f(x)=2x+1
g(x)=x^2+2
Find g(f(x))

The value of the expression is 4/25.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

The given expression is,

-16/25 - (-12/15)

Two negatives become positive.

-16/25 - (-12/15) = (-16/25) + (12/15)

Doing the cross multiplication,

-16/25 - (-12/15) = [(-16 × 15) + (12 × 25)] / [25 × 15]

                         = 60 / 375

                         = 12/75

                         = 4/25

Hence we get the resulting value as 4/25.

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The lower bound for a 95% confidence interval for the average length of the entire population of fish is 65.492.

Let the sample mean be ( x ) = 66.7

Standard deviation for the given sample be = s = 8.5

random sample of 190 fish is collected from the ocean so ( n )= 190

Confidence level be 95% so the Z-score be 1.959 ≈ 1.96.

By using the formula ,

x ± [tex]Z\frac{s}{\sqrt{n} }[/tex]

= 66.7 ± 1.96 (8.5/√190)

= 66.7 ± 1.208

where 1.208 indicates margin error (E).

So upper bound be 66.7 + 1.208 = 67.908

and lower bound be 66.7 - 1.208 = 65.492.

95% of samples contain the population mean (μ) within the confidence interval x ± E.

"A confidence interval is the range of values, obtained from sample statistics, that is likely to include the value of an unknown population parameter," according to the definition.

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The angle of 135 degrees is an obtuse angle.

An angle is a space shared by two rays that are joined at the same vertex. We can find different types of angles according to their amplitude.

If the amplitude is larger than 90º (90 degrees) and less than 180º (180 degrees) that tells us that it is an obtuse angle.

An obtuse angle is also defined as an angle that is formed when a ray rotates between 90º and 180º around a point.

Visually, this angle is more than a quarter of a circle but less than half of a circle. So, if we divide a circle into four parts, an obtuse angle will always occupy between 1/4 and 1/2 of a circle.

Thus, the angle of 135 degrees is an obtuse angle.

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The required  three types of solutions for a system of equation are Unique solution, no solution, infinite many solution.

simultaneous equations, system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

Systems of linear equations can be classified as follows:

Dependent: There are countless possible solutions to the system. The same lines are shown on the equation graphs. ...

Independent: There is only one answer to the problem. The equations' graphs come together at a single point. ...

Inconsistent: There is no fix for the system.

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Line 'b' is perpendicular to line 'a'. Then the slope of line 'b' is 5/4.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

The points are given below.

(7, 10) and (2, 14)

The slope of the line 'a' is given as,

m = (14 - 10) / (2 - 7)

m = - 4 / 5

Line 'b' is perpendicular to line 'a'. Then the slope of the line 'b' is given as,

Slope = - 1 / m

Slope = - 1 / (-4/5)

Slope = 5/4

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The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:

y = a(x - r(1))(x - r(2))

A quadratic expression that is the product of two factors, each of which is a linear expression, is referred to as having a "factored form."

When an equation is in factored form, it can be expanded to recreate it in standard form by multiplying out the components. The act of factoring involves summarizing the parts of a given integer or algebraic expression.

The equation y = a[tex]x^2[/tex] + bx + c is in factored form when it is written as:

y = a(x - r(1))(x - r(2))

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Answer:

x = 22, y = -13

Step-by-step explanation:

4x + 3y = 49

- x - 2y = 4

x + 2y = -4

4x + 8y = -16

Subtract both equations,

5y = -65

y = -13

x - 26 = -4

x = 22

Cheers

The inequality x > - 3 is represented by a line with an open circle at - 3 going toward infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, An inequality x + 6 > 13 represented by a number line.

So, x + 16 > 13.

x > 13 - 16.

x > - 3.

A line with an open circle at - 3 and a direction toward infinity is used to illustrate the inequality x > - 3.

