For all values of x f(x) = 2x-3 and g(x) = x² + 2 (c) Solve fg(x) = gf(x)​

The inequalities that the given number line represents are:

(A) x > 8

(B) x -4

A connection that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics.

On the number line, size comparisons between two numbers are typically conducted.

The outcome is (x/a) > (y/a) when x > Y and a > 0, and (x/a) (y/a) when x Y and a > 0.

The division of both sides of an inequality by a negative integer, on the other hand, produces an analogous inequality if the inequality sign is inverted.

So, the inequality that the given number line represents:

(A) x > 8 is the inequality in the first equation.

(B) Given that the second graph is a dot, the inequality for it is x -4.

Therefore, the inequalities that the given number line represents are:

(A) x > 8

(B) x -4

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By shifting the appropriate numbers to the appropriate locations, the equations become true with [tex]f(-6) = 5, f(x) = 3[/tex] , and  [tex]x = -5,[/tex] and  [tex]f(7) = 8[/tex] .

An equation is a claim that two expressions are equivalent in mathematics. Usually, it has one or more factors, which stand in for the unknowable elements we're trying to figure out how to calculate.

Equations can be used to depict actual-world circumstances or to explain relationships between various mathematical things.

For instance, the equation  [tex]"x + 3 = 7"[/tex] indicates that the total of the constant "3" and the variable "x" equals 7. By taking 3 out of both parts of the equation, we can find "x" and get [tex]"x = 4"[/tex] as a result.

Given

To make the equations true, move the right values to the right places in the table below:

[tex]f(-6) = 5[/tex]

[tex]f(x) = 3; x = -5[/tex]

[tex]f(7) = 8[/tex]

By shifting the appropriate numbers to the appropriate locations, the equations become true with  [tex]f(-6) = 5, f(x) = 3,[/tex] and [tex]x = -5[/tex] , and [tex]f(7) = 8[/tex] .

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The complete question is :- Use the table below to drag the correct numbers to their appropriate spots to make the equations true:

(Fill in the blank)

X                                      f(x)

-6                                     8

7                                        3

4                                      -5

3                                      -2

-5                                     12

Answer:

Volume = length x width x height

3 in x 8 in x 8 in = 192 cubic inches

To rewrite a number with a radical in the denominator without the radical, we can use the conjugate of the denominator. The conjugate of a binomial expression a + b is a - b, and the conjugate of a - b is a + b.

Suppose we have a number with a radical in the denominator, such as 1/√2. To rewrite this without the radical, we multiply the numerator and denominator by the conjugate of the denominator, which is

√2: 1/√2 = (1/√2) * (√2/√2) = √2/2

Note that the product of the denominator and its conjugate is always a difference of squares, which can be simplified to an integer without a radical.

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Answer:

$4.50

Step-by-step explanation:

There are 12 inches in a foot. 18 inches is 1.5 feet.

1 foot of wire is $3.00 and a half of foot should be $1.50.

1.5 feet of wire should cost $4.50

1.5 ft × $3/ft

= $4.50

Answer: 6 pounds

Step-by-step explanation:

If 1 pound of raw spaghetti makes 5 cups of cooked spaghetti, then we can set up a proportion:

1 pound raw spaghetti : 5 cups cooked spaghetti = x pounds raw spaghetti : 30 cups cooked spaghetti

To solve for x, we can cross-multiply and simplify:

1 * 30 = 5 * x

30 = 5x

x = 6

Therefore, 6 pounds of raw spaghetti noodles would be needed to make 30 cups of cooked noodles.

Answer:

8

Step-by-step explanation:

2x² + 3x - 6

plug in x with 2

2(2)^2+3(2)-6

2(4)+6-6

8+6-6

14-6

8

Answer:

x²  + 4x - 6

Step-by-step explanation:

x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left

= x(x + 1 + x + 2x)  - 3(x² - x + 2)

= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis

= 4x² + x - 3x² + 3x- 6 ← collect like terms

= x² + 4x - 6

Answer:

4.3

Step-by-step explanation:

The correct option for this question is (d) "No, none of the sides are parallel."

why it is and what is a Quadrilateral?

To determine if quadrilateral CDEF is a trapezoid, we need to check if it has exactly one pair of parallel sides.

We can find the slopes of the line segments CD and EF as follows:

slope of CD = (5 - (-6)) / (-8 - (-1)) = 11 / (-7) = -1.57 (approx.)

slope of EF = (8 - 5) / (3 - 4) = 3 / (-1) = -3

Since the slopes are different, CD and EF are not parallel, and therefore, CDEF is not a trapezoid.

