find the inverse of each function f(x) = x-3/2

This question is about to determine the conditional statement,  proposition and either that is true or false.

The explanation of each part in this question is given below:

a) The given proposition can be written as the conjunction of two conditional statements as follows:

If a = 2 (mod 8), then [tex](a^2 + 4a) = 4 (mod 8)[/tex].

If [tex](a^2 + 4a) = 4 (mod 8)[/tex], then a = 2 (mod 8).

b) To prove the first conditional statement, assume a = 2 (mod 8). Then, there exists an integer k such that a = 8k + 2. Substituting this value of a into [tex](a^2 + 4a)[/tex], we get:

[tex]a^2 + 4a = (8k + 2)^2 + 4(8k + 2) = 64k^2 + 36k + 8[/tex]

Reducing this expression modulo 8, we get:

a^2 + 4a ≡ 64k^2 + 36k + 8 ≡ 0 + 4k + 0 ≡ 4 (mod 8)

Therefore, we have shown that if a = 2 (mod 8), then (a^2 + 4a) = 4 (mod 8).

To prove the second conditional statement, assume (a^2 + 4a) = 4 (mod 8). Then, there exists an integer k such that (a^2 + 4a) = 8k + 4. Substituting this value of (a^2 + 4a) into the equation a^2 + 4a - 8k = 0, we can use the quadratic formula to solve for a:

a = (-4 ± √(16 + 32k))/2 = -2 ± √(4 + 8k)

Since a is an integer, it follows that √(4 + 8k) must be an integer as well. This implies that 4 + 8k is a perfect square. The only perfect squares that are congruent to 4 (mod 8) are those of the form 8m + 4 for some integer m. Therefore, we have:

4 + 8k = 8m + 4

k = m

Substituting k = m back into the expression for a, we get:

a = -2 + √(4 + 8k) = -2 + √(8m + 4) = -2 + 2√(2m + 1)

Since a is an integer, it follows that √(2m + 1) must be an integer as well. This implies that 2m + 1 is a perfect square. The only perfect squares that are congruent to 1 (mod 8) are those of the form 8n + 1 for some integer n. Therefore, we have:

2m + 1 = 8n + 1

m = 4n

Substituting m = 4n back into the expression for a, we get:

a = -2 + 2√(2m + 1) = -2 + 2√(8n + 1) = 2(√(2n + 1) - 1)

Therefore, we have shown that if (a^2 + 4a) = 4 (mod 8), then a = 2 (mod 8).

Since both conditional statements have been proven, the given proposition is true.

(c) The given proposition is true, as shown in the proofs of the two conditional statements in part (b).

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A: The correct statement is c. Statistics are used to estimate parameters.

Statistics is the science of collecting and analyzing data to gain insight into a population of interest. It involves the collection, organization, analysis, interpretation, and presentation of data. The goal of using statistics is to draw conclusions about a population of interest and to estimate parameters of the population.

A parameter is a numerical value that is used to describe a population. For example, the mean of a population is a parameter. Statistics are used to estimate parameters of a population from a sample of the population. This process is called estimation. A statistic is a numerical value that is used to describe a sample.

For example, the sample mean is a statistic that is used to estimate the population mean. Estimation is done using the formula for a sample statistic, which is given by:

Estimate= (Statistic) / (Sample Size)

Here, the statistic is the sample mean, and the sample size is the number of observations in the sample. For example, if the sample mean is 10 and the sample size is 5, then the estimate of the population mean is 2 (10/5).

Statistics can also be used to construct confidence intervals to describe population parameters, such as means and proportions. A confidence interval is an interval of values around a sample statistic, such as a mean or a proportion, that is expected to contain the population parameter with a certain level of confidence.

In conclusion, statistics are used to estimate parameters of a population from a sample of the population. Estimation is done using the formula for a sample statistic, and confidence intervals can be used to describe population parameters.

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one possible explanation for why there are two different ways of adding up the symbols on the tablet is given below.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The ancient Egyptian number system was based on hieroglyphs, and it used a decimal system with hieroglyphs representing the powers of 10. However, without seeing the specific symbols on the tablet, it is difficult to provide an accurate answer.

Assuming that the tablet is using a basic arithmetic operation such as addition, and each symbol represents a different number,

it is possible that there are two different ways to add up the numbers represented by the symbols on the tablet.

