For each sequence, decide whether it could be arithmetic, geometric, or
neither.
1. 27, 9, 3, ...
2. 4, 8, 12,...
3. 50, 56, 60, ...
4. 36, 12, 4, ...
5. 4, 24,...

#1

\(\\ \sf\longmapsto f(x)=-5x+4\)

\(\\ \sf\longmapsto f(6)\)

\(\\ \sf\longmapsto -5(6)+4=-30+4=-26\)

#2

\(\\ \sf\longmapsto g(x)=3x^3+5\)

\(\\ \sf\longmapsto g(-2)=3(-2)^3+5=3(-8)+5=-24+5=-19\)

The inradius of the triangle of the given dimensions will be equal to the value 2.

To find the inradius of a triangle, we need to know the semi perimeter of the triangle, which is half of the perimeter. The perimeter of a triangle is the sum of the lengths of its sides. So, the semi perimeter of triangle ABC is (6+8+10)/2 = 12.

Now that we know the semi perimeter, we can use the formula for the inradius of a triangle:

inradius = √(s-a)(s-b)(s-c)/s

where a, b, and c are the lengths of the sides of the triangle and s is the semi perimeter.

Plugging in the values for a, b, c, and s, we get:

inradius = √(12-6)(12-8)(12-10)/12 = √(6)(4)(2)/12 = √48/12} = √4 = 2

Therefore, the inradius of triangle ABC is 2.

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Answer:

A. I only

Step-by-step explanation:

Given the functions

h(x)= -2x - 1 g(x)= -1/2x + 1/2

h(g(x) =h( -1/2x + 1/2)

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

We are to replace x in h(x) with -x+1/2

h((-x+1)/2) = -2(-x+1)/2 + 1

h((-x+1)/2) = -(-x+1)+1

h((-x+1)/2)= x-1+1

h((-x+1)/2) = x

h(g(x) = x

Also for g(h(x))

g(h(x)) = g(-2x-1)

Since g(x) = -x+1/2

g(-2x-1) = -(-2x-1)+1/2

g(-2x-1) =2x+1+1/2

g(-2x-1) = 2x+2/2

g(-2x-1) = 2(x+1)/2

g(-2x-1) = x+1

Sine g(h(x)) ≠ h(g(x)), hence both functions are not inverses of each other

Hence I. The function h(g(x)) = x is the only correct option. Option A is correct

The correct option is: A. I only

We have functions:

\(h(x)= -2x - 1 \\g(x)= -\frac{1}{2} x +\frac{1}{2} \\h(g(x)) =h(-\frac{1}{2} x +\frac{1}{2}) \\h(g(x))=f(\frac{-x+1}{2} )\)

Now, replace x in h(x) by \(\frac{-x+1}{2}\)

So,

\(h(\frac{-x+1}{2} ) = -2(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} ) = -(\frac{-x+1}{2}) + 1\\h(\frac{-x+1}{2} )= x-1+1\\h(\frac{-x+1}{2} )=x\\h(g(x)) = x\)

Now, g(h(x))

g(h(x)) = g(-2x-1)

Since \(g(x) = \frac{-x+1}{2}\)

\(g(-2x-1) = \frac{-(-2x-1)+1}{2} \\g(-2x-1) =\frac{2x+1+1}{2}\\g(-2x-1) =\frac{2x+2}{2}\\g(-2x-1) = x+1\)

As g(h(x)) ≠ h(g(x)),

Therefore, both functions are not inverses of each other.

Hence A. I only

The function h(g(x)) = x is the only correct option.

So, option A is correct.

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Answer:

(x + 5)(3x + 5)

Step-by-step explanation:

(x - 5)(x + 8) + (x + 5)(2x - 3) ← factor out (x + 5) from each term

= (x + 5)(x + 8 + 2x - 3)

= (x + 5)(3x + 5)

We want to rewrite an expression as a product between two factors.

The expression (x+5)(x+8) + (x+5)(2x - 3) can be written as the product of (x + 5) and (3x + 5)

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*(3x + 5)

To get that expression, we need to remember the distributive property of the product:

A*(C + B) = A*C + A*B

Here we start with:

(x+5)(x+8) + (x+5)(2x - 3)

Note that the factor (x + 5) appears in both terms.

