Find the next 2 numbers in the sequence: 7, 28, 49,70, ....

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

Basic Formula: ax + by = c

where a 0 and a, b, and c are all real numbers. m ...

Form of the Slope Intercept: y = mx + b

where (x,y) is a line connecting the points y and x.

In two-point form, y y 1 = m (x x 1) y y 1 = m (x x 1)

In the case where (x1,y1) (x 1, y 1) and (x2,y2) (...

Form of Intercept:

x/ x0 x 0 and y/ y0 y 0 equal 1.

where y0 y 0 = y-in and x0 x 0 = x-intercept...

Different forms of a two-variable linear equation are possible, including standard form, intercept form, and point-slope form. For instance, the equation 2x+3y=9 may be expressed using either of the following forms: 2x+3y-9=0 (standard form), y = (-2/3)x + 3, and Form of the Intercept: y - 5/3 = -2/3(x + (-2)) (point-slope form).

Find the value of the variable that causes the equation to be true in order to solve linear equations. Utilize the inverse of the variable's multiplier and divide or multiply both sides by it. To obtain the variable value, simplify the result. Put your solution back into the equation to verify it.

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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 quotient is 2x2+5x2+2.

The rational root theorem, also known as the rational root test, is an algebraic theorem that states that for a polynomial equation in one variable with integer coefficients to have a solution (root) that is a rational number, both the constant term (the term without a variable) and the leading coefficient (the coefficient of the highest power) must be divisible by the fraction's denominator.

Since we have already provided it

[tex]\frac{(6x^2+15x^3+10x^2+10x+4)}{(3x^2+2)}[/tex]

We will now factor the numerator to determine the quotient:

Use the theorem that says [tex]a_0=4[/tex] and [tex]a_n=6[/tex].

[tex]a_0[/tex] divisions are 1, 2, and 4.

[tex]a_n[/tex] is divided into 1, 2, 3, and 6.

Check the following logical figures as a result: ±[tex]\frac{1,2,4}{1,2,3,6}[/tex]

[tex]-\frac{2}{1}[/tex] is a root of the expression, so factor out [tex]x+2[/tex]

[tex]=(x+2)\frac{6x^4+15x^3+10x^2+10x+4}{x+2}[/tex]

[tex]= \frac{6x^4+15x^3+10x^2+10x+4}{x+2} \\=6x^3+3x^2+4x+2[/tex]

We'll factor it in once more now:

[tex]=(6x^3+3x^2)+(4x+2)\\=2(2x+1)+3x^2(2x+1)\\=(2x+1)(3x^2+2)[/tex]

Finally, we have our factored form:

[tex]= (x+2)(2x+1)(3x^2+2)\\=\frac{(x+2)(2x+1)(3x^2+2)}{3x^2+2} \\=(x+2)(2x+1)\\=2x^2+5x+2[/tex]

The complete question is:-

What is the quotient: (6x4 + 15x3 + 10x2 + 10x + 4) ÷ (3x2 + 2)?

a. 2x2 – 5x + 2

b. 2x2 + 5x – 2

c. 2x2 + 5x + 2

d. 2x2 – 5x – 2

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By using the concept of algebraic expression, it can be calculated that-

Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)

What is algebraic expression?

An algebraic expression is an expression that consists of numbers, variables, and operations such as addition, subtraction, multiplication, and division. Algebraic expressions can be used to represent relationships between numbers, or to represent solutions to equations. These expressions are often used in mathematics, engineering, and computer programming. Algebraic expressions can also be used to create equations or to solve problems. Algebraic expressions can be written in both standard form and expanded form, and can be evaluated to find values for the variables.

The given expression is 18x + 6y - 3

Now,

18x + 6y - 3

3(6x + 2y - 1)

Expression equivalent to 18x + 6y - 3 is 3(6x + 2y - 1)

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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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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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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.

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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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 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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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 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 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 roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .. A polynomial equation of the second degree can be used to define quadratics.

A quadratic issue in mathematics involves multiplying a variable by itself, often known as "squaring," which is a mathematical operation. This vocabulary is based on the fact that a square's area is equal to the product of its side length and itself. Quadratum, the Latin word for square, is the source of the word "quadratic."

here

= 3[tex]x^{2}[/tex] - 10x + 8 = 0

= 3[tex]x^{2}[/tex]+ 2x  - 12x + 8 = 0

=  2 ( x + 4 ) + 3x( x + 4 )

=  ( x + 4 )( 3x + 2 )

x = -4 and x = -2/3

The roots of equation in quadratic form 3[tex]x^{2}[/tex]- 10x + 8 = 0 are: x= -2/3 , -4 .

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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

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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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:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Answer:

это будет 1000000000000

Answer:

there is supplementary angle

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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Enter 5/100 for five hundredths to divide the numerator by the denominator using a forward slash. Make sure there is space between the whole and fraction components when using mixed numbers.

The procedure used to express repeated multiplication is known as exponentiation in mathematics. As an illustration, 10 can be expressed as "10 raised to 3," which equals [tex]10^{3}[/tex] , if it is multiplied three times.

here ,

Exponentiation: 2/5^ 2  = 4/25

Or, two fifths raised to the power of squared is equal to four twenty-fifths. The mathematical equivalent of multiplying a number by itself a certain number of times is what is known as the number's exponential value.

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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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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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The probability P(A and B) has a value of 0.08

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

These mean that

P(A) = 0.2

P(B) = 0.4

From the question, we have

The events are independent events

The probability A and B is calculated as

P(A and B) = P(A) * P(B)

Substitute the known values in the above equation, so, we have the following representation

P(A and B) = 0.2 * 0.4

Evaluate

P(A and B) = 0.08

Hence, value is 0.08

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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:

5x and 3x are like term

Step-by-step explanation:

as per the question 5x plus 9 is equal to 3x The common is X that means 5x and 3x as 5 plus 3 is nine

The expression 5xyz2 3zy have 5 and -3. It is possible to compare expressions and phrases.

In the expression

5xyz² – 3zy, the terms are 5xyz² and –3zy.

Coefficient of xyz² in the term 5xyz² is 5.

coefficient of zy in the term –3zy is –3.

In the expression 1 + x + x² , the terms are 1, x and x²

Therefore,

5xyz² = 5

- 3zy = -3

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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