One way to approach this problem is to try to find two different sets of numbers that when added, produce the same result.

For example, if the symbols represent the numbers 2, 3, and 5, then one way to add them up would be:

2 + 3 + 5 = 10

Another way to add them up would be:

3 + 7 = 10

In this case, the symbol for 2 would represent the number 7, and the symbol for 5 would represent the number 3. This would be one possible explanation for why there are two different ways of adding up the symbols on the tablet.

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sorry but without seeing the actual tablet then we cant work it out to get a correct answer

The percentage scored by Curry is 39.3% oby halftime.

To find the percentage of his team's points that Curry scored, we can use the following formula:

percentage = (part / whole) x 100

Where

Part = 22 points

Whole = 56 points

Substitute the known values in the above equation, so, we have the following representation

Percentage = (22 / 56) x 100%

Evaluate

Percentage = 39.3%

Hence, Curry scored 39.3% of his team's points by halftime.

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Answer:c

Step-by-step explanation:

because

Accumulated depreciation account is used to calculate an asset's net book value, which is the value of an asset carried on the balance sheet.

The accumulated depreciation account is a contra asset account on a company's balance sheet. It represents a credit balance. It appears as a reduction from the gross amount of fixed assets reported. Accumulated depreciation specifies the total amount of an asset's wear to date in the asset's useful life.

One of the uses of accumulated depreciation account is that is used to calculate an asset's net book value, which is the value of an asset carried on the balance sheet.

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The values missing sides of the figures are calculated below.

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

NUMBER 7

Scale factor is the ratio of two corresponding sides of similar figures. Since the scale factor from A to B = 3:5. We have:

A : B = 3:5

(x+11) : 30 = 3 : 5

(x+11) /30 = 3 / 5

x + 11 = (30*3)/5

x + 11 = 90/5

x + 11 = 18

x = 18 - 11

x = 7

NUMBER 8

(2x-12) : 12 = 1:3

(2x-12) /12 = 1/3

2x-12 = 12/3

2x-12 = 4

2x = 4 + 12

2x = 14

x = 14/2

x = 7

NUMBER 9

AB : FG = BC:GH

104/39 = 112/x

x = 42

NUMBER 9

TK:KL = KU:KM

14/91 = 12/x

x = 78

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(a) The probability that the system functions on a rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.7 of functioning.

We can calculate this probability using the binomial distribution:

P(system functions on a rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.7)

Using a calculator or statistical software, we find:

P(system functions on a rainy day) = 0.8482

(b) The probability that the system functions on a non-rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.9 of functioning. Again, we can use the binomial distribution:

P(system functions on a non-rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.9)

Using a calculator or statistical software, we find:

P(system functions on a non-rainy day) = 0.9970

(c) To find the probability that the system will function tomorrow, we need to use the law of total probability. Let R be the event that it rains tomorrow and NR be the event that it doesn't rain tomorrow. Then:

P(system functions tomorrow) = P(system functions on a rainy day)P(R) + P(system functions on a non-rainy day)P(NR)

Using the probabilities from parts (a) and (b), and the fact that P(R) = 0.2 and P(NR) = 0.8, we can calculate:

P(system functions tomorrow) = (0.8482)(0.2) + (0.9970)(0.8) = 0.9746

Therefore, the probability that the 4 out of 6 systems will function tomorrow is 0.9746, assuming a 0.2 probability of rain.

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Mathematical relationships could be found in a linear programming model are (b) 2A - 2B = 30 (e) 1A + 1B = 9 (f) 2A + 6B + 1AB ≤ 36

Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.

(a) -1A + 2B ≤ 20 : Cannot be found in linear programming model as linear programming model can only consists of positive linear numbers and this equation contain negative number.

(b) 2A - 2B = 30 : Can be found in linear programming model

(c) 1A - 6B2 ≤ 10 : Cannot be found in linear programming model as equation includes square variable.

(d) 3√A + 2B ≥15 : Cannot be found in linear programming model as equation includes square root variable.

(e) 1A + 1B = 9 : Can be found in linear programming model

(f) 2A + 6B + 1AB ≤ 36 : Can be found in linear programming model

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The lengths of the missing sides associated with geometric systems formed by similar triangles are listed below:

Case 10: 49

Case 12: 36

In this problem we have the case of two geometric systems formed by two similar right triangles. These figures are similar if they have congruent internal angles but their sides are not congruent though proportional. Hence, missing sides can be found by proportion formulas. Now we proceed to determine the missing side for each case:

Case 10

x / 7√33 = 7√33 / 33

x = 7²

x = 49

Case 12

x / 6√13 = 6√13 / 13

x = 6²

x = 36

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Answer:

False, No.

