Can anybody help me quick 21 points

Can Anybody Help Me Quick 21 Points

Answers

Answer 1
Let the number of apartments be x. We know that the cost of the digits is $1 each, and that the total cost of the digits is $282. Therefore, we can set up the following equation:

1x + 1(x+1) + 1(x+2) + ... + 1(x+(n-1)) = 282

Simplifying this equation, we get:

nx + n(n-1)/2 = 282

We can solve for n using the quadratic formula:

n = (-1 ± sqrt(1 + 4(2*282)))/2

n = 21.06 or n = -20.06

Since the number of apartments must be a positive integer, we can round up to the nearest integer, giving us n = 22. Therefore, Tabitha will be numbering 22 apartments.

Extra: On Monday, the store sells 1s for half price, or $0.50. This means that the total cost of the digits would be:

1x + 0.5(x+1) + 0.5(x+2) + ... + 0.5(x+(n-1)) = 141

Simplifying this equation, we get:

nx + n(n-1)/4 = 141

Using the quadratic formula again, we get:

n = (-1 ± sqrt(1 + 4(4*141)))/2

n = 16.76 or n = -15.76

Rounding up to the nearest integer, we get n = 17. Therefore, if Tabitha had bought the digits on Monday, she could have saved 5 digits, or $5.

Related Questions

Share your own multi-step combination problem

Answers

My own multi-step combination problem is given below:

Amanda  was planning a dinner party for 10 people, and she want to choose a menu of 3 fruit , 2 meat pie, and 2 desserts. Amanda  have a total of 5 fruit , 4 meat pie, and 3 desserts to choose from. How many different dinner menus can Amanda  create?

How do you solve the multi-step combination?

To solve this problem, Amanda  need to use the formula for combinations and it is:

nCr = n! / (r! x (n-r)!)

where:

n = total number of items to select from

r is the number of items to select.

First, we have to calculate the number of ways to select 3 fruit from 5, hence it will be:

5C3

=  5! / (3! x (5-3)!)

= 10

Next, we have to calculate the number of ways to select 2 meatpie from 4 and it will be

4C2

= 4! / (2! x  (4-2)!)

= 6

Lastly,, we need to calculate the number of ways to select 2 desserts from 3 and it will be:

3C2

= 3! / (2! x  (3-2)!)

= 3

To have the total number of dinner menus, we have to multiply these three numbers together:

= 10 x 6 x 3

= 180

Therefore, one can say that Amanda have 180 different dinner menus that she can be create.

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The lion population in a certain reserve drops by 5% every year. Currently, the population's size is 325. i.Write a function that gives the lion population size,P(t), t years from today ii. What will the population be in 4 years. Write an exponential function for all three

Answers

Answer:

1. The function that gives the lion population size P(t), t years from today is:

P(t) = 325(0.95)^t

2. To find the population in 4 years, we can substitute t=4 in the function:

P(4) = 325(0.95)^4

P(4) = 279.14

So the population will be approximately 279 lions in 4 years.

3. The exponential function for all three years is the same as in part 1:

P(t) = 325(0.95)^t

Need answers to this by 20 min please!

Dividing cubic polynomials by linear divisor

Answers

The solution to each of the given polynomials are:

1)  x² + 3x - 4

2) x² - 4x + 4

3) x² - 7x + 8

4) x² - 13 - (15/(x + 3)

How to carry out polynomial division?

1) We want to divide the polynomial. Thus:

          x² + 3x - 4

x + 2| x³ + 5x² + 2x - 8

     -   x³ + 2x²

                 3x² + 2x

               - 3x² + 6x

                        - 4x - 8

                      -  -4x - 8

                                0

2) We want to divide the polynomial. Thus:

        x² - 4x + 4

x - 2| x³ - 6x² + 12x - 8

     -  x³ - 2x²

              - 4x² + 12x

              - -4x² + 8x

                         4x - 8

                      -  4x - 8

                                0

3) We want to divide the polynomial. Thus:

         x² - 7x + 8

x + 3| x³ - 4x² - 13x + 24

      -  x³ + 3x²

              - 7x² - 13x

              - -7x² - 21x

                         8x + 24

                      -  8x + 24

                                0

4) We want to divide the polynomial. Thus:

        x² - 13

x + 3| x³ + 3x² - 13x - 15

      -  x³ + 3x²

              - 0x² - 13x

              - -7x² - 13x

                       0 - 15

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What is the area of sector GHJ , given that θ=pi/4 radians. Express your answer in terms of pi and as a decimal rounded to the nearest tenth. Show your work.

