Joe's taxable income is $67,825. Use this tax schedule to calculate the total amount he owes in taxes. If taxable income is over-- But not over-- The tax is: $0 $7,825 10 percent of the amount over $0 $7,825 $31,850 $782.50 plus 15 percent of the amount over 7,825 $31,850 $77,100 $4,386.25 plus 25 percent of the amount over 31,850 $77,100 $160,850 $15,698.75 plus 28 percent of the amount over 77,100 $160,850 $349,700 $39,148.75 plus 33 percent of the amount over 160,850 $349,700 no limit $101,469.25 plus 35 percent of the amount over 349,700 A. $8,993.75 B. $4,386.25 C. $12,348.80 D. $13,380.00

The graph representing the piecewise-defined function is the top right graph, shown on the image at the end of the answer.

A piecewise-defined function is a function that has different definitions, one for each interval of the input x of the function.

In the context of this problem, the intervals are as follows:

Constant functions are represented by horizontal lines, hence the horizontal lines for each interval are given as follows:

Hence the second graph, the top right graph is correct.

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Answer:

8

Step-by-step explanation:

In order to answer this question we need to find the greatest common divisor of the two quantities which will give us the maximum number by which both can be divided.

The greatest common divisor of a group of integers is the largest common divisor that divides each of the integers. The first step to find it is write down the integers as a product of primes, so we have:

\(56=(28)(2)=(14)(2)(2)=(7)(2)(2)(2)= 2^3\)·\(7\)

\(72=(24)(3)=8(3)(3)=2^3\)·\(3^2\)

Now, in order to find the gcd we are going to take the factors that they have in common. In this case they both share the \(2^3\).

Thus, \(2^3=8\) is the greatest common divisor and therefore the maximum value of weight which can measure the weight of the rice exact number of times.

Answer:√ 25

log

13 ( 28 )

√ 75

Step-by-step explanation:

Answer: it just depends on how much each lawn pays him

Answer:

(1,-1)

Step-by-step explanation:

If you try plugging in the numbers for x in the equation y > Ix + 1I - 1, you'll find the answer.

No, it is not it true that for any integer n ≤ 2, φ(n) has a primitive root

In modular arithmetic, a number g is called a primitive root modulo n if every number  coprime to n is congruent to a power of  modulo . Mathematically, g is a primitive root modulo n if and only if for any integer  a such that gcd(a, n)=1 , there exists an integer k such that:

.\(g^{k}\)≡ a (mod n)

Now,

Existence of Primitive root modulo n exists if and only if:

So,

if n be a positive integer. A primitive root mod n is an integer g such that every integer relatively prime to n is congruent to a power of g mod n.

For example,

As ϕ(11)=10, the order of 2(mod11) must divide 10.  

So we check 22≡4(mod11) and 25≡10(mod11).

Since neither of these are 1, and

we know 2ϕ(11)=210≡1(mod11) by Euler's Theorem,

ord112=ϕ(11), making 2 a primitive root modulo 11.

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Move all terms not containing y to the right side of the

equation.

y= X/2+4

Rewrite in slope-intercept form.

y=1/2x+4

Use the slope-intercept form to find the slope and y

intercept.

Slope: 1/2

y-intercept: (0,4)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values. Answer: (0,4) (2,5)

Answer:

\(\large\boxed{(2, -3)}\)

Step-by-step explanation:

\(\textsf{We are asked for the Center Coordinates given a circle.}\)

\(\large\underline{\textsf{What is a Circle?}}\)

\(\textsf{A Circle is a curved shape that is commonly used to present a equidistant (same}\)

\(\textsf{distance apart) from a Center point.}\)

\(\textsf{When we create an equation for a circle, we should keep in mind of what the}\)

\(\textsf{coordinates of the center point are, and the Radius. For this problem an equation}\)

\(\textsf{has been given to us.}\)

\(\boxed{\begin{minipage}{20 em} \\ \underline{\textsf{\large Equation of a Circle (Standard Form);}} \\ \\ \tt \tt (x-h)^{2} + (\tt y-k)^{2} = r^{2} \\ \\ \underline{\textsf{\large Where;}} \\ \textsf{h represents the x-coordinate of the center.} \\ \textsf{k represents the y-coordinate of the center.} \\ \tt r^{2} \ \textsf{represents the radius of a circle squared.} \end{minipage}}\)

