A business invests $25,000 in an account that earns 5.1% simple interest annually.
What is the value of the account after 4 years?

The only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).

It should be noted that to determine which equation is a polynomial identity, we need to simplify both sides of each equation and see if they are equal for all values of c and d.

(A) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ - d³ + 3cd(c + d)

The left-hand side can be expanded using the binomial formula. The right-hand side is a polynomial of degree 3, so we can see that equation (A) is a polynomial identity.

(B) (c+d) = c + d³ + 3cd(c + d)

= d³ + c³ + 3cd(c + d) + c + d - c³

= d³ + c³ + 3cd(c + d) + c + d

The right-hand side can be simplified, but it is not equal to the left-hand side for all values of c and d. Therefore, equation (B) is not a polynomial identity.

(C) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ + d³ + 3cd(c + d) + cd(c - d)

The right-hand side is not equal to the left-hand side for all values of c and d, so equation (C) is not a polynomial identity.

(D) (c+d)³ = c³ + 3c²d + 3cd² + d³

= c³ - d³ + 3cd(c - d) + c³ + d³

= 2c³ + 3cd(c - d)

The right-hand side is not equal to the left-hand side for all values of c and d, so equation (D) is not a polynomial identity.

Therefore, the only equation that is a polynomial identity is (A), (c+d)³ = c³ - d³ + 3cd(c + d).

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there are 3,360 ways in which the top 3 cars can finish the race.

How to Determine the number of ways?

To determine the number of ways in which the top 3 cars can finish the race, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, the order of the cars finishing the race matters.

The number of ways to determine the first place finisher is 16, as any of the 16 cars can finish in first place. Once the first place finisher has been determined, there are only 15 cars remaining, and any one of them can finish in second place. Therefore, there are 15 possible ways to determine the second place finisher.

Similarly, once the first and second place finishers have been determined, there are 14 cars remaining, and any one of them can finish in third place. Therefore, there are 14 possible ways to determine the third place finisher.

To find the total number of ways in which the top 3 cars can finish the race, we can multiply the number of possibilities for each place together:

16 x 15 x 14 = 3,360

Therefore, there are 3,360 ways in which the top 3 cars can finish the race.

It is important to note that this calculation assumes that each car is unique and that there are no ties for any of the top 3 positions. If there were ties, the calculation would become more complicated and would involve combinations as well as permutations.

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The answers are: A)H0: μ1 − μ2 = 0; Ha: μ1 − μ2 ≠ 0

(b)  Means: Company A___50.6___ min.; Company B___52.75___ min.

c)The t-value is -0.30107., The p-value is 0 .764815.

A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon

A)H0: μ1 − μ2 = 0

i.e there is no difference between the means of delayed flight for two different airlines

Ha: μ1 − μ2 ≠ 0

i.e there is a difference between the means of delayed flight for two different airlines

(b)

Company A___50.6___ min.

Company B___52.75___ min.

Mean of Company A = x`1= ∑x/n =34+ 59+ 43+ 30+ 3+ 32+ 42+ 85+ 30+ 48+ 110+ 50+ 10+ 26+ 70+ 52+ 83+ 78+ 27+ 70+ 27+ 90+ 38+ 52+ 76/25

= 1265/25= 50.6

Mean of Company B = x`2= ∑x/n =

=46+ 63+ 43+ 33+ 65+ 104+ 45+ 27+ 39+ 84+ 75+ 44+ 34+ 51+ 63+ 42+ 34+ 34+ 65+ 64/20

= 1055/20= 52.75

Difference Scores Calculations

Company A

Sample size for Company A= n1= 25

Degrees of freedom for company A= df1 = n1 - 1 = 25 - 1 = 24

Mean for Company A= x`1=  50.6

Total Squared Difference (x-x`1) for Company A= SS1: 16938

s21 = SS1/(n1 - 1) = 16938/(25-1) = 705.75

Company B

Sample size for Company B= n1= 20

Degrees of freedom for company B= df2 = n2 - 1 = 20 - 1 = 19

Mean for Company B= x`2=  52.75

Total Squared Difference (x-x`2) for Company B= SS2=7427.75

s22 = SS2/(n2 - 1) = 7427.75/(20-1) = 390.93

T-value Calculation

Pooled Variance= Sp²

Sp² = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22)

Sp²= ((24/43) * 705.75) + ((19/43) * 390.93) = 566.65

s2x`1 = s2p/n1 = 566.65/25 = 22.67

s2x`2 = s2p/n2 = 566.65/20 = 28.33

t = (x`1 - x`2)/√(s2x`1 + s2x`2) = -2.15/√51 = -0.3

The t-value is -0.30107.