Then we can use it as a common factor and write:

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*( (x + 8) + (2x - 3))

                                          = (x + 5)*(x + 8 + 2x - 3)

                                          = (x + 5)*(3x + 5)

Then we have:

(x+5)(x+8) + (x+5)(2x - 3) = (x + 5)*(3x + 5)

So the expression (x+5)(x+8) + (x+5)(2x - 3) can be written as the product of (x + 5) and (3x + 5)

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The domain of the inverse function h^(-1)(x) is y > 1, indicating that the input values of h^(-1)(x) must be greater than 1. The range of h^(-1)(x) is x <= -2.

To determine the domain and range of the inverse function h^(-1)(x) for the given function h(x) with a domain of x <= -2 and a range of y > 1, we need to consider the interchanged roles of the independent and dependent variables.

The domain of the inverse function, h^(-1)(x), will be the range of the original function, h(x), and the range of the inverse function will be the domain of the original function.

Given that the domain of h(x) is x <= -2, it means that h(x) is defined only for values of x less than or equal to -2. Therefore, the range of h(x) is y > 1, indicating that the output values of h(x) are greater than 1.

When we find the inverse function, h^(-1)(x), the roles of x and y are interchanged. So, the domain of h^(-1)(x) will be the range of h(x), which is y > 1. Therefore, the domain of h^(-1)(x) is y > 1.

Similarly, the range of h^(-1)(x) will be the domain of h(x), which is x <= -2. Hence, the range of h^(-1)(x) is x <= -2.

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The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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The approximate diameter of the circle is 5.77 cm

Given that :

area of circle = 28.3 cm²

How is Area of circle is calculated ?

Area of circle is calculated using formula :

A= πr²

where "π" represents 3.14 and r is radius. So now, according to given information,

Where Pi = 3.14

Hence,

A= πr²

Substitution the value of A in above formula :

28.3 = πr²

28.3 = 3.14r²

r² =28.3/3.14

r² =8.323

√r²=√8.323

r = 2.885

r = 2.885 cm Approximately.

d = 2r

d = 5.77 Approximately.

Therefore, the diameter of the circle is 5.77 cm

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Answer:

Width = 7 units

Step-by-step explanation:

Width = x

Length = 3x + 1

2x + 2(3x+1) = 58

2x + 6x + 2 = 58

8x = 58-2

x = 56/8

x = 7

Fractions equivalent to 1/2 are 2/4, 3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18/ 10/20, 12/24, 14/28.

Just a couple of them above. Hope all of this helps you out

The fractions that are equivalent to 1/2 are:

2/4, 3/6, 4/8, 5/10, 6/12, 7/14, 8/16, 9/18, 10/20.

The fractions that are equivalent to 1/2 are:

1/2 (itself)

2/4

3/6

4/8

5/10

6/12

7/14

8/16

9/18

10/20

and so on.

These fractions are equivalent to 1/2 because they represent the same value when simplified.

When the numerator and denominator are divided by their greatest common divisor, they result in the simplified fraction of 1/2.

For example, if we simplify 2/4, we divide both the numerator and denominator by 2, resulting in 1/2

Similarly, if we simplify 6/12, we divide both the numerator and denominator by 6, again resulting in 1/2. This pattern holds for all the listed fractions.

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The value of x is 22.

Given is a parallelogram ABCD, in which angle B and C are 4x+12 and 3x+14, we are asked to find the value of x,

We can make use of the fact that a parallelogram's adjacent angle sum equals 180 degrees.

According to the given information, the adjacent angles B and C are 4x + 12 and 3x + 14, respectively.

The equation:

(4x + 12) + (3x + 14) = 180

Combine like terms:

7x + 26 = 180

Subtract 26 from both sides:

7x = 154

Divide both sides by 7:

x = 22

Therefore, the value of x is 22.

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The value of x given as x + 2 > 3x - 8 in the inequality is x < 5.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Here, they are denoted by the symbols ≥ < > ≤.

It was given that we should solve the inequality using the algebraic approach: x + 2 greater-than 3 x minus 8.

From the information, the inequality is given as:

x + 2 > 3x - 8

In this case, it is important to collect the like terms

Collect the like terms

x - 3x > - 8 - 2

-2x > -10

Then we have to divide through by 2 in order to get the value of x.

Divide

x < 10 / 2

x < 5

Therefore, the calculation shows that x is less than 5.

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The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared. The correct option is C, 0.32.

The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.

It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r” in a simple regression model.

fraction of the variability in data values = (coefficient of correlation)² = r²

For the given data, the correlation can be found as shown below. Therefore, the value of r is -0.56. Since we need the value of  r², the value of r² is,

r² = (-0.56)²

r² = 0.3136 ≈ 0.32

Hence, the correct option is C, 0.32.

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The random variable x, which represents the amount of rain (in inches) that fell this spring, is a continuous random variable.

In this context, a continuous random variable is one that can take on any value within a certain range. The amount of rain can be measured with different levels of precision, such as 2.5 inches or 2.5342 inches, indicating that there is an infinite number of possible values between any two given points.

On the other hand, a discrete random variable would involve countable outcomes or a finite number of possible values. For example, if we were counting the number of rainy days during the spring, the random variable would be discrete since it can only take whole number values.

In the case of measuring the amount of rain, there can be infinitely many possible values within any given range, and therefore, it is considered a continuous random variable. So, the correct answer is option A.

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The complete question is:

Decide whether the random variable x is discrete or continuous. Explain your reasoning Let x represent the amount of rain (in inches) that fell this spring. Is the random variable x discrete or continuous? Choose the correct answer below.

A. Continuous, because x is a random variable that cannot be counted.

B. Discrete, because x is a random variable that can be counted.

The solution to the initial value problem y' = 2yx, y(1) = 1/4 is  \(y = (1/(4e)) * e^(^x^2^)\)

To find the solution, follow these steps:

Step 1: Identify the given differential equation and initial condition.
The differential equation is y' = 2yx, and the initial condition is y(1) = 1/4.

Step 2: Separate variables.
Divide both sides of the equation by y to isolate dy/dx:

(dy/dx) / y = 2x

Now, multiply both sides by dx to separate the variables:

(dy/y) = 2x dx

Step 3: Integrate both sides.
Integrate the left side with respect to y, and the right side with respect to x:

\(∫(1/y) dy = ∫(2x) dx\)

ln|y| = x^2 + C₁ (Remember to add the constant of integration, C₁)

Step 4: Solve for y.
To remove the natural logarithm, take the exponent of both sides:

\(y = e^(x^2 + C₁)\)

We can rewrite this as:

\(y = e^(^x^2^) * e^(^C^_1)\)
Since e^(C₁) is also a constant, let C = e^(C₁):

\(y = C * e^(^x^2^)\)

Step 5: Apply the initial condition to find the constant C.
Use the initial condition y(1) = 1/4 and substitute x = 1:

1/4 = C * e^(1^2)

1/4 = C * e

Now, solve for C:

C = 1/(4e)

Step 6: Write the solution.
Substitute the value of C back into the equation for y:

\(y = (1/(4e)) * e^(^x^2^)\)

This is the solution to the initial value problem y' = 2yx, y(1) = 1/4.

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The volume of ball is 32.49 cubic centimeter.

What is volume ?

 Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here ,

The volume of a ball = 32490 cubic millimeters

To convert into cubic millimeter into cubic centimeter by dividing by 1000, Then,

=>  32490/1000

=> 32.49 cubic centimeter.

Hence the volume of ball in cubic centimeter is 32.49 .

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Answer:its 5

Step-by-step explanation: cuz

Answer:

C) The sum of the measures of the interior angles of a triangle is 180°.

Step-by-step explanation:

I got it correct on edge

The fact to prove ΔABC and ΔTRS are similar is The sum of the measures of the interior angles of a triangle is 180, option third is correct.

It is defined as the law to prove that the two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two triangles shown in the picture.

Angle B = 46 degrees

Angle C = 45 degrees

Angle A = 180 - 45 - 46 = 89 degrees

Angle R = 46 degrees

Angle S = 180 - 46 - 89 = 45 degrees

Angle T = 89 degrees

Thus, the fact to prove ΔABC and ΔTRS are similar is The sum of the measures of the interior angles of a triangle is 180, option third is correct.