\(\textsf{*Note that if we are given the formula, the radius is already squared, unless}\)

\(\textsf{specified in the directions.}\)

\(\tt (x-2)^{2} + (y+3)^{2} = 9\)

\(\textsf{Our main focus should be h and k. Notice how both point values are negative.}\)

\(\textsf{The Center Point is represented as the opposite given to us in the formula.}\)

\(\underline{\textsf{Find the Opposite of -2 and 3;}}\)

\(\tt -2 \rightarrow \boxed{2}\)

\(3 \rightarrow \boxed{-3}\)

\(\underline{\textsf{Center Coordinates;}}\)

\(\large\boxed{(2, -3)}\)

A reasonable prediction for the number of times a pink paper clip will be drawn is 18. Option D.

To determine a reasonable prediction for the number of times a pink paper clip will be drawn when a random paper clip is drawn and replaced 50 times, we need to consider the relative proportions of each color of paper clip in the bag.

The bag contains a total of 9 pink paper clips out of a sum of 9 + 7 + 5 + 4 = 25 paper clips in total. To find the probability of drawing a pink paper clip in a single draw, we divide the number of pink paper clips by the total number of paper clips: 9 / 25 = 0.36.

Since each draw is independent and the paper clip is replaced after each draw, the probability of drawing a pink paper clip remains constant at 0.36 for each subsequent draw. This means that in a large number of draws, we would expect approximately 36% of the draws to result in a pink paper clip.With 50 draws in total, we can predict the number of times a pink paper clip will be drawn by multiplying the probability of drawing a pink paper clip (0.36) by the total number of draws (50): 0.36 * 50 = 18.

Therefore, a reasonable prediction for the number of times a pink paper clip will be drawn is 18, SO Option D is correct.

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Answer:

a

Step-by-step explanation:

the answer is a because adding -3 to 12 will make 9 and -3 × 12 is -36.

a) By strong induction, any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

b) By strong induction, any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

c) By strong induction, any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

a. Prove that any amount of postage worth 8 cents or more can be made from 3-cent or 5-cent stamps.

Base case: For postage worth 8 cents, we can use two 4-cent stamps, which can be made using a combination of one 3-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 8, can be made from 3-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 8, we can use the induction hypothesis to make k cents using 3-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with a 5-cent stamp to get the same value. If the last stamp we added was a 5-cent stamp, we can replace it with two 3-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3-cent or 5-cent stamps.

b. Prove that any amount of postage worth 24 cents or more can be made from 7-cent or 5-cent stamps.

Base case: For postage worth 24 cents, we can use three 8-cent stamps, which can be made using a combination of one 7-cent stamp and one 5-cent stamp.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 24, can be made from 7-cent or 5-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 24, we can use the induction hypothesis to make k cents using 7-cent or 5-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 5-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with three 5-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 7-cent or 5-cent stamps.

c. Prove that any amount of postage worth 12 cents or more can be made from 3-cent or 7-cent stamps.

Base case: For postage worth 12 cents, we can use one 3-cent stamp and three 3-cent stamps, which can be made using a combination of two 7-cent stamps.

Induction hypothesis: Assume that any amount of postage worth k cents or less, where k is greater than or equal to 12, can be made from 3-cent or 7-cent stamps.

Induction step: Consider any amount of postage worth (k+1) cents. Since k is greater than or equal to 12, we can use the induction hypothesis to make k cents using 3-cent or 7-cent stamps. Then, we can add one more stamp to make (k+1) cents. If the last stamp we added was a 3-cent stamp, we can replace it with two 7-cent stamps to get the same value. If the last stamp we added was a 7-cent stamp, we can replace it with one 3-cent stamp and two 7-cent stamps to get the same value. Therefore, any amount of postage worth (k+1) cents can be made from 3

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Answer:

Scale factor is 1/4

Step-by-step explanation:

You can easily calculate the scale factor of anything by dividing the new length by the old one. Then just simplify if necessary.

