is not a valid solution.

If we round x down to 11, then each van and each bus had 11 students. The total number of students in the vans and buses is:

10(11) + 12(11) = 220 + 264 = 484

This is not equal to the given total of 256, so rounding down to 11 is not a valid solution either.

Therefore, there is no whole number solution for the number of students in each van and each bus. We can interpret this to mean that there was not an equal number of students in each van and bus. Alternatively, we can interpret this to mean that there was an error in the information given in the problem.

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The probability that the arrival time between vehicles is 12 seconds or less found using exponential distribution is 0.6306.

What is meant by exponential distribution?

The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process. The crucial characteristic of the exponential distribution is that it has no memory. Either more little values or fewer larger values can make up the exponential random variable. 

Given,

Mean = 12s

Mean = 1/λ = 12

λ = 1/12 = 0.083

Now we have to find CDF at 12s.

The probability that an observation from an exponential distribution, with the scale parameter, is smaller than or equal to x is returned by the CDF function for the exponential distribution.

CDF = F(x) = [tex]1- e^{-\lambda\*x}[/tex]

When x = 12

F(12) = [tex]1- e^{-0.083*12}[/tex] = 0.6306

Therefore the probability that the arrival time between vehicles is 12 seconds or less found using exponential distribution is 0.6306.

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Answer:

Step-by-step explanation:

Part A: The population for this sample survey is all people who live in Virginia, and the sample is the random group of 48,548 people who were interviewed for the survey.

Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves selecting individuals from the population at random, so that each person in the population has an equal chance of being selected. This can be done using a random number generator or by selecting names from a list of the population.

Part C: It's difficult to say whether the estimates are close to the truth about the entire population without more information about the survey methodology and potential sources of bias. However, assuming that the survey was conducted using sound sampling techniques and that the sample is representative of the population, it's possible that the estimates are reasonably accurate. Nevertheless, it's important to keep in mind that survey estimates always have some degree of sampling error, so the true population values could be slightly different from the survey results. Additionally, the survey may not capture people who don't have access to healthcare or who choose not to seek medical care, so the estimates may not be fully representative of the entire population.

Answer: Part A: The population for this sample survey is all people who live in Virginia, while the sample is the 48,548 people who were interviewed in the Virginia Health Survey.

Part B: One method that could have been used to obtain the random sample is simple random sampling. This involves randomly selecting individuals from the population using a random number generator or other randomization method to ensure that each member of the population has an equal chance of being selected. Another method could be stratified random sampling, which involves dividing the population into strata based on relevant characteristics (such as age or income), and then randomly selecting individuals from each stratum in proportion to their representation in the population.

Part C: It is difficult to determine whether these estimates are close to the truth about the entire population without additional information. However, if the sample was selected using appropriate sampling methods (such as simple random sampling or stratified random sampling) and had a large enough sample size, then the estimates are likely to be relatively accurate. The margin of error, which depends on the sample size and variability in the population, can also be calculated to provide an estimate of the range in which the true population value is likely to fall. Overall, the accuracy of the estimates will depend on the quality of the sampling method used, the size of the sample, and the representativeness of the sample in relation to the population.

The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.

What is meant by the mode of a data set?

The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.

a)2, 2, 2, 5, 6, 7, 9, 10

Here most repeated value is only 2.

So the mode is 2.

b) 5, 6, 8,10, 11, 11, 15, 18

Here most repeated value is only 11.

So the mode is 11.

c)12, 12, 13, 13, 14, 14, 15, 15

Here the values 12,13,14 and 15 are repeated twice.

So this has 4 values as mode.

d) 21, 22, 22, 24, 25, 26, 28, 28

Here 22 and 28 are repeated twice.

So this data set has 2 values for the mode.

Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.

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Answer:

D

Step-by-step explanation:

here is a pic for proof

Answer:

To simplify the expression −8(1+x)+7x, we can use the distributive property of multiplication over addition, which states that a(b+c) = ab + ac. Applying this property, we get:

−8(1+x) + 7x = −81 − 8x + 7x (distributing the -8)

= -8x - 8 + 7x (simplifying the multiplication)

= -x - 8 (combining like terms)

Therefore, the simplified form of the expression −8(1+x)+7x is −x − 8.

The value of sin -1(square root 2/2) is π/4 or 45 degrees.

Inverse sine, also known as arcsine, is a trigonometric function that is the inverse of the sine function. It is denoted as sin^-1(x), where x is a number between -1 and 1.

The inverse sine function is used to find the angle in a right triangle that has a given sine value. In other words, if we know the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle, we can use the inverse sine function to find the measure of that angle.

The inverse sine function returns an angle in radians, which can be converted to degrees if needed. It has a domain of -1 ≤ x ≤ 1 and a range of -π/2 ≤ sin^-1(x) ≤ π/2.

Like other inverse trigonometric functions, the inverse sine function is a multivalued function. This means that for a given value of x, there can be multiple angles that satisfy sinθ = x. To address this, the principal value of the inverse sine function is defined as the angle between -π/2 and π/2 that satisfies sinθ = x.

The inverse sine function has many applications in mathematics, physics, engineering, and other fields. It is used in the calculation of angles in a variety of contexts, such as in the design of structures and in the analysis of wave phenomena. It is also used in calculus and other advanced mathematics courses to solve integrals and differential equations.

To see why, we can use the definition of the inverse sine function, which gives us the angle whose sine is equal to the input value. In this case, we have:

sin -1(square root 2/2) = θ

where sin(θ) = square root 2/2.

We know that the sine of 45 degrees (or π/4 radians) is also equal to square root 2/2. Therefore, we have:

sin(45 degrees) = square root 2/2

Taking the inverse sine of both sides gives us:

sin -1(square root 2/2) = 45 degrees = π/4

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Answer:

84 deg

Step-by-step explanation:

cos(x)=sin(90-x)

90-x=6

x=84

The solution to the system of equations is x =5 and y = -6

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

12x + 9y = 6

7x + 6y = −1

Multiply (2) by 1.5

So, we have the following representation

12x + 9y = 6

10.5x + 9y = −1.5

Subtract the equations to eliminate y

1.5x = 7.5

So, we have

x = 5

Recall that

12x + 9y = 6

So, we have

60 + 9y = 6

This gives

9y = -54

Divide

y = -6

SO, the value of y is -6

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Answer:

B. 10 yd., 14 yd., 17 yd.

Step-by-step explanation:

In a right triangle, the squares of the sums of the two shorter sides must equal the square of the longer side(which is the hypotenuse)

From the combinations given only the set 10 yd, 14 yd. and 17 yd does not obey this rule

10² + 14² = 296
17² = 298
So this does not match

Answer:20

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