Answers

The area of sector GHJ is:

3.125π cm² (in terms of pi)

9.8 cm² (As a decimal rounded to the nearest tenth)

How to find the area of sector GHJ?

The formula for area of a sector when the angle is in radians is:

A = (1/2) * r²θ

Where θ is the angle subtended at the center and r is the radius of the circle.

In this case, r = 5 cm and θ = π/4

Substituting:

A = (1/2) * 5² * π/4

A = 3.125π cm² (in terms of pi)

As a decimal rounded to the nearest tenth:

A = 3.125 * 22/7

A = 9.8 cm²

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A pharmaceutical company receives large shipments of ibuprofen tablets and uses an acceptance sampling plan. This plan randomly selects and tests 29 tablets, then accepts the whole batch if there is at most one that doesn't meet the required specifications. What is the probability that this whole shipment will be accepted if a particular shipment of thousands of ibuprofen tablets actually has a 15% rate of defects?

Answers

Answer:

Step-by-step explanation:

This problem can be solved using the binomial distribution, which gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

Let p be the probability that a single ibuprofen tablet has a defect, which is given as 15% or 0.15. Then, the probability that a single ibuprofen tablet does not have a defect is 1 - p = 0.85.

The acceptance sampling plan requires that at most one tablet does not meet the required specifications out of 29 tablets. This means that the shipment will be accepted if there are 0 or 1 defective tablets in the sample of 29.

The probability of getting exactly k defective tablets in a sample of n tablets is given by the binomial probability formula:

P(k) = (n choose k) * p^k * (1 - p)^(n - k)

where (n choose k) = n! / (k! * (n - k)!) is the number of ways to choose k defective tablets out of n, and ! denotes the factorial function.

To find the probability that the whole shipment will be accepted, we need to find the probability that there are 0 or 1 defective tablets in the sample of 29:

P(0 or 1 defects) = P(0 defects) + P(1 defect)

= (29 choose 0) * 0.15^0 * 0.85^29 + (29 choose 1) * 0.15^1 * 0.85^28

≈ 0.1098

Therefore, the probability that the whole shipment will be accepted is approximately 0.1098 or 10.98%

Use the general form of the equation for an ellipse with center (0,0) with a vertex at (5,0) and a co-vertex at (2,0)​

Answers

The general form of the equation for an ellipse with center (0,0) and semi-axes lengths a and b is:

(x^2/a^2) + (y^2/b^2) = 1

Since the vertex is at (5,0), we know that a = 5. Since the co-vertex is at (2,0), we know that b = 2.

Plugging these values into the equation, we get:

(x^2/5^2) + (y^2/2^2) = 1

Simplifying, we get:

x^2/25 + y^2/4 = 1

Therefore, the equation of the ellipse with center (0,0), a vertex at (5,0), and a co-vertex at (2,0) is x^2/25 + y^2/4 = 1.

8.G.1.2 A mathematical puzzle uses four triangles with the dimensions show below. Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P

Answers

The triangles which are congruent are P and Q. So, the correct answer is A).

Triangles are congruent if they have the same shape and size. This means that all corresponding angles and sides are equal. In this case, we can use the side lengths to determine which triangles are congruent.

Triangle P and Q have the same side lengths, so they are congruent (A). Triangle Q and R do not have the same side lengths, so they are not congruent (not B). Triangle R and S do not have the same side lengths, so they are not congruent (not C).

Triangle S and P do not have the same side lengths, so they are not congruent (not D). Therefore, the answer is A. Triangles P and Q are congruent.

