Using composition, determine if the functions are inverses: f(x)=(2)/(3)x-8 and g(x)=(3)/(2)x+12

Answer:

5 2/3

Step-by-step explanation:

all you need is to add because the fraction is the same.

a) The probability of selecting two different colors is obtained as 9/10.

b) The probability of not selecting a yellow marble is obtained as 3/20.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

a) To find the probability of selecting two different colors, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

So the probability of selecting two different colors can be found by calculating the probability of selecting two marbles of the same color and subtracting that from 1.

The probability of selecting two marbles of the same color from the first bag is (2/5) x (1/4) = 1/10, since there are 2 red marbles out of 5 total marbles in the bag, and the probability of selecting a second red marble is 1/4.

The probability of selecting two marbles of the same color from the second bag is 0, since there is only one marble of each color.

So the probability of selecting two different colors is -

1 - (1/10 + 0) = 9/10

Therefore, the probability value is 9/10.

b) To find the probability of not selecting a yellow marble, we can again use the complement rule.

The probability of not selecting a yellow marble is equal to 1 minus the probability of selecting a yellow marble from either bag.

The probability of selecting a yellow marble from the first bag is 1/5, since there is one yellow marble out of 5 total marbles in the bag.

The probability of selecting a yellow marble from the second bag is also 1/4, since there is one yellow marble out of 4 total marbles in the bag.

So the probability of not selecting a yellow marble is -

1 - (1/5 + 1/4) = 3/20

Therefore, the probability value is 3/20.

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Hence, the sum of the fixed expenses ($75 + $25 = $100) and the expressions variable charges ($15 per person) would equal the total cost for catering.

Mathematically speaking, you can multiply, divide, add, or subtract. This is how an expression is constructed: Math operation, expression, and numerical value Functions, parameters, and numbers make up a mathematical expression. It is feasible to use opposing words and phrases. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical operation between them. As an instance, the phrase 4m + 5 is made up of the phrases 4m and 5, as well as the variable m from the provided equation, which are all separated by the mathematical symbol +.

Finding the slope of the line will allow you to compute the rate of change for Smokey Joe's catering. The slope in this instance is $15, which indicates that the price will rise by $15 for each extra person served. The variable cost that Smokey Joe's incurs every person served is represented by this rate of change.

If Smokey Joe's charges a $25 delivery fee, this will be an extra set expense that they will pay no matter how many customers they serve. Hence, the sum of the fixed expenses ($75 + $25 = $100) and the variable charges ($15 per person) would equal the total cost for catering.

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The set is linearly independent.

Yes, the given set is linearly independent. To prove this, we can use the determinant method. To calculate the determinant, arrange the columns of the array in a 3x3 matrix. This gives us the following matrix:

$$\begin{bmatrix}1 & -1 & -2\\-1 & 0 & 1\\0 & 1 & -1\end{bmatrix}$$

The determinant of this matrix is 1, which is not equal to 0. This shows that the given set is linearly independent.

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In the congruent geometry ,  length of EH is 14 meters .

What is congruent geometry?

In a congruent geometry, the shapes that are so identical. can be superimposed on themselves.

Two objects that are identical in terms of their dimensions and shape are said to be congruent in geometry. Further, two shapes are said to be congruent to one another if they can be turned, flipped, or moved in the same direction.

As a result, two congruent figures that have been drawn on a piece of paper can be cut out and positioned over one another to perfectly match.

Here, The figure shows the design and its photocopy. The ratio of BC: FG is 1:2.

Since the two figures are congruent

BC/FG= AD/EH

1/2 = 7/EH    (from figure AD = 7 )

EH = 2*7

EH = 14 m

Thus, the required length of EH is 14 meters.

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The simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

The given expression is ((-4m4n-4)3) / ((mn)2).

To simplify the expression ((-4[tex]m^{(4)}[/tex] ) (([tex]n^{(-4)[/tex])[tex])^{(3))}[/tex]/ ((mn[tex])^{(2)}[/tex]), we will use the power rules of exponents.