Alternatively, we can also find the slopes of the line segments CF and DE as follows:

slope of CF = (-5 - (-6)) / (4 - (-1)) = 1/5

slope of DE = (8 - 5) / (3 - (-8)) = 3/11

Since the slopes are different, CF and DE are not parallel, and therefore, CDEF is not a trapezoid.

Therefore, the answer is option (d) "No, none of the sides are parallel."

A quadrilateral is a geometric shape that has four straight sides and four vertices (corners). It is a two-dimensional polygon with four sides and four angles. The sum of the interior angles of a quadrilateral is always 360 degrees.

There are many types of quadrilaterals, including squares, rectangles, rhombuses, parallelograms, trapezoids, and kites.

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The volume of the prism is equal to 40x m³.

The volume of the cylinder is equal to 72π m³.

The value of x to the nearest tenth is equal to 5.7 meters.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

Substituting the given parameters into the formula for the volume of a rectangular prism, we have;

Volume of a rectangular prism, V = 5 × x × 8

Volume of a rectangular prism, V = 40x m³.

For the volume of the cylinder, we have:

Volume of a cylinder, V = πr²h

Volume of a cylinder, V = π × 3² × 8

Volume of a cylinder, V = 72π m³.

Next, we would solve for x;

40x = 72π

40x = 226.1947

x = 226.1947/40

x = 5.7 meters.

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Complete Question:

Rectangular prism and a cylinder both have a height of 8 m, and their cross-sectional areas are equal at every level parallel to their respective bases.

A rectangular prism and a cylinder both have a height of 8 meters. The rectangle has base dimensions of 5 meters by x. The cylinder has a radius of 3 meters.

Complete the steps to find the width of the prism.

Find the volume of the prism.

V = m3

Find the volume of the cylinder.

V = m3

Set the volumes equal to each other and solve for x. Round to the nearest tenth.

x = m

The probability that a stranger on the street has an IQ below 98 is 0.4470, or 44.70%.

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

According to our question-

z= x-a/u

98-100/15

Hence, A chance of a random individual on the street having an IQ below 98 is 0.4470, or 44.70%.

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Answer:

90 cubes in the box.

Step-by-step explanation:

To find how many cubes would fit into the box, first we must find the volume of each cube. 2cm x 2cm x 2cm= 8 cubic centimeters. The entire volume of the box is 720 cubic centimeters, so we can divide 720 by 8.

720/8=90

90 cubes can fit into the box.

Answer: 90

Step-by-step explanation:

First, we need to calculate the volume of one cube of sugar:

V = s³, where s is the side length of the cube

V = 2³ = 8 cm³

To find the number of cubes that can fit in a box of 720 cm³, we need to divide the volume of the box by the volume of one cube:

720 cm³ ÷ 8 cm³/cube = 90 cubes

Therefore, 90 cubes of sugar can fit in a box with a volume of 720 cm³.

The sum of the interior angles of a quadrilateral is 360°. We can use this fact to find the measures of the other two angles.

Let x be the measure of one of the two angles in the 2:3 ratio. Then, the measure of the other angle is 3x (since the two angles are in a ratio of 2:3).

We know that:

252° + 63° + 2x + 3x = 360°

Simplifying this equation, we get:

5x + 315° = 360°

5x = 45°

X= 9°

Therefore, one of the angles has a measure of 2x = 18°, and the other angle has a measure of 3x = 27°.

Answer:

The 4 angles of the quadrilateral are : 252, 63, 18 and 27

Step-by-step explanation:

252 + 63 + 2x + 3x = 360

315 + 5x = 360

5x = 45 ( 360-315 )

x = 9

Therefore, 1st angle = 2x = 18

2nd angle = 3x = 27

The sum of the geometric progression is the sum S₃ = 32

The sum of terms of a geometric progression is given by

Sₙ = a(rⁿ - 1)/(r - 1) where

Given the geometric progression, aₙ = 4(2)ⁿ⁻¹ comparng it with the general term of a geometric sequence aₙ = arⁿ⁻¹, then

Now, we desire S₃, that is Sₙ when n = 3.

So, S₃ = a(r³ - 1)/(r - 1)

= 4(2³ - 1)/(2 - 1)

= 4(8 - 1)/1

= 4(8)

= 32

So, the sum S₃ = 32

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"A point that moves on a coordinate line is said to be in simple harmonic motion if its distance d from origin at time t is given by either d = a sinωt or d = a cosωt."