The total degrees of freedom is = n1+n2- 2= 25+20-2=43

The critical region for two tailed test at significance level ∝ =0.05 is

t(0.025) (43) = t > ±2.017

Since the calculated value of t=  -0.30107.  does not fall in the critical region t > ±2.017, null hypothesis is not rejected that is there is no difference between the means of delayed flight for two different airlines.

The p-value is 0 .764815. The result is not significant at p < 0.05.

C) Do not reject H0. There is no statistical evidence that one airline does better than the other in terms of their population mean delay time.

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The value of Cscθ is 1/y.

What is a trigonometric function?

The right-angled triangle's angle and the ratio of its two side lengths are related by the trigonometric functions, which are actual functions. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Here, we have

Given: if p(x,y) is the point on the unit circle defined by the real number theta.

We have to find the value of the csc theta.

P(x,y) is the point on the unit circle  (the unit circle has a radius of 1 and center (0,0))

Now in a diagram, we can see that

OA= x

AP= y

radius OP =1

∠POA =θ

Now in ΔAOP

Cscθ = hypotenuse/opposite side

Cscθ = OP/AP

Cscθ = 1/y

Hence, the value of Cscθ is 1/y.

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Answer:

20 ..............................

If NP and QS are parallel lines and ∠NOM = 130° then the value of ∠POM is 50°.

Parallel lines are two or more lines in a plane that do not intersect, regardless of how far apart they are.

Despite being located at different distances from one another, parallel lines always have the same slope, which is the same steepness and direction.

Since NP and QS are parallel lines, we have:

∠NOM + ∠MOP = 180° (because NOM and MOP are on a straight line)

Also, the alternate interior angles NOM and POM are equal, so:

∠NOM = ∠POM

Substituting this into the first equation gives:

∠POM + ∠MOP = 180°

We can now solve for ∠POM by substituting the given value:

130° + ∠POM = 180°

∠POM = 50°

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Answer: The altitude of the triangle is [tex]h = 7 \sqrt{3}.[/tex]

Step-by-step explanation:

Suppose that we separate the equilateral triangle with the altitude of the triangle, as shown in the diagram I attached.

Then the length of the altitude [tex]h[/tex] can be found through the Pythagorean theorem:

[tex]h = \sqrt{14^2-\left( \frac{14}{2} \right)^2} = \sqrt{147} = \boxed{7 \sqrt{3}}.[/tex]

Therefore, the altitude of the equilateral triangle is [tex]h = 7 \sqrt{3}.[/tex]

The diameter of the semicircle is with an area of 76.97 square yards is 14 yards.

Semicircle is half that of a circle, hence the area will be half that of a circle. Area of semi circle = 1/2 × πr²

Where r radius and π is constant pi.

Since we are given the area of the semicircle as 76.97 square yards, we can set up the following equation:

76.97 = 1/2 × (πr²)

Multiplying both sides by 2, we get:

153.94 = πr²

Dividing both sides by π, we get:

r² = 49

Taking the square root of both sides, we get:

r = 7

Therefore, the diameter of the semicircle is: d = 2r  = 2(7) = 14 yards

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The amount of taxes owed on a taxable income of $51, 100 is $6,919.00. The correct option is B.

To determine the amount of taxes owed on a taxable income of $51,100, we need to use the federal income tax brackets and rates for the tax year in question.

For the tax year 2021, the federal income tax brackets and rates for single filers are:

10% on taxable income from $0 to $9,950

12% on taxable income from $9,951 to $40,525

22% on taxable income from $40,526 to $86,375

24% on taxable income from $86,376 to $164,925

32% on taxable income from $164,926 to $209,425

35% on taxable income from $209,426 to $523,600

37% on taxable income over $523,600

To calculate the taxes owed on a taxable income of $51,100, we need to determine the amount of income that falls into each tax bracket, and then apply the corresponding tax rate to each portion of income.

Income up to $9,950 is taxed at 10%. This gives us a tax of 0.10 x $9,950 = $995.

Income from $9,951 to $40,525 is taxed at 12%. This gives us a tax of 0.12 x ($40,525 - $9,951) = $3,384.48.

Income from $40,526 to $51,100 is taxed at 22%. This gives us a tax of 0.22 x ($51,100 - $40,526) = $2,312.72.

Adding these three amounts together, we get the total tax owed:

$995 + $3,384.48 + $2,312.72 = $6,692.20

Therefore, the closest answer choice is B) $6,919.00.

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The amount of taxes owned on a taxable income of $51100 is $11242 which is approximately equal to option (c).

An income refers to the money that an individual or organization receives on a regular basis from various sources, such as employment, investments, or business activities. It is typically reported as gross income before taxes and other deductions are taken out.

Tax is a mandatory financial charge imposed by the government on individuals, businesses, and other entities, based on their income or property value. The revenue generated from taxes is used to fund public services and infrastructure.

