Pedro and Paola are married and file their taxes jointly.Paola's taxable income was $40,675 and Pedro's was $32.802.Paola's employer withheld $4,654 in federal taxes.Pedro's employer withheld $4,345 Will they get a refund or do they owe?(WWrite "refund" or 'owe" as your answer.) how much?

Answer:

The answer is "0.1190".

Step-by-step explanation:

Given:

\(\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190\)

Answer:

A.) 4 - 6x + 1 = 36x

B.) 5/6 - x = 6x

F.) 5 = 42x

Step-by-step explanation:

edge.

Answer:

  77.27 ft

Step-by-step explanation:

You want the length of rope between you and an anchor on a cliff if you are 20 ft from the cliff and the angle of elevation is 75°.

We can model the geometry as a right triangle. The relation between the angle and the distances of interest is ...

  Cos = Adjacent/Hypotenuse

  cos(75°) = (20 ft)/(rope length)

Solving for rope length gives ...

  rope length = (20 ft)/cos(75°) ≈ 77.27 ft

The length of the rope to the anchor is about 77.27 feet.

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The equation of a line y=2x+8.

The equation of a straight line can be represented in the slope-intercept form, y = mx + c

Where c = intercept

Slope, m =change in the value of y on the vertical axis/change in the value of x on the horizontal axis

Looking at the given line,

y = 2x + 7

Compared with the slope-intercept equation,

Slope, m = 2

If a line is parallel to another line, it means that both lines have equal or the same slope. This means that the slope of the line passing through the point (-2, 4) is 2

Substituting m= 2, y = 4 and x = -2 into the equation, y = mx + c , it becomes

4 = 2 × - 2 + c

4 = - 4 + c

c = 4 + 4 = 8

The equation becomes y=2x+8.

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According to BODMAS rule...

We would first solve...

Bracket i.e.(4+7)

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

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Step-by-step explanation:

we can idnetify that it is arithmetic due to it being a linear sequnce. Therefore we find Tn and equate it to the last term to find the number of terms. We then use that to find the sum of the series using the following formula where n is the number of terms, a is the first term and L represents your last term.

By using pythagorean theorem, the length of the missing side is 12 feet.

What is the Pythagorean theorem?

Pythagoras' theorem is a fundamental principle in geometry that relates to the three sides of a right-angled triangle. It states that:

"In a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides."

In mathematical terms, if a, b, and c are the lengths of the sides of a right-angled triangle, where c is the hypotenuse, then the theorem can be written as:

\(c^2 = a^2 + b^2\)

We can use the Pythagorean theorem to determine the length of the missing side if we know that the given sides form a right triangle.

In this case, we have two sides of the triangle given: 7.2 feet and 9.6 feet. Let's assume that c is the length of the hypotenuse.

If the triangle is a right triangle, then we can use the Pythagorean theorem to solve for c:

\(c^2 = 7.2^2 + 9.6^2\)

\(c^2 = 51.84 + 92.16\)

\(c^2 = 144\)

\(c = \sqrt{144}\)

c = 12 feet

Therefore, if the triangle is a right triangle, then the length of the missing side is 12 feet.

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1888 ounces bags of dried dill can be made

Addition: Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined

let us consider that, x = dried cilantro , y = dried dill

so by the given information we can write addition of dried cilantro an dried dill is equal to 253

x + y = 253

and also said that container of dried cilantro is 17 pounds heavier than that of container of dried dill so we can write, x = y + 17

substitute the value of x in the 1st equation

y + 17 + y = 253

2y + 17 = 253

2y = 253 - 17

2y = 236

y = 236/2

y = 118

so there is 118 pounds of

and it will be sold in 1 ounce bags

we know, 1 pound = 16 ounces

so 118 pounds = (118×16) = 1888 ounces

which will make 1888 ounces bags

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Answer:

You may make dried dill in 1888 ounce bags.

Step-by-step explanation:

What does addition mean?

One of the four fundamental operations in mathematics is addition. The other three are subtraction, multiplication, and division. When two whole numbers are added, the sum or total of those values is obtained.