First, we will apply the power rule to the numerator:

((-4)[tex])^{3}[/tex])([tex]m^{(4*3)}[/tex])([tex]n^{(4*3)}[/tex]) = (-64)([tex]m^{(12)}[/tex])([tex]n^{(12)}[/tex])

Next, we will apply the power rule to the denominator:

([tex]m^{(2)}[/tex])([tex]n^{(2)[/tex]) = [tex]m^{(2)}[/tex][tex]n^{(2)[/tex]

Now we can simplify the expression by canceling out the common terms in the numerator and denominator:

((-64)([tex]m^{12}[/tex])([tex]n^{12}[/tex])/([tex]m^{(2)}[/tex][tex]n^{(2)}[/tex])

= (-64)([tex]m^{12-2}[/tex])([tex]n^{12-2}[/tex])

= (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex])

Finally, we can write the final expression in simplified form:

(-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

Therefore, the simplified expression is (-64[tex]m^{(10)}[/tex])/([tex]n^{(14)}[/tex]).

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Therefore , the solution of the given problem of unitary comes out to be child can purchase 39 roller coaster excursions with 273 ride tickets as a result.

To finish the job using the unitary technique, the expression from this nano section should be multiplied by two. In essence, when a wanted object is present, both the characterised by either a group and the pigment sections are omitted from the unit method. A variable fee of Inr ($1.01), for instance, would be paid for 40 pens. It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait.

Here,

The boy can purchase the following amount of roller coaster rides:

39 trips using 273 ride tickets at 7 tickets each (rounded down to the nearest whole number)

The child can purchase 39 roller coaster excursions with 273 ride tickets as a result.

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The equatiοn οf the least squares regressiοn line which mοst clοsely matches the data set is y = 3.5 x + 43.8

Tο sοlve fοr the data set, lets lοοk at the table,

X            1190         1992          1994         1996           1998

Y             45             51               57            61               75

Let the equatiοn that shοws the abοve data be

y = b + a x ---------(1)

Where, a = Σy Σx² - Σx Σxy

And, b = (Σxy - Σx Σy) / n Σx² -(Σx)²

By the abοve table,

Σx=20

Σxy = 1296

Σx² = 120

Σy=289

By substituting these values in the abοve value οf a and b,

We get b = 43.8 and a = 3.5

Substitute this value in equatiοn (1)

We get, the equatiοn that shοws the given data is,

y = 3.5 x + 43.8

Therefοre, οptiοn 3 is cοrrect.

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The eigenvalues of matrix A are 11 and -1, and the corresponding eigenvectors are [1, -3, 0] and [1, 0, 0].

Eigenvalues and eigenvectors are important concepts in linear algebra. The eigenvalues of a matrix are the values that satisfy the equation Ax = λx, where A is the matrix, x is the eigenvector, and λ is the eigenvalue. The eigenvectors are the corresponding vectors that satisfy this equation.

To find the eigenvalues and eigenvectors of the matrix A=​2−15​013​00−3​​, we need to follow these steps:

1. Find the characteristic equation of the matrix A by subtracting λ from the diagonal elements and taking the determinant:
|A-λI| = |2-λ -1 5| = (2-λ)(-3-λ) - (-1)(5) = 0
|0 1 3|
|0 0 -3-λ|

2. Solve the characteristic equation to find the eigenvalues:
(2-λ)(-3-λ) - (-1)(5) = 0
-6 + 3λ + 2λ - λ² + 5 = 0
λ² - 5λ - 11 = 0
(λ - 11)(λ + 1) = 0
The eigenvalues are λ = 11 and λ = -1.

3. Find the eigenvectors by substituting the eigenvalues back into the equation Ax = λx and solving for x:
For λ = 11:
(2-11)x₁ - x₂ + 5x₃ = 0
x₂ + 3x₃ = 0
-3x₃ = 0
x = [1, -3, 0]
For λ = -1:
(2+1)x₁ - x₂ + 5x₃ = 0
x₂ + 3x₃ = 0
3x₃ = 0
x = [1, 0, 0]
The eigenvectors are x = [1, -3, 0] and x = [1, 0, 0].

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(a) The height of the ball when it leaves the child's hand is 3 feet.

(b) The maximum height of the ball is 19 feet.

(c) The ball will strike the ground approximately 33.44 feet from the child.

