Write the number 1. 8 in the form , using integers, to show that it is a rational number.

a) A procedure for identifying outliers is identifying if there are values that are more than 1.5 IQR from the quartiles. Thus, the value of 810 is an outlier in the given distribution.

b) As the distribution contains a high outlier, it means that the distribution is right skewed.

The first quartile of a data-set is the element that represents the 25th percentile of the distribution.

For a distribution of 34 students, the first half of the distribution has 16 values, hence the first quartile is the mean of the 8th and 9th values.

From the stemplot, these values are 170 and 180, hence:

Q1 = (170 + 180)/2 = 175.

The third quartile is the 75th percentile of the distribution, hence it is the mean of the 8th and 9th values of the second half of the distribution.

From the stemplot, these values are 39 and 41, hence:

Q3 = (390 + 410)/2 = 400.

The IQR is the difference between the quartiles, hence:

IQR = Q3 - Q1 = 400 - 175 = 225.

Values that are more than 1.5 IQR from the quartiles are considered outliers, hence the bounds are given as follows:

Hence the value of 810 is a high outlier. This high outlier will influence the mean, making it higher than the median, and thus the distribution is right skewed.

The stemplot is given by the image shown at the end of the answer.

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a) Differential equation (initial value problem) for the mass of the copper sulfate would be dm/dt = 0

b) m(t)=0

What is Differential equation?

A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to create a relationship between the two.

a) Solution is flowing out of the tank. This can be expressed mathematically as:

dm/dt = (flow rate of solution into tank) - (flow rate of solution out of tank)

= (2 l/min) - (2 l/min)

= 0

Therefore, the differential equation for the mass of the copper sulfate in the tank is:

dm/dt = 0

This is a simple differential equation with a constant coefficient of 0, and it can be easily solved by integrating both sides of the equation with respect to time.

b. To solve the differential equation, we can write:

m(t) = integral(0, t, dm/dt)

= integral(0, t, 0)

= 0

Since the coefficient of the derivative is 0, the solution to the differential equation is a constant function with a value of 0. This means that the mass of the copper sulfate in the tank will remain constant over time, regardless of the flow rates of the solution into and out of the tank.

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The factors of polynomial P(x)= 2x² -7x + 3 is x =1/2 and x =3.

Factoring polynomials is the opposite method of the multiplication of things of polynomials. An expression of the shape

axⁿ + bxⁿ⁻¹+kcxⁿ⁻² + ….+kx+ l, wherein every variable has a regular accompanying it as its coefficient is known as a polynomial of diploma ‘n’ in variable x. hence, a polynomial is an expression wherein a mixture of a regular and a variable is separated with the aid of an addition or a subtraction signal.

For a polynomial of the form:

ax²+ bx +c, rewrite the middle term as a sum of two terms whose product is a × c =2×3 = 6 and whose sum is b= −7.

Now,

Factor −7 out of −7x

2x²−7(x)+3

Rewrite −7 as −1 plus −6

2x²+ (−1−6)x +3

Apply the distributive property.

2x²−1x−6x+3

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(2x²−1x)− 6x + 3

Factor out the greatest common factor (GCF) from each group.

x(2x−1)−3(2x−1)

Factor the polynomial by factoring out the greatest common factor,

(2x−1)(2x-1)(x−3)

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The volume of a cube is 15.625 cubic cm.

What is the volume of a cube?

A cube is a three-dimensional shape having 6 square faces, all the faces are of equal length, breadth, and height.

The volume of the cube is given by side * side * side.

The volume of a cube is given by:

V = a³,

where a is the side length of the cube.

Each side of a cube is 2.5 cm long.

Then, the volume of the cube will be:-

V = (2.5)³,

=  15.625

Hence, the volume of a cube is 15.625 cubic cm.

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The area of the rectangle is 12 square units which vertices are P(2, 3), Q(4, -1), R(-8, -7), and S(-10, -3).

To find the area of the rectangle, we need to first find the side lengths of the rectangle. We can do this by using the coordinates of the points to find the distances between them.

The side length of the rectangle along the x-axis is the distance between points P and Q, which is 4 - 2 = 2 units.

The side length of the rectangle along the y-axis is the distance between points P and S, which is 3 - (-3) = 6 units.

Now that we know the side lengths of the rectangle, we can use the formula for the area of a rectangle, which is length x width, to find the area.

The area of the rectangle is 2 x 6 = 12 square units.

Therefore, the answer is 12 square units.

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The average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

What is Standard deviation?

Standard deviation is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.

To determine whether there is evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years at a 5% level of significance, we need to perform a one-tailed t-test. A one-tailed t-test is used to test whether the mean of a sample is significantly greater than (or less than) a certain value.

To perform the t-test, we first need to calculate the t-statistic, which is defined as:

      [tex]t = (mean - null value) / (standard error / \sqrt{n} )[/tex]

where mean is the mean age of the sample of lifeguards, null value is the value that the null hypothesis is testing against (in this case, 24 years), standard error is the standard error of the mean age, and n is the number of lifeguards in the sample.