=$51100* 22/100

=$11242

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The difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

Assume that the data is n-sized as follows:

x1, x2, x3 .....xn

Let the mean of this data be: x'

The mean of the absolute differences between the observations and the mean of the data to which they belong, then, is the mean absolute deviation of such a data.

It is determined by:

M.A.D = ∑ |xi - x'| / n  (i = 1 ....n)

Hence, mean absolute deviation is the average deviation of the data values, regardless of whether it is above or below the mean.

Due to the fact that:

The mean absolute deviation of the monthly temperatures in New Orleans is 43.5°F, which implies that on average, the temperature deviates 43.5°F from the average monthly temperature.

where mean displays New Orleans, Louisiana's typical monthly temperature.

Thus, the difference between the monthly mean temperature and the average monthly temperature for New Orleans, Louisiana, is typically about 43.5°F.

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Answer: 32

Step-by-step explanation:

     We will use the Order of Operations. First, we will do parentheses (), then brackets [], then lastly the braces {}, then lastly add 12.

Given:

     {[2+(11+9)]-2)+12

Add 11 to 9:

     {[2+20]-2)+12

Add 2 to 20:

     {22-2)+12

Subtract 2 from 20:

     20 + 12

Add 20 and 12:

     32

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

The statistical question that can result in numerical data is "How many hours this week did you spend on homework?"

This is because the question is asking for a numerical response that can be measured and counted. The other options are not statistical questions that can result in numerical data.

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The solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

What is inequality?

In mathematics, the inequality of two lines refers to the relationship between the slopes and y-intercepts of two different lines on a coordinate plane. Specifically, if the slope of one line is greater than the slope of another line, and their y-intercepts are not equal, then the inequality symbol (< or >) can be used to represent their relationship. For example, if line A has a slope of 2 and a y-intercept of -3, and line B has a slope of 1 and a y-intercept of 1, we can write A > B to represent that line A is steeper than line B.

To solve this problem, we need to use the information given to us to set up an inequality that represents the total number of seats in the theater and then use that inequality to determine the maximum number of people that can be in the theater while still meeting the fire safety regulations.

Let's start by calculating the total number of seats in the theater. We know that there are 90 seats in the balcony and 15 rows on the floor. We don't know the exact number of seats in each row, but we do know that each row has the same number of seats, which we will call x. Therefore, the total number of seats in the theater is 90 + (15 × x)

Now we can set up an inequality to represent the maximum number of people that can be in the theater while still meeting the fire safety regulations. We know that this number must be less than or equal to 240. Therefore, our inequality is 90 + (15 × x) ≤ 240

Now we can solve for x by first subtracting 90 from both sides of the inequality,

15 × x ≤ 150

Next, we can divide both sides of the inequality by 15,

x ≤ 10

Therefore, the solution to the inequality is x ≤ 10, which means that each row of seats on the floor must have 10 seats or fewer in order to meet the fire safety regulations.

To check this solution, we can plug x = 10 into our expression for the total number of seats,

Total number of seats = 90 + (15 × 10) = 240

This confirms that the maximum number of people in the theater is 240, which is the limit imposed by the fire safety regulations.

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Answer:

if question is a fraction then -0.001429, if not then 624.0235948

The shaded area covers around 0.8664 square feet of space.

The mean and standard deviation of the standard normal distribution are 0 and 1, respectively. The standard deviation shows how much a particular measurement deviates from the mean, and the standard normal distribution is centred at zero.

Using a conventional normal distribution table, we must first determine the areas to the left of z= -1.5 and z=1.5, and then subtract those two areas to determine the area of the shaded zone.

Using a standard normal distribution table, we find that the area to the left of z= -1.5 is 0.0668, and the area to the left of z=1.5 is 0.9332. As a result, the darkened region's area is:

0.9332 - 0.0668 = 0.8664

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Answer:

We can use the Law of Cosines to find the distance between points a and b.

Using the angles given, we can find the angle between points a and b:

Angle C = 180 - (76 + 32) = 72 degrees

Next, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the distance between points a and b, a is the distance between point c and point a (210 ft), b is the distance between point c and point b (150 ft), and C is the angle between points a and b (72 degrees).

Plugging in the values:

c^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

c^2 ≈ 21069.27

Therefore, the distance between points a and b is approximately:

c ≈ 145.2 ft

We can condense and find n's solution: 3n + 24 = 2n - 4

Since n = -14, the unknowable number is also -14.

A mathematical expression called an algebraic expression includes variables, integers, and mathematical operations including addition, subtraction, multiplication, and division. Algebraic expressions can be straightforward, like "2x," or they can be more complicated, like

[tex]3x^2+4y-5[/tex].

Variables are used to represent unknown quantities and have a range of possible values. In problems requiring unknown values or to represent connections between quantities, algebraic expressions are widely used.

A mathematical expression that includes variables, constants, and operations involving algebra (addition, subtraction, etc.) is known as an algebraic expression. Terms comprise expressions.

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Answer:

1500

Step-by-step explanation:

Number of boxes = 12

Number of pencils in each box = 125

Total number of pencils

= 12 × 125

= 1500 pencils

The perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

To find the perimeter of the regular octagon inscribed in a circle with radius 14 inches, we need to use the formula:

Perimeter of octagon = 8 x length of one side

Since the octagon is regular, all sides are congruent. Let s be the length of one side of the octagon.

The radius of the circle is 14 inches, which is also the distance from the center of the circle to any vertex of the octagon. We can divide the octagon into eight congruent isosceles triangles, each with base s and legs of length 14 inches. We can then use the Pythagorean theorem to find the length of the base s:

s² = 14² - (s/2)²

s² = 196 - s²/4

5s²/4 = 196

s² = 156.8

s ≈ 12.52

Therefore, the perimeter of the octagon is:

Perimeter = 8s ≈ 100.16 inches (rounded to 2 decimal places).

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1. The total amount of your emergency fund will be $11,403.75.

2. $8,552.81 is in the CD, and $2,850.94 is in the regular savings account.

Your FICA deduction is 7.65% of your gross income:

7.65% of $4,520.00 = $345.98

Your federal tax withholding is 11.75% of your gross income:

11.75% of $4,520.00 = $531.40

Your state tax withholding is 8.5% of your gross income:

8.5% of $4,520.00 = $384.40

Your total deductions are:

= $345.98 + $531.40 + $384.40

= $1,261.78

Your monthly income after deductions is:

= $4,520.00 - $1,261.78

= $3,258.22

Your fixed expenses are 30% of your realized income:

= 30% of $3,258.22

= $977.47

Your monthly savings amount is:

= $3,258.22 - $977.47

= $2,280.75

You saved 5 months' worth in an emergency fund, so the total amount in your emergency fund is:

= 5 x $2,280.75

= $11,403.75

Regenerate response

You placed 75% of your emergency fund in a 60-day CD at a 5.25% APR:

= 75% of $11,403.75 = $8,552.81

You placed the remaining 25% of your emergency fund in a regular savings account at a 3.8% APR:

= 25% of $11,403.75

= $2,850.94.

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Answer:

x = 7

Step-by-step explanation:

8x + 5 + 3x + 8 = 90

11x + 5 + 8 = 90

11x + 13 = 90

11x = 77

x = 7

Let's Check

8(7) + 5 + 3(7) + 8 = 90

56 + 5 + 21 + 8 = 90

61 + 21 + 8 = 90

82 + 8 = 90

90 = 90

So, x = 7 is the correct answer!

Answer:

7

Step-by-step explanation:

First, collect common factors. This means put the x's together and the regular numbers together.

8x+3x=11x

5+8=13

11x+13=90

Subtract 13 from both sides

11x+13=90

    -13  -13

11x=77

Divide 77 by 11

x=7

Hope this helps! :)

Answer:

2004

Step-by-step explanation:

The equation a² + b² = c² represents the Pythagorean theorem.

This is a theorem that  states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.

To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:

If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):

Plug in the known values for a and b into the equation and solve for c.

Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.

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The percentage of females with brown eyes as follows is 25%.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:

Move the constant term to the right side of the equation:

x^2 + 4x = 11

Complete the square by adding the square of half the coefficient of x to both sides of the equation:

x^2 + 4x + (4/2)^2 = 11 + (4/2)^2

Simplifying the left side:

x^2 + 4x + 4 = 11 + 4

Factor the perfect square on the left side of the equation:

(x + 2)^2 = 15

Take the square root of both sides of the equation:

x + 2 = ±√15

Solve for x by subtracting 2 from both sides:

x = -2 ± √15

Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.

Step-by-step explanation:

w = width

2w + 2 =  Length

Area = W x L  = 84 = w (2w+2)

                          84 = 2w^2 + 2w

                            0 = 2w^2 + 2w - 84        Use Quadratic Formula

                                                                 a = 2    b=2    c = -84

to find  

W = 6      then     L =  14 inches

In 5 minutes, the camel can drink = 1.5 x 5 = 7.5 gallons of water.

So, the camel can drink 7.5 gallons of water in 5 minutes.

The unitary method is a mathematical technique used to solve problems related to proportionality.

It involves finding the value of a single unit and using it to determine the value of a given quantity or multiple quantities.

The unitary method is useful in solving problems that involve direct proportion or inverse proportion.

To find out how much water the camel can drink in 5 minutes, we can use the unitary method.

We know that the camel can drink 15 gallons of water in 10 minutes.

So, in 1 minute, the camel can drink = 15/10 = 1.5 gallons of water.

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