How do you determine if two pairs of functions are inverses?

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Let x= the average for all three classes combined. So x=85.25.

When you add two or more numbers and divide the result by the number of numbers you added together, you obtain an average.

The arithmetic mean is determined by adding a collection of numbers, dividing by their count, and obtaining the result.

average  =  total points / number of students

total points = average*number of students

Let the total number of students in  each class = a , b  and x

The total number of points the first class amassed  was   80a

The total number of points amassed by the second class was  85b

The total number of points amassed by the third class = 89c

For the first two classes we have

[ 80a + 85b ] / [ a + b] = 83

80a + 85b = 83a + 83b  

subtract  80a, 83b from both sides    

3a = 2b

a = 2/3b

For the second two classes we have

[ 85b + 89c ]  / [ b + c ]  =  87  

[  85b + 89c ]  = 87 [b + c]

85b + 89c = 87b + 87c      

subtract  85b, 87c from both sides

2c = 2b  

b  = c

For the three classes.....

Total points by all three classes /  number of class members  = the average for all three classes

[ 80a + 85b  + 89c ] /  [ a + b + c ]   =[sub for  a and c ]  

[80 (2/3)b  + 85b  + 89b]  /  [ (2/3)b  + b  + b ]  

b [ 80 (2/3)  + 85  + 89 ]  / [  b [( 2/3) + 1 + 1] ]       [cancel the b's ]

[ 80 (2/3) + 85 + 89]  [  8/3 ]

[ 160/3 + 85 + 89 ] /  [8/3] =

[ 160/3  + 255/3 + 267/3]  / [8/3]     multiply  top/bottom by 3

[160 + 255 + 267 ] / 8  =  

85.25  = average for all three classes

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Answer:

297

Step-by-step explanation:

297 ≈ 12 * √(12^2 + 4 * 11.124^2) + 12^2

Answer:

Use the distributive property to multiply 6 by (2x+1)

Answer:

Answer down below!

Step-by-step explanation:

Since they are only asking for the first step, we don't solve it

In this case, you have to remember your Distributive Property rules.

You multiply:

6 * 2x

6 * 1

Then, rewrite the equation

12x + 6 = 18

Answer:

C is closest to the actual result, $1126.03.

Step-by-step explanation:

Use the Compound Amount formula:  A = P(1 + r/n)^(nt), where:

 P is the original principal; r is the interest rate as a decimal fraction; n is the number of compounding periods per year, and t is the number of years.

Then we have A = $1000(1 + 0.04/4)^(4*3), or

                            = $1000(1.01)^12  =  $1126.03

Data from a voluntary response sample, which is not representative of the population, are included in the histogram.

A histogram is a bar graph-like data visualization that groups various class levels into columns along the horizontal x-axis. Each column's data count or percentage of occurrences are shown on the vertical y-axis. Data distribution patterns can be seen visually using columns.

A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.

Histograms show numerical or quantitative data, whereas bar charts show categorical factors.

Therefore, the correct answer is option b) The histogram includes data from a voluntary response sample which is not representative of the population.

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The vertex of the function g(x) = 3\(x^{2}\) - 12x + 7 is at (2, -5).

The vertex of a parabola in the form of y = a\(x^{2}\) + bx + c can be found using the formula x = -b/2a for the x-coordinate of the vertex and then substituting this value into the equation to find the y-coordinate.

For the function g(x) = 3\(x^{2}\) - 12x + 7, we can see that a = 3 and b = -12. We can use the formula to find the x-coordinate of the vertex:

x = -b/2a = -(-12)/(2*3) = 2

So the x-coordinate of the vertex is 2. To find the y-coordinate, we can substitute x = 2 into the equation:

g(2) = 3 \((2)^{2}\)- 12(2) + 7 = -5

Therefore, the vertex of the function g(x) = 3\(x^{2}\) - 12x + 7 is at (2, -5).

So the correct answer is (c) (2, −5).

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1) The Combination, Probability is (5C2 x 12C3) / 30C5

2) The Combination, Probability is (C(4,7) x C(2,5)) / C(6,12)

3) The Combination, Probability is (C(3,5) x C(3,5)) / C(6,10)

4) The Permutation, Probability is 1 / P(50,3)

1) This situation is describing a combination because the order in which the students are chosen does not matter. The probability of randomly choosing 2 blonde girls and 3 dark-haired boys can be found as follows:

Number of ways to choose 2 blonde girls out of 5 = C(5, 2) = 10

Number of ways to choose 3 dark-haired boys out of 12 = C(12, 3) = 220

Total number of ways to choose 5 students out of 30 = C(30, 5) = 142,506

Probability = (10 x 220) / 142,506 = 0.0154

Therefore, the probability of randomly choosing 2 blonde girls and 3 dark-haired boys if 5 students are randomly chosen to be class representatives is 0.0154.

