Define Boolean logic

please detail this as much as you can

The inverse of the function f(x) = 15x - 45 is g(x) = x + 45 / 15

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f-1 or F-1.

In this problem, f(x) = 15x - 45, we can find the inverse as;

To determine the inverse function, switch x and y and solve the resulting equation for x

If the initial function is not one-to-one, then there will be more than one inverse.

y = 15x - 45

x = 15y - 45

Let's solve for y

15y = x + 45

y = x + 45 / 15

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Considering the vertical asymptote and the intercepts, the rational function is given by:

\(r(x) = \frac{4(x - 2)}{(x + 2)(x - 4)}\)

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.

From the graph, there are vertical asymptotes at x = -2 and x = 4, hence the denominator is given by:

(x + 2)(x - 4).

The x-intercept of a function f(x) is the value of x when y = 0. For a rational function, they are the zeroes of the denominator.

For this problem, there is a x-intercept at x = 2, hence the numerator is given by:

a(x - 2).

Then the function is:

\(r(x) = \frac{a(x - 2)}{(x + 2)(x - 4)}\)

When x = 0, r(x) = 1, hence we use it to find a.

-2a/-8= 1

2a/8 = 1

2a = 8

a = 4.

Hence the function with the leading coefficient is:

\(r(x) = \frac{4(x - 2)}{(x + 2)(x - 4)}\)

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Answer:

a) At $3,300 for 600 seats, the average price per seat is 3300/600 = $5.50. The mix of tickets that results in that average can be found using an X diagram as shown below. The numbers on the right are the differences along the diagonals. When they are multiplied by 2, they add to 600. This shows that the required sales for revenue of $3,300 are

 200 adult tickets

 400 student tickets

b) When 3 student tickets are sold for each adult ticket, the average seat price is

 (3*$4.50 +7.50)/4 = $5.25

Then the shortfall in revenue is ...

 $3,300 -480*$5.25 = $780

The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".

When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.

In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.

a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.

b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.

c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.

d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.

Therefore, "time(length)" is the most suitable and appropriate name for the function.

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On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17,  10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .

What is Addition ?

Addition can be defined as the performing addition operation by using operand + between two operators.

3 + 7 = 10

2 + 9 = 11

4 + 6 =10

5 + 9 =14

12 + 5 =17

6 + 3 =9

8 + 3 =11

10 + 0 = 10

9 + 8 = 17

1 + 9 = 10

7 + 6 = 13

9 + 3 =12

6 + 8 = 14

0 + 3 = 3

3 + 6 = 9

7 + 1 = 8

4 + 2 =6

4 + 7 = 11

11 + 3 = 14

7 + 7 = 14

9 + 7 = 16

12 + 9 =21

Hence, On performing addition exercises we get 10 , 11 , 10 , 14 , 17 , 9 , 11 , 10 , 17,  10 , 13 , 12 , 14 , 3 , 9 , 8 , 6 , 11 , 14 , 14 , 16 , 21 .

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The value of m in terms of other variables of the right angle triangle is: m = √(p² - n²)

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

However, it can also be written in the form of c² = a² + b²

From the given triangle, we can write as:

p² = m² + n²

m² = p² - n²

m = √(p² - n²)

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Answer:

x =5

Step-by-step explanation:

Distribute the 7

leaves you with 14x - 28 =42

Add 42 to both sides, cancelling out the 28 on the left

left with 14x = 70

70/14 = 5

x = 5

Answer:

\(( x + 4 )^2 + ( y - 7 )^2 = 36\)

Step-by-step explanation:

Use the circle equation, \(( x - h )^2 + ( y - k )^2 = r^2\)

Plug in the center and radius:

\(( x + 4 )^2 + ( y - 7 )^2 = 6^2\)

Simplify:

\(( x + 4 )^2 + ( y - 7 )^2 = 36\)

So, the equation is \(( x + 4 )^2 + ( y - 7 )^2 = 36\)

Answer:

22 1/2

Step-by-step explanation:

Answer:

V = 27

Step-by-step explanation:

62 = −19 + 3v

Swap sides so that all variable terms are on the left-hand side.

−19 + 3v = 62

Add 19 to both sides.

3v = 62 + 19

Add 62 and 19 to get 81.

3v = 81

Divide both sides by 3.

v = 81/3

​Divide 81 by 3 to get 27.

v = 27

I hope this will help you! :)

Answer:

18

Step-by-step explanation:

6 / (1 / 3) = 6 * 3 = 18

Answer:

18

Step-by-step explanation:

I did it and got it right

Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

Maureen's pension would be $50,035.20.

What is Percentage?

To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.