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--The given question is incomplete, the complete question is given

" 8.G.1.2 A mathematical puzzle uses four triangles with the dimensions show below. Which of the following triangles are congruent? A. P and Q B. Q and R C. R and S D. S and P "--

Help with this pleaseee

Answers

The reduced form of the matrix is [tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

A matrix is a rectangular array of numbers arranged in rows and columns. In linear algebra, matrices can be used to represent linear transformations and solve systems of linear equations.

In the given matrix, we need to perform a row operation to get a 1 in row 1, column 1. Row operations are operations performed on the rows of a matrix to transform it into another matrix that is equivalent in terms of solutions to a system of linear equations.

The three types of row operations are:

Swapping two rows.

Multiplying a row by a non-zero constant.

Adding a multiple of one row to another row.

To perform this row operation, we first multiply row 1 by 12 to get a multiple of 12 in the first column of row 1:

[tex]\begin{bmatrix}84 &-48 &96 \\-12& 7& -13\end{bmatrix}[/tex]

Next, we add row 1 to row 2 multiplied by 2 to get a 0 in column 1 of row 2:

[tex]\begin{bmatrix}84 &-48 &96 \\0& 11& 79\end{bmatrix}[/tex]

Finally, we can divide row 1 by 84 to get a 1 in row 1, column 1:

[tex]\begin{bmatrix}1 &-\frac{4}{7} &\frac{4}{7} \\0& 11& 79\end{bmatrix}[/tex]

Now we have a 1 in row 1, column 1, and the matrix is in row echelon form.

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The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?

Answers

The first step is to copy a segment and an angle, and the second step is to fix the width of the compass to the length of the segment. Then last, draw a perpendicular line.

What is geometry?

Geometry is a branch of mathematics that deals with the study of spatial relationships, shapes, sizes, positions, and dimensions of objects. It involves the study of points, lines, angles, planes, curves, surfaces, and solids, and how they relate to each other in space.

According to the given information:

Considering that, we must define the first stage, which is the process of copying a line segment in order to ensure that the new line segment is the same length as the original line segment. In a first stage, an angle and a segment must be replicated. The illustration depicts the copying construction.

The compass width must then be changed to match the section length. The new angle is now commensurate with the old angle. This is the following step.

The next step is to draw a perpendicular line. It is shown here how to draw a line perpendicular to the specified line across a point.

As a result, the first step is to copy a segment and an angle, and the second step is to set the width of the compass to the length of the segment. Then last, draw a perpendicular line.

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A triangle with area 184 square inches has a height that is two less than six times the width. Find the height and the width of the triangle.

Answers

The height of the triangle is √(115) - 1 inches and the width is (1 + √(115)) / 6 inches.

Let's begin by assigning variables to the height and width of the triangle. We'll use h for height and w for width.

From the problem statement, we know that the area of the triangle is 184 square inches:

Area = (1/2) * base * height

where the base is equal to the width. We can rearrange this formula to solve for the height:

height = 2 * Area / base

Since the area is given as 184 square inches and the base is equal to the width, we can write:

h = 2 * 184 / w

We also know that the height is two less than six times the width. Writing this as an equation, we have:

h = 6w - 2

Now we can substitute the expression for h from the second equation into the first equation:

2 * 184 / w = 6w - 2

Multiplying both sides by w gives:

2 * 184 = w * (6w - 2)

Expanding the right side gives:

2 * 184 = 6w² - 2w

Simplifying further gives:

6w² - 2w - 368 = 0

This is a quadratic equation that we can solve using the quadratic formula:

w = (-b ± √(b² - 4ac)) / 2a

where a = 6, b = -2, and c = -368. Plugging in these values gives:

w = (2 ± √(2² - 4 * 6 * (-368))) / 2(6)

Simplifying further gives:

w = (1 ± √(115)) / 6

Taking the positive value gives:

w = (1 + √(115)) / 6

Plugging this value back into either equation for h gives:

h = 6w - 2 = 6((1 + √(115)) / 6) - 2 = 1 + √(115) - 2 = √(115) - 1

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please help with an explanation

Answers

It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.