Plugging in the values from the problem, we get:

           [tex]t = (24.7 - 24) / (standard \ error / \sqrt{36} )\\\\= 0.7 / (standard\ error / 6)[/tex]

The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:

   [tex]standard \ error = population \ standard\ deviation / \sqrt{(n)}[/tex]

Plugging in the values from the problem, we get:

standard error = / sqrt(36) = / 6 =

Substituting this value back into our expression for t, we get:

    t = 0.7 / ( 6)

      = 1.8

For a one-tailed t-test at a 5% level of significance, the critical value is 1.645. This means that if the t-statistic is greater than 1.645, we can reject the null hypothesis and conclude that there is evidence to support the claim.

So we can reject the null hypothesis and conclude that there is evidence to support the claim that the average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.

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Answer:

это будет 1000000000000

The slope of the line that passes through (6, 1) and (10, 8) is 7 / 4.

The slope of a line is the change in dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.

In other words, the slope of a line is a measure of its steepness.

Hence, let's find the slope of the line that passes through (6, 1) and (10, 8).

Therefore,

slope = Δy / Δx

slope = y₂ - y₁ / x₂ - x₁

x₁ = 6

x₂ = 10

y₁ = 1

y₂ = 8

Therefore,

slope = 8 - 1 / 10 - 6

slope = 7 / 4

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Answer: 7/4 is the slope

Answer:

Step-by-step explanation:

Yes, he is correct because writing a negative symbol with a denominator and numerator makes the sense same. Because the negative is as a whole not only the numerator and not only the denominator. As it is a fraction which is a whole single identity.

3/4= 0.75, Therefore in each above three always the

-0.75= -0.75= -0.75 will give same value in each.

Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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Answer:

See the picture.

Step-by-step explanation:

No, y = 4 is not a linear function.

A linear function is a function that has a constant rate of change, meaning for every input (x), the output (y) always increases or decreases by the same amount. This can be expressed algebraically as a linear equation in the form y = mx + b, where m is the rate of change (slope) and b is the y-intercept.

For example, y = 3x + 2 is a linear function because for every increase of 1 in the input (x), the output (y) increases by 3.

In contrast, y = 4 does not have a constant rate of change because the output (y) is always 4, no matter what the input (x) is. Therefore, y = 4 is not a linear function.

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Answer:

If 10% of the school brings lunch, and it's 31 people, we know that there are a total of 310 students. 10 times 31 is 310.

To check this, 90% of 310 is 279, and 310-279=31!

Answer:

310

Step-by-step explanation:

100 / 10 = 10

31 * 10 = 310

The equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

The equation y = 2x - 4 can be written in slope-intercept form as y = 2x + b, where b is the y-intercept. To find the slope and y-intercept of the equation, we need to solve for b.

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can set x equal to 0 in the equation to get y = 2(0) - 4. This simplifies to y = -4, so the y-intercept is -4.

The slope is the rate at which the line rises. To find the slope, we can take the coefficient of x, which is 2. So the slope of the equation y = 2x - 4 is 2.

In summary, the slope of the equation y = 2x - 4 is 2 and the y-intercept is -4. We can write the equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

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A graph is a diagram representing data in an organized manner.

The examples are line graphs, histograms, pie charts, bargraphs.

A graph can simply be defined as the pictorial representation or given a diagram representing data or values in an organized manner.

Points on a graph mostly represents the relationship between two or more elements.

It is also referred to as a mathematical diagram that explains the relationship between two or more sets of data, measurements or elements.

The data on a graph is mostly arranged in an organized manner.

The examples of a graph;

Hence, a graph is an organized diagram.

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Answer:

y=-2x+5

Step-by-step explanation:

First, find the slope:

m=(y2-y1)/(x2-x1)  ==> slope formula where m is the slope

(–1, 7), (1, 3)  ==> (x1=-1, y1=7), (x2=1, y2=3)

m=(3 - 7)/(1 - (-1)) ==> plugin y2=3, y1=7, x2=1, and x1=-1 into the slope formula

m=(-4)/(1 + 1)  ==> simplify

m=(-4)/2

m=-2  ==> the slope is -2

y=mx+b  ==> slope-intercept equation

3=(-2)(1)+b  ==> plugin the slope(m=-2) and point B(1, 3)  ==> (x=1, y=3)

3=-2+b  ==> solve for b

3+2=-2+2+b  ==> add 2 on both sides to isolate b

b=5  ==> simplify

y=-2x+5  ==> plugin the slope and b=5 into the equation

The level of a line's slope indicates its steepness.

The slope is computed mathematically as "rise over run" (change in y divided by change in x).

In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.

The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.

Now, let's take an example ,

2x - 3y ≤ 12

or, - 3y ≤ 12 - 2x

or, 3y ≤ 2x - 12

or y ≤ (2/3)x - 4

So, here slope (m) = 2/3, graph is shown below:

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Answer:

20+7k=8k+16

Step-by-step explanation:

8(k+2)

8 x k = 8k

8 x 2 = 16

Therefore, its  20+7k=8k+16

Answer:

8k+16

Step-by-step explanation:

20 + 7k = 8(k + 2)

20 + 7k = (8)(k) + (8)(2)

20 + 7k = 8k + 16

Answer:

there is supplementary angle

Discontinuous classes can be made continuous by using interpolation, which expression values between known points. For example, a discontinuous class of heights can be made continuous by using interpolation to estimate heights between known points.