First, we need to calculate the average of Maureen's three highest salaries:

Average = (107,000 + 107,800 + 108,198) / 3

Average = 322,998 / 3

Average = 107,666

Next, we need to calculate 1.56% of this average:

Percentage = 1.56% * 107,666

Percentage = 1,667.84

Finally, we multiply this percentage by the number of years worked to find the pension:

Pension = 30 * 1,667.84

Pension = 50,035.20

So, Maureen's pension would be $50,035.20.

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Answer:

a) 27 b) 5 c) 16 d) 7

Step-by-step explanation:

Step-by-step explanation:

To calculate the correlation coefficient (r) given SSxx, SSxy, and other information, we need to use the following formula:

r = √(SSxy / SSxx)

Given SSxx = 950 and SSxy = 205.2, we can substitute these values into the formula:

r = √(205.2 / 950)

Calculating the value:

r = √(0.216)

r ≈ 0.465

The correlation coefficient (r) is approximately 0.465.

Interpretation: The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the value of r = 0.465 indicates a positive linear relationship between the variables, but it's not a strong relationship. The closer the value of r is to 1 or -1, the stronger the relationship. Since r = 0.465 is relatively close to zero, it suggests a weak positive linear association between the variables being an analyzed.

hope it help you

The Pearson's correlation coefficient (r) based on given data is approximately 0.44, implying a moderate positive correlation.

The formula for calculating Pearson's correlation coefficient (r) in this case is given as: r = SSxy / sqrt(SSxx * SSyy). However, we don't have the value for SSyy directly, but we can calculate it. We know that SSyy = Σy² -(Σy)² / n. Given that Σy² is 2028 and Σy is 120 and number of samples n is 12, we can calculate SSyy as: SSyy = 2028 - (120)² / 12 = 52. Now, substitute SSxx = 950, SSxy = 205.2 and SSyy = 52 in the formula to find r: r = 205.2 / sqrt(950 * 52), giving us an r-value of approximately 0.44. This value of r suggests a moderate positive correlation between the variables in the dataset.

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Answer:

107 adults 16 children

Step-by-step explanation:

can i get brainlest

X varies directly as y , that x = 9 when y = 3,the value of x when y = 12 by  the constant of Variation , value of x is 36.

X  varies directly as y, it means that there is a constant ratio between x and y. We can express this relationship using the formula:

x = ky

where k is the constant of variation.

To find the value of k, we can use the given information that x = 9 when y = 3. Substituting these values into the formula, we have:

9 = k * 3

Solving for k, we divide both sides of the equation by 3:

k = 9/3

k = 3

Now that we have the value of k, we can find x when y = 12 by substituting it into the formula:

x = 3 * 12

x = 36

Therefore, when y = 12, the corresponding value of x is 36.

if x varies directly as y and we are given that x = 9 when y = 3, we can find the value of x when y = 12 by determining the constant of variation (k) and using the formula x = ky. In this case, the constant of variation is 3, so when y = 12, x equals 36.

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Answer:

a^x/y=1              x: 0

Step-by-step explanation: w.k.t,        a^0=1( any variable raised to 0 is 1)

                                    so, here the exponent is x/y which should have been 0 so that answer was 1.

Answer:

---------------------------------

Real distance is 4.4 miles and on the map it is 8 inches.

The scale is:

or

In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.

The given polynomial equation  can be expressed as ;

x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6

We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation

x = -8

[(-8)³ + 6(-8)² - 40(-8)]

= 192

[-512 + 384 + 320]

= 192

x = -4,

[(-4)³ + 6(-4)² - 40(-4)]

[-64 + 96 + 160 ]

= 192

x = 6

[(6)³ + 6(6)² - 40(6) ]

216 + 216 - 240

= 192

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Answer:

Step-by-step explanation:

A,B

x = –8

x = –4

(a) The mean of the data item from the group data is 161.

(b) The deviation from the mean for each data is -6,-5,1,3 and 7. respectively.

(c) The sum of the deviation is 0

Grouped data are data formed by aggregating individual observations of a variable into groups, so that a frequency distribution of these groups serves as a convenient means of summarizing or analyzing the data.

(a) To find the mean of the data, we use the formula below.

Formula:

Where:

Substitute these values into equation 1

(b) To calculate the deviation from the mean (M') for each of the data item we use the formula below.

M' = x-M

For data 115,

For data 156,

For data 162,

For data 164,

For data 168,

(c) The sum of the deviation is

Hence, the mean, the diaviation from the mean is -6,-5,1,3 and 7  and the sum of the deviation of the data is 161 and 0 respectively,

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IF([Balance] >=10000, 0.015,0.035) is the correct formula if Balance field in the query is more than 10000. Else it should be 0.015.

What does TIF stand for?

What is TIF? Tax Increment Financing, or TIF, is a geographically targeted economic development tool. It captures the increase in property taxes, and sometimes other taxes, resulting from new development, and diverts that revenue to subsidize that developmen

We know that freezing point is a coligative property hence it depends on the number of solute particles present.