Consider that x represents dried cilantro and y represents dry dill.

So, using the information provided, we can say that adding dry cilantro and dried dill equals 253.

x + y = 253

and added that a container of dried cilantro weighs 17 pounds more than a container of dried dill, leading us to derive the equation x = y + 17

substitute the value of x in the 1st equation

y + 17 + y = 253

2y + 17 = 253

2y = 253 - 17

2y = 236

y = 236/2

y = 118

so there is 118 pounds of

and it will be sold in 1 ounce bags

we know, 1 pound = 16 ounces

so 118 pounds = (118×16) = 1888 ounces

which will make 1888 ounces bags.

x1 and x2 are uncorrelated random variables.

Given that y1 and y2 are independent random variables with mean 0 and variance σ^2, and x1 and x2 are related to y1 and y2 as follows:

x1 = y1 and x2 = ρy1√(1-ρ^2)y2

We can find the mean and variance of x1 and x2 as follows:

Mean of x1:

E(x1) = E(y1) = 0 (since y1 has mean 0)

Variance of x1:

Var(x1) = Var(y1) = σ^2 (since y1 has variance σ^2)

Mean of x2:

E(x2) = ρE(y1)√(1-ρ^2)E(y2) = 0 (since both y1 and y2 have mean 0)

Variance of x2:

Var(x2) = ρ^2Var(y1)(1-ρ^2)Var(y2) = ρ^2(1-ρ^2)σ^2 (since y1 and y2 are independent)

Now, let's find the covariance between x1 and x2:

Cov(x1, x2) = E(x1x2) - E(x1)E(x2)

= E(y1ρy1√(1-ρ^2)y2) - 0

= ρσ^2√(1-ρ^2)E(y1y2)

= 0 (since y1 and y2 are independent and have mean 0)

Therefore, x1 and x2 are uncorrelated random variables.

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No matter what the shape of the parent population is, as long as our sample size is 10 or greater, we can conclude that the sampling distribution of the sample mean is approximately normally distributed. This statement is False.

We know that,

the Central limit theorem says that no matter what the distribution of the population is, as long as the sample is "large", meaning of size 30 or more, the sample mean is approximately normally distributed. If the population is normal to begin with then the sample mean also has a normal distribution, regardless of the sample size.

So therefore we need sample size greater than 30 and we have given 10 or greater.

Hence the given statement is false.

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Answer:

Son's Age: 11

Mary's Age: 33

Step-by-step explanation:

Let set Mary and her son as variables,

M = Mary's age

S  = Mary's son age

Breakdown:

"Mary is three times as old as her son"

M = 3S

"In 12 years, Mary's age will be one less than twice her son's age"

M + 12 = 2(S + 12) - 1

we add 12 to both sides as it will be in 12 years for both

We know that M = 3S, so we plug this in

3S + 12 = 2(S + 12) - 1

Now solve for S (son's age),

3S + 12 - 12 = 2(S + 12) - 1 - 12

3S = 2(S + 12) - 13

3S = 2S + 24 - 13

3S - 2S = 2S - 2S + 24 - 13

S = 24 - 13

S = 11

To find Mary age, plug in her son age ,

M = 3S

M = 3(11)

M = 33

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We are given that P(A) = 0.30 and P(B) = 0.40, which means the probability of A given B (P(A | B)) must also be 0 since P(A ∩ B) = 0. Therefore, P(A ∩ B) = 0 and P(A | B) = 0.

1. P(A ∩ B) = 0 since the events are mutually exclusive.

2. P(A | B) = 0 since P(A ∩ B) = 0.

The two events are mutually exclusive, which means that they cannot occur at the same time. This implies that the probability of both A and B occurring together, P(A ∩ B), must be 0. We are given that P(A) = 0.30 and P(B) = 0.40, which means the probability of A given B (P(A | B)) must also be 0 since P(A ∩ B) = 0. Therefore, P(A ∩ B) = 0 and P(A | B) = 0.