Discontinuous classes can be made continuous by using interpolation. Interpolation is a mathematical process that estimates values between known points. This can be done in a variety of ways, such as linear interpolation which estimates values using the slope between two known points, or polynomial interpolation which uses a polynomial equation to estimate the values between known points. For example, if you have a discontinuous class of heights, you can use interpolation to estimate values between the known heights. This would result in a continuous class of heights, which may be more useful than the discontinuous class. Interpolation can also be used to estimate other types of values, such as temperature, pressure, or any other type of value that can be represented on a continuous scale.

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The coefficient of the expression 3x² is the number 3

The coefficients are the numbers on the left side or before each variable.

Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

If the expression of a single term is:. 3x²

Then the only coefficient will be the number that is placed before it and it is:

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It derives its name from the famous rock on the Capitoline Hill in Rome from where prisoners were hurled to their deaths in ancient times.

This question isn't history; it's mathematics.

However, the solution is as follows:

Given

f(x) = 3x²

Domain = {-2, -1, 0}

Required

Calculate the Range

To calculate the range, we simply plug in the values of the domain in the given function

Let the domain be represented by x; such that

x = {-2, -1, 0}

When x = -2

f(x) = 3x²

f(-2) = 3 * (-2)²

f(-2) = 3 * 4

f(-2) = 12

When x = -1

f(x) = 3x²

f(-1) = 3 * (-1)²

f(-1) = 3 * 1

f(-1) = 3

When x = 0

f(x) = 3x²

f(0) = 3 * 0²

f(0) = 3 * 0

f(0) = 0

The range are the values of f(-2), f(-1) and f(0)

Hence, Range = {12, 3, 0}

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Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

The limit of a graph can be read by a function is said to have a limit if the value of the function is less than or equal to a particular value.

Limit

One way to think about the limit of a function at a number at x = an is as the value that the function begins to take as it gets closer to that value. Approaching the location where x = a can be done from either the left or the right side.

From a limx to a f (x)

As an illustration, if f(x) is defined as the limit of x, then x is the highest value that f can take. A function is said to have a limit if the value of the function is less than or equal to a particular value. For a given function, there can be multiple limits, but only one of them can be larger than the others.

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To solve an equation for vertical asymptotes using a calculator, just input the denominator of the given equation to calculator to solve for x, the obtained values of x will give the vertical asymptotes for the given equation.

A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a.

Vertical asymptotes are significant because they demonstrate the boundaries of an undefined function. This can be crucial when examining a function's behavior and comprehending its characteristics.

To calculate the vertcial asymptotes on a calculator (eg. fx-991EX) follow the steps below to input the denominator of the given equation:

1. Press MENU button

2. Press Alpha + A to select equation/Func options

3. Press 2 to select Polynomial option

4. Select the degree of denominator

5. Enter the respective coefficients and press equal to button to get the vertical asymptote.

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The median for the next batch of observations is 5.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=2,5,7,9

n=4

median=(4)/2

=2nd term

=5

The median for following set of observation is 5.

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Santa's workshop staff traditionally consists of six elves with names. His elves construct the toys, wrap the presents, and craft the magic.

Manufacturing toys for Christmas presents, caring for the reindeer, baking cookies, making sweets, setting up Santa's sleigh, and helping Santa with other jobs are all responsibilities of a Christmas elf. Making toys all year long is one of the main responsibilities of Christmas elves.

They numbered 144 in total. Twelve became their base number and 144 their greatest number as all elves were discovered in groups of twelve (for a long time). There was no common name for a larger number in any of the later Elvish languages.

The typical image of a Christmas elf is one who is dressed in green or red, has big, pointy ears, and a pointy cap. They are frequently shown as humanoids, yet occasionally as fuzzy, tail-equipped mammals.

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Answer:

Step-by-step explanation:

-2+x=22 one step equations

just add 2 to 22

-2 + x = 22

x = 24

----------------------

check

-2 + 24 = 22

22 = 22

the answer is good

Answer:

x = 24

Step-by-step explanation:

- 2 + x = 22 ( isolate x by adding 2 to both sides )

x = 22 + 2 = 24

Answer: $24 after 4 years

Step-by-step explanation:

1.5% = 0.015

Take 400 times 0.015 = $6 per year

6 times 4 = $24 after 4 years

The mean of 1, 2, 3, 4, and 5 is 3, and the standard deviation is 1.58.

To find the mean, you add up all the numbers and divide by the number of numbers you have.

To find the standard deviation, you first find the difference between each number and the mean, square each of these differences, add them up, and divide by the number of numbers you have. Then, you take the square root of this result.

Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3

Standard deviation = sqrt(((1 - 3)^2 + (2 - 3)^2 + (3 - 3)^2 + (4 - 3)^2 + (5 - 3)^2) / 5) = sqrt((4 + 1 + 0 + 1 + 4) / 5) = sqrt(10 / 5) = sqrt(2) = 1.58

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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