(a) This is because when x = 0 (the point at which the ball is thrown), the equation simplifies to y = 3.

(b) The maximum height of the ball can be found by finding the vertex of the parabola. The x-coordinate of the vertex is -b/2a, where a = -1/16 and b = 2. So, x = -2/(-1/8) = 16. Plugging this value back into the equation gives us the maximum height: y = -1/16(16)² + 2(16) + 3 = 19 feet.

(c) The ball strikes the ground when y = 0. Setting the equation equal to 0 and solving for x gives us:

0 = -1/16 x² + 2x + 3

Multiplying both sides by 16 to eliminate the fraction gives us:

0 = -x² + 32x + 48 = x² - 32x - 48

Using the quadratic formula, we find that x = (32 ± 8√19)/2 or x ≈ 33.44 and x ≈ -1.44

Taking the positive value, the distance from the child to where the ball strikes the ground is approximately 33.44 feet.

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Answer:

right one is correct explanation

f(x) can be factored into f(x) = 2(x + 5)(x + 3/2)(x - 3)(x - 5/2).

To find the real zeroes of f(x) = 2x^(4) + 17x^(3) + 35x^(2) - 9x - 45 using synthetic division, the Rational Root Theorem, and the Remainder Theorem, we need to follow these steps:

1. Using the Rational Root Theorem, we can find the possible rational roots of f(x) by taking the factors of the constant term (-45) and dividing them by the factors of the leading coefficient (2). The possible rational roots are:

±1, ±3, ±5, ±9, ±15, ±45, ±1/2, ±3/2, ±5/2, ±9/2, ±15/2, and ±45/2.

2. Next, we will use synthetic division to test these possible roots and find the real zeroes of f(x). We will start with the smallest possible root, -45/2, and divide f(x) by (x + 45/2) using synthetic division. The result is a polynomial of one degree less than f(x).

3. We will then use the Remainder Theorem to check if the remainder of the synthetic division is 0. If the remainder is 0, then -45/2 is a real zero of f(x) and we can use the Factor Theorem to factor f(x) into (x + 45/2)(2x^(3) - 8x^(2) - 80x + 90).

4. We will repeat steps 2 and 3 with the remaining possible rational roots until we find all the real zeroes of f(x).

5. Once we have found all the real zeroes of f(x), we can use the Factor Theorem to factor f(x) into the product of linear factors and a constant. The real zeroes of f(x) are -5, -3/2, 3, and 5/2.

Therefore, f(x) can be factored into f(x) = 2(x + 5)(x + 3/2)(x - 3)(x - 5/2).

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Answer:

You are 78 years old.

Answer:

Naw bro you're 0

Step-by-step explanation:

We fοund the inequality tο be  14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.

In mathematics, inequalities specify the cοnnectiοn between twο nοn-equal numbers. Equal dοes nοt imply inequality. Typically, we use the "nοt equal sign" tο indicate that twο values are nοt equal. Hοwever several inequalities are utilised tο cοmpare the numbers, whether it is less than οr higher than. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the expressiοn οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa. Literal inequalities are relatiοnships between twο algebraic expressiοns that are expressed using inequality symbοls.

Given,

 The gallοns οf fuel that the car hοlds = 14 gallοns

Amοunt οf fuel used each day = 0.6 gallοns

When the remaining fuel is 1.5 gallοns οr less, warning lights cοme οn.

We can write an inequality fοr this situatiοn.

If x is the number οf days the car is used, then the warning lights cοme οn when,

 14 - 0.6x ≤ 1.5

This is the inequality expressiοn.

Sοlving,

12.5 ≤ 0.6x

x ≥ 12.5/0.6

x ≥ 20.8

Therefοre we fοund the inequality tο be 14 -0.6x ≤ 1.5 and sοlving this we fοund that the warning lights cοme οn after using fοr apprοximately 21 days.

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Answer:

1 < x < 15

Step-by-step explanation:

To find the range of values for the third side, you must subtract and add the other known sides. The lower limit for the range of the third side will be 8 - 7, which equals 1. The upper limit for the range of the third side will be 8 + 7, which equals 15

Answer:

1<x<15

Step-by-step explanation:

Triangle inequalities state that the sum of two sides of any triangle must be less than the other. This is true for all three sides of the triangle.