To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.

Option 1: Replace the old boat with the new fuel-efficient model

If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).

The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).

Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.

Option 2: Continue to use the old boat until it wears out

If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.

However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).

In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.

Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.

Conclusion

Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.

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There are 8 blue marbles, 6 red marbles, 2 green marbles and 4 black marbles in a box.
What is the probability that the marble is not green?

Answers

The probability that the marble choose is not green is 9/10

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1.

Probability is expressed as;

probability = sample space/total outcome

total number of marble = 8+6+2+4 = 20marbles

Probability that it is green = 2/20 = 1/10

therefore probability that Is not green = 1-1/10

= 10-1)/10

= 9/10

therefore the probability that a marble chosen is not green is 9/10.

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Participants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.

Of all those who participated in the study, 80% received medication A.
Of those who received medication A, 76% reported an improvement.
Of those who received the placebo, 62% reported no improvement.
I see the other answers about the same question, but I still don't understand some of it

Answers

To find P(placebo and improvement), we need to use the information given in the problem and apply the formula for conditional probability:

P(A and B) = P(A) x P(B|A)

where P(A) is the probability of event A, and P(B|A) is the conditional probability of event B given that event A has occurred.

In this case, we want to find the probability of two events occurring together: receiving the placebo and reporting an improvement. Let's use a tree diagram to organize the information:

```
A (80%)
/ \
Imp No imp
/ \
B No B
```

From the diagram, we can see that:

- P(placebo) = 1 - P(medication A) = 1 - 0.8 = 0.2
- P(improvement | medication A) = 0.76
- P(no improvement | placebo) = 0.62

Now we can use the formula to find P(placebo and improvement):

P(placebo and improvement) = P(placebo) x P(improvement | placebo)

P(placebo and improvement) = 0.2 x (1 - P(no improvement | placebo))

P(placebo and improvement) = 0.2 x (1 - 0.62)

P(placebo and improvement) = 0.2 x 0.38

P(placebo and improvement) = 0.076

Therefore, the probability of receiving the placebo and reporting an improvement is 0.076, or approximately 0.08, which means that about 8% of the participants received the placebo and reported an improvement.

1. A survey conducted by a national research center asked a random sample of 920
teenagers in the United States how often they use a video streaming service.
From the sample, 59% answered that they use a video streaming service every day.
a. Construct and interpret a 95% confidence interval for the proportion of all
teenagers in the United States who would respond that they use a video
streaming service every day.
b. Based on the confidence interval in part (a), do the sample data provide
convincing statistical evidence that the proportion of all teenagers in the United
States who would respond that they use a video streaming service every day is
not 0.5? Justify your answer.


Mean Standard Deviation Sample Size
Standard care 0.57 0.26 56
New treatment 0.69 0.27 56

2. Patients experiencing symptoms of a heart attack are routinely transported to a
hospital in an ambulance. In a study of a new treatment thought to reduce damage to
the heart, patients experiencing symptoms of a heart attack were randomly assigned to
one of two groups. During transportation to the hospital, patients in one group received
standard care, and patients in the other group received the new treatment consisting of
standard care and the application of a blood pressure cuff.
The response variable measured for each patient was a number between 0 and 1,
referred to as the myocardial salvage index (MSI). A higher MSI value indicates a more
positive outcome for the patient. Summary statistics for the MSI responses of the two
groups are shown in the table.
Do the data provide convincing statistical evidence that the new treatment results in a
higher mean MSI value than does the standard care among people similar to the
patients in the study?

Answers

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

How to solve

a. The 95% confidence interval for the proportion of teenagers using video streaming services daily is (0.5579, 0.6221). This means we're 95% confident that 55.79% to 62.21% of US teenagers use such services daily.

b. The results demonstrate that the proportion is not 0.5 because the full confidence interval is higher than 0.5.2. We obtain a t-value of roughly 2.51 with 108.52 degrees of freedom using a two-sample t-test.