Step-by-step explanation:

No, it is not possible to create a regular tessellation with a regular heptagon. A regular tessellation, also known as a tiling, is a repeating pattern of identical regular polygonal shapes that cover a plane without any gaps or overlaps. The only regular polygonal shapes that can be used to form a regular tessellation are the equilateral triangle, square, and hexagon. These shapes have interior angles that are multiples of 60 degrees, which allows them to fit together seamlessly to form a repeating pattern. The interior angle of a regular heptagon is roughly 128.5714 degrees, which does not divide evenly into 360 degrees, so it cannot be used to form a regular tessellation.

Answer:

The example that demonstrates the greatest distance traveled is Brenan diving to a depth of -12.76 feet, as it has the highest absolute value.

Answer:

Step-by-step explanation:

Right Answer: Add to eliminate X

[tex]4x+ (-4x)+5y+9y=-6+(-22)\\14y=-28\\y=\frac{-28}{14} \\y=2[/tex]

Answer:

Step-by-step explanation:

14.0

Answer:

[tex]x=11.5[/tex]

The third option listed

Step-by-step explanation:

We can use the sine function to evaluate [tex]x[/tex].

The definition of the sine function is

[tex]\sin \theta=\frac{O}{H}[/tex]

Note

[tex]\theta[/tex] is the angle

[tex]O[/tex] is the side opposite to the angle

[tex]H[/tex] is the hypotenuse

In this example we are given the hypotenuse and the angle.

Knowing these 2 values we can evaluate the opposite side ([tex]x[/tex]).

Lets solve for [tex]O[/tex].

[tex]\sin \theta=\frac{O}{H}[/tex]

Multiplying both sides by [tex]H[/tex] lets us isolate [tex]O[/tex] ([tex]x[/tex]).

[tex]O=H*\sin \theta[/tex]

Numerical Evaluation

We are given

[tex]\theta=35\textdegree\\H=20[/tex]

Inserting those values into our equation for [tex]O[/tex] ([tex]x[/tex]) yields

[tex]O=20*\sin 35[/tex]

[tex]O=11.4715287[/tex]

Rounding to the nearest tenth gives us

[tex]O=11.5[/tex]

[tex]x=11.5[/tex]

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Answer:

Step-by-step explanation:

Answer: $81,686

Step-by-step explanation:

$148,520 - 45% = $81,686

Alternative

$148,520 x 0.55 = $81,686

The missing angles in triangle RST and LMN are 121° and 15° respectively.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

Angle position describes how a line interacts with another line or plane. The amount of rotation of the body relative to the reference position is used to calculate the angle of position.

Theta (), the sign used to represent the angular position, can represent the angle in degrees (°), radians (rads), or revolutions.

So, in the triangle RST:

Missing angle:

44 + 15 + x = 180

x = 180 - 59

x = 121°

In triangle LMN:

121 + 44 + x = 180

x = 180 - 165

x = 15°

Therefore, the missing angles in triangle RST and LMN are 121° and 15° respectively.

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Using a telephone directory as the sampling frame can lead to under-coverage and bias, and it is generally not considered a representative sampling method.

Other more representative sampling methods, such as random digit dialing, address-based sampling, or a combination of methods, may be used to obtain a more accurate representation of the population.

Selecting a sample of households from the telephone directory can result in under-coverage and bias for several reasons.

Concept: When random sampling is not used, bias or regular flaws in the way the sample mean the population can occur.

Voluntary reply to samples, in which respondents choose their own respondents, and benefit samples, in which people who live nearby are included in the sample, are particularly biased.

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Answer:

Step-by-step explanation:

10000

Answer:10000

Step-by-step explanation:

dimosure

Answer:

8

Step-by-step explanation:

plug in the values of x and y into the equation

4(4) / (2)

16 / 2 = 8

A graphing utility such as Desmos or Wolfram Alpha can be used to graph the function. The graph shows that the maximum value occurs at t = 13 and the minimum value occurs at t = 7, which confirms our calculations.