TS is 8, and T'S' is 2, so:

\(\frac{2}{8}=\frac{1}{4}\)

edit: fixed fraction

The function that describes the population of Martin is\(P(t) = 12,420 \times (1 + 0.016)^t\)

The predicted population of Martin in 2015 is 14557

The predicted  population of Martin in 2002 is 10,658

The function that describes the population of Martin as a function of the number of years t, since 2005, can be written as:

\(P(t) = 12,420 \times (1 + 0.016)^t\)

where P(t) is the population of Martin t years since 2005.

To predict the population of Martin in 2015, we need to substitute t = 10 into the equation:

P(10) = 12,420 × (1 + 0.016)¹⁰

= 14556.5

Therefore, the predicted population of Martin in 2015 is approximately 14556.5 people.

To predict the population of Martin in 2002, we need to find the number of years between 2005 and 2002, which is 3 years.

We can substitute t = -3 into the equation:

P(-3) = 12,420 × (1 + 0.016)⁻³)

= 10,658

Therefore, the predicted population of Martin in 2002 is approximately 10,658 people.

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Answer:

you are correct it is a

Step-by-step explanation:

Answer:

Its A

Step-by-step explanation:

Answer:

4.72500

Step-by-step explanation:

Answer:

6.75% of 70 is 4.725.

Step-by-step explanation:

6.75% as a decimal is 0.0675.

70 × 0.0675 = x

4.725 = x

6.75% of 70 is 4.725.

The total cost of software F over time is $5000.

For questions involving Customer Satisfaction Score, "Satisfaction Rate" is computed. It's calculated to provide you with an overall satisfaction rating of your respondents' responses to your goods and services.

Cost of Software F = $10000

Satisfaction rate with Software F = 90%

Cost of satisfaction level = $0

Cost of dissatisfaction level = $5000

Percentage of not satisfied = 10%

The total cost of Software F over time is :

= {($10000 x 90% - $0) + ($10000 x 10% - $5000)}.

= $5000

Therefore, cost of software F over time is $5000.

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Answer:

30,775.14 mm²

Step-by-step explanation:

area - πr²

3.14 x (99)²

30,775.14 mm²

If Howard, in his new lightweight running shoes, was able to walk at the rate of 0.83 meters per second in which his coach timed his walking at this steady pace for seconds. . The distance he walk during that time is 10.126.

Given data:

Distance walk in 1 second = 0.83 meters per second

Walk at steady pace = 12.2 seconds

Now let find the distance that Howard have to walked in 12.2 seconds

Distance walked in 12.2 seconds =  0.83 meters per second × 12.2 seconds

Distance walked in 12.2 seconds = 10.126

Therefore the distance is 10.126.

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The complete question is:

Howard, in his new lightweight running shoes, was able to walk at the rate of 0.83 meters per second. His coach timed his walking at this steady pace for 12.2 seconds. How far did he walk during that time? Use paper and a pencil to show your work, and then check your answer with a calculator.

Answer:

The domain of the function are values of x that respect the following condition: \(x \geq 7\)

Step-by-step explanation:

We are given the following function:

\(f(x) = \sqrt{x - 7}\)

Domain of the square root function:

The square root does not exist for negative values, so the domain of a square root function:

\(g(x) = \sqrt{h(x)}\)

Is \(h(x) \geq 0\)

In this question:

\(f(x) = \sqrt{x - 7}\)

Then:

\(h(x) = x - 7\)

\(x - 7 \geq 0\)

\(x \geq 7\)

The domain of the function are values of x that respect the following condition: \(x \geq 7\)

Answer:

the answer is 8 and x>or equal 7 and the only option greater than 7 is 8

Step-by-step explanation:

Answer: 17/42 of shape B is shaded.

Step-by-step explanation:

You are trying to find the shaded part of shape A minus the unshaded part of shape C.