In this case, we know two sides. Let us set a variable for the third, as x.

So the sum of 8 and 7 has to be bigger than x:

8+7>x

15>x

8 and x have to be greater than 7:

8 +x >7

x>-1

And 7 and x have to be greater than 8:

7 + x>8

x>1

Looking at the inequalities between x, we must choose the most inclusive ones. x>-1, but 1 is within that, so we can go with x>1. x<15 is a statement that cannot change because it is the only end value given. Therefore, the answer is 1<x<15

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Answer: See attached for the graph. There is an undefined slope and no y-intercept.

Step-by-step explanation:

      See attached for a graph. Since this is only greater than, (>) we will use a dashed line. Then we will shade everything greater than -4.

      The slope of this graph is undefined because this line is straight up and down. If we try to write it as an equation, you end up dividing by zero (which ends up undefined)

      Lastly, there is no y-intercept. Since this line does not cross the y-axis, there is no point of intersection.

The slope is 3. After 1 second, the car's distance increases by 7 feet.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, we have the following equation that represents the relationship between distance and time;

y = 3x + 4

At x = 1 second, the distance is given by;

y = 3(1) + 4

y = 3 + 4

y = 7 feet.

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Answer:

A megabyte is 1,000,000 bytes

A gigabyte is 1,000,000,000 bytes

A terabyte is 1,000,000,000,000 bytes

A kilobyte is 1,000 bytes

A byte has 8 bits

This is the appropriate set notation for the set J, which includes all integers between -5 and -3.

The set J can be rewritten by listing its elements in the appropriate set notation. Since the set J contains all integers between -5 and -3, we can list the elements as follows:

An integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers.

J = {-5, -4}

In set notation, this can be written as:

J = {x | x is an integer and -5 <= x < -3}

Therefore, the set J can be rewritten as:

J = {-5, -4}

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The inequality for the statement "5 is greater than or equal to a" is 5 ≥ a.

To write an inequality for the statement "5 is greater than or equal to a," we can use the greater than or equal to symbol (≥) to represent the relationship between 5 and a. The inequality would be written as:
5 ≥ a
This inequality can also be written as a ≤ 5, which means that a is less than or equal to 5. Both of these inequalities represent the same relationship between 5 and a, and either one can be used to represent the statement "5 is greater than or equal to a."

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

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The statement "If the system of a linear equation has the unique solution, then the system is inconsistent." is False since a single solution is an indication that the equations intersect at a specific point, making it consistent.

A system of linear equations is a set of two or more linear equations that contain two or more variables. A solution to the system of linear equations is a set of values for the variables that satisfies all the equations in the system.

The system of linear equations having a single solution is a consistent system since a single solution is an indication that the equations intersect at a specific point. This contradicts the notion that the system is inconsistent. An inconsistent system is one that has no solutions.

Thus, if a system of linear equations has a unique solution, it must be consistent.

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Answer:

36

Step-by-step explanation:

do x to the second power then multiply 4 to get your answer

We have shown that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗 as required.

The given statement is that F and G are two cumulative distribution functions on the real line, and they have no common points of discontinuity in the interval (a, b). We need to show that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗

First, we can use the fact that F and G are cumulative distribution functions to write the integral of G(x)dF(x) as the difference of the product of F and G at the endpoints of the interval:

∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)〗

Similarly, we can write the integral of F(x)dG(x) as the difference of the product of F and G at the endpoints of the interval:

∫_((a,b])▒〖F(x)dG(x)=F(b)G(b)-F(a)G(a)〗

Subtracting the second equation from the first gives us:

∫_((a,b])▒〖G(x)dF(x)-∫_((a,b])▒〖F(x)dG(x)=F(b)G(b)-F(a)G(a)-F(b)G(b)+F(a)G(a)〗

Simplifying the right-hand side of the equation gives us:

∫_((a,b])▒〖G(x)dF(x)-∫_((a,b])▒〖F(x)dG(x)=0〗

Therefore, we have shown that ∫_((a,b])▒〖G(x)dF(x)=F(b)G(b)-F(a)G(a)-∫_((a,b])▒〖F(x)dG(x)〗〗 as required.