At a significance level of 0.05, the critical t-value for a one-tailed test is approximately 1.66.

Since the calculated t-value is greater than the critical t-value, we reject the null hypothesis, concluding that there's convincing evidence that the new treatment results in a higher mean MSI value than standard care.

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The formula A = 252e^.049t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 373 thousand?

Answers

Answer:  Approximately the year 2006

Roughly 8 years after 1998

================================================

Work Shown:

A = 373 represents a population of 373 thousand.

Plug in this value of A and solve for t. We'll need natural logs (LN) to isolate the variable.

[tex]A = 252e^{0.049t}\\\\373 = 252e^{0.049t}\\\\373/252 = e^{0.049t}\\\\1.4801587 \approx e^{0.049t}\\\\[/tex]

Apply natural logs to both sides.

[tex]\text{Ln}(1.4801587) \approx \text{Ln}\left(e^{0.049t}\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*\text{Ln}\left(e\right)\\\\\text{Ln}(1.4801587) \approx 0.049t*1\\\\\text{Ln}(1.4801587) \approx 0.049t\\\\t \approx \text{Ln}(1.4801587)/0.049\\\\t \approx 8.0030472\\\\[/tex]

It takes about 8 years for the population to reach 373 thousand.

Since t = 0 starts at 1998, we get to the year 1998+8 = 2006.

The times to run a mile are 7,
9, 10, 11, 11, and 12.
What is the mean?

Answers

Answer:

10

Step-by-step explanation:

When you think of the mean of a data set, think of the word average. 'Mean' and 'average' are the same thing when you're talking about a set of data.

To find the mean, you have to divide the sum of all values in your data set, by the number of values.

7 + 9 + 10 + 11 + 11 + 12 = 60

60/6 = 10

Therefore, the mean of this data set would be 10.

see attachment
3(3m+N)

Answers

Answer:

Step-by-step explanation:

The reciprocal of h.C.F and lcm of two number are 1/12 and 1/312 respectively. If one of the number is 24. Find the other number?

Answers

The other number is 156.

Let a and b be two numbers, with a = 24.

We know that the product of two numbers' HCF and LCM is equal to the product of the two numbers.

So, we have:

HCF × LCM = a × b

We are given that the reciprocal of HCF is 1/12.

So, HCF = 1 / (1/12) = 12.

We are also given that the reciprocal of LCM is 1/312.

So, LCM = 1 / (1/312) = 312.

12 × 312 = 24 × b

Simplifying, we get:

b = (12 × 312) / 24 = 156

Therefore, the other number is 156.

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Parametric Equations Question

A drone traveling horizontally at 100 m/s over flat ground at an elevation of 4500 meters must drop an emergency package on a target on the ground. The trajectory of the package is given by [tex]x=100t, y=-4.9t^2 +4500, t\geq 0[/tex]where the origin is the point on the ground directly beneath the drone at the moment of release. How many horizontal meters before the target should the package be released in order to hit the target? Round to the nearest meter.

Answers

the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

what is  rounded to the nearest  ?

"Rounded to the nearest" means finding the nearest value of a specified degree of accuracy. For example, rounding a number to the nearest whole number means finding the closest whole number to that number. If the number is equally close to two whole numbers, it is rounded up to the higher number.

In the given question,

The trajectory of the package can be modeled using the equation:

y = -0.5 * g * x² / v² + tan(∅) * x + h

where:

y = height of the package above the ground at horizontal distance x

g = acceleration due to gravity (9.8 m/s²)

v = horizontal velocity of the drone (100 m/s)

theta = angle at which the package is released

h = initial height of the package above the ground (4500 meters)

To hit the target, we want the package to land on the ground, which means its final height should be zero. So, we can set y = 0 and solve for x to find the horizontal distance at which the package should be released. This gives:

0 = -0.5 * 9.8 * x² / 100² + tan(∅) * x + 4500

Simplifying and rearranging, we get:

0.049 * x² + tan(∅) * x - 4500 = 0

Using the quadratic formula, we can solve for x:

x = (-tan(∅) ± √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Since we want the package to land in front of the target, we take the positive root of the equation:

x = (-tan(∅) + √(tan²(∅) + 0.049 * 4500 * 4)) / (0.098)

Now, we need to find the value of theta that will make the package hit the target. Since the drone is traveling horizontally, the package will also have a horizontal velocity of 100 m/s when it is released. So, we can use trigonometry to find the angle at which the package should be released. This gives:

tan(∅) = 4500 / x

Substituting this into the equation for x, we get:

x = (-4500 / x + √((4500 / x)²+ 0.049 * 4500 * 4)) / (0.098)

Simplifying and rearranging, we get:

x² = 4500 * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x) / 0.098

Squaring both sides, we get:

x⁴ = 4500² * (√((4500 / x)² + 0.049 * 4500 * 4) - 4500 / x)² / 0.009604

Expanding and simplifying, we get:

x⁴ = 900000000 * (1 + 0.00012345679 * x² - 0.00012345679 * 4500 * x / √(x² + 202500)) / 0.009604

We can solve for x using numerical methods, such as using a graphing calculator or an online solver. Using such a method, we find that:

x ≈ 9,932 meters

Therefore, the package should be released about 9,932 meters before the target to hit the target, rounded to the nearest meter.

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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answers

The answer of x is 16.

Each state sets its own state income tax rate. Table 1 shows 3 individuals'
incomes and taxes owed. Table 2 shows the income tax rates for several
states.
Table 1:
Name Income Taxes Owed
Beatrice $35,000
Gregory $55,000
Melinda $72,000
O $4,602.50
O $19,725
$2,450
$4,400
$3,600
O $46,025
O $61,147.50
Table 2:
State
Alabama
Georgia
Maine
If Anthony lives in Georgia and has an income of $65, 750, how much money
will he have left after he pays state income taxes?
Income Tax Rate
5%
7%
8%

Answers

From Table 2, we can see that Georgia's income tax rate is 7%.

To find the amount of state income taxes Anthony will owe, we can multiply his income by the tax rate:

State income tax = (Anthony's income) x (Georgia's tax rate)

State income tax = $65,750 x 0.07

State income tax = $4,602.50

Therefore, Anthony will owe $4,602.50 in state income taxes. To find out how much money he will have left after he pays these taxes, we can subtract the tax amount from his income:

Money left after paying state income taxes = Anthony's income - State income tax

Money left after paying state income taxes = $65,750 - $4,602.50

Money left after paying state income taxes = $61,147.50

Therefore, Anthony will have $61,147.50 left after he pays state income taxes.

what are the answers? thank you.​

Answers

Answer:

2, area=42.39 arc length=14.13

3, area=604.9 arc length=71.1

PLSSS HELP AND PLEASE SHOW WORK ASWELL


Collin has 100 feet of fencing to enclose a pen for his puppy. He is
trying to decide whether to make the pen
circular or square. He plans to use all of the
fencing.

Part A.) If Collin uses all of the fencing, what
would be the area of each pen? Use 3.14
for pie. Round to the nearest hundredth if
necessary.

Part B.) To have the largest possible area for the pen, which pen should Collin build?

Answers

Answer:

A.

circular: ≈ 795.77 square feet

square: 625

Step-by-step explanation:

the circular pen would have a larger area.

Solving for the radius, we have:

r = 100 / (2 × 3.14) = 15.92 feet (rounded to two decimal places)

Therefore, the area of the circular pen would be:

Area = πr^2 = 3.14 × (15.92 ft)^2 ≈ 795.77 square feet

For a square pen with side length s, the perimeter is given by:

4s = 100

s = 25

The area of a square pen with side length s is given by:

A = s^2 = 25^2 = 625

Part A:

Let's first consider the circular pen. The circumference of a circle is given by 2πr, where r is the radius. In this case, we have 100 feet of fencing, so:

2πr = 100

Solving for r, we get:

r = 100/(2π) = 15.92 feet (rounded to two decimal places)

The area of the circular pen is given by πr^2, so:

Area = π(15.92)^2 = 795.77 square feet (rounded to two decimal places)

Now let's consider the square pen. If we use all 100 feet of fencing, then each side of the square will be 25 feet long. Therefore, the area of the square pen is:

Area = 25^2 = 625 square feet

Part B:

To have the largest possible area for the pen, Collin should build the circular pen. We can see from the calculations above that the area of the circular pen is larger than the area of the square pen. This is because a circle has the largest area for a given perimeter, which in this case is 100 feet.

Of all the registered automobiles in Colorado, 5% fail the state emissions test. Ten automobiles are selected at random to undergo an emissions test. Round the answers to at least four decimal places.

Answers

The probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

what is binomial distribution?

The number of successes in a certain number of independent trials is modelled by the binomial distribution, which has just two potential outcomes for each trial, commonly referred to as "success" and "failure."

We can solve this problem by using the binomial distribution formula:

[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]

where:

P(X=k) is the probability of getting exactly k automobiles that fail the emissions test

n is the number of automobiles being tested, in this case, n = 10

k is the number of automobiles that fail the emissions test

p is the probability of a single automobile failing the emissions test, in this case, p = 0.05

Using this formula, we can calculate the probability of getting exactly k failures for k = 0, 1, 2, ..., 10, and then add up these probabilities to get the probability of getting at least one failure.

The probability of getting exactly k failures is:

[tex]P(X=k) = (10\ choose\ k) * 0.05^k * 0.95^{(10-k)[/tex]

Using a calculator or statistical software, we can calculate these probabilities:

[tex]P(X=0) = (10 choose 0) * 0.05^0 * 0.95^10 = 0.5987\\P(X=1) = (10 choose 1) * 0.05^1 * 0.95^9 = 0.3151\\P(X=2) = (10 choose 2) * 0.05^2 * 0.95^8 = 0.0746\\P(X=3) = (10 choose 3) * 0.05^3 * 0.95^7 = 0.0119\\P(X=4) = (10 choose 4) * 0.05^4 * 0.95^6 = 0.0013\\P(X=5) = (10 choose 5) * 0.05^5 * 0.95^5 = 0.0001\\[/tex]

[tex]P(X=6) = (10 choose 6) * 0.05^6 * 0.95^4 = 0.0000\\P(X=7) = (10 choose 7) * 0.05^7 * 0.95^3 = 0.0000\\P(X=8) = (10 choose 8) * 0.05^8 * 0.95^2 = 0.0000\\P(X=9) = (10 choose 9) * 0.05^9 * 0.95^1 = 0.0000\\P(X=10) = (10 choose 10) * 0.05^10 * 0.95^0 = 0.0000\\[/tex]

The probability of getting at least one failure is:

[tex]P(X > =1) = 1 - P(X=0) = 1 - 0.5987 = 0.4013[/tex]

Therefore, the probability of getting at least one automobile that fails the emissions test is approximately 0.4013 or 40.13%.

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In AJKL, m/J = (8x - 7), m/K = (x + 7)°, and m/L= (2x + 15)°. What
is the value of x?

Answers

Therefore, the equation for that value x = 6, and m(A) = 90.

What is a formula or equation?

A mathematical equation expresses two things as being equal to one another, or as having the same value and worth. A specific equation that expresses a significant link between variables and numbers is called a formula.

The fact that the sum of a triangle's angles is 180 degrees must be used to determine the value of x. Angles J, A, and K in the triangle AJK allow us to write:

m(J) + m(A) + m(K) = 180

We can substitute the given angle measures into this equation:

(8x - 7) + m(A) + (x + 7) = 180

Simplifying this equation, we get:

9x + m(A) = 180 - 7 - 7

9x + m(A) = 166

We can use the same reasoning for triangle AJL:

m(J) + m(A) + m(L) = 180

Substituting the given angle measures, we get:

(8x - 7) + m(A) + (2x + 15) = 180

Simplifying this equation, we get:

10x + m(A) = 172

The two unknowns in our current set of equations are x and m(A). By removing the first equation from the second, we can find m(A):

10x + m(A) = 172

(9x + m(A) = 166)

x = 6

Now that we know x, we can substitute it into either equation to find m(A):

8x - 7 + m(A) + x + 7 = 180

15x + m(A) = 180

m(A) = 180 - 15x

Substituting x = 6, we get:

m(A) = 180 - 15(6) = 90

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Which linear equation is represented in the graph?
A. y = 2x – 1

B. y = –2x – 1

C. y = –2x + 1

D. y = 2x + 1

Answers

I would say it's D but not 100 percent sure.

Suppose that the functions and are defined as follows.

Answers

1) (f - g) (x) = f(x) - g(x) = x ≤ 1/4  

Domain of the function is : [1/4, infinity)

2) → [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]        

Domain of the function : (1/4, infinity)

We have the function are as follows:

f(x) = -x + 4

g(x) = [tex]\sqrt{4x+1}[/tex]

To find the f - g and f/g and also their domains using interval  notation.

Now, (f - g) (x) = f(x) - g(x)

                       = [tex]-x+4-\sqrt{4x+1}[/tex]

                       = 4x + 1 ≤ 0

                       = x ≤ 1/4            

Domain of the function is : [1/4, infinity)

→ [tex]\frac{f}{g}(x) =\frac{f(x)}{g(x)} = \frac{-x+4}{\sqrt{4x-1} }[/tex]

=> 4x - 1 > 0

=> x > 1/4

Domain of the function : (1/4, infinity)

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PLEASE HELP

Construct the indicated confidence interval for the population mean u using the t-distribution. Assume the population is normally distributed.
C=0.90, x=13.7, s =3.0, n= 10

Answers

The 95% confidence interval using a t-distribution for the population mean μ using the t-distribution is  (9.7, 14.7).

Here, we have,

1. Identify the given information:

 - Confidence level (c) = 0.95

 - Sample mean (x) = 12.2

 - Sample standard deviation (s) = 3.0

 - Sample size (n) = 8

2. Determine the degrees of freedom (df) for the t-distribution:

 - df = n - 1 = 8 - 1 = 7

3. Find the t-value corresponding to the 0.95 confidence level and 7 degrees of freedom:

 - You can use a t-table or an online calculator for this.

 - The t-value for a 0.95 confidence level and 7 df is approximately 2.365.

4. Calculate the margin of error (ME) using the t-value, sample standard deviation (s), and sample size (n):

 - ME = t-value * (s / sqrt(n))

 - ME = 2.365 * (3.0 / sqrt(8)) ≈ 2.5

5. Construct the 95% confidence interval using the sample mean (x) and the margin of error (ME):

 - Lower limit: x - ME = 12.2 - 2.5 ≈ 9.7

 - Upper limit: x + ME = 12.2 + 2.5 ≈ 14.7

So, the 95% confidence interval for the population mean μ using the t-distribution is (9.7, 14.7).

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Please help me understand this

Answers

Answer:

To find the value of y, we can use the slope formula:

slope = (y2 - y1) / (x2 - x1)

We know that the slope is 5, and the two points on the line are (5,y) and (4,1). We can substitute these values into the slope formula to get:

5 = (y - 1) / (5 - 4)

Simplifying this equation gives:

5 = y - 1

Adding 1 to both sides gives:

y = 6

Therefore, the value of y is 6.

Step-by-step explanation:

El perímetro de un campo rectangular es 300 m . Si la longitud del campo es 88 , ¿cuál es su anchura?

Answers

Based on the above, the width of the field is 62 meters.

What is the width?

Based on the question, Let's say that the width of the field is  denoted with 'w'.

Note that the formula for the perimeter (P) of a rectangle is:

P = 2(l + w)

where"

l = length

w =  width.

Fixing the values into the equation, it will be:

300 = 2(88 + w)

So, Divide both sides by 2:

150 = 88 + w

Subtract 88 from both sides:

w = 150 - 88

w = 62

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Se text below

The perimeter of a rectangular field is 300 m. If the length of the field is 88 , what is its width?

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