To find the absolute extrema of the function h(t) = t^2 - 6 on the closed interval [7, 13], we can start by taking the derivative of the function and setting it equal to zero to find any critical points:

h'(t) = 2t = 0

t = 0

However, t = 0 is not in the interval [7, 13], so we only need to check the endpoints of the interval and any other critical points that may lie within the interval.

Since there are no critical points in the interval, we only need to evaluate the function at the endpoints:

h(7) = 7^2 - 6 = 43

h(13) = 13^2 - 6 = 163

Thus, the absolute maximum of h(t) on the interval [7, 13] is 163, which occurs at t = 13, and the absolute minimum is 43, which occurs at t = 7.

To verify our results using a graphing utility, we can graph the function h(t) = t^2 - 6 on the interval [7, 13] and visually observe the maximum and minimum values.

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Answer:

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

Step-by-step explanation:

I'm sorry, but I cannot see the graph you are referring to. However, I can still answer some of your questions based on the information provided.

When the diameter of the cylinder is 2 cm, the radius is equal to half the diameter, which is 1 cm.

To express the volume of a cube of side length s as an equation, we use the formula for the volume of a cube:

Volume of cube = s^3

Making a table for the volume of the cube at different side lengths, we get:

Side Length (cm) Volume (cm^3)

        0                                    0

        1                                     1

        2                                     8

        3                                     27

To compare the volume of the cube when the side length is 3 cm and the volume of the cylinder when the diameter is 3 cm, we need to find the radius of the cylinder first.

When the diameter is 3 cm, the radius is half the diameter, which is 1.5 cm. The height of the cylinder is also equal to the radius, so the volume of the cylinder can be found using the formula:

Volume of cylinder = πr^2h

Substituting r = 1.5 cm and h = 1.5 cm, we get:

Volume of cylinder = π(1.5)^2(1.5) ≈ 10.602 cm^3

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

Answer: To find the selling price of the karaoke machine with a 49.5% markup, you need to first calculate the amount of the markup. You can do this by multiplying the cost of the machine (52.75) by the markup rate (49.5%) expressed as a decimal:

52.75 * 0.495 = 26.067375

Next, add this markup amount to the cost of the machine:

52.75 + 26.067375 = 78.817375

So, the selling price of the karaoke machine with a 49.5% markup would be $78.82.

Step-by-step explanation:

Answer:

Step-by-step explanation:10299

Answer:

We can use the formula speed = distance / time to calculate the speed of the plane.

The total distance traveled by the plane is 3,000 + 600 = 3,600 miles.

The total time taken by the plane is 2 hours 30 minutes, which is equivalent to 2.5 hours.

Therefore, the speed of the plane is:

speed = distance / time

     = 3,600 / 2.5

     = 1,440 miles per hour

So the answer is (A) 1440mph

Answer:

x = 30, -40

Step-by-step explanation:

This a right triangle, so you can use the Pythagorean Theorem.

[tex]a^{2}+ b^{2}=c^{2}[/tex], now in place of the a, b and c use x, x +10 and 50.

so a = x, b =x+10 and c = 50

[tex]x^{2} + (x+10)^{2} =50^{2}[/tex]

[tex]x^{2} +x^{2} +20x +100 = 2500[/tex]

The maximum sustainable rate of harvest which is possible for the growth of fish P(t)  according to the differential equation " P' = 4P - 4P^2 - h " will be at the harvest rate of h=3.

In order to calculate the maximum sustainable harvest rate possible, we are required to find the equilibrium solutions of the differential equation firstly. Equilibrium solutions occur when P' = 0, so we can set the right-hand side of the differential equation at 0.

4P - 4P² - h = 0

Now a quadratic equation is formed in terms of P, which can be used to obtain P.

P = (1 ± √(1 + h))/2

There are two equilibrium solutions, obtained by these two values of P.

Now, in order to obtain a maximum sustainable harvest rate, we are required to have both equilibrium solutions to as positive ( as negative populations don't make any sense in this context).

Therefore, we have to find the largest value of h for which both of these equations have positive solutions:

(1 + √(1 + h))/2 > 0

(1 - √(1 + h))/2 > 0

On camparing both the inequalities, it can be concluded that the first inequality is always true, since the square root of a positive number is always positive. The second inequality is true when h < 3.

Hence, the maximum sustainable harvest rate is is found to be at h = 3. If the harvesting rate is greater than 3, then there will be no positive equilibrium solutions and the population will eventually be perished.

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