Q. If the replacement set for x is the set of real numbers, which graph represents the inequality x + 16 > 13?

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Answer:

(3, 9 )

Step-by-step explanation:

x + y = 12 → (1)

y = 3x → (2)

substitute y = 3x into (1)

x + 3x = 12

4x = 12 ( divide both sides by 4 )

x = 3

substitute x = 3 into (2) and solve for y

y = 3x = 3 × 3 = 9

solution is (3, 9 )

Answer:

-3+-1

(simplifies to -4)

Step-by-step explanation:

keep change change

On using subtraction it can be seen that Simone needs more 8 inches space in her room to fit the chest beside the bed. So, the chest cannot fit in Simone's room with the measurements of room = 100 inches and bed  = 74 inches.

What is subtraction?

The process of subtracting one number from another is called subtraction. The way to calculate the difference between two numbers is by using the basic arithmetic operation of subtraction, which is represented by the symbol (-).

The measurement for Simone's room is, a = 100 inches.

The measurement for Simone's bed is, b = 74 inches.

The amount of space left in Simone's room = a - b.

Using the arithmetic operation of subtraction -

= 100 - 74

= 26

Hence, 26 inches of space is left in Simone's room.

The measurement for chest that Simone wants to fit in her room next to bed is 85 centimeters.

To convert 85 cm to inches divide the length by 2.5 -

Using the arithmetic operation of division -

85/2.5 = 34

Hence, the measurement of the chest in inches is 34 inches.

26 < 34

Using the arithmetic operation of subtraction -

34 - 26 = 8

So, Simone has 26 inches space left and the size of chest is 34 inches, which cannot be fitted in the room.

Therefore, Simone cannot fit the chest in her room.

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1. The angle pair is straight angle pair or linear pair.

2. m∠4 = 80°

3. m∠5 = 100°

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In a normal distribution, approximately 68% of the scores fall within one standard deviation of the mean, and approximately 95% of the scores fall within two standard deviations of the mean.

IQ scores are often distributed in a bell-shaped curve, which is known as the normal distribution.

In a normal distribution, the mean is the center of the curve and the standard deviation is a measure of how spread out the scores are. In most IQ tests, the average score is 100 and the standard deviation is 15. If a score is 2 standard deviations above the average, it falls in the upper 2.5% of all scores.

This is because the normal distribution is symmetric, which means that the same percentage of scores falls above and below the average. In this case, if you took an IQ test and your score was 2 standard deviations above average, your score would be higher than approximately 97.5% of all IQ test takers, which is a relatively rare score.

However, it's important to note that IQ tests have many limitations and not all IQ tests have the same mean and standard deviation.

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Answer:

28/10

Step-by-step explanation:

To find out scale factor, you need to divide both sides which means

7/2.5 is 2.8 and if we turn that into a fraction we get 28/10

The initial cost, which is zero, is 4.25 less than the plotted value of the stock, which is 4.25. So, "The stock is equation  4.25 less than the initial value, and the absolute value is 4.25" is the right response.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Based on the information provided, a vertical number line with tick marks every half unit starts at minus 7 and goes all the way up to 0. The number line displays the value of the negative 4.25.

The initial cost, which is zero, is 4.25 less than the plotted value of the stock, which is 4.25. So, "The stock is 4.25 less than the initial value, and the absolute value is 4.25" is the right response.

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The inverse of the function f(x) = 2x + 1 is [tex]f^{-1}[/tex](x) = [tex]\frac{x-1}{2}[/tex]

Let y=f(x)

x=[tex]f^{-1}[/tex](y)

Given, f(x)=2x+1

y=2x+1

2x=y−1

x=[tex]\frac{y-1}{2}[/tex]

[tex]f^{-1}[/tex] (y)=[tex]\frac{y-1}{2}[/tex]

Replace y by x, we get,

[tex]f^{-1}[/tex](x)=[tex]\frac{x-1}{2}[/tex]

This is the inverse of function.

A function that can reverse into another function is known as an inverse function or anti function. In other words, if any function "f" takes x to y, then the inverse of that function will take y to x. When a function is written as "f" or "F," its inverse is written as "[tex]f^{-1}[/tex]" or "[tex]F^{-1}[/tex]." Here, (-1) should not be confused with an exponent or a reciprocal.