2) This situation is describing a permutation because the order in which the smartphones are sold matters. The probability that exactly four of the first six sold have cracked screens can be found as follows:

Number of ways to choose 4 cracked screens out of 7 = C(7, 4) = 35

Number of ways to choose 2 intact screens out of 5 = C(5, 2) = 10

Number of ways to arrange the 6 chosen smartphones = P(6, 6) = 720

Probability = (35 x 10 x P(6, 6-4)) / P(12, 6) = 0.078

Therefore, the probability that exactly four of the first six sold have cracked screens is 0.078.

3) This situation is describing a combination because the order in which the songs are listened to does not matter. The probability that exactly three country songs are listened to can be found as follows:

Number of ways to choose 3 country songs out of 5 = C(5, 3) = 10

Number of ways to choose 3 pop songs out of 5 = C(5, 3) = 10

Total number of ways to choose 6 songs out of 10 = C(10, 6) = 210

Probability = (10 x 10) / 210 = 0.476

Therefore, the probability that exactly three country songs are listened to is 0.476.

4) This situation is describing a permutation because the order in which the hurdlers finish matters. The probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants can be found as:

Probability = 1 / P(50, 3) = 1 / 117,600

Therefore, the probability of randomly choosing the correct finishing order of the first, second, and third place for the hurdlers out of 50 contestants is approximately 0.0000085.

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Good evening,

Answer: B

Step-by-step explanation:

-1/2(2+6x(-1)) = 3(3-(-1))-10

-1/2(2+-6) = 3(3+1))-10

-1/2(-4) = 3x4-10

2=3x4-10

2=12-10

2=2

Answer:

160 trust me

Step-by-step explanation:

we multiply the length by the width which is the formula of finding rectangular areas'  

The algebraic solutions to the system of equations are given as follows:

\((3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)\)

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Replacing the second equation in the first:

x² + (2x - 2)² = 25

x² + 4x² - 8x + 4 = 25

5x² - 8x - 21 = 0.

Which is a quadratic equation with coefficients a = 5, b = -8, c = -21, then:

\(\Delta = (-8)^2 - 4(5)(-21) = 484\)

\(x_1 = \frac{-(-8) + \sqrt{484}}{2(5)} = 3\)

\(x_2 = \frac{-(-8) - \sqrt{484}}{2(5)} = -\frac{7}{5}\)

Then, the solutions for y are:

Thus, the solutions are:

\((3,4), \left(-\frac{7}{5}, -\frac{24}{5}\right)\)

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Answer:

300 new employees

Step-by-step explanation:

1:3

x + 3x = 1,200

4x = 1200

x = 300

Answer:

Step-by-step explanation:

2.  30 minutes

3. 985 years

4. 75 degrees

5. -5 degrees

6. 30340 feet

7. 49 degrees

The probability that the first failed inspection occurs on Fatima's 5th inspection i.e P(c = 5) is 0.05..

In probability and statistics,the geometric distribution defines the probability of the first success occurring after k trials. The probability of success is p

P r ( X = k ) = ( 1 − p )⁽ᵏ⁻¹⁾ p.

We have given that,

An emissions inspections on cars is conducted by Fatima.

Probability that car fail the inspection, p = 6% = 0.06

let c denoted the number of cars that are inspected until one car fail to inspection.

The random variable c here. Here c follow geometric probability distribution with probability of success (0.06).

Plugging all known values in above formula we get, p(c= 5) = (1-0.06)⁴ × 0.06

= (0.94)⁴ (0.06)

=0.0468449376~ 0.05

so, the answer is 0.05

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Complete question:

Fatima conducts emissions inspections on cars. She finds that 6%, percent of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.

Required:

Find the probability that the first failed inspection occurs on Fatima's 5th inspection

Given the `simplevector.h` definition, the file needs to be modified to implement the template. The updated file with modifications is given below: Updated simplevector.h file templateclass SimpleVector {private: T *aptr; int arraySize; void subError().

The `class` keyword and `template` keyword are used to declare and define a template class `SimpleVector`. The template parameter type is `T`.The implementation is defined inside the class declaration itself. Hence, `SimpleVector::` is prefixed to the function definitions.The member functions include `SimpleVector()` as a constructor, `SimpleVector(int)` as a constructor.

`SimpleVector(const SimpleVector&)` as a copy constructor, `~SimpleVector()` as a destructor, `size()` function to return the size of the array, `operator[]` function to perform subscripting, `print()` function to print the contents of the array, and a private `subError()` function to throw an exception when an index out of bounds error occurs.

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Answer:

2.5

Step-by-step explanation:

Taking eguation i

4x+y=13

x= 13-y/4

Taking equation ii

x-y = 2

Substituting the value of x in eq i from ii

x- y =2

13-y/4- y=2

13-y-y=2×4

13-2y =8

-2y=8-13

y=-5/-2

Therefore y=2.5

Answer:

156 jackfruits

Step-by-step explanation:

Let there are 6x jackfruit in baseket P, 2x in basket Q and 5x in basket R.

The total number of jackfruit  in basket P is 48 more than the number of  jackfruit in basket Q. ATQ,

6x = 48 + 2x

Solving for x.

6x - 2x = 48

4x = 48

x = 12

Jackfruits in basket P = 6x = 6(12) = 72

Jackfruits in basket Q = 2x = 2(12) = 24

Jackfruits in basket R = 5x = 5(12) = 60

Total no of jackfruits = 72 + 24 + 60

= 156

So, there are 156 jackfruits in the three baskets.

Jake is considering his career options or career aspirations.

Jake is at a stage in his life where he is contemplating his future and the different career paths he could pursue. He has identified three potential professions: teacher, lawyer, and singer. Jake's talent and intelligence indicate that he has the potential to excel in any of these fields. His vow not to be satisfied in a dead-end job suggests that he is motivated and ambitious, seeking a fulfilling and successful career.

At this point, Jake is likely evaluating various factors such as his interest, skills, personal values, and long-term goals to determine which career path aligns best with his aspirations. He may be considering the level of satisfaction, growth opportunities, financial stability, and societal impact associated with each profession. Exploring these factors will help Jake make an informed decision about his future career and choose a path that will provide him with the fulfillment and success he desires.

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Answer:

RM3,500

Step-by-step explanation:

Salary=RM375 per week

5% commission per week

If she target a minimum of RM 550.

Let x=minimum Sales

RM550=RM375 + 5% of x

RM550=RM375 + 0.05x

RM550 - RM375=0.05x

RM175=0.05x

Divide both sides by 0.05

RM175/0.05=0.05x/0.05

RM3,500=x

For Azila to earn a minimum of RM550 in a week, her salary will be RM375 plus 5% commission on the sales of RM3,500 value of product.

Check:

5% of RM3,500

=0.05*3,500

=RM175

Plus

Salary of RM375

RM175 + RM375=RM550

Answer:

1 = 51  

2=18    

3=123

4=39

Step-by-step explanation:

Answer:

No it's not a function

Step-by-step explanation:

Every point line up evenly when it's vertical. just take your pencil and put it on the circle vertically and you will see that the points will line up

So it's not. function

pls mark brainiest because i didn't waste your time lol

Answer:

no

Step-by-step explanation:

the answer is no because each value in the domain is associated with exactly one point in the codomain, but a line passing though the circle generally intersects the circle at two points

Answer: 0.8? i'm not sure lol check explaination

Step-by-step explanation:
slope formula: y2-y1/x2-x1
5-1/3-(-2)=4/5=0.8

The diameter of the ball is approximately 16.67 meters.

To find the diameter of the ball, we can use the relationship between the distance traveled and the number of revolutions.

The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter.

Given that the ball rolls a distance of 3.5 meters and makes 15.0 revolutions, we can calculate the circumference of the path it travels:

C = 3.5 m * 15.0 = 52.5 m

Since each revolution covers the circumference of the ball, we have C = πd. Plugging in the known value for C, we can solve for the diameter (d):

52.5 m = πd

Dividing both sides of the equation by π, we get:

d = 52.5 m / π

Using a calculator, we can evaluate this expression:

d ≈ 16.67 meters

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Answer:

your answer is 2.02

6(x-2) > 15

6x - 12 > 15

6x > 27

x > 27/6

Hope it helps!

Answer:

x>4.5

Step-by-step explanation:

6(x-2)>15

We do this is as if it were an equation:

6(x-2)>15

Expand the brackets:

6x-12>15

Add 12 to both sides:

6x-12+12>15+12

Simplify:

6x>37

Now we divide both sides by 6:

6x÷6>37÷6

x > 4.5

If we put 5 into the original equation as it is more than 4.5, we get:

6(5-2)>15

We can simplify the brackets or expand first:

Simplifying the brackets first:

6(3)>15

18>15 ✅

Expanding first:

6(5-2)>15

30-12>15

18>15 ✅

Answer:

a line of symmetry is a line divide an object in to two equal parts. answer is A

Answer:

Root( c square -9)

Step-by-step explanation:

The answer u have is the answer for a^2

Answer:

Root (c square -9)

Step-by-step explanation:

Using the elimination method, the solution to the system of linear equations is: x = 4.5 and y = -5.

Solving a system of linear equations by elimination involves eliminating one of the variables, then solve to find the other variable.

Given the equations:

6x + 5y = 2 --> eqn. 1

4x + 2y = 8 --> eqn. 2

Multiply eqn. 1 by 2 and eqn. 2 by 5:

12x + 10y = 4 --> eqn. 3

20x + 10y = 40 --> eqn. 4

Subtract

-8x = -36

x = 4.5

Substitute x = 4.5 into eqn. 2

4(4.5) + 2y = 8

18 + 2y = 8

2y = 8 - 18

2y = -10

y = -5

The solution is: x = 4.5 and y = -5.

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Answer:

Yes, if it is a square or rectangle.

Step-by-step explanation:

Answer:  

31 is prime. and it’s prime factorization is just 31....

Step-by-step explanation: