if f(x) - x ^ 2 + 1 6(x) = 3x and fg(x) = gf(x) find the value of x​

The area of the folded piece of paper is 30 inches square

The paper is folded in the shape of a trapezium. The area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 4 inches

b = 4 + 2 + 2 = 8 inches

h = 5 inches

area of the trapezium = 1 / 2 (4 + 8)5

area of the trapezium = 1 / 2 (12)5

area of the trapezium = 60 / 2

area of the trapezium = 30 inches square

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The force between the two charges is 1.69 x[tex]10^-^1^5[/tex] N

The force between two electric charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

F = k * (q1 * q2) / d²

where F is the force, k is Coulomb's constant (9 x 10⁹ N m² / C²), q1 and q2 are the magnitudes of the two charges, and d is the distance between them.

Substituting the given values, we get:

F = (9 x [tex]10^9[/tex] N m² / C²) * (0.000003 C) * (0.0000009 C) / (0.06 m)²

Simplifying this expression gives:

F = 1.69 x[tex]10^-^1^5[/tex] N

Therefore, the force between the two charges is 1.69 x [tex]10^-^1^5[/tex] N.

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If he visited all the cities in order A(O,4), B(4,1). C(3. 1) and D(-1. 2). then he traveled 12.3 units distance ( nearest tenth).

John visited four cities that form a rectangle on a coordinate grid at A(0, 4), B(4, 1), C(3, 1), and D(-1, 2). If he visited all the cities in order and ended up where he started, the distance he traveled can be found by calculating the perimeter of the rectangle.

Calculate the distance between consecutive points.
AB = √[(4-0)^2 + (1-4)^2] = √[16 + 9] = √25 = 5
BC = √[(3-4)^2 + (1-1)^2] = √[1 + 0] = √1 = 1
CD = √[(-1-3)^2 + (2-1)^2] = √[16 + 1] = √17 ≈ 4.1 (rounded to nearest tenth)
DA = √[(0-(-1))^2 + (4-2)^2] = √[1 + 4] = √5 ≈ 2.2 (rounded to nearest tenth)

Calculate the total distance traveled (perimeter of the rectangle).
Total Distance = AB + BC + CD + DA = 5 + 1 + 4.1 + 2.2 = 12.3

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a)The amount in the account after 5 years, compounded annually, will be approximately $60,625.06.

b) The amount in the account after 5 years, compounded semiannually, will be approximately $61,588.88.

The amount in the account after 5 years can be calculated using the compound interest formula. For an initial investment of $47,000 at an annual interest rate of 5%, compounded annually or semiannually, the amount in the account will be different.

(a) For compounding annually:

The compound interest formula is given by:

A = P(1 + r/n)^(nt)

where:

A = the amount after time t

P = principal amount (initial investment) = $47,000

r = annual interest rate = 5% or 0.05 (as a decimal)

n = number of times interest is compounded per year = 1 (since it is compounded annually)

t = time period = 5 years

Plugging in the given values, we get:

A = 47000(1 + 0.05/1)^(1*5)

A = 47000(1.05)^5

A ≈ $60,625.06

So, the amount in the account after 5 years, compounded annually, will be approximately $60,625.06.

(b) For compounding semiannually:

The only difference from the above calculation is the value of 'n', which is the number of times interest is compounded per year. In this case, 'n' will be 2, as interest is compounded semiannually (twice a year).

Plugging in the given values, we get:

A = 47000(1 + 0.05/2)^(2*5)

A = 47000(1.025)^10

A ≈ $61,588.88

So, the amount in the account after 5 years, compounded semiannually, will be approximately $61,588.88.

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Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.

Step 1: Arrange the data in ascending order.

54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99

Step 2: Determine the range of the data.

The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.

Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).

5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9

Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.

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Answer:

(8/√2)^2 = 64/2 = 32 square inches

P(X ≤ 1) = P(X = 0) + P(X = 1) ≈ 0.901

So the probability that at most 1 customer in the sample orders for delivery is approximately 0.901, rounded to three decimal places.

To solve this problem, we can use the binomial distribution since we have a fixed number of trials (6) and each trial can result in one of two outcomes (ordering for delivery or not).

Let X be the number of customers in the sample who order for delivery. Then X follows a binomial distribution with parameters n = 6 and p = 0.11 (the probability of ordering for delivery).

We want to find the probability that at most 1 customer orders for delivery. This can be written as:

P(X ≤ 1) = P(X = 0) + P(X = 1)

To calculate these probabilities, we can use the binomial probability formula:

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

where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n distinct items.

Using this formula, we can calculate:

P(X = 0) = (6 choose 0) * 0.11^0 * [tex]0.89^6[/tex] ≈ 0.530

P(X = 1) = (6 choose 1) * 0.11^1 * 0.89^5 ≈ 0.371

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Answer: 80

Step-by-step explanation: The question is tell us that a certain company  we don't know which one, but it says a certain company has 400 shoes. that is important to note. also 20% of the shoes are black. and One shoe is chosen and replaced. Then the second shoe is chosen. The question is What is the probability that the shoes chosen are black?

Well, take 400 and mutipy it by 20% which changes to 0.20 in decimal form then mutiply your answer by one and you get 80. so the answer is the probability that shoes chosen are black is 80%.

By the rule of indices the  given expression is equivalent to x⁻² y⁻⁵.(option B)

What is index?

In mathematics, Index in plural indices  is the power or exponent which is raised to a number or a variable. For example, for the number 2⁵, 5 is the index of 2. Which gives the value 32.

Given expression is y⁻⁸ y³ x⁰ x⁻²

Here we use the law of indices.

By the law of indices it can be stated that the indices at the time of multiplication is being added up. That is zᵃ × zᵇ = zᵃ⁺ᵇ.

Using this concept of indices the given expression can be rewritten as

 y⁻⁸⁺³ x⁰⁻²

= y ⁻⁵ x⁻²

= x⁻² y⁻⁵

Hence, the given expression is equivalent to x⁻² y⁻⁵.

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If the line has a positive slope, it means that the amount is increasing, and if it has a negative slope, it means that the amount is decreasing.

Based on the given information, the function models the amount of money a new business has made over x months. Therefore, we can assume that the function is a linear function, and its graph is a straight line.

Given that negative values represent debt, we can assume that the slope of the line is positive over the interval where the function takes positive values. Therefore, the interval over which the amount is increasing is from zero to infinity, which means that the business is making money and not in debt.

It's essential to note that if the function has a negative slope over any interval, then the amount is decreasing, and the business is losing money. However, we cannot determine this information from the given function's information.

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Answer:

67. 50

Step-by-step explanation:

15x4.50= 67.5

Using the sine function and the given information, we can find that length of  y is approximately 203.3 feet.

We know that exterior angle of a triangle is equal to the sum of its opposite interior angles. So, we can find angle BAC as follows

BAC + ABC = 180 degrees

As sum of interior angles of a triangle

BAC + 90 = 180

BAC = 90 degrees

Now, we can use the sine ratio to find y

sin(31) = y/400

y = 400 * sin(31)

y ≈ 203.3 ft

Therefore, y is approximately 203.3 ft when rounded to the nearest tenth.

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

" Find y. Round to the nearest tenth:

In triangle ABC, 31° is the outer angle at A which is in between a line extended from A parallel to BC.

X  is CA

у is AB

400 ft is BC

Angle B is right angle

y = [ ? ]ft Enter"--

The absolute value inequality in form |x-b| < c that has the solution set x<-5 or x>7 is |x-1| < 7

To write an absolute value inequality in the form |x-b| < c, we need to think about what this form means.

The expression |x-b| represents the distance between x and b on the number line. Therefore, |x-b| < c means that the distance between x and b is less than c.

Now, let's consider the given solution set: x < -5 or x > 7. We can see that the midpoint between -5 and 7 is 1, so we choose b = 1. Then, we need to determine c, which is the maximum distance between b and any of the solutions.

If we take x = -6 (which is less than -5), then |x-b| = |-6-1| = 7. Similarly, if we take x = 8 (which is greater than 7), then |x-b| = |8-1| = 7. Therefore, the maximum distance is 7.

Putting it all together, we get the absolute value inequality:

|x-1| < 7

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P(Dead l WH) = 0.23/0.48 = 0.4792

Here the western red cedar is relatively young.

(a) P(Dead l RC) = 0.02/0.20 = 0.10

P(Dead l DF) = 0.16/0.32 = 0.50

P(Dead l WH) = 0.23/0.48 = 0.4792

Here the western red cedar is relatively young.

(b) P(sapling l RC) = 0.08/0.20 = 0.4

P(sapling l DF) = 0.00/0.32 = 0

P(sapling l WH) = 0.04/0.48 = 0.08333

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"t" increases, and the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

The function s(t) = 31,500(1.034)^t gives an approximation of the number of digital subscriptions s as a function of t months after the launch of the advertising campaign.

The parameters of the function s(t) are:

31,500: This is the initial number of digital subscriptions at t = 0, when the advertising campaign is launched.

1.034: This is the growth rate of the number of digital subscriptions per month. It represents the percentage increase in the number of subscriptions each month due to the advertising campaign. Specifically, each month the number of subscriptions is multiplied by 1.034, which is the same as increasing it by 3.4%.

t: This is the time in months after the launch of the advertising campaign. It is the independent variable of the function that determines the number of digital subscriptions at any given time t.

Statements interpreting the parameters of the function s(t) are:

The initial number of digital subscriptions at t = 0 is 31,500.