Any function which is written in the form 'a sin(ωt+Ф)' and 'a cos(ωt+Ф)' is said to be a simple harmonic motion.

One definition of a periodic motion is a straightforward harmonic motion. The acceleration of the particle at any location is directly proportional to the displacement from the mean position in simple harmonic motion, which is an oscillatory motion.

Simple harmonic motion, or SHM, is a specific type of repeated or periodic motion that describes the motion of the pendulum. The oscillating object's location changes sinusoidally over time.

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The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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The correct option A) There is a cluster, and as x decreases, y increases.

The table represents a set of data containing two variables, x and y. By analyzing the data, we can observe a cluster of values around x = 4 with corresponding y values in the range of 42-45. As we move towards smaller x values, there is a general trend of increasing y values. However, there are a few outliers. Based on these observations, statement A is the most accurate description of the data in the table. It is important to note that the accuracy of the statement is limited to the given data, and further analysis or additional data may reveal a different trend or pattern.

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Complete question:

The table below shows a set of data. Which statement about the table is true?

x: 1.6, 1.9, 2.3, 3.4, 3.8, 4.2, 4.3, 4.6, 4.8.

y: 39, 38, 42, 40, 41, 44, 42, 45, 44

Which statement about the table is true?

A) There is a cluster, and as x decreases, y increases.

B) There is a cluster, and as x increases, y increases.

C) There is not a cluster, and as x increases, y increases.

D) There is not a cluster, and as x decreases, y increases.

The approximate probability that more than 10% of the sample would report that they experienced extreme levels of stress during the past month, obtained using the z-score for the proportion of the sample, and the standard error, is about 96.327%

The z-score of a sample proportion, z can be obtained using the formula;

z = (p - π)/√(π·(1 - π)/n)

Where;

p = The sample proportion

π = The proportion of the population

n = The sample size

The percentage of the students out of the 1750 students that experienced extreme levels of stress in the school, p = 15%

The number of students in the sample used by the newspaper, n = 160 students

The number of students in the sample that replied "yes" = 10%

The true proportion of the students that experience stress = 15%

The probability that ,more than 10% of the sample would report that they experienced extreme levels of stress during the past month can be found as follows;

The standard error is; SE = √(p × (1 - p)/n)

Therefore;

SE = √(0.15 × (1 - 0.15)/160) ≈ 0.028

The z-score is therefore;

z = (0.1 - 0.15)/0.028 ≈ -1.79

z = -1.79

The z-score indicates the number of standard deviations the proportion of the sample is from the true proportion

The proportion on the of the sample which is larger than 10% is obtained from the area under the normal curve, to the right of the z-score of -1.79, which is obtained as follows;

The z-value at z = -1.79 is 0.03673, which indicates that the area to the left of the z-value is 0.03673, and the area to the right is; (1 - 0.03673) = 0.96327

The probability observing a sample proportion more than 10% if the actual proportion is 15% is therefore; 0.96327 = 96.327%

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The direction of the current in the current-carrying wire that produces the field indicated in the figure is given below.

Conventionally, a positive charge would go in the same direction as an electric current. As a result, the battery's positive terminal receives less current in the external circuit than its negative counterpart. Indeed, electrons would go in the reverse direction across the cables.

According to Fleming's right-hand rule gives which direction the current flows. The right hand is held with thumb, index finger & middle finger mutually perpendicular to each other. The thumb is pointed in direction of motion to magnetic field of conductor relative to magnetic field.

(A) from right hand rule direction of current is towards left.

(B) Out of the Screen.

(C) Lower left to upper right.

According to Fleming's Right Hand Rule, if the thumb, forefinger, and middle finger are arranged in a straight line on the right hand, the thumb will point in the direction of the conductor's motion in relation to the magnetic field, the forefinger will point in the direction of the magnetic field, and the middle finger will point in the direction of the induced current.

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Answer:

1 : 3.5

Step-by-step explanation:

Rewrite the ratio 6:21 as 1 : n .

Divide each side by 6.

6/6 : 21/6

1 : 3.5

Answer:

Step-by-step explanation:

Because we want to know how many three-fourths there are, we have to make groups of 3 fourths, or divide the number of fourths we have by 3. So there are (2\times 4)\div 3 = 8\div 3 = 2 \fraction three-fourths in 2.

Answer:

To multiply a whole number and a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator the same.

