Find the first 5 terms.

The eight types of functions are  Linear Functions, Quadratic Functions, Polynomial Functions, Exponential Functions , Logarithmic Functions, Trigonometric Functions, Rational Functions, Piecewise Functions.

1. Linear Functions: Linear functions are equations of the form y = mx + b, where m and b are constants and x is an independent variable. The equation describes a straight line when graphed. The slope of the line is m, and the y-intercept, where the line crosses the y-axis, is b.

2. Quadratic Functions: Quadratic functions are equations of the form y = ax^2 + bx + c, where a, b, and c are constants and x is an independent variable. These equations describe parabolas when graphed. The vertex of the parabola is the point (x, y) where the curve changes direction and is given by (-b / 2a, c - b^2 / 4a).

3. Polynomial Functions:  Polynomial functions are equations of the form [tex]y = a_nx^n + ... + a_1x + a_0,[/tex] where a_n, ..., a_1, a_0 are constants and x is an independent variable. These equations can describe many different shapes when graphed.

4. Exponential Functions: Exponential functions are equations of the form [tex]y = a^x[/tex], where a is a constant and x is an independent variable. These equations describe exponential growth or decay when graphed. The rate of growth or decay is determined by the value of a.

5. Logarithmic Functions: Logarithmic functions are equations of the form y = log_a x, where a is a constant and x is an independent variable. These equations describe logarithmic curves when graphed. The base of the logarithm is determined by the value of a.

6. Trigonometric Functions: Trigonometric functions are equations of the form y = f(x), where f is a trigonometric function (e.g. sin, cos, tan, cot) and x is an independent variable. These equations describe sine and cosine curves when graphed.

7. Rational Functions: Rational functions are equations of the form y = (ax + b) / (cx + d), where a, b, c, and d are constants and x is an independent variable. These equations can describe many different shapes when graphed.

8. Piecewise Functions: Piecewise functions are equations of the form y = f(x) if x is in a certain interval, and y = g(x) if x is in another interval. These equations can describe many different shapes when graphed.

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Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.

The number is derived by multiplying the square root of a positive integer by itself.

For instance, the square root of 25 is 5, since 5 x 5 is 25.

As you can see, 5 is also the square root of 25 because (5) (5) = 25.

The square root of a number is always represented by the symbol, which is √.

Here,

The square root symbol, which has the value of 1.414, is used to symbolize the square root of 2, also known as root 2.

Mathematicians frequently utilize this number.

Because Root 2 has an unlimited number of decimals and cannot be stated as a fraction, it is an irrational number.

and 2 has a value of 2.

Thus,

=> √2 ≠ 2

as

=> 1.414 ≠ 2.00

Therefore , the given expression of the problem √2 = 2 is a false statement the true statement is √2 ≠ 2.

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A set of points equidistant from a fixed point in a plane figure is called a circle where the distance between each of the set of the points and the fixed point forms the radius of the circle.

A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.

In two-dimensional Euclidean geometry, the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.

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Answer:

  acute, because 10²+12²>15²

Step-by-step explanation:

You want to classify a triangle with sides 10 in, 12 in, and 15 in.

The "form factor" (f) of the triangle can be computed as ...

  f = a² +b² -c²

where a, b, c are the side lengths in increasing order. This is positive for an acute triangle, negative for an obtuse triangle, and zero for a right triangle.

  f = 10² +12² -15² = 100 +144 -225 = 19

  f > 0

That is to say 10² +12² > 15², so the triangle is acute

__

Additional comment

The largest angle in the triangle is arccos(f/(2ab)). In this triangle, that is ...

  arccos(19/(2·10·12)) ≈ 85.46°, an acute angle

The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. The two roots can be calculated using the quadratic formula.

The equation x² + 6x + 9 has two real roots, because the discriminant (b² - 4ac) is greater than zero. This can be seen by calculating b² - 4ac, which in this case gives (6² - 4*1*9) = 36 - 36 = 0. A discriminant of zero or higher means that the equation has two real roots. The two roots can be calculated using the quadratic formula, which is x = [-b ± Â√(b² - 4ac)] / 2a. In this case, a = 1, b = 6, and c = 9, so the formula becomes x = [-6 ± Â√(6² - 4*1*9)] / 2, which simplifies to x = [-6 ± Â√0] / 2, or x = [-6 ± 0] / 2. So the two roots are x = -3 and x = -3, which means that the equation has two equal real roots.

x² + 6x + 9

b² - 4ac = (6² - 4*1*9) = 36 - 36 = 0

x = [-6 ± Â√(6² - 4*1*9)] / 2

x = [-6 ± Â√0] / 2

x = [-6 ± 0] / 2

x = -3 and x = -3

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Pascal's law statement states that pressure is equal to the force divided by the area on which it acts.

According to Pascal's law, pressure applied to a fluid inside of a container will be transmitted without a change in magnitude to every point within the fluid as well as the container's walls. Any point in the fluid experiences equal pressure in all directions.

The force multiplied by the surface area on which it acts produces pressure. Pascal's principle states that a pressure increase on one piston in a hydraulic system causes an equal increase in pressure on another piston in the system.

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Answer:

Below

Step-by-step explanation:

At the y-axis intercept, the value of x = 0      <==== put '0' in for 'x' and calculate the y-axis intercept

Answer: 2% is equivalent to 1/50

Step-by-step explanation:

We first need to divide the numerator by the denominator.

1 ÷ 50 = 0.02

Once we have the fraction in a decimal format, the answer is then multiplied by 100 to get the correct percentage:

0.02 × 100 = 2%

On solving the provided question, we can say that - there are 67 numbers less than 100 are divisible by 3

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

= n(A ∪ B)

= n(A) + n(B) - n(A ∩ B)

= 33 + 50 - 16

= 67

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The total cost for the meal with tax and tip is $22.26.

This can be calculated using the following formula:

Total Cost with Tax and Tip = Meal Cost + (Meal Cost * Sales Tax Rate) + (Meal Cost * Tip Rate)

In this case, the formula would be:

Total Cost with Tax and Tip = 17.00 + (17.00 * 0.07) + (17.00 * 0.18)

This simplifies to:

Total Cost with Tax and Tip = 17.00 + 1.19 + 3.06

Which yields a final total cost of 22.26.

To explain in more detail, the meal cost is the original cost of the meal, which in this case is 17.00. Then, the sales tax rate is applied to the meal cost, which is 7% or 0.07. This gives us an additional cost of 1.19 (17.00 * 0.07). Lastly, the tip rate is applied to the meal cost, which is 18% or 0.18. This gives us an additional cost of 3.06 (17.00 * 0.18). Adding the meal cost of 17.00, the tax cost of 1.19, and the tip cost of 3.06 together gives us a total cost of 22.26.

Therefore, the total cost for the meal with tax and tip is $22.26.

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An equation is given as y=3x+c, an equivalent equation can be created by by solving for c in terms of y and x as y-3x.

An equation is given as y=3x+c , the concept that can be used to find the expression of c is the subject of the formular.

It should be noted that the  subject of a formula is the variable that is being worked out which is been recognised as the letter on its own on one side of the equals sign.

y=3x+c

c= y-3x

Then solving for c in terms of y and x will give us (y-3x)

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The 12 types of sets are empty set, singleton set, finite set, infinite set, subset, equal set, universal set, power set, proper subset, superset, equivalent set and proper superset.

An empty set does not contain any element, while a singleton set contain only one element.

If the number of elements in  a set is finite, the set is a finite set. If the number of elements in  a set is not finite, that is not countable it is an infinite set.

A set, say A contain only elements of another set, say B but not necessarily all elements, than set A is a subset of set B.

Whenever a set A is a subset of set B, we say the B is a superset of A. If A and B are two sets, then A is called the proper subset of B if A is a subset of B but B is not a subset of A i.e., A ≠ B.

If a set contains all and only elements of another set, then both set are said to be equal sets.

A universal set contains all elements of related sets.

Power set is the collection of all subsets of a particular set.

The set B is the proper superset of set A, then all the elements of set A are in B, but set B must contain at least one element which is not present in set A.

Equivalent sets are sets that have same number of elements.

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The statistical mode of a set of numbers is the number that occurs most frequently in the set. In the set {9, 10, 6, 5, 6}, the number 6 occurs twice, which is more than any other number. Therefore, the mode of this set is 6.

The field of statistics, which is applied mathematics, encompasses the gathering, describing, analyzing, and drawing of conclusions from quantitative data. The fundamental mathematical ideas in statistics include calculus of differential and integrals, linear algebra, and probability theory.

When attempting to estimate the population of a town, it is vital to determine the percentage of its residents who watch TV. This context makes reference to the sample, which is a condensed selection from the population.

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The age of the son is 10 years old.

Lets simplify the above problem ,

Let assume man's age = a

Let assume son's age = b

If  a man is 4 times as old as his son, then

=> a= 4b

In 5 years, he will only be 3 times as old as his son, then

= a+5

= 3(b+5)

Apply substitution method :

4b+5

=3b+15

b=10

a =40

Hence the son age is 10 years old.

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Answer:

Step-by-step explanation:

value of y is 87*

because linear pair always sum up to give 180*

we know 93+y=180

so y=180-93=87

y= 87°

180-93 = 87

The fraction of the instructions that used the word off is [tex]\frac{9}{25}[/tex]

Answer:

m=-2

Step-by-step explanation:

Recall slope (m) can be found using the following:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

For this problem, let:

[tex](x_1,y_1)=(-9,-4)\\(x_2,y_2)=(-3,-16)[/tex]

So,

[tex]m=\frac{(-16)-(-4)}{(-3)-(-9)}\\m=\frac{(-16)+4}{(-3)+9}\\m=\frac{-12}{6}\\m=-2[/tex]

The distance driven is a linear function of the hours traveled, due to the constant addition every time the number of hours is increased by one.

A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.

The points of the function in the table are given as follows:

(1,55), (2,110), (3, 165), (4,220).

(time input, distance output).

The increases to the output when the input time is increased by one are given as follows:

As the increases are constant, the distance driven, in fact, is a linear function of the hours traveled.

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Answer:

its a commutative property becaus its just changing the order

Answer:

x/3

Step-by-step explanation:

like x divided by 3

The reported rate of return is not reasonable i.e. the rate of return on the investment is  -0.20% .

What is Return ?

The annual return on an investment, expressed as a percentage of the initial investment.an investment of $200 earns $12 for a year, so the Rate of Return is 12/200 = 0.06 = 6%.

Given, for an investment of $26,245, a quarterly statement reports that the account balance is $26,192 and rate of return for the same quarter was -0.02 %.

Here, we'll calculate the rate of return as follows:

Rate of return = (change in investment/ Initial investment) × 100

                        = ($26,192 - $26,245)/$26,245 × 100

                        = -53/26245 × 100

                        = - 0.20 %

Hence, The correct rate f return will be -0.20 %, not -0.02%.

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The nature of the roots of a quadratic equation is known by a value known as the discriminant,  which is calculated by seeing the equation and comparing it with the standard equation which is given by -

ax^2 + bx +c , where a , b , c are constants .

The root of the equation is given by -

x= [(-b )± (b^2 - 4ac)] / 2a

Here, the term (b^2 - 4ac) is called the discriminant of the quadratic equation .

This discriminant is the defining factor of the nature of the roots.

Now, here arise three cases-

(i) If (b^2 - 4ac) > 0, the roots are real and distinct .

(ii) If (b^2 - 4ac) = 0 , the roots are real and equal.

(iii) If (b^2 - 4ac) < 0 , the roots are not real and they are imaginary i.e. they are complex in nature and of the form a+ib.

For example , we have an equation x^2 + 2x + 1.

Here, a =1, b=2 and c=1.

Putting these values in the discriminant , we get -

b^2 - 4ac = 4-4(1)(1) = 0.

So, the roots of the equation are real and equal i.e. x=2,2.

Hence, it is the discriminant which determines the nature of roots.

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The term "infinity" in mathematics refers to something that is bigger than a natural number.

Given that,

We have to find what is infinity means.

We know that,

Something that has no beginning is said to be infinite. It is generally something that has no restrictions. It is a condition in which there are no boundaries in terms of time, space, or any other kind of quantity.

Infinity is denoted by ∞.

If there is a one-to-one relationship between a set of numbers and a suitable subset of itself, that set can be said to be infinite.

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Answer:

corrine got 66006 vote

bill got 53450 vote

Answer:

Bill Randall= 53450 votes.

Corrine Brown= 66006 votes.

Step-by-step explanation:

Bill Randall = X

Corrine Brown = 1x

Bill Randall= x+1x+12556=119456

2x+12556=119456

2x=119456-12556

2x=106900

x=106900/2

x=53450

Corrine brown = 53450+12556

                        = 66006

Recall that the transform() and predict() functions only operate on test data, while the fit transform() function only operates on training data.

The mean and standard deviation for a particular feature are calculated using the fit(data) approach and then scaled. Scaling with mean and standard deviation determined by the. fit() method is done using the transform(data) method. The methods fit transform() and transform are both used for fits.

Predict() makes predictions based on the parameters it learned during fit on the testing examples, while the fit() method applies the model to the input training instances. Fit Transform is a mathematical expression that means to calculate, then transform (say calculating the means of columns from some data and then replacing the missing values). In order to alter the training set, you must also calculate it.

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As our sample size is large and grade point average follows normal curve, we use parametric test.

The normal curve is a statistical measurement which refer that the available data presented in a large number close to the mean value.

The test is used to determine an approximate value of a set of data.

hence, we use parametric test for determining an approximate value.

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The required mean of the given data is 5.71.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset.

The term "average" is frequently used to describe this measure of central tendency.

So, we have the data set:

2, 2, 4, 6, 8, 8, 10

Mean formula: Sum of terms / Number of terms

Now, calculate the mean as follows:

Mean: Sum of terms / Number of terms

Mean: 40 / 7

Mean: 5.71

Therefore, the required mean of the given data is 5.71.

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Answer: 216 small balls

Step-by-step explanation:

The volume of a ball:

                                [tex]\displaystyle\\V=\frac{4}{3} \pi R^3[/tex]

Let us calculate the volume of a big metallic ball:

[tex]\displaystyle\\V_{big}=\frac{4}{3} (3)(3^3)\\\\ V_{big}=4(27)\\\\V_{big}=108 \ cm^3[/tex]

Now let us calculate the volume of a big small ball:

[tex]\displaystyle\\V_{small}=\frac{4}{3} (3)(0.5^3)\\\\ V_{small}=4(0.125)\\\\V_{small}=0.5 \ cm^3[/tex]

Thus, the number of identical small balls should work:

[tex]\displaystyle\frac{V_{big}}{V_{small}} =\frac{108}{0.5} \\\\\frac{V_{big}}{V_{small}} =216\ units[/tex]

Yes,△TSR is Congruent to △QRS ( i.e,△QRS ≅ △TRS) by SAS , because there is all enough information to prove that the triangles are congruent by SAS rule.

The word "congruent" for figures means the same thing in all respects, mainly shape and size. The relationship between two congruent entities is described by congruence. SAS congruence is a term also known as side angle side congruence. According to this rule, two triangles are congruent if two sides of a triangle are equal to two sides of another triangle and the angles formed by those sides of the two triangles are equal. We have two triangles, △TSR and △QRS as we can see in above figure and we get ,

Thus, two sides and one angle of triangle is similar to corresponding sides and angle of other triangle, so SAS Congruence criteria is applicable here. Therefore, △QRS ≅ △TRS by the SAS Congruence Postulate.

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Complete question :

Can TSR and QRS be proven congruent by SAS ? and the triangles are shown above figre.

Based on the given task content; the percent chance is 1 out of 20 is 5%.

Percentage refers to the amount, number or rate of something, regarded as part of a total of 100.

The percent chance is 1 out of 20

= 1/20 × 100

= 0.05 × 100

= 5%

Un conclusion, 5% is the percent chance is 1 out of 20

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