For every month after the launch of the advertising campaign, the number of digital subscriptions increases by 3.4%, or a factor of 1.034.

The parameter t represents the time in months after the launch of the advertising campaign. As t increases, the number of digital subscriptions grows exponentially at a rate of 3.4% per month.

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The probability that the smallest bell rings the first three days in a row is 1/27. when Each day three church bells are rung in a random order

In the given data there are 3 bells in the church in which there is a small bell and the three bells are rung in a random order. we need to find the probability that the smallest bell rings the first three days in a row.

The probability that the smallest bell rings on any given first day can be given as  = 1/3

Because there are three bells and each bell has an equal chance of being rung first. The probability that this happens three days in a row is given as

= (1/3) × (1/3) × (1/3)

= 1/27

Therefore, the probability that the smallest bell rings the first three days in a row is 1/27

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Answer:

34/73

Step-by-step explanation:

37 + 34 + 2 = number of customers = 73

73 is our denominator.

34 is the number of people who used a credit card.

34 is our numerator.

Put the two together, and you get 73! Enjoy!

The height of the cylindrical ornament is approximately 5.7 centimetres (option b).

To find the height of the cylindrical ornament given that 450 cubic centimetres of wood is used and the radius of the base is 5 centimetres, you can use the formula for the volume of a cylinder: V = π × radius² × height.

Step 1: Write down the given values.
Volume (V) = 450 cubic centimetres
Radius (r) = 5 centimetres

Step 2: Plug the given values into the formula.
450 = π × (5)² × height

Step 3: Solve for the height.
450 = π × 25 × height
450 = 78.54 × height

Step 4: Divide both sides by 78.54 to find the height.
height = 450 / 78.54
height ≈ 5.7 centimetres

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You are an scalene triangle.

You are a scalene triangle.

A scalene triangle is a type of triangle where all three sides have different lengths, and no two angles are congruent. In this case, you mentioned that one of the angles has a measure of 100 degrees.

Here's a simple diagram of a scalene triangle to help illustrate:

    \

     \

      \

       \

        \

         \

In the diagram, the angles are not drawn to scale, but it represents a scalene triangle where one angle measures 100 degrees. The sides of the triangle would have different lengths, distinguishing it from an equilateral or isosceles triangle where at least two sides are congruent.

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The number name of 346. 725 is three hundred forty-six point seven two five.

A number name refers to the name that is used to describe the number in words. This is helpful in communicating it orally.

To convert the given number to word form, we do as follows:

1. We check the digits of the number before decimals

In this case, the number of digits in the question is 3

2. The highest place value is then checked.

It comes out to be hundreds

3. We name it accordingly and add a suffix to the face value

This is 3 and the name comes out to be Three hundred

4. We continue it till we encounter the decimal

We get the number as Three hundred forty-six

5. Then we mention the word decimal or point

The result is Three hundred forty-six point

6. The number after the decimal is written as it is

Hence, the name comes out to be Three hundred forty-six point seven two five.

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The probability of the adults being chosen this way by chance is less than 0.01 interprets that group is more likely to choose men over women

A group conducting a survey randomly selects adults in a certain region. Of the 2,500 adults selected, 1,684 are men. The men and women have an equal chance The result of the survey is significant at the 0.01 level which means that the probability of group selection being the result of chance is 0.01 or less because the event is least likely to happen the group is more likely to select men over women.

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The domain of the rational function is: option (2)  {x ∈ ℝ | x ≠ -4, 3, 4}

A rational number is any number that can be expressed as the ratio or fraction of two integers, where the denominator is not zero. In other words, a rational number is a number that can be written in the form of p/q, where p and q are integers, and q is not equal to zero.

The domain of a rational function is the set of all real numbers for which the function is defined, and the denominator is not equal to zero. So, we need to find the values of x for which the denominator of the given rational function is not zero.

The denominator of the given rational function is:

x³ - 3x² - 16x + 48

We can factor this polynomial using synthetic division or polynomial long division:

x³- 3x² - 16x + 48 = (x - 4)(x - 3)(x + 4)

So, the denominator of the rational function is not defined when:

x - 4 = 0 or x - 3 = 0 or x + 4 = 0

Solving these equations, we get:

x = 4 or x = 3 or x = -4

Therefore, the domain of the given rational function is:

{x ∈ ℝ| x ≠ –4, 3, 4}

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The probability of hitting the bulls eye (center circle) when we shoot an arrow with radius of the bulls eye is 2ft and the radius of the target is 6ft is 11.1%.

Assuming that we are shooting randomly at the target and the arrow can land anywhere within the target area, the probability of hitting the bull's eye (center circle) can be calculated as the ratio of the area of the bull's eye to the area of the entire target.

The area of the bull's eye can be calculated as follows:

Area of bull's eye = π x (radius of bull's eye)²
Area of bull's eye = 3.14 x 2²
Area of bull's eye = 12.56 square feet

The area of the entire target can be calculated as follows:

Area of target = π x (radius of target)²
Area of target = 3.14 x 6²
Area of target = 113.04 square feet

Therefore, the probability of hitting the bull's eye can be calculated as:

Probability of hitting bull's eye = Area of bull's eye / Area of target
Probability of hitting bulls eye = 12.56 / 113.04
Probability of hitting bulls eye = 0.111 or approximately 11.1%

So, the probability of hitting the bull's eye (center circle) when we shoot an arrow randomly at the target is approximately 11.1%.

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If Mr. Vara's square pyramid post caps have a volume of 94.5 cubic centimeters, and he assumes that the height and side length are equal, then the side length of each cap should be approximately 6.04 centimeters.

Mr. Vara is designing post caps in the shape of a square pyramid for his fence. The caps are solid wood and have a volume of 94.5 cubic centimeters. To calculate the dimensions of the pyramid, we need to use the formula for the volume of a square pyramid, which is V = (1/3)bh, where b is the area of the base and h is the height of the pyramid.

Since the caps are square pyramids, the base is a square. Let's call the side length of the base s. Then the area of the base is s². We can rearrange the formula for volume to get h = (3V)/b. Plugging in the given volume of 94.5 cubic centimeters, we get:

h = (3 x 94.5) / s²
h = 283.5 / s²

We still need to find the side length s. We can use the fact that the volume of the pyramid is also equal to [tex](1/3)s^{2h[/tex]. Plugging in the volume and height from above, we get:

94.5 = (1/3)s²(283.5 / s²)
94.5 = 94.5

This equation simplifies to 1 = 1, which doesn't give us any information about s. However, we can make an assumption about the dimensions of the pyramid. Let's say that the height h is equal to the side length s. Then we can solve for s using the volume formula:

[tex]94.5 = (1/3)s^{2s[/tex]
94.5 = (1/3)s³
283.5 = s³
s = 6.04

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To find the revenue function, we need to multiply the price (p) by the quantity sold (x). The price function given is p = 5,300 - dollars, so we can substitute this into our revenue function as follows:

Revenue = p * x
Revenue = (5,300 - dollars) * x

We also know that production is limited to 100 units, so we need to take that into account when determining the revenue function. If x is greater than 100, then the revenue will be limited to 100 units sold. If x is less than or equal to 100, then the revenue will be based on the actual quantity sold.

To incorporate this constraint into our revenue function, we can use a piecewise function:

Revenue = { (5,300 - dollars) * 100           if x > 100
             (5,300 - dollars) * x             if x <= 100 }

Simplifying the piecewise function, we get:

Revenue = { 530,000 - (dollars * 100)        if x > 100
             (5,300 - dollars) * x             if x <= 100 }

Therefore, the revenue function for this monopoly is:

Revenue = { 530,000 - 100 * dollars        if x > 100
             (5,300 - dollars) * x             if x <= 100 }
Hi! To find the revenue function, we first need to determine the total revenue, which is the product of the price per unit (p) and the number of units sold (x). Given the demand function p = 5,300 - x dollars and the average cost function C = 3,010 + 2x dollars, we can find the revenue function as follows:

Revenue function, R(x) = p * x
R(x) = (5,300 - x) * x

By simplifying the equation, we get:
R(x) = 5,300x - x^2

So, the revenue function for this monopoly is R(x) = 5,300x - x^2.

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If you select a marble without looking and then put it back if you do this 90 times, the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

If you select a marble without looking and then put it back, the probability of selecting any particular marble on any given trial is the same for all marbles. Assuming there are only two possible outcomes - selecting an orange marble or a pink marble - the probability of selecting an orange or a pink marble on any given trial is 1/2 or 0.5.

Since the probability of selecting an orange or a pink marble on each trial is the same, the best prediction for the number of times you will select an orange or a pink marble out of 90 trials is an equal number of times for each color. Therefore, the best prediction for the number of times you will select an orange or a pink marble is 45 times each.

This is only a prediction based on probability, and the actual number of times you select an orange or a pink marble may differ from the prediction due to chance. However, over a large number of trials, the actual outcomes should approach the predicted probabilities.

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Answer: X= 4/5x + 8

Step-by-step explanation: Distribution factor

The amount of interest paid for missing the payment in the eight month would be C. $87.28

First, find the total cost of the computer including the sales price :

= 875 x ( 1 + 0. 05 )

= 875 x 1. 05

= $ 918. 75

Then, find the monthly rate of interest :

= 14. 25 / 12

= 1. 1875 %

This leads to an eight month interest rate of :

= 8 x 1. 1875 %

= 9. 5 %

The interest to be paid:

= 9. 5 % x 918. 75

= $ 87. 28

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Full question is:

You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. 58.19