So, 3 x 3/5 = (3 x 3)/5 = 9/5

Therefore, 3 x 3/5 = 9/5.

Answer:

Step-by-step explanation:

9x/5

The value of n for the ascending powers of x is found to be 20.

A series expansion is just a representation of a specific function as the sum of powers in a single of its variables or by the sum of powers of this other function, typically an elementary one.

For several popular functions, we give series expansions (most Maclaurin, most Laurent, and some Puiseux). The above-mentioned equation for Taylor's series can be thought of to be the expansion of f(x+h) around the origin x. A function f(x) is frequently expanded around the point x = 0.

Using the expansion of the function-

ⁿC₁= (n!)/(n – 1)!1! = (n(n – 1)!)/(n – 1)!1!= n/1!= n.

(1 + 2x)ⁿ= ⁿC₀(1)ⁿ ⁻ ⁰(2x)⁰ + ⁿC₁(1)ⁿ ⁻ ¹(2x)¹ + ...

            = 1 + n(1)(2x) + ...

(1 + 2x)ⁿ  = 1 + 2nx + ...

Now,

The second term is 2nx.

2n= 40

n = 40/2= 20.

Thus, the value of n for the ascending powers of x is found to be 20.

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Answer:

6

Step-by-step explanation:

We know that a dozen is the value of 12 so to find half a dozen we simply need to half it!

This means that there are 6 eggs in a half dozen.

FUN FACT:

A baker's dozen is 13, one more than a regular dozen!

Hope this helps, have a lovely day!

Answer:

Step-by-step explanation:

its 60

Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called the dependent variable. The variable you are using to predict the other variable's value is called the independent variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Using linear regression on the given data the equation we got in the form of y =mx + c is y = 243x - 16.50

What is linear regression?

A variable's value can be predicted using linear regression analysis based on the value of another variable. The dependent variable is the one you want to be able to forecast. The independent variable is the one you're using to make a prediction about the value of the other variable.

To find the equation for the linear function that best fits the given data, we can use linear regression. Using a calculator or software, we can find the following:

The mean of x is 3.5 and the mean of y is 150.

The variance of x is 2.5 and the variance of y is 2203.5.

The covariance of x and y is 607.5.

Using these values, we can calculate the slope of the regression line:

m = covariance of x and y / variance of x = 607.5 / 2.5 = 243

We can also calculate the y-intercept of the regression line:

b = mean of y - m * mean of x = 150 - 243 * 3.5 = -16.5

Therefore, the equation for the linear function that best fits the given data is:

y = 243x - 16.5

Rounding both numbers to two decimal places, we get:

y = 243x - 16.50

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Answer:

54°

Step-by-step explanation:

AB = BC = CD = AD (Because all sides of a rhombus are equal)

Let's consider the triangle DBC:

BC = DC => ∠DBC = 36°

The angle DCB is equal to:

180° - 36*2 = 180° - 72° = 108°

In a parallelogram, opposite angles are equal.

Then the angle DAB = DCB = 108°

Also, we know that the diagonals of a rhombus are the bisectors of the angles from which they come.

So, the angle DAE = EAB = 108° / 2 = 54°

f(x) = (x+4)^2(x-3) has polynomial function with the following zeros: double zero at -4 simple zero at 3.

If a polynomial has a double zero at -4, it means that it can be factored as (x+4)^2.

If it also has a simple zero at 3, then the factorization must include (x-3).

Therefore, the polynomial function with these zeros is :-

f(x) = (x+4)^2(x-3)

This polynomial has a double zero at -4, because $(x+4)^2$ has a zero of order 2 at -4, and a simple zero at 3, because $(x-3)$ has a zero of order 1 at 3.

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Because the resultant is the closing side of the triangle according to the triangle law of vector addition, the resultant vector's magnitude would be 13.93 metres.

A vector quantity is what?

The vector quantities are those that include both the direction and the magnitude of the quantities.

The vector quantities include things like force, acceleration, and displacement.

Scalar quantities only have the magnitude of the quantity measured; they do not have information about the direction.

The triangle law of vector addition can be used to calculate the resultant vector.

Using the right-angled triangle's Pythagoras theorem

[tex]Base^{2} + Height^{2} = Resultant^{2}[/tex]

[tex]132 + 52 = Resultant^{2}[/tex]

Outcome 2 = 194

The outcome is 194

=13.93 m

According to the triangle law of vector addition, the resultant vector would have a magnitude of 13.93 metres since it is the triangle's closing side.

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