suppose the scores on an exam are normally distributed with a µ = 72 points, and σ =5. a) a student is randomly selected. what is the probability that the student scored between 75 and 81 points?

For a taxable income of $1,80,900, the effective tax rate is 21.11%.

Marginal tax is the tax rate applied to an individual’s last dollar of income. It is the additional tax that must be paid on any additional income earned. In other words, it is the tax rate that applies to an individual’s income after all deductions. For example, if an individual’s income is $50,000 and the marginal tax rate is 25%, then the individual must pay an additional $12,500 in taxes on top of the $25,000 in taxes already paid on their $50,000 income.

Marginal tax rates are progressive, meaning that as an individual’s income increases, the marginal tax rate will increase as well. The marginal tax rate is important to understand because it helps individuals determine how much additional income they will need to earn in order to make up for the taxes they will have to pay on that income. It is also important to understand how marginal tax rates can affect tax planning strategies.

To determine the effective tax rate for a taxable income of $180,900, calculate the sum of the marginal tax rates for each tax bracket that the $180,900 falls into. The taxable income of $180,900 is greater than $89,075 and less than $170,050. The marginal tax rates for these two tax brackets are 22% and 24%, respectively. The sum of the marginal tax rates is 46%. Divide the sum by the taxable income of $180,900 to get the effective tax rate of 21.11%. Round the final answer to the nearest hundredth to get 21.11%.

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Answer:

Step-by-step explanation:

f(x)=x^2+1

f(x^2+1)

f(x^2+1):x^4+2x^2+2

f(f(x))=x^4+2x^2+2

2nd answer

Hope this helps!^^

There are 15,504 different committees that can be chosen from the 20-member student council to form a committee of 15 students.

To calculate the number of different committees that can be chosen from a 20-member student council to form a committee of 15 students, we can use the combination formula.

The number of combinations of selecting 'r' items from a set of 'n' items is given by the formula:

C(n, r) = n! / (r!(n - r)!)

In this case, we want to select 15 students from a pool of 20 members, so the formula becomes:

C(20, 15) = 20! / (15!(20 - 15)!)

Calculating this value:

C(20, 15) = 20! / (15! * 5!)

The factorial notation represents the product of all positive integers up to a given number. Evaluating the factorials:

20! = 20 * 19 * 18 * 17 * 16 * 15!

15! = 15 * 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5!

By canceling out common factors:

C(20, 15) = (20 * 19 * 18 * 17 * 16) / (5 * 4 * 3 * 2 * 1)

Simplifying:

C(20, 15) = 15,504

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A line is defined by the equation [x, y, z] = [-2, 3, 7] + t[3, -2, 5].

Parametric equations for the line are:  x = -2 + 3ty = 3 - 2ty = 7 + 5t

To determine if the line contains the point (10, -5, 22),  

we need to substitute x = 10, y = -5, z = 22 in the equation and check if there exists a value of t that satisfies the equation.

Using the above equations, we get:10 = -2 + 3t-5 = 3 - 2t22 = 7 + 5t

Solving the above system of equations, we get:t = 4

Substituting this value of t in the given equation, we get:[x, y, z] = [-2, 3, 7] + t[3, -2, 5][10, -5, 22] = [-2, 3, 7] + 4[3, -2, 5][10, -5, 22] = [10, -5, 22]

Yes, the point (10, -5, 22) lies on the given line since it satisfies the equation.

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Answer: 156

Step-by-step explanation:

80 x 195% = 156

OR

80 x 1.95 = 156

Answer:

The answer is 38.

Step-by-step explanation:

You have to substitue c = -4 into the expression :

Let c = -4,

\( {( - 4)}^{2} - 5( - 4) + 2\)

\( = 16 + 20 + 2\)

\( = 38\)

Answer: 35ft

Step-by-step explanation:

The area for a rectangle or square is Width times Length (W*L)

So we can take our given measurements and multiply them

\(5*7=35\)

To find a quadratic equation with the y-intercept and vertex, follow these steps: identify the coordinates of the y-intercept and vertex, substitute them into the general form of the quadratic equation, solve for the coefficients, and substitute the coefficients back into the equation. For example, if the y-intercept is (0, 3) and the vertex is (-2, 1), the quadratic equation would be y = x^2 + x + 3.

To find a quadratic equation with the y-intercept and vertex, we can follow these steps:

For example, let's say the y-intercept is (0, 3) and the vertex is (-2, 1). We can substitute these coordinates into the general form of the quadratic equation:

3 = a(0)^2 + b(0) + c

1 = a(-2)^2 + b(-2) + c

Simplifying these equations, we get:

c = 3

4a - 2b + c = 1

By substituting c = 3 into the second equation, we can solve for a and b:

4a - 2b + 3 = 1

4a - 2b = -2

2a - b = -1

By solving this system of equations, we find a = 1 and b = 1. Substituting these values back into the general form of the quadratic equation, we obtain the final equation:

y = x^2 + x + 3

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To find a quadratic equation with a given y-intercept and vertex, you need the coordinates of the vertex and one additional point on the curve.

Example:

Suppose we want to find a quadratic equation with a y-intercept of (0, 4) and a vertex at (2, -1).

To find a quadratic equation with a given y-intercept and vertex, you can use the vertex form of a quadratic equation and substitute the coordinates to obtain the equation. Then, use the y-intercept to find an additional point on the curve and solve a system of equations to determine the coefficients. Finally, substitute the coefficients into the standard form of the quadratic equation to get the final equation.

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Generally speaking, a S corporation is put up to reduce the tax obligations. It is Option (3).

A business form known as a S corporation is one that is allowed by the tax code to distribute its taxable income, credits, deductions, and losses to its shareholders directly. This provides it certain advantages over the more popular C corp. The S corp, an alternative to the limited liability company, is only available to small firms with 100 or fewer stockholders (LLC). S corporations and LLCs are both referred to as "pass-through entities" since they don't pay corporate taxes, instead, they pay their owners, who are then in charge of paying the necessary taxes.

One sort of legal corporate structure that is popular among small businesses is the S corporation, commonly referred to as a S corp or S corp or S subchapter. Another is a limited liability company (LLC). A corporation with 100 shareholders or fewer can profit from incorporation while still being taxed as a partnership thanks to the requirements of a S corp. S corporations and LLCs are both pass-through companies, which means they don't pay corporate taxes and provide their owners and principals with limited liability protection. LLCs, however, offer more flexibility.

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Correct Question:

An S corporation is generally set up to:

1. implement an expansion strategy

2. attract capital

3. reduce tax burdens

4. easy entry into an industry

5. take advantage of limited liability

Janet can customize a car in 630 different ways.

To determine the number of ways Janet can customize a car, we need to multiply the number of options for each customization choice.

Number of car models: 10

Number of exterior colors: 7

Number of interior colors: 9

To calculate the total number of ways, we multiply these numbers together:

Total number of ways = Number of car models × Number of exterior colors × Number of interior colors

= 10 × 7 × 9

= 630

Therefore, the explanation shows that Janet has a total of 630 options or ways to customize her car, considering the available choices for car models, exterior colors, and interior colors.

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Answer:

17.

Step-by-step explanation:

\(a^2+b^2 = c^2\) is the formula used to find the hypotenuse (also known as the Pythagora's Theorem).

Substitute the given values into the equation.

\(8^2+15^2=c^2\)

64 + 225 = \(c^2\)

289 = \(c^2\)

\(\sqrt{289}\) = c

c = 17

\(\left( \dfrac 49 \right) \div \left( \dfrac{18} 3 \right)\\\\\\=\dfrac 49 \div6\\\\\\=\dfrac 49 \times \dfrac 16\\\\\\=\dfrac{2}{9\times 3}\\\\\\=\dfrac{2}{27}\)

The variable X has a binomial distribution in the following distributions:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

In a binomial probability distribution, the number of "Successes" in a series of n experiments is represented as either success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 p), depending on the outcome's boolean value.

In a binomial distribution, we have a fixed number of independent trials (in this case, the number of patients), and each trial has only two possible outcomes (success or failure). The probability of success remains the same for each trial (in this case, the probability of the medicine working is 30%).

Option B does not represent a binomial distribution since it counts the number of patients for whom the medicine does not work, which is the complement of success. Option D is not a binomial distribution as it counts the number of doses each patient needs to take, which is not a success/failure outcome.

So, the correct answers are:

A. When the medicine is tried with two patients, X is the number of patients for whom the medicine worked.

C. When the medicine is tried with six patients, X is the number of patients for whom the medicine worked.

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0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.

According to collect from the data

Let us assume that the data as followed by

How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.

Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.

2,3,3,4,4,4

now then:

= 8!/2!3!3!4!4!4!

= 8.7.6.5.4!/2×6×6×24×24×4!

= 35/864

Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .

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In summary, the joint density of the continuous random variables X1 and X2 is given by k(1 – X2) f(X1, X2) if 0 < X1 < X2 < 1, and 0 elsewhere. To make this a probability density function, the value of k is determined to be 6.

Now, let's calculate the probability P(X1 < X2). We integrate the joint density function over the region where X1 is less than X2. The limits of integration for X1 are 0 to X2, and for X2, it is from X1 to 1. Evaluating the integral, we find that P(X1 < X2) = 32.

Next, we need to find the marginal density functions for X1 and X2. The marginal density function of X1, denoted as f1(x1), is obtained by integrating the joint density function over all possible values of X2. Similarly, the marginal density function of X2, denoted as f2(x2), is obtained by integrating the joint density function over all possible values of X1. After performing the integrations, we find that f1(x1) = 3(1 – x1) for 0 < X1 < 1, and f2(x2) = 6x2(1 – x2) for 0 < X2 < 1.

Finally, let's compute the probability P(X2 < X1|X1 < 3). We integrate the joint density function over the region where X2 is less than X1 and X1 is less than 3. The limits of integration for X2 are 0 to X1, and for X1, it is from 0 to 3. Evaluating the integral, we find that P(X2 < X1|X1 < 3) = 32.

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Answer:

4 hours

Step-by-step :

If Sunny runs twice as fast as Moonbeam

Given the assumed data:

Sunny's speed = 12m/h

Moonbeam's speed= 6m/h

Therefore, if they run for 2 hours, Sunny would have covered 12 * 2 = 24 miles

While Moonbeam would have covered 6 *2 = 12 miles in the same 2 hours.

This given illustration shows that given that all parameters are equal, except the x2 speed of Sunny to that of Moonbeam, he would always be 2x faster than Moonbeam.

If they run for 4 hours, Sunny would have covered 12 * 4 = 48 miles

While Moonbeam would have covered 6 *4 = 24 miles in the same 4 hours.

Answer:

just remove the parentheses and add the numbers

Step-by-step explanation:

Answer:

\(1.0 - 0.8 \\ = 0.2\)

Answer:

boxes count from top to bottom

Answer:

its too small, i cant read it, sorry

Step-by-step explanation:

If c > 0, then lim_(x->c) (x^c - c^x) / (x - c) = 1 - inc/1+inc.

To show that if c > 0, then lim Xc - Cx / Xx - Cc = 1, we need to make use of L'Hopital's Rule and some algebraic manipulations. Here's how to do it:

Given that c > 0, let f(x) = x^c - c^x and g(x) = x - c.

Then, the given limit is equivalent to: lim_(x->c) f'(x) / g'(x)

By differentiating f(x) and g(x), we get: f'(x) = c * x^(c-1) - c^x * ln(c) and g'(x) = 1.

So, the limit becomes: lim_(x->c) [c * x^(c-1) - c^x * ln(c)] / 1

Now, let's rewrite the numerator: [c * x^(c-1) - c^x * ln(c)] = c * (x^(c-1) - c^(x-1) * ln(c))

Therefore, the limit becomes: lim_(x->c) [c * (x^(c-1) - c^(x-1) * ln(c))] / 1

Now, we can use L'Hopital's Rule to evaluate the limit:

lim_(x->c) [c * (x^(c-1) - c^(x-1) * ln(c))] / 1

= lim_(x->c) [c * ((c-1) * x^(c-2) - (x-1) * c^(x-2) * ln(c))] / 0

= -c * ln(c) * lim_(x->c) (x-1) * c^(x-2) / ((c-1) * x^(c-2))

Now, let's evaluate the limit inside the parentheses:

lim_(x->c) (x-1) * c^(x-2) / ((c-1) * x^(c-2))

= lim_(x->c) (x/c)^(c-2) * (x-1)/(c-1)

We can simplify the above expression as follows:

(x-1)/(c-1)

= (x-c+c-1)/(c-1)

= (x-c)/(c-1) + (c-1)/(c-1)

= (x-c)/(c-1) + 1

Therefore, the limit becomes:

lim_(x->c) -c * ln(c) * [(x-c)/(c-1) + 1]

= lim_(x->c) -c * ln(c) * (x-c)/(c-1) - c * ln(c)

= 1 - inc/1+inc

Hence, we have shown that if c > 0, then lim_(x->c) (x^c - c^x) / (x - c) = 1 - inc/1+inc.

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Show that if c > 0, then lim Xc-Cx/Xx-Cc=1 - Inc/1+ Inc1+ Inc

Answer: To solve -x²-2x=0 by factoring, we can factor out x from the left-hand side:

x(-x-2) = 0

This equation is true if either x = 0 or -x-2 = 0. Solving for x in the second equation:

-x-2 = 0

-x = 2

x = -2

Therefore, the solutions to the equation -x²-2x=0 are x = 0 and x = -2.

To solve x²-4x-8--6x by factoring, we can simplify it first by combining like terms:

x²-10x-8 = 0

To factor this quadratic, we need to find two numbers that multiply to -8 and add to -10. These numbers are -2 and -8, so we can write:

x²-2x-8x-8 = 0

(x²-2x) - (8x+8) = 0

x(x-2) - 8(x+1) = 0

(x-8)(x-2) = 0

Therefore, the solutions to the equation x²-4x-8--6x are x = 8 and x = 2.

To solve 3x² +12=-21x-24 by completing the square, we first need to move all the terms to one side:

3x² + 21x + 36 = 0

Next, we divide both sides by 3 to simplify the coefficient of x²:

x² + 7x + 12 = 0

To complete the square, we need to add and subtract (7/2)² = 49/4 inside the parentheses:

x² + 7x + 49/4 - 49/4 + 12 = 0

(x + 7/2)² = 1/4

Taking the square root of both sides and solving for x, we get:

x + 7/2 = ±1/2

x = -7/2 ± 1/2

Therefore, the solutions to the equation 3x² +12=-21x-24 by completing the square are x = -4 and x = -3.

To solve -x²-3x-13 = -2x² by using the quadratic formula, we first need to move all the terms to one side:

-x² + x - 13 = 0

Next, we identify the coefficients a, b, and c:

a = -1, b = 1, c = -13

Substituting these values into the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

x = (-1 ± sqrt(1² - 4(-1)(-13))) / 2(-1)

x = (-1 ± sqrt(1 + 52)) / (-2)

x = (-1 ± sqrt(53)) / (-2)

Therefore, the solutions to the equation -x²-3x-13 = -2x² by using the quadratic formula are approximately x = -3.25 and x = 4.25.

Step-by-step explanation:

The periodic transfer of a portion of the cost of an intangible asset to expense is known as amortization. This is the process of spreading the cost of an intangible asset over its useful life, similar to how depreciation is used for tangible assets like buildings and equipment.

Intangible assets, such as patents, copyrights, and trademarks, do not have a physical existence but still have value to the company. Amortization recognizes the decline in value of these assets over time and helps to accurately reflect their impact on the company's financial statements.

The amount of amortization each period is calculated by dividing the cost of the asset by its estimated useful life. It is important for companies to track and properly account for their intangible assets, including amortization, as it can have a significant impact on their financial statements and overall financial health.

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We are given these two numbers:

4*10^(-7) and 1.08*10^(-9).

What is similar is that they are in scientific notation, that is, the base of both is

between 1 and 9.

The difference is in the exponent. 0.0000004 is lesser than 1, so the exponent will be negative, while 1,080,000,000 is greater than 1, so the exponent will be positive.

The area of a rectangle is given by the product of its length and width. Therefore, we need to factor the given polynomial into two factors that represent the length and width of the table. We can do this by using the quadratic formula or by factoring the polynomial by grouping. Here, we will use factoring by grouping.

First, we group the terms in pairs:

7x^2 + 75x + 50 = (7x^2 + 35x) + (40x + 50)

Next, we factor out the greatest common factor from each pair of terms:

7x(x + 5) + 10(4x + 5)

We now have a common binomial factor of (x + 5), which we can factor out:

(7x + 10)(x + 5)

Therefore, the dimensions of the table are 7x + 10 and x + 5. We can check this by multiplying the dimensions:

(7x + 10)(x + 5) = 7x^2 + 35x + 10x + 50 = 7x^2 + 75x + 50

This confirms that the given polynomial represents the area of a rectangular table with dimensions of 7x + 10 and x + 5.

Algebraic rule

The algebraic rule for this rotation is:

Description in words

This is a rotation of 180º about the origin

Answer:

--------------------

The experimental probability is the ratio of actual outcomes and total outcomes:

Answer:

$165

Step-by-step explanation:

120÷8=15

15×11=165

Thus, the concept of multiplying decimals by powers of 10 is used.

a) 8.7 x 10 = 87.0

b 8.7 x 100 = 870.0

C 8.7 x 1,000 = 8700.0

d 8.7 x 0.1 = 0.87.

e 8.7 x 0.01 = 0.087.

a) When we multiply 8.7 by 10, we move the decimal point one place to the right, giving us 87.0. However, the zero at the end is not significant, so we can drop it, leaving us with 8.7.

b) When we multiply 8.7 by 100, we move the decimal point two places to the right, giving us 870.0. Again, the zero at the end is not significant, so we drop it, leaving us with 87.

c) When we multiply 8.7 by 1,000, we move the decimal point three places to the right, giving us 8,700.0. Once again, we drop the zero at the end, leaving us with 8,700.

d) When we multiply 8.7 by 0.1, we move the decimal point one place to the left, giving us 0.87.

e) When we multiply 8.7 by 0.01, we move the decimal point two places to the left, giving us 0.087.

f) If we look at the answers for parts a through e, we can see that the number of zeroes and the position of the decimal point change based on the power of 10 we are multiplying by. When we multiply by a larger power of 10, we add more zeroes and move the decimal point further to the right. When we multiply by a smaller power of 10, we move the decimal point to the left and the number of zeroes decreases.

In conclusion, multiplying decimals by powers of 10 can change the position of the decimal point and the number of significant figures in the answer. It is important to pay attention to the placement of the decimal point and the number of zeroes in the answer to ensure accuracy.

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