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From the given information provided, A is crest, B is wavelength, C is  trough, D is amplitude, E is equilibrium line in the transverse wave.

Amplitude: The maximum displacement of wave from its equilibrium position. In other words, it is the height of the wave measured from the midpoint (or equilibrium position) to the crest or trough.

Wavelength: The distance between two consecutive crests or troughs of a wave. It is usually denoted by Greek letter lambda (λ) and measured in meters.

Crest: The highest point or peak of a wave. It is the point on the wave with maximum positive displacement from the equilibrium position.

Trough: The lowest point of a wave. It is the point on the wave with maximum negative displacement from the equilibrium position.

Equilibrium: The position where there is no net force acting on an object. In the context of waves, the equilibrium position is the position where there is no displacement of the medium through which the wave is travelling.

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Answer:

$2.48

Step-by-step explanation:

50 coins in all

16% of 50 is 8. (50 x 0.16 = 8)

That means we have 14 Nickels

34% of 50 is 17. (50 x 0.34 = 17)

Multiplying each number by their value (i.e. 14 x 5 for Nickels)

We get 248. We can assume we don't have 248 dollars, and more likely have $2.48 instead.

Answer: y = -2x + 2 3/7

Step-by-step explanation:

The slope-intercept form is y = mx + b

Start:

14x + 7y = 17

Subtract 14 from each side to get y alone:

7y = -14x + 17

Divide by 7 on each side:

y = -2x + 2 3/7

Hope this helps!

The figure represented here is a square pyramid.

With a square base and fοur triangular sides that are cοnnected at a vertex, a square pyramid is a three-dimensiοnal geοmetric οbject. It has a pentahedrοn shape with five faces.

Fοur triangles are jοined at each vertex tο a square fοundatiοn tο fοrm a square pyramid. It has a square fοundatiοn, and triangles with a shared vertex make up its side faces.

We can get the squared pyramidal figure by fοlding the triangles οf equal size frοm all the sides.

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The two integer values of a for which the quadratic equation x² + ax + 8a = 0 have integer solutions are

A quadratic equation is an polynomial in which the highest power of the variable is 2.

Since we have the equation x² + ax + 8a = 0, we desire to find how many integer values of a that will make the equation have integer solution.

To do that, we use the discriminant of a quadratic equation

D = b² - 4ac where

Now, for a quadratic equation to have real solutions D ≥ 0

So, b² - 4ac ≥ 0

Now from the equation we have that

So, substituting the values of the variables into D, we have that

D = b² - 4ac

a² - 4(1)(8a) ≥ 0

a² - 32a ≥ 0

For integer values of a

a² - 32a = 0

a(a - 32) = 0

a = 0 or a - 32 = 0

a = 0 or a = 32

So, we have two integer values of a which are

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a. The average velocity between 1s and 5s is -30 m/s.
b. The average velocity between 5s and 9s is -70 m/s
c. The velocity at -5 is -50 m/s.

A. The average velocity between 1 s and 5 s can be calculated by finding the displacement divided by the time interval. The displacement is the difference between the final and initial positions, which can be found by plugging in the values of t into the equation s(t) = 500 - 5t^2.
So, s(1) = 500 - 5(1)^2 = 495 m and s(5) = 500 - 5(5)^2 = 375 m.

The displacement is 375 - 495 = -120 m. The time interval is 5 - 1 = 4 s.

Therefore, the average velocity is -120 m / 4 s = -30 m/s.

B. The average velocity between 5 s and 9 s can be calculated in the same way. s(5) = 375 m and s(9) = 500 - 5(9)^2 = 95 m.

The displacement is 95 - 375 = -280 m. The time interval is 9 - 5 = 4 s.

Therefore, the average velocity is -280 m / 4 s = -70 m/s.

C. The velocity at t = 5 can be found by taking the derivative of the position function s(t) = 500 - 5t^2.

The derivative is s'(t) = -10t. Plugging in t = 5 gives s'(5) = -10(5) = -50 m/s.

So the velocity at t = 5 is -50 m/s.

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