A line plot has a range of 4, from 1 to 5, with 5 modes. How would you describe the graph?

A. There is not enough information.

B. The data is clustered around 3.

C. Each column will be the same height.

D. The graph has an outlier.

Roots of a quadratic equation using the factorisation method, we need to find two numbers that multiply to the constant term of the equation and add up to the coefficient of the linear term. Then, we can use these two numbers to factor the quadratic expression and solve for the roots.

a) For the quadratic equation x^2 - 10x + 16 = 0, we need to find two numbers that multiply to 16 and add up to -10. These numbers are -2 and -8, so we can write the quadratic as (x - 2)(x - 8) = 0. Setting each factor equal to zero, we get x - 2 = 0 and x - 8 = 0, which give us the roots x = 2 and x = 8.

b) For the quadratic equation 2x^2 + 3x - 9 = 0, we need to find two numbers that multiply to -18 (since 2*(-9) = -18) and add up to 3. These numbers are 6 and -3, so we can write the quadratic as 2x^2 + 6x - 9x - 9 = 0. Factoring by grouping, we get 2x(x + 3) - 9(x + 3) = 0, which simplifies to (2x - 9)(x + 3) = 0. Setting each factor equal to zero, we get 2x - 9 = 0 and x + 3 = 0, which give us the roots x = 9/2 and x = -3.

c) For the quadratic equation x^2 - 5x = 0, we can factor out an x to get x(x - 5) = 0. Setting each factor equal to zero, we get x = 0 and x - 5 = 0, which give us the roots x = 0 and x = 5.

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a) there are 32 possible subsets of C.

b)The cardinality of set M is the sum of these numbers, which is 781.

C) there are an infinite number of possible strings, the cardinality of set K, which contains all possible strings using letters from C, is also infinite.

a) The cardinality of set C is 5, as there are 5 distinct elements in the set. The cardinality of the power set of C, denoted as P(C), is 2^5 = 32, as there are 32 possible subsets of C.

b) A tree showing all possible strings of letters of length 5 or less starting with the letter z would look like:

z

├── v

│   ├── v

│   ├── w

│   ├── x

│   └── y

├── w

│   ├── v

│   ├── w

│   ├── x

│   └── y

├── x

│   ├── v

│   ├── w

│   ├── x

│   └── y

├── y

│   ├── v

│   ├── w

│   ├── x

│   └── y

└── z

   ├── v

   ├── w

   ├── x

   └── y

The cardinality of set M, which contains all possible strings of length 5 or less with letters from C, is equal to the sum of the cardinalities of all sets of strings of each length. Thus,

Set of strings Number of strings

Length 1 1

Length 2 5

Length 3 5^2 = 25

Length 4 5^3 = 125

Length 5 5^4 = 625

The cardinality of set M is the sum of these numbers, which is 1 + 5 + 25 + 125 + 625 = 781.

c) A tree showing all possible strings of any length would have an infinite number of branches. Each node in the tree would represent a different string, and the branches emanating from each node would represent the next letter that could be added to the string. Since there are an infinite number of possible strings, the cardinality of set K, which contains all possible strings using letters from C, is also infinite.

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The inverse of f(x) is: [tex]f^{-1(x)}[/tex] = (x - 8)/5 switched the variables, so instead of [tex]f^{-1(x)}[/tex] , we wrote it as [tex]f^{-1(x)}[/tex] .

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

To find the inverse of the function f(x) = 8 + 5x, we need to solve for x in terms of f(x).

Let y = f(x) = 8 + 5x

To find the inverse, we need to isolate x on one side of the equation:

y = 8 + 5x

y - 8 = 5x

x = (y - 8)/5

Therefore, the inverse of f(x) is:

[tex]f^{-1(x)}[/tex] = (x - 8)/5

Or, we can write it as:

[tex]f(x)^{-1}[/tex] = (x - 8)/5

Note that we switched the variables, so instead of [tex]f^{-1}[/tex] , we wrote it as [tex]f^{-1(x)}[/tex] .

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The function graphed on the axes above should be expressed as a piecewise function as follows;

f(x) = -3x - 8    {x ≤ -2}

    = 6x - 17     {x > 3}

In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 2)/(-4 + 2)

Slope (m) = 6/-2

Slope (m) = -3.

At data point (-2, -2) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = -3(x + 2)  

y = -3x - 8

For the second line, we have:

Slope (m) = (7 - 1)/(4 - 3)

Slope (m) = 6/1

Slope (m) = 6.

At data point (3, 1) and a slope of 6, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 6(x - 3)  

y = 6x - 17

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The continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex].

To evaluate this convolution integral, we first need to express the integrand as a piecewise function. Since u(t) is 1 for t >= 0 and 0 for t < 0, we can rewrite u(t+2)-u(t) as a piecewise function:

u(t+2)-u(t) =

1, 0 <= t < 2

0, t >= 2

0, t < 0

Now we can evaluate the convolution integral using the definition:

y(t) = ∫[tex]_0^t[/tex] x(τ)h(t-τ)dτ

Substituting the given functions for x(t) and h(t) and simplifying using the piecewise function for u(t+2)-u(t), we get:

y(t) = k ∫[tex]_0^t[/tex] [tex]e^}(-yt)}[/tex]dτ = [tex]k[-(1/y)e^{(-yt)}]_0^t = k(1 - e^{(-yt)})/y[/tex], t >= 0

Therefore, the continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex] for t >= 0.

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1. I imagine buying 100 shares of Amazon.com Inc. on January 3, 2020, when the stock price was $93.75, investing $9,375.  

Today, October 31, 2022, the stock price of Amazon.com Inc. is $102.44.

2. The real return on my investment in Amazon.com Inc was a net loss of  7.12% or $667.60.

3. The company I selected to buy its stock three years ago was Amazon.com Inc.

4. I decided on Amazon.com Inc., hoping to earn spectacular returns since it is a multinational technology company.

5. When I consider the actual return on the stock investment in Amazon.com Inc., I think it was an unwise investment.

6. The investment returned a negative real value because I realized less than I initially invested; I actually lost about $667.60 overall.

Stock investment is the purchase of shares for an ownership interest in a publicly-listed company.

The investor makes the investment with the hope that the investee will grow and perform well over some period, enabling the investor to earn some real returns (in the form of dividends and capital appreciation).

Purchase of 100 shares Jan. 3, 2020 = $9,375 (100 x $93.75)

Sales of 100 shares Oct. 31, 2022 = $10,244 (100 x $102.44)

Tax (10%) = $1,024.40 ($10,244 x 10%)

Inflation (3%) = $307.32 ($10,244 x 3%)

Administration fee on sales (2%) = $204.88 ($10,244 x 2%)

Real Returns in dollars = $8,707.40 ($10,244 - $1,024.40 - $307.32 - $204.88)

Loss on returns = $667.60 ($8,707.40 - $9,375)

Loss percentage = 7.12% ($667.60/$9,375 x 100)

Unfortunately, Amazon.com Inc. did not pay any dividends during the period of my investment, and I really lost funds to taxes, inflation, and administration fees when I sold it.

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Answer:

87 feet.

Step-by-step explanation:

To solve the problem, we can use the tangent function, which relates the opposite side of a right triangle (the height of the tree in this case) to the adjacent side (the horizontal distance from the base of the tree to the point directly below the kite) through the angle between them (44 degrees):

tan(44) = height / distance

We know the angle and the distance (90 feet), so we can solve for the height:

height = distance * tan(44)

height = 90 * tan(44)

The value of tan(44) is approximately 0.9656887, which means that if we multiply it by 90, we get:

90 * tan(44) = 90 * 0.9656887

Using a calculator, we get:

90 * 0.9656887 = 86.908983

However, this is not the final answer, because we were asked to round to the nearest whole foot. Since 86.908983 is closer to 87 than to 86, we round up to 87. Therefore, the approximate height of the tree is 87 feet.

The left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.

(i) To show that the limit of (1/x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or they both go to infinity. Let's consider the right-hand limit:

lim x→0+ (1/x^2) = +∞ (the limit goes to infinity)

Now let's consider the left-hand limit:

lim x→0- (1/x^2) = +∞ (the limit goes to infinity)

Since the left-hand limit and the right-hand limit are both infinite and not equal, the limit does not exist.

(ii) To show that the limit of (1/√x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ (1/√x^2) = lim x→0+ (1/|x|) = +∞ (the limit goes to infinity)

Now let's consider the left-hand limit:

lim x→0- (1/√x^2) = lim x→0- (1/|x|) = -∞ (the limit goes to negative infinity)

Since the left-hand limit and the right-hand limit are not equal, the limit does not exist.

(iii) To show that the limit of (x+(x)) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ (x+(x)) = 0+0 = 0

Now let's consider the left-hand limit:

lim x→0- (x+(x)) = 0+0 = 0

Since the left-hand limit and the right-hand limit are equal, the limit exists and equals 0.

(iv) To show that the limit of sin(1/x) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:

lim x→0+ sin(1/x) does not exist

This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the right-hand side, and the limit does not approach any single value.

Now let's consider the left-hand limit:

lim x→0- sin(1/x) does not exist

This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the left-hand side, and the limit does not approach any single value.

Since the left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.

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Answer:

First, we need to calculate the total exemptions for Kareem, his wife, and their child:

Total exemptions = 3 x 4,050 = 12,150

Next, we subtract the standard deduction and exemptions from their adjusted gross income to find their taxable income:

Taxable income = 92,600 - 12,600 - 12,150 = 67,850

Therefore, the correct answer is (B) 67,850.

Step-by-step explanation:

Branliest please

In scenario a, the function c(x) represents the density of traffic on a straight road, measured in cars per mile, where x is the number of miles east of a major interchange. The product c(x) · Ax has units of cars, as it represents the number of cars in a certain segment of the road. The definite integral ∫ c(x) dx and its Riemann sum approximation given by 1/n ∑ c(xi) · Δx have units of cars per mile, as they represent the average density of traffic over a certain distance. When evaluating the definite integral ∫ c(x) dx, we get a value that represents the total number of cars on the road between two given points.

In scenario b, the function B(x) represents the distribution of the weight of books on a shelf, in pounds per inch, where x is the number of inches from the left end of the shelf. The product B(x) · Ax has units of pounds, as it represents the weight of books in a certain segment of the shelf. The definite integral ∫ B(x) dx and its Riemann sum approximation given by 1/n ∑ B(xi) · Δx have units of pounds, as they represent the total weight of books on the shelf. When evaluating the definite integral ∫ B(x) dx, we get a value that represents the total weight of books on the shelf.
a. i. The units on the product c(x) · Δx are cars per mile (from c(x)) multiplied by miles (from Δx), resulting in cars.

a. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product c(x) · Δx, which are cars.

a. iii. To evaluate the definite integral, we have:

∫(200 + 100e^(-0.12x)) dx

Using the integral rules, we get:

[200x - (100/0.12)e^(-0.12x)] (evaluate this from 0 to a specific value to find the total cars between 0 and that value)

The meaning of the value is the total number of cars on the road between 0 miles and the specified value of x miles east of the major interchange.

b. i. The units on the product B(x) · Δx are pounds per inch (from B(x)) multiplied by inches (from Δx), resulting in pounds.

b. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product B(x) · Δx, which are pounds.

b. iii. To evaluate the definite integral, we have:

∫(0.5 + (x+1)^2) dx

Using the integral rules, we get:

[0.5x + (1/3)(x+1)^3] (evaluate this from 0 to 72 to find the total weight of books on the shelf)

The meaning of the value is the total weight of the books on the 6-foot-long shelf.

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The probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.

a. The mean of the sample mean (my) can be calculated using the formula:

my = population mean = 606 megabytes per month

b. The standard deviation (standard error) of the sample mean can be calculated using the formula:
standard error = [tex]\frac{standard deviation}{\sqrt{sample size} }[/tex]
standard error = [tex]\frac{240}{\sqrt{64} }[/tex]
standard error = 30

Therefore, the standard error of the sample mean is 30 megabytes per month.

c. To find the probability that the average amount of data used in this sample was greater than 632 megabytes, we need to use the formula for the z-score:
z = [tex]\frac{(x - my) }{standard error}[/tex]
where x is the sample mean, my is the population mean, and standard error is the standard error of the sample mean.
z = [tex]\frac{(632 - 606) }{30}[/tex]
z = 0.87

Using a z-table or calculator, we can find that the probability of getting a z-score of 0.87 or higher is 0.1922. Therefore, the probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.

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5, instances of the number 5 will be stored in this 2D array. Option B.

To count the instances of the number 5 in the 2D array, we need to iterate through all the elements of the array and count the occurrences of 5.

Starting from the top-left element, we see that it is not a 5. Moving to the right, we find a 5 in the second column. Continuing to the right, we find another 5 in the same row. So far, we have counted 2 instances of 5.

Moving to the next row, we find no 5s in the first column. In the second column, we find two 5s in the same row. This brings our total count to 4. Moving to the last row, we find a single 5 in the second column, bringing our final count to 5.

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To find the maximum distance between the point (1,3) and a point on the circle of radius 4 centered at the origin, we can use the distance formula. Let (x,y) be a point on the circle, then the distance between (1,3) and (x,y) is given by:

d = √((x-1)^2 + (y-3)^2)

Since the point (x,y) lies on the circle of radius 4 centered at the origin, we have:

x^2 + y^2 = 16

We can solve for y in terms of x:

y = ±√(16 - x^2)

Substituting into the distance formula, we get:

d = √((x-1)^2 + (±√(16 - x^2) - 3)^2)

Simplifying and squaring, we get:

d^2 = (x-1)^2 + (±√(16 - x^2) - 3)^2

d^2 = x^2 - 2x + 1 + (16 - x^2 - 6√(16 - x^2) + 9)  (or d^2 = x^2 - 2x + 1 + (16 - x^2 + 6√(16 - x^2) + 9))

d^2 = -x^2 - 2x + 26 ± 6√(16 - x^2)

To maximize the distance, we want to maximize d^2. Note that the maximizing distance should be at least 4, which means that we only need to consider the positive root of d^2. The critical points of d^2 occur when the derivative is zero, so we differentiate with respect to x:

d(d^2)/dx = -2x - 2(±3x/√(16 - x^2))

Setting this equal to zero, we get:

x = ±4/√5, ±2√2/√5, 0

Note that x = 0 corresponds to the point (0,4) on the circle, which has distance 5 from (1,3), so it is not a critical point. The other critical points correspond to the points where the circle intersects the x-axis and the y-axis. Evaluating d^2 at these critical points, we get:

d^2 = 18 ± 6√6

The maximum distance is therefore √(18 + 6√6), which occurs when x = ±4/√5.

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Isaac pay for the cost of racket is 39.9.

The cost of a pair of shoes is three times the cost of a bag, so we can write:

Cost of shoes = 3b

Similarly, the cost of the racket is twice the cost of the bag, so we can write:

Cost of racket = 2b

Now we can use the given information to set up an equation:

Cost of racket + Cost of bag + Cost of shoes = $119.70

Substituting the expressions we found above, we get:

2b + b + 3b = $119.70

Simplifying the equation:

6b = $119.70

Dividing both sides by 6:

b = $19.95

So the cost of the bag is $19.95.

We can use this to find the costs of the shoes and racket:

Cost of shoes = 3b = 3($19.95) = $59.85

Cost of racket = 2b = 2($19.95) = $39.90

Therefore, Isaac paid $39.90 for the racket.

A cost is an expenditure required to produce or sell a product or get an asset ready for normal use. In other words, it's the amount paid to manufacture a product, purchase inventory, sell merchandise, or get equipment ready to use in a business process.

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Check the picture below.

so the circle has a radius of 3 and a center at (-2 , 1)

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{3}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~3^2\implies (x+2)^2 + (y-1)^2 = 9[/tex]

Based on the provided information, f'(x) changes from positive to negative at x=1, indicating that the function has a local maximum at this point.

Since y=f(x) is continuous for all real numbers and the interval is [0, ∞), there is an absolute maximum at x=1. The best description of the absolute extrema is: "There is an absolute maximum at x=1." Based on the sign chart for the first derivative, we know that the function is increasing from negative infinity to x=-1, and then decreasing from x=-1 to positive infinity. This means that there is an absolute maximum at x=-1 since the function is increasing to that point and decreasing after it. Therefore, the correct statement is: "There is an absolute maximum at x=-1."

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The series of transformations correctly show that △CAT≅△DOG is rotate ACAT 180° about the origin, the correct option is A.

We are given that;

△CAT≅△DOG

Now,

To show that ACAT and ADOG are congruent, we need to find a sequence of rigid transformations that maps one onto the other.

One possible sequence is:

This will map A to D, C to O, A to G, and T to O.

Translate the image 2 units left. This will align the image with ADOG.

Therefore, by transformation the answer will be rotate ACAT 180° about the origin.

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8.19 divided by 4.2 is approximately equal to 1.94047624, which can be rounded to 1.94 (to two decimal places).

In mathematics, division is a basic arithmetic operation that involves separating a quantity or a number into equal parts or groups. The division operation is denoted by the symbol "/", or in some cases, the symbol "÷"

When we divide one number by another, we are essentially finding out how many times the second number "fits into" the first number

To divide 8.19 by 4.2, we can use long division as follows:

     1.9 4 0 4 7 6 2 4 3 3 3...

  --------------------------

4.2| 8.1 9 0 0 0 0 0 0 0 0 0

    8 4

    ----

    2 6 0

    2 5 2

    -----

      8 0 0

      7 1 4

      -----

      8 5 0

      8 4 8

      -----

        2 0 0

        1 6 8

        -----

        3 1 0

        2 5 2

        -----

          5 8

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Based on the average daily balance, the finance charge for this credit card that charges 10.5% APR is $2.10.

The finance charge consists of the interest and other fees that lenders charge borrowers.

One of the methods for computing the finance charge is the average daily balance, which takes the sum of the daily balances and divides by the number of days in the billing cycle.

APR interest rate = 10.5%

Monthly period days = 30

Days 1-3: $200 (initial balance)        3 days      $600 ($200 x 3)

Days 4-20: $300 ($100 purchase)  17 days   $5,100 ($300 x 17)

Days 21-30: $150 ($150 payment)  10 days   $1,500 ($150 x 10)

Total balances = $7,200

Average daily balance = $240 ($7,200 ÷ 30)

Finance charge = $2.10 ($240 x 10.5% x 30/360)

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Rounding to the nearest cent, Sasha will pay $35.10 in interest this month. Therefore, the correct answer is option A.

To calculate the interest that Sasha will pay, we need to use the following formula:

Interest = (Balance * APR * Days in a billing cycle) / 365

where Balance is the amount owed after the payment, APR is the annual percentage rate, and Days in the billing cycle are the number of days in the billing cycle.

Since we do not know the number of days in the billing cycle, we will assume it to be 30 days for simplicity. Therefore, the balance owed after the payment is:

Balance = $3200 - $300 = $2900

Substituting the values into the formula, we get:

Interest = ($2900 * 0.1875 * 30) / 365

= $35.09

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The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.

To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form

(y - x₁)(y - x₂) = 0

where y is the variable in the quadratic equation.

Substituting the given values of the zeros, we get

(y - (-6))(y - 2) = 0

Simplifying this expression, we get

(y + 6)(y - 2) = 0

Expanding this expression, we get

y² - 2y + 6y - 12 = 0

Simplifying this expression further, we get

y² + 4y - 12 = 0

So the quadratic equation with zeros at -6 and 2 is

y² + 4y - 12 = 0

This is the standard form of a quadratic equation, which is

ax² + bx + c = 0

where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.

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It will take God approximately 32 days to use up all the gas in his tanker and need a refill.

If God filled his gas tanker with 19/5/9 tank of gas and uses 1 5/6 gallons of gas each day, we can calculate how many days it will take for him to need a refill.

First, we need to convert the mixed number 19/5/9 to an improper fraction:

19/5/9 = (19 * 9 + 5) / 9 = 176/9

So God has 176/9 tanks of gas in his tanker.

Next, we can calculate how much gas God uses each day:

1 5/6 = (6 * 1 + 5) / 6 = 11/6

So God uses 11/6 gallons of gas each day.

To find out how many days it will take for God to need a refill, we can divide the amount of gas in his tanker by the amount of gas he uses each day:

(176/9) / (11/6) = (176/9) * (6/11) = 32

Therefore, it will take God approximately 32 days to use up all the gas in his tanker and need a refill.

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The actual error is:
|4194 - 4787.9476| = 593.9476
Since the bound for the error is 0.371, which is much smaller than the actual error of 593.9476, we can say that the Composite Simpson Rule with n=4 provides a very good approximation to the integral.

Sure! We can approximate the integral ∫10.5x4 dx using the Composite Simpson Rule with n=4.

First, let's split the interval [1,4] into 4 subintervals of equal width:

h = (4-1)/4 = 0.75

x0 = 1, x1 = 1.75, x2 = 2.5, x3 = 3.25, x4 = 4

Next, we need to evaluate the function at the endpoints and midpoints of each subinterval:

f(x0) = f(1) = 10.5(1)^4 = 10.5
f(x1) = f(1.75) = 10.5(1.75)^4 = 100.2842
f(x2) = f(2.5) = 10.5(2.5)^4 = 528.125
f(x3) = f(3.25) = 10.5(3.25)^4 = 1841.7969
f(x4) = f(4) = 10.5(4)^4 = 3360

Now, we can apply the Composite Simpson Rule formula:

∫10.5x4 dx ≈ h/3 [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)]

≈ 0.75/3 [10.5 + 4(100.2842) + 2(528.125) + 4(1841.7969) + 3360]

≈ 4787.9476

To find a bound for the error using the error formula, we can use the following formula:

|E| ≤ K*h^4*(b-a)/180

where K is a constant, h is the width of each subinterval, and (b-a) is the length of the interval.

Since f''''(x) = 840, we can use K = 840.

|E| ≤ 840*(0.75)^4*(4-1)/180

≈ 0.371

To compare this to the actual error, we can find the exact value of the integral using the antiderivative:

∫10.5x4 dx = 10.5(1/5)x^5 + C

evaluated from x=1 to x=4:

= 10.5(1/5)(4^5 - 1^5)

= 4194

The actual error is:

|4194 - 4787.9476| = 593.9476

Since the bound for the error is 0.371, which is much smaller than the actual error of 593.9476, we can say that the Composite Simpson Rule with n=4 provides a very good approximation to the integral.

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Answer:

Set your calculator to degree mode.

cos(48°) = y/35

y = 35cos(48°)

tan(20°) = x / 35cos(48°)

x = 35cos(48°)tan(20°) = 8.5 inches

Answer:

8.5 in

Step-by-step explanation:

Find height, h, of the triangle:

cos48 = h/35

h = cos48(35) = 23.42

tan20 = x/23.42

x = tan20(23.42) = 8.524 ≈ 8.5 in

Answer:

78° + 95° + (2x + 115)° + 72° = 360°

(2x + 360)° = 360°, so x = 0.

The surface area of the prism is determined as 300 yd².

The surface area of the prism is calculated as follows;

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 5 (12) + (5 + 12 + 13) x 8

S.A = 60 yd² + 240 yd²

S.A = 300 yd²

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The proportion of individuals with the common attribute in the first sample is 0.525, while in the second sample, it is 0.728.

We have,
To analyze these samples, we can calculate the proportion of individuals with a common attribute in each sample.

Step 1: Calculate the proportion for the first sample
Divide the number of people with the common attribute (21) by the total number of people in the sample (40).
Proportion 1 = 21/40 = 0.525

Step 2: Calculate the proportion for the second sample
Divide the number of people with the common attribute (1528) by the total number of people in the sample (2100).
Proportion 2 = 1528/2100 = 0.728

Thus,

The proportion of individuals with the common attribute in the first sample is 0.525, while in the second sample, it is 0.728.

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Answer:

1, 768

2, 2088

3, 7789

4, 1828

5, 1435.

Answer:

center = -1, -3

radius = 6

Step-by-step explanation:

x² + y² + 2x + 6y = 26

x² + 2x + y² +6y = 26

equation of a circle is,

(x - h)² + (y - k)² = r²

where center of a circle is (h,k)

radius = r

x² + 2x + y² + 6y = 26

finding the middle point for mid term breaking of the equations,

(2/2)² = 1

(6/2)² = 9

x² + 2x + 1 + y² + 6y + 9 = 26 + 1 +9

to balance the equation we have to add the midpoints at both sides,

thus we have equation of a circle,

(x + 1)² + (y + 3)² = 36

so,

centre of a circle = -1, -3

radius = 6

We can see here that the vertices will be:

The vertex, in geometry, is the intersection of two or more lines, curves, or edges. It can also refer to the vertex of a parabola, which is where a function reaches its highest or lowest value.

We can see here that the equation of the hyperbola is seen in standard form. It is known that the center of the hyperbola is at (h, k) is (2, 1).

The distance between the center and vertices = a

where a² = coefficient of the positive term

So we see that  a² = 16

a = 4.

Also, the distance between the center and co-vertices = b

where b² = 4

b = 2.

Thus,

Vertex 1 = (2 + 4, 1) = (6, 1)

Vertex 2 = (2 - 4, 1) = (-2, 1).

Therefore, the vertices are:

(6, 1) and (-2, 1).

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