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Answer:

f(x)=(x-1)^2+3

Step-by-step explanation:

Both equations vertexes equal (1, 3) while the rest do not match.

f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.

We can use the technique of completing the square to rewrite the given function f(x) in vertex form.

f(x) = 4 + x² - 2x

f(x) = (x² - 2x) + 4

Adding and subtracting (1) inside the parentheses

f(x) = (x² - 2x + 1) + 4 - 1

f(x) = (x - 1)² + 3

So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.

Therefore, the correct option is f(x) = (x - 1)² + 3.

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The values of T(0) = e(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), r''(t) = 8e^(2t) + 8e^(-2t).

We are given that r(t) = e^(2t), e^(-2t), te^(2t). To find T(0), we need to evaluate the unit tangent vector T(t) at t=0. The formula for the unit tangent vector is T(t) = r'(t)/|r'(t)|, where |r'(t)| is the magnitude of r'(t).

r'(t) = 2e^(2t) - 2e^(-2t), so r'(0) = 2 - 2 = 0.

Thus, T(0) = r'(0)/|r'(0)| = 0/|0|, which is undefined.

However, since r'(0) = 0, we can use the normal vector instead to find the direction of the tangent line at t=0.

The normal vector N(0) is given by N(t) = T'(t)/|T'(t)|. To find T'(t), we differentiate r'(t) with respect to t:

r''(t) = 4e^(2t) + 4e^(-2t)

So, r''(0) = 4 + 4 = 8. Thus, T'(0) = r''(0)/|r'(0)| = 8/0, which is undefined.

To find r'(t), we can differentiate r(t) using the product rule:

r'(t) = 2e^(2t), -2e^(-2t), 2te^(2t) + e^(2t)

To find r''(t), we can differentiate r'(t):

r''(t) = 4e^(2t), 4e^(-2t), 4te^(2t) + 4e^(2t)

Thus, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

Therefore, T(0) = e^(0) = 1, r''(0) = 8, r'(t) = 2e^(2t) - 2e^(-2t), and r''(t) = 8e^(2t) + 8e^(-2t).

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The converse of the statement "If a figure is a square, its diagonals divide it into isosceles triangles" would be:

"If a figure's diagonals divide it into isosceles triangles, then the figure is a square."

The converse statement is not necessarily true. While it is true that in a square, the diagonals divide it into isosceles triangles, the converse does not hold. There are other shapes, such as rectangles and rhombuses, whose diagonals also divide them into isosceles triangles, but they are not squares. Therefore, the converse of the statement is not always true.

Therefore, the converse of the given statement is not true. The existence of diagonals dividing a figure into isosceles triangles does not guarantee that the figure is a square. It is possible for other shapes to exhibit this property as well.

In conclusion, the converse statement does not hold for all figures. It is important to note that the converse of a true statement is not always true, and separate analysis is required to determine the validity of the converse in specific cases.

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A number is divisible by another number if it yields a whole number when divided by that number. For example, 8 is divisible by 2 because 8/2 = 4, and 4 is a whole number.

Then, let us verify the options.

• 13860 is divisible by 4?

3465 is a whole number. Thus, 13860 is divisible by 4.

• 13860 is divisible by 7?

1980 is a whole number. Thus, 13860 is divisible by 7.

• 13860 is divisible by 9?

1540 is a whole number. Thus, 13860 is divisible by 9.

• 13860 is divisible by 11?

1260 is a whole number. Thus, 13860 is divisible by 11.

Answer: $135

Step-by-step explanation: x(40/100)=54. x represents the original price and 40/100 is the discount while 54 is the money saved from the discount. This ultimately shows us 40% of something is 54 and that something is represented by x and x equals 135.

The conclusion that the building managers can draw based on the given data is; D: Riding to work is more common among tech company employees than at the other modes of transportation.

The results of the survey are shown in the two-way frequency table below.