Shaded part of shape A: 4/7

Unshaded part of shape C: 1 - 5/6 = 1/6

Shaded part of shape A minus unshaded of shape C:

4/7 - 1/6

= 24/42 - 7/42

= 17/42

Answer:

h = √65, length of diagonal = √117

Step-by-step explanation:

1) FE = DC since △FEA congruent to △CBD. Therefore FE per say  = 23-15/2 = 4.   Respectively we can find height "AE" using Pythagorean theorem;

AE = √(9)^2-(4)^2 = √81-16  = √65 units

h = √65

2) The diagonal of this rectangle forms two smaller triangles, each of which have legs of length 4 + 2 & 4 + 4 respectively. Use Pythagorean Theorem and determine the length of the diagonal;

Legs =  6 & 8

6^2 +9^2 = diagonal^2,

length of diagonal = √6^2 + 9^2

                               = √117 units

diagonal = √117

If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is a Sophie Germain prime.

Sophie Germain was a French mathematician who used these primes to investigate Fermat's Last Theorem, a famous mathematical conjecture that was finally proved in 1994 by Andrew Wiles. A safe prime is a prime number of the form 2p+1, where p is also a prime number, and it is called "safe" because it has some cryptographic properties that make it useful in certain encryption schemes.                                                                                                                                          In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

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Answer:

??

Step-by-step explanation:

there is not enough information

Appropriate hypotheses for performing a significance test: Null hypothesis: The mean weight of loaves of bread produced at the bakery is equal to 1 pound. Alternative hypothesis: The mean weight of loaves of bread produced at the bakery is less than 1 pound.

Parameter of interest: The mean weight of loaves of bread produced at the bakery.b. There is some evidence for the alternative hypothesis since the p-value is 0.00806, which is less than the level of significance of 0.01. This means that the results are statistically significant, and it is unlikely to get this result due to chance alone.c. At the α level of 0.01, the conclusion would be to reject the null hypothesis since the p-value is less than the level of significance.

This means that there is sufficient evidence to support the alternative hypothesis, which is that the mean weight of loaves of bread produced at the bakery is less than 1 pound. In summary, data markers are used in charts to represent individual data points. They are often used in combination with other chart elements, such as axes, gridlines, and legends, to help viewers understand the data being presented. The column, bar, area, dot, pie slice, or other symbol in a chart that represents a single data point is a data marker. Data markers provide you with a visual representation of the data in a chart. For example, in a column chart, each column represents a single data point.

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Answer:

4.24

Step-by-step explanation:

3.64 + 3/5

3.64 + 0.6 <--- 3/5 = 0.6 as a decimal

= 4.24 <--- Final answer

Logos is the use of evidence and reasoning to persuasively support a claim.

A principle originating in classical Greek thought which refers to a universal divine reason, immanent in nature, yet transcending all oppositions and imperfections in the cosmos and humanity.

Evidence

Evidence is that which tends to prove or disprove something, ground for belief, proof. something that makes plain or clear, an indication or sign, His flushed look was visible evidence of his fever.

Logos

logos is when we use cold arguments – like data, statistics, or common sense – to convince people of something, rather than trying to appeal to an audience's emotions.

data

data is information that has been translated into a form that is efficient for movement or processing.

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The number 7 emerged in human history through cultural and mathematical developments.

The significance of the number 7 can be observed in various aspects of human history. One of the earliest instances is found in ancient Mesopotamia, where the Sumerians developed a base-60 numeral system called sexagesimal.

This system contributed to the use of 60 as a highly divisible number and influenced the concept of dividing the day into 24 hours, each consisting of 60 minutes.

In ancient Egypt, the division of the week into seven days was based on the observation of celestial bodies.

The Egyptians associated each day with a different planet or celestial object, namely Sunday (Sun), Monday (Moon), Tuesday (Mars), Wednesday (Mercury), Thursday (Jupiter), Friday (Venus), and Saturday (Saturn). These planetary associations were later adopted by the Romans, and their names in English still reflect these origins.

The number 7 also holds religious and symbolic significance. In Judaism, the seventh day of the week, Saturday, is considered a day of rest, known as the Sabbath.

This tradition is rooted in the biblical story of creation, where God rested on the seventh day. In Christianity, the Book of Genesis describes the world being created in six days, with the seventh day being designated as holy.

Furthermore, the number 7 appears in mathematics and geometry. The seven colors of the rainbow, the seven musical notes, and the seven wonders of the ancient world are all examples of the cultural significance attributed to this number.

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Answer:

P(40) = 64, P(50) = 70, P(60) = 72,

P(70) = 70

60 minutes is correct.