Covalent substances do not break up into ions, hence they do not produce many particles in solution unlike ionic substances. Hence, ionic substances have a far higher freezing point than covalent molecules.

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Answer:

y = 10x + 3

Step-by-step explanation:

According to the quantity theory of money, changes in the money supply will lead directly to changes in the price level if velocity and real GDP are unaffected by the change in the money supply.Velocity can change over time, and changes in velocity may be caused by various factors.

For example, changes in velocity can be caused by shifts in payment practices, changes in the use of credit, changes in the availability of bank deposits or cash, or shifts in demand patterns.Changes in velocity may be related to changes in the money supply.

For example, if the money supply increases, the demand for money may increase, causing the velocity of money to decrease. Conversely, if the money supply decreases, the demand for money may decrease, causing the velocity of money to increase.

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Answer:

\(\dfrac{155}{18} \pi \textrm{ cm}\)

Step-by-step explanation:

This problem asks us to find the length of an arc ACB on the circumference of a circle with center O and a radius of 5 cm.

We first must solve for the total circumference (perimeter) of the circle. This is represented by the formula C = 2πr. Hence, the circumference of this circle is:

C = 2π(5) cm

C = 10π cm

Next, we have to find what fraction of 360º the major arc ACB is in order to deduce how much of the circle's total circumference the arc takes up.

\(\dfrac{(360 - 50)\textdegree}{360\textdegree} = \dfrac{31}{36}\)

Finally, we can multiply the amount of circumference that arc ACB takes up by the length of the whole circumference to get the length of arc ACB.

\(\textrm{Length of arc } ABC = \dfrac{31}{36} \cdot 10\pi\)

\(= \dfrac{310}{36} \pi\)

\(= \dfrac{155}{18} \pi \textrm{ cm}\)

Answer:

\(\textsf{Length of major arc $\overset{\frown}{ACB}$}: \;\; \boxed{\dfrac{155}{18}\pi\; \sf m}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $= \pi r\left(\dfrac{\theta}{180^{\circ}}\right)$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in degrees.\\\end{minipage}}\)

Angles around a point sum to 360°.  Therefore:

\(\begin{aligned}\implies m \angle BOA&=360^{\circ}-m \angle AOB\\&=360^{\circ}-50^{\circ}\\&=310^{\circ}\end{aligned}\)

Therefore, the given values are:

To find the length of the major arc ACB, substitute the given values into the arc length formula:

\(\begin{aligned}\implies \overset{\frown}{ACB}&=\pi \cdot 5 \cdot \left(\dfrac{310^{\circ}}{180^{\circ}}\right)\\\\&=5\pi \cdot \dfrac{31}{18}\\\\&=\dfrac{155}{18}\pi\; \sf m\end{aligned}\)

Answer:90

Step-by-step explanation:

Trust me bro

The degrees of rotation that will carry the regular pentagon onto itself is 72,144,216,288

In geometry, a pentagon is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°.

Given here: A regular pentagon is rotated clockwise about center P.

Now  Since you have 5 vertices, your starting vertex can land in 5 different starting places and still come up with the same figure. So if you take 360/5 you get 72 degree rotations to each consecutive vertex.

or more specifically 360/5=72

Again therefore the pentagon will coincide itself after every integral multiple of 72

Thus 72, 144,216,288 are the required angles of rotation.

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Answer:

D. Angle A corresponds to Angle D

Step-by-step explanation:

Since Triangle ABC is reflected over the x axis, Triangle DEF is just a mirrored version of it. Which means that B corresponds to E, C corresponds to F, and A corresponds to D. We can also figure this out by the sequence of letters.

ABC

DEF

They correspond to each other based on the order.

Angle ∠A corresponds to ∠D.

Option D is the correct answer.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

ΔABC is reflected over the x-axis to produce image ΔDEF.

So,

From the figure,

We see that,

AB corresponds to ED.

BC corresponds to EF.

AC corresponds to FD.

∠A corresponds to ∠D.

∠B corresponds to ∠E.

∠C corresponds to ∠F.

Thus,

∠A corresponds to ∠D.

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Answer: 4/5

Step-by-step explanation:

Answer:

The value is \(w = 6.7 \%\)

Step-by-step explanation:

Generally the productivity rate is mathematically represented as

\(P_r = K * Z\)

Here K is the ha the farmer could harvest in an hour and Z is a typical yield of corn in kg/ha

Now considering 1970

The productivity rate is

\(P_r = 0.75 *5000\)

=> \(P_r = 3750 \ kg/h \)

Now considering 1940

The productivity rate is given as \(P_R = 250 \ kg/h \)

Generally the productivity ratio is mathematically ration is mathematically represented as

\(w = \frac{P_R}{P_r} * 100\)

=> \(w =  \frac{250}{3750}  * 100\)

=> \(w = 6.7 \%\)