From the table we can see that;

Total Cars = 55

Total Number of Buses = 46

Total Number of Walks = 36

Total Number of Bikes = 48

Total Number of Subways = 80

Total Number of  Tech company = 98

Total Number of Law Firms = 73

Total Number of Finance Groups = 94

Option A; There are 16 people who use buses from the tech company while there are 26 people who use subway from the Law firm. Thus, the statement is false.

Option B; There are 12 people who walk to work  at the finance group while there are a total of 10 people who walk to work at the law firm. Thus the statement is false.

Option C; Percentage of walkers at law firm = 10/73 * 100% = 13.7%

Percentage of car drivers at the tech firm = 10/98 * 100% = 10.2%

Thus, the statement is false

Option D; This is true

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Answer:

It is more common to find a bus rider who works at the tech company than a person on the subway who works at the law firm.

Step-by-step explanation:

got it right on edmentum

The area of rhombus can be found using the formula A = (d1 x d2)/2, where d1 and d2 are the lengths of the diagonals. Using area formula, we get A = (24 x 18)/2 the area of the rhombus is 24√(119) square meters.

Let's start by finding the other diagonal of the rhombus.

We know that the perimeter of a rhombus is four times the length of one of its sides. So, if the perimeter is 80 m, then each side has a length of 80/4 = 20 m.

We also know that the diagonals of a rhombus are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Therefore, each leg of one of these right triangles is half of one of the diagonals of the rhombus.

Let's call the other diagonal of the rhombus d. Then, using the Pythagorean theorem in one of the right triangles, we have

(20/2)² + (d/2)² = 24²

100 + d²/4 = 576

d²/4 = 476

d = 2√(119)

Now that we have both diagonals, we can find the area of the rhombus by multiplying them and dividing by 2

Area = (24 * 2√(119))/2

Area = 24√(119)

Therefore, the area of the rhombus is 24√(119) square meters.

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

"  The area of a rhombus whose perimeter is 80 m and one of whose diagonal is 24 m is ..........."--

Answer:

I believe the answer is 13.

Step-by-step explanation:

According to the question Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

To calculate the probability of obtaining a straight flush in a five-card poker hand, we need to determine the number of possible straight flush hands and divide it by the total number of possible five-card hands.

A straight flush consists of five consecutive cards of the same suit. There are four suits in a standard deck of cards (hearts, diamonds, clubs, and spades), and for each suit, there are nine possible consecutive sequences (Ace, 2, 3, 4, 5, 6, 7, 8, 9; 2, 3, 4, 5, 6, 7, 8, 9, 10; etc.). Therefore, there are \(\(4 \times 9 = 36\)\) possible straight flush hands.

The total number of possible five-card hands can be calculated using the concept of combinations. In a standard deck of 52 cards, there are \(\({52 \choose 5}\)\) different ways to choose five cards. The formula for combinations is \(\({n \choose k} = \frac{n!}{k!(n-k)!}\), where \(n\)\) is the total number of items and \(\(k\)\) is the number of items being chosen.

Using the formula, we have \(\({52 \choose 5} = \frac{52!}{5!(52-5)!} = 2,598,960\).\)

Therefore, the probability of obtaining a straight flush in a five-card poker hand is:

\(\[\frac{\text{{number of straight flush hands}}}{\text{{total number of five-card hands}}} = \frac{36}{2,598,960} \approx 0.00001385\]\)

Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

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Answer:

-2x^2+12x

Step-by-step explanation:

Answer:

36 red, 22 blue

37 red, 21 blue

38 red, 20 blue

39 red, 19 blue

40 red, 18 blue

Step-by-step explanation:

Total number of pens: 58

More red pens than blue pens.

At least 36 red pens.

No more than 40 red pens.

Possible number of pens:

36 red, 22 blue

37 red, 21 blue

38 red, 20 blue

39 red, 19 blue

40 red, 18 blue

The given triangle ABC and DEF are similar

From the properties of the similar triangle :

The ratio of the corresponding sides of similar traingle are equal and the ratio of perimeter is also equal to the ratio of corresponding sides

In the triangle ABC, AC=9, BC=6, and the angle B is 90 degree

then apply pythagoras to find the third side of triangle:

Pythagoras Theorem: The square of sum of base and perpendicular is equal to the square of Hypotenuse.