Inverse functions f and g result in f(x) = y if and only if g(y) = x.

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What is the inverse of the function f(x) = 2x + 1?

A) Evaluate f(0)

f(0) = 6*0 - 4 = -4

What does a math function mean?

a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

B) Evaluate f(2)

f(2) = 6*2 - 4 = 8

C) Evaluate f(-2)

f(-2) = 6*(-2) - 4 = -12

D) Evaluate f(4)

f(4) = 6*4 - 4 = 20

E) Evaluate f(-3)

f(-3) = 6*(-3) - 4 = -16

Note: In the given function, x is replaced by z, so in order to evaluate the function for the given values of x, we need to replace x with z.

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If no two men are to sit next to each other, there are 144 ways to arrange four men and four women at a round table.

Combinations are mathematical operations that count how many possible combinations there are for a given set of components, regardless of the order in which they were chosen. One can choose the components of combos in any order.

First, arrange the four women so that there is a free seat between each pair of them at the round table. These four women can be seated at the round table in 3 different ways, for a total of 6 possible arrangements. This is written as 3! = 6.

Then, the four vacant seats will be occupied by the four men and this is written as ⁴P₄=4!=24. Then, the required number of ways to seat the two men who are not adjacent to each other is 6×24=144 ways.

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What is the rational expression?

A rational expression is an expression of the form (p(x))/(q(x)) where p(x) and q(x) are polynomials. The expression is called a rational expression because it is the ratio of two polynomials.

A rational expression that is equal to the given expression when x doesn't equal 2 or -3 is:

5x / (x+3)

This is obtained by canceling the common factor of (x-2) in the numerator and the denominator of the original expression. Note that, this is only true when x doesn't equal 2 or -3, because the original expression is not defined when x = 2 or x = -3, as it would result in a division by zero.

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The given rational expression can be simplified by canceling out the common factor of (x-2) in the numerator and denominator, which results in the following simplified rational expression:

5/(x+3)

A rational expression is an expression of the form (p(x))/(q(x)) where p(x) and q(x) are polynomials. The expression is called a rational expression because it is the ratio of two polynomials.

A rational expression that is equal to the given expression when x doesn't equal 2 or -3 is:

5x / (x+3)

This is obtained by canceling the common factor of (x-2) in the numerator and the denominator of the original expression. Note that, this is only true when x doesn't equal 2 or -3, because the original expression is not defined when x = 2 or x = -3, as it would result in a division by zero.

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Answer: 9

Step-by-step explanation:

        Noah's Playlist- 36 divided by 4 = 9

Answer:Pr(4.19 ≤ X ≤ 4.81)

Step-by-step explanation:

First of all, let's calculate the mean;

x¯ = (4.3 + 5.1 + 3.9 + 4.5 + 4.4 + 4.9 + 5.0 + 4.7 + 4.1 + 4.6 + 4.4 + 4.3 + 4.8 + 4.4 + 4.2 + 4.5 + 4.4)/17

x¯ = 76.5/17

x¯ = 4.5

We are given standard deviation; s = 0.31

Now, z-value for a 68% Confidence interval is 1

Range in which the data falls is;

Range = x¯ ± zs

Range = 4.5 ± (1 × 0.31)

Range is;

Pr[(4.5 - 0.31) ≤ X ≤ (4.5 + 0.31)]

Pr(4.19 ≤ X ≤ 4.81)

Two ordered pairs of the equation -x+6y=8

are (0, 4/3) and (-8, 0).

Here we want to find an ordered pair for the given equation:

-x + 6y = 8

To find an ordered point we just need to evaluate the equation in any value of x or y that we want.

For example, if we use x = 0 we will get:

-0 + 6y = 8

6y = 8

y = 8/6

y = 4/3

So we have the ordered pair (0, 4/3)

And if we evaluate in y = 0, we willg et:

-x + 6*0 = 8

-x = 8

x = -8

We have the point (-8, 0)

So these are two examples of ordered pairs of the equation.

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A polygon has as many angles as it has sides. A pentadecagon has 15 sides and 15 angles.

What is polygon ?

A Polygon is a closed figure made up of line segments (not curves) in a two-dimensional plane. Polygon is the combination of two words, i.e. poly (means many) and gon (means sides). A minimum of three line segments is required to connect end to end, to make a closed figure.

A pentadecagon is a two-dimensional geometric shape that has 15 straight sides and 15 angles. It is a type of polygon, which is a closed shape that is made up of a finite number of straight line segments. The sum of the angles in a pentadecagon is equal to (15-2) x 180 = 2160 degrees. The interior angles of a regular pentadecagon are equal to (15-2) x 180/15 = 144 degrees. The formula to calculate the area of a regular pentadecagon is (15/4) x (apothem)^2 x (cot (180/15)) where apothem is the distance from the center of the shape to the midpoint of a side.

A polygon has as many angles as it has sides. A pentadecagon has 15 sides and 15 angles.

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The answer of 10 more than 23 is 33.

The answer of 10 more than 23 is 33 which can be derived using simple mathematical calculations.

To find 10 more than 23, you can add 10 to the original number 23.

10 + 23 = 33

It's a simple arithmetic operation where you add a specific number, in this case 10, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 10 more than 23 is 33.

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The difference of the given fractions lie between 0 and 1/2

A proper fraction is a fraction which has its numerator value less than the denominator. For example, ⅔, 6/7, 8/9, etc. are proper fractions.

Given here: 7/8-6/11= 77-48 /88

                                =0.32 or 8/25

but  0<0.32<1/2<1

Hence, the difference of the given fractions lie between 0 and 1/2

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The Total weekly revenue of Mae Ling is 570$ with a five percentage commission.  

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

Given, Mae Ling earns a weekly salary of $355 plus a 5.0% commission on sales at a gift shop.

Since she sold $4,300 worth of merchandise

Her commission would be = 4300 * 5%

Commission = 4300 * 5/100

Commission = 215$

Her total salary = commission + weekly wage

Her total salary = 215 + 355 = 570

Therefore, the Total weekly salary of Mae Ling is 570$ with a 5 percent commission.

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An independent system is a system that does not interact with its environment or any other system. A dependent system, on the other hand, is a system that interacts with its environment or other systems. In other words, the behavior of a dependent system is affected by external factors, whereas the behavior of an independent system is not.

Independent systems are self-sufficient and don't rely on external factors to function or operate. They can function and make decisions on their own without being affected by anything else. For example, a calculator is an independent system, it performs mathematical operations on its own and does not depend on anything else to work.

On the other hand, dependent systems are not self-sufficient and rely on external factors to function or operate. They are affected by and interact with their environment, and their behavior is influenced by external factors. For example, a car is a dependent system, it needs gasoline to run and is affected by the road conditions, traffic, and weather.

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I'm not aware of any concrete information to support the assertion that New Yorkers travel less than 12,200 miles per year on average.

The average number of miles driven can vary significantly based on a number of variables, including population density, demography of urban and rural areas, transportation infrastructure, and individual preferences.

The availability of alternate modes of transportation, changes in fuel prices, and changes in the general state of the economy can all have an impact on data on average miles driven.

It's impossible to say for sure whether the typical amount of miles driven in New York is less than 12,200 without access to particular data or a research.

However, because sample data can be influenced by bias and other kinds of inaccuracy, if this statistic was obtained from a sample of data, it might not correctly reflect the general average for the entire state.

A thorough and representative study would need to be carried out to precisely establish the typical amount of miles travelled in New York.

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The Average snowfall in Boston is 44.6 inches

Average is a single value that is taken as prototypically of a set or list of numbers. Depending on the context the average might have statistically different meanings like median or mode.

Average= sum of observation/number of observations

The temperature in january=32.8

the temperature in february= 56.4

∴Average= 32.8+56.4/2

=89.2/2

=44.6

Therefore, the Average snowfall in Boston over this period is 44.6 inches.

Some properties of average are:

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