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Answer:

\(y=\frac{-3}{2}x+8\)

Step-by-step explanation:

y=mx+b

b is where the line touches the y-intercept

mx is the slope...rise over run (positive slope) OR fall over crawl (negative slope)

b= 8

mx= -3/2

y= -3/2x+8

From the AAS property of congruency the side ab≅ac in the isosceles triangle.

Congruency generally shows the similarities between two triangles or any other shape for the similarity of the two shapes they should have any three properties same like their three sides, Three angles or one angle two sides and so on.

Now for an Isosceles triangle abc given in the figure

\(\angle bad=\angle cad\)

\(\angle abd=\angle acd\)

\(ad=ad\)   (common side)

So from the AAS property, the triangle \(\Delta bad=\Delta acd\) are congruence

The side ab will also be equal to the side ac.

So from the AAS property of congruency is the side ab≅ac in the isosceles triangle.

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Answer:

The answer would be "A". Converse of the isosceles triangle theorem.

Step-by-step explanation:

You're Welcome :)

Reporting on a mission, initiative, or the data obtained from it is known as debriefing. Debriefing can reduce problems associated with the use of deception by a researcher. So option a is correct.

Debriefing is the act of reporting on a mission, project, or the data gleaned from it. After an activity or event, a structured procedure examines the actions performed.

Technically speaking, it refers to a method of active intervention that is specialized and developed into more formal meanings like operational debriefing. It is divided into various categories, including, among others, psychological, military, and experiential debriefing.

The following crucial components are often included in effective debriefings:

1. Active participation that goes beyond merely taking criticism in a passive manner.

2. Developmental aim centred on growth and learning

3. A discussion of particular incidents

4. Information from several sources

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

the answer is y = 7x - 9

Step-by-step explanation:

hope this helps

Answer:

42.56 mph

Hope this helps!

The length of missing side of triangle is 11cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angled triangle.

In the triangle hypotenuse is 12cm, opposite side is 4.8cm.

We need to find the adjacent side which is represented by x.

By pythagoras theorem we find the missing side

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides

12²=4.8²+x²

144=23.04+x²

subtract 23.04 on both sides

120.96=x²

Take square root on both sides

x=10.99

x=11

Hence, the length of missing side of triangle is 11cm.

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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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The American section will be 84°.

Given is circle, we need to find the central angle for America,

So, given that,

The frequency of German is 4, American is 7, Italian is 13 and of Other 6,

So,

The total frequency = 4 + 7 + 13 + 6 = 30

So, for American section = 7/30 x 360 = 84

Hence the American section will be 84°.

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If x is the quantity of trick skis sold and y is the quantity of slalom skis sold, and x and y are both nonnegative numbers, then x 0 and y 0.

We can see from the first row of the table that 6x + 4Y 216 because 6x indicates the work hours required to make x number of trick skis and 4y is required to make y number of slalom skis. We get at 6X + 4Y 216 since the sum (6x+4y) cannot be greater than 216 hours.

Using a similar logic, the second row provides us with the following inequality:

X + Y ≤ 40

X 0 Y 0 6 X + 4 Y 216 X + Y 40

The points at the vertices are:

A = (0, 0)\sB = (0, 40)\sC = (12, 28)\sD = (33, 0) (33, 0)

By intersecting the border lines, one can locate each vertex point. For instance, the intersection of the boundary lines 6x+4y = 216 and x + y = 40 is point C.

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Big O notation focuses on the worst-case scenario analysis, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

Imagine that you're a teacher with a student named Ram. You want to find his records, so you use a simple search algorithm to go through your school district's database.

You know that a simple search takes O(n) times to run. This means in the worst case, you'll have to search through every single record to find Ram

After a simple search, you find that Ram records are the very first entry in the database. You don't have to look at every entry.

Did this algorithm take O(n) time Or did it take O(1) time because you found Ram records on the first try?

In this case, 0(1) is the best-case scenario – you were lucky that Ram records were at the top. But Big O notation focuses on the worst-case scenario, which is 0(n) for a simple search. It’s a reassurance that a simple search will never be slower than O(n) time.

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