Perimeter of Triangle is express as the sum of the length of all the sides of traingle

The scale Factor :

Since the ratio of perimeter of triangle ABC and DEF are same as the ratio of thier corresponding sides

So,

So, Perimeter of triangle DEF = 38.69 unit

Answer:

y=1/2x-5

Step-by-step explanation:

Parallel lines always have the same slope. Thus, since you know y=1/2+1 is parallel you know the slope is 1/2 as in y=mx+b, m is the slope. In addition, you know the y-intercept as -5. So the equation is y=1/2x-5

Answer:

y=1/2x-5

Step-by-step explanation:

to be parallel it needs to have the same slope so the slope is the same

0,-5 is the y intercept so -5 is the y intercept

The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

The domain of a function is the set of all possible input values (also known as the independent variable) for which the function is defined.

In other words, it is the set of values of x for which the function has a corresponding output value (also known as the dependent variable).

Here we have

f(x) = 4x + 3

g(x) = x² - 5x + 6  

Then f(x) · g(x) can be calculated as follows

=> (4x + 3) [ x² - 5x + 6 ]

Using distributive property, we get:

=> 4x (x² - 5x + 6) + 3(x² - 5x + 6)

=> 4x³ - 20x² + 30x + 3x² - 15x + 18

=> 4x³ - 17x² + 15x + 18  

Hence, f(x).g(x) = 4x³ - 17x² + 15x + 18    

The domain of the function f(x) = 4x³ - 17x² + 15x + 18 is all real numbers since there are no restrictions or conditions that would make the function undefined for any value of x.

Therefore,

The function f(x).g(x) = 4x³ - 17x² + 15x + 18 and the domain of this function is (-∞, +∞).

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Given:

The recursive formulae.

To find:

The correct explicit formulae for the given recursive formulae.

Solution:

If the recursive formula of a GP is \(f(n)=rf(n-1), f(1)=a, n\geq 2\), then the explicit formula of that GP is:

\(f(n)=ar^{n-1}\)

Where, a is the first term and r is the common ratio.

The first recursive formula is:

\(f(1)=5\)

\(f(n)=3f(n-1)\) for \(n\geq 2\).

It is the recursive formula of a GP with a=5 and r=3. So, the required explicit formula is:

\(f(n)=5(3)^{n-1}\)

Therefore, the required explicit formula for the first recursive formula is \(f(n)=5(3)^{n-1}\).

If the recursive formula of an AP is \(f(n)=f(n-1)+d, f(1)=a, n\geq 2\), then the explicit formula of that AP is:

\(f(n)=a+(n-1)d\)

Where, a is the first term and d is the common difference.

The second recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+5\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=5. So, the required explicit formula is:

\(f(n)=5+(n-1)5\)

\(f(n)=5+5(n-1)\)

Therefore, the required explicit formula for the second recursive formula is \(f(n)=5+5(n-1)\).

The third recursive formula is:

\(f(1)=5\)

\(f(n)=f(n-1)+3\) for \(n\geq 2\).

It is the recursive formula of an AP with a=5 and d=3. So, the required explicit formula is:

\(f(n)=5+(n-1)3\)

\(f(n)=5+3(n-1)\)

Therefore, the required explicit formula for the third recursive formula is \(f(n)=5+3(n-1)\).

The ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

Given is that a granola recipe calls for 3 cups of oats, 1 cup of almonds. 1 cup of pecans, and 1 cup of dried fruit

The ratio of nuts to fruits is -

r = (3 oat cups + 1 almond cup + 1 pecan cup)/(1 dried fruit cup)

r = 5/1

5 : 1

For every 5 cups of nuts, there is 1 cup of dried fruit cup.

Therefore, the ratio of nuts to fruits is 5 : 1 and for every 5 cups of nuts, there is 1 cup of dried fruit cup.

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Answer:

9

Step-by-step explanation: