Consider the integral I= | 1914, d.o. + x2 0 This integral can be evaluated both numerically and analytically. Thus the objective is to verify the numerical result against one obtained in closed-form analytically. This integral has the exact answer I= ln(2). To that end, answer the following questions: (a) Evaluate the preceding integral numerically by using the composite Simpson's rule for number of subintervals n = 4 and 8. Estimate the error in each case. Compare your answers with the exact result.

The x-intercepts with multiciplity greater than 1 is x = 0

The number of distinct intercepts is 3 and the number of zeros is 4

From the question, we have the following parameters that can be used in our computation:

f(x) = x²(x + 2)(x - 7)

The x-intercepts with multiciplity greater than 1 is the factor that has a power greater than 1

So, we have

x² = 0

This gives

x = 0

The number of distinct intercepts is the number of factors i.e. 3

The number of zeros is the sum of powers

i.e. Zeros = 2 + 1 + 1

Zeros = 4

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Answer:

a=-1

Step-by-step explanation:

a(n) = -6+3(n-1)

a(n) = -6+3n-3

a(n) -n=-6+3n-n-3

a=-6+3-3

+3 +3

a3=-3

---- ----

3 3

a=-1

Answer:

-15

Step-by-step explanation:

g(x) = 3x + 3

Let x = -6

g(-6) = 3*-6 + 3

           = -18 +3

            = -15

The answer to the given question is option B, which is (-1.74 and 1.74).

Step-by-step explanation:

Now, we need to find the z values that will enable us to fail to reject the null hypothesis. The p-value for the given level of significance is:

p = 0.0819.

As it is a two-tailed test, the significance level is divided into two equal parts.

The equal parts would be 0.0819/2 = 0.04095.

The z-score corresponding to the probability 0.04095 is -1.74, and the z-score corresponding to the probability 0.95905 (1 - 0.04095) is 1.74.

Therefore, the z-values that will enable us to fail to reject the null hypothesis at the 0.0819 significance level in a two-tailed test is option B, which is (-1.74 and 1.74).

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Answer:

cost of 1 dozen cupcake =30$

cost 12 cupcake =30$

cost of 1 cupcake=30/12

=2.5$

Answer:

1200

Step-by-step explanation

3800+p=5000

5000-3800=1200

Answer:where is the graph?

Step-by-step explanation:

Answer: m=5 b=12

Step-by-step explanation:

This equation is already set up in slope intercept form of y=mx+b.

So y=5x+12 would mean that 5= slope and 12= y-intercept. They just wanted you to be able to identify the slope and y-intercept from the equation given.

If you look at another example like: y=12x+6 then the slope would be = 12 and the y-intercept would be = 6.

Juana would have to pay approximately $29.40 in interest for the $10,686.00 loan over a 20-day period, assuming an annual interest rate of 5.79%.

The interest Juana would have to pay in 20 days can be calculated using the formula:

Interest = Principal × Interest Rate × Time

In this case, the principal amount is $10,686.00 and the interest rate is 5.79% per annum. To calculate the interest for 20 days, we need to convert the time to a fraction of a year. Since there are 365 days in a year, the time in years would be 20/365.

Using the formula and substituting the values:

Interest = $10,686.00 × 0.0579 × (20/365)

Calculating this expression, we find that the interest amount Juana would have to pay in 20 days is approximately $29.40.

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The original equation  provided (74.94 * 1000), we can see that multiplying 74.94 by 1,000 is equivalent to adding three zeros to the end of the number. Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000.  So, the answer to the equation is simply 74,940.

we need to understand the concept of exponents and how they relate to the number of zeros in a number. An exponent is a way of showing how many times a number should be multiplied by itself. For example, 10 raised to the power of 3 (written as 10^3) means 10 multiplied by itself three times, which is equal to 1,000.
Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000. When this number is written without an exponent, we can simply write it as 1 followed by three zeros, which is 1,000. Therefore, the answer to your question is that the number 10 with a 3 exponent has three zeros when it is written without an exponent.
When you multiply 74.94 by 1000, you are essentially moving the decimal point three places to the right because the number 10 with a 3 exponent (10^3) has three zeros when it is written without an exponent.
1. Identify the number to be multiplied (74.94) and the exponent of 10 (3).
2. Convert 10^3 to its standard form, which gives us 1000 (three zeros).
3. Move the decimal point of the number (74.94) three places to the right due to the three zeros in 1000.
So, 74.94 * 1000 = 74940.

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The original equation  provided (74.94 * 1000), we can see that multiplying 74.94 by 1,000 is equivalent to adding three zeros to the end of the number. Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000.  So, the answer to the equation is simply 74,940.

The concept of exponents and how they relate to the number of zeros in a number. An exponent is a way of showing how many times a number should be multiplied by itself. For example, 10 raised to the power of 3 (written as 10^3) means 10 multiplied by itself three times, which is equal to 1,000.

Now let's consider the number 10 with a 3 exponent, which we know is equal to 1,000. When this number is written without an exponent, we can simply write it as 1 followed by three zeros, which is 1,000. Therefore, the answer to your question is that the number 10 with a 3 exponent has three zeros when it is written without an exponent.

When you multiply 74.94 by 1000, you are essentially moving the decimal point three places to the right because the number 10 with a 3 exponent (10^3) has three zeros when it is written without an exponent.

1. Identify the number to be multiplied (74.94) and the exponent of 10 (3).

2. Convert 10^3 to its standard form, which gives us 1000 (three zeros).

3. Move the decimal point of the number (74.94) three places to the right due to the three zeros in 1000.

So, 74.94 * 1000 = 74940.

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Answer:

x^2+16x+64=(x+8)^2

Step-by-step explanation:

For the first spot you find the perfect square of the equation

This is found by doing (1/2 16)^2

1/2 16 = 8

8^2 = 64

The second spot is factoring, where you would put half of 16 or the square root of 64

1/2 16 = 8

root 64 = 8

Answer:

vertical angles

Step-by-step explanation:

angles 6 and 7 are formed by the same two lines and are on opposite sides  of the intersection point

Answer

Step-by-step explanation:

Answer:

C. 20

Step-by-step explanation:

Use the Pythagorean theorem which is \(a^{2} +b^{2} =c^{2}\).

\(a^{2}\) and \(b^{2}\) are the sides of the triangle squared, AB and AC. \(c^{2}\) is the hypotenuse (the slanted side of the triangle) or BC.

So, \(12^{2} + 16^{2} =400^{2}\). Then you square root 400 to get your answer.

\(\sqrt{400}\) = 20.

20 is your answer.

To evaluate the indefinite integral ∫t/(1 - t^3) dt as a power series, we can use the geometric series expansion. First, rewrite the integrand as t * (1/(1 - t^3)). Then, use the geometric series formula to expand the denominator.

Finally, integrate each term of the power series and simplify. To evaluate the indefinite integral as a power series, we start by rewriting the integrand as t * (1/(1 - t^3)). This allows us to use the geometric series expansion. The geometric series formula is given by: 1/(1 - r) = 1 + r + r^2 + r^3 + ...

In our case, the denominator of the integrand is 1 - t^3, which can be rewritten as (1 - (-t^3)). This is in the form 1 - r, where r = -t^3. By substituting -t^3 into the geometric series formula, we get: 1 - t^3 + (t^3)^2 - (t^3)^3 + ...

Next, we integrate each term of the power series. The integral of t^n is (t^(n+1))/(n+1). So, integrating each term in the power series gives us: t - (t^4)/4 + (t^7)/7 - (t^10)/10 + ... Finally, we simplify the integral by writing it as an infinite sum of terms.

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Therefore, there are 53,248 different super subs that can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from at Sandwich Station.

The super sub at Sandwich Station consists of 4 different toppings and 3 different condiments. The question is asking how many different super subs can be made if there are 8 toppings, 6 condiments, and 6 types of homemade bread to choose from.

To solve this problem, we can use the multiplication principle of counting. The multiplication principle states that if there are m ways to do one thing and n ways to do another thing, then there are m x n ways to do both things.

Let's use the multiplication principle to solve this problem. There are four different toppings, and we can choose any of the eight toppings for each of the four spots.

Using the multiplication principle, there are

8 x 8 x 8 x 8 = 4096

ways to choose the toppings. Similarly, there are

6 x 6 x 6 = 216

ways to choose the condiments. Lastly, there are 6 different types of homemade bread to choose from. Using the multiplication principle again, there are

4096 x 216 x 6 = 53,248,

which means there are 53,248 ways to make the super subs.

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Answer:

12 is the median

Step-by-step explanation:

as u have to cancel each number out at each side together till you reach the middle

The median of the given data in the box-and-whisker plot is 9.5. Therefore, option C is the correct answer.

A box and whisker plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your data, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.

From the given box-and-whisker plot

Minimum is 3

Maximum is 15

Q₁ is 7

Q₃ is 13

Median is 9.5

The median of the given data in the box-and-whisker plot is 9.5. Therefore, option C is the correct answer.

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DD earned a gross profit of $15,000 from the sale of the merchandise inventory.

DD sold merchandise inventory for cash to customers for $45,000. This means that DD received $45,000 in cash from its customers for the sale of its merchandise inventory.

DD had purchased the merchandise inventory sold for $30,000. This means that DD bought the merchandise inventory that it sold to its customers for $30,000.

The difference between the amount received from the sale of the merchandise inventory and the cost of the merchandise inventory is the gross profit. In this case, the gross profit is $45,000 - $30,000 = $15,000. This means that DD earned a gross profit of $15,000 from the sale of the merchandise inventory.

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The values of r for which the differential equation has solutions of the form y = ert are r = -2 and r = -3.

To find the values of r for which the differential equation y'' + 5y' + 6y = 0 has solutions of the form y = ert, we can substitute y = ert into the differential equation and solve for r.

First, let's find the derivatives of y with respect to t:

y' = re^rt

y'' = r^2e^rt

Substituting these derivatives into the differential equation, we get:

r^2e^rt + 5re^rt + 6e^rt = 0

Now, we can factor out the common term e^rt:

e^rt(r^2 + 5r + 6) = 0

Since e^rt is never zero, we can set the expression inside the parentheses equal to zero:

r^2 + 5r + 6 = 0

Now we can solve this quadratic equation for r. Factoring the quadratic, we have:

(r + 2)(r + 3) = 0

Setting each factor equal to zero, we get:

r + 2 = 0  -->  r = -2

r + 3 = 0  -->  r = -3

So, the values of r for which the differential equation has solutions of the form y = ert are r = -2 and r = -3. There are two values of r in this case.

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Answer:

all real numbers

Step-by-step explanation:

The domain is the values that x can take

There are no restrictions as to what x can be in this function

In the function given, it can take any x variable without it causing any problems in the function when solved.

So, any value can be x (all real numbers)

Best of Luck!

The number of baby camels at the zoo is 44.

Given: The number of adult camels is 6 and the number of baby camels is 5 for every 6 camels respectively.

To find :We have to find how many baby camels are at the zoo.

Explanation:

Step 1:The ratio of adult camels and baby camels is 6:5

Step 2:Let the number of adult camels = 6x .

Step 3:Let the number of baby camels = 5x

Step 4:It is given that the total number of adult camels and baby camels is 44 at the zoo. So According to the questions,

⇒6x+5x=44

⇒11x=44

⇒x=44/11

⇒x=4

∴The number of adult camels = 6×4

                                               = 24

And the number of baby camels at the zoo.

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Answer:

C.

Step-by-step explanation

make a line with that dots, and you will find the y-intercept, -2.

To approximate the definite integral I = ∫[0.5 to 0] x^4 * e^(-x^2) dx with an error less than 0.001, we can use a series expansion. The series expansion of the integrand function is derived, and terms are added until the desired accuracy is achieved.



To approximate the definite integral, we can use a Taylor series expansion of the integrand function x^4 * e^(-x^2). The Taylor series expansion of e^(-x^2) is well-known as the Maclaurin series for the exponential function. By multiplying the Taylor series expansion of e^(-x^2) by x^4, we obtain a power series representation of the integrand.

Next, we integrate the power series term by term. Integrating a power series can be done by term-by-term integration, and we obtain a new power series representation for the integral. Since we have an upper limit of 0.5 for the definite integral, we only need to evaluate the power series up to the desired accuracy at x = 0.5.

We continue adding terms to the power series until the absolute difference between consecutive partial sums falls below 0.001. This ensures that the error in the approximation is within the desired accuracy range. The accuracy of the approximation can be increased by adding more terms to the power series expansion.By utilizing this approach, we can approximate the definite integral I = ∫[0.5 to 0] x^4 * e^(-x^2) dx with the specified accuracy requirement of |error| < 0.001.

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Answer:

C

Step-by-step explanation:

Formula for Surface Area of cube :

6  x  \(a^{2}\)

In our case, the edges are 8, meaning would we would subsuite a with 8 in the equation. We would do 6 x 64, since \(8^{2}\) is 64. 6 x 64 is 384, hence our answer is 384.

The Surface Area of the cube is 384 unit².

Surface area is the amount of space covering the outside of a three-dimensional shape.

Given: the edge of the cube, l= 8 units

Surface area of the cube =  6*l²

                                           = 6*8*8

                                           = 6*64

                                          = 384 unit²

Hence, the surface area of the cube is 384 unit².

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If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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Answer:

Step-by-step explanation:

I believe that since both circles C & D are congruent, and TU is bisected into TW and WU, PS = 7.4/2 = 3.7

PS = 3.7

Answer:

it is 6.9

Step-by-step explanation:

i took the test

Answer:

There's nothing there just repost it and don't forget the link

Step-by-step explanation:

Good Mornin' Dude  

* inserts Bruno Mars "Uptown Funk"

Answer:

C is the answer!!

Step-by-step explanation:

The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Using Pythagoras theorem the hypothenuse of the figure is 32.5 feet

Pythagoras theorem is defined as “In a right-angled triangle,  the square of the hypotenuse must be equal to the sum of squares of the other two sides". The sides of this triangle  are legs and hypotenuse. The hypotenuse is the longest side, as it is opposite to the angle 90°.

The formula of Pythagoras theorem is given as

c² = a² + b²

Taking the two sides given, we can find the hypothenuse of the right angle triangle figure

c² = 26² + 19.5²

c² = 676 + 380.25

c = √1056.25

c = 32.5

The distance from the top of the pole to the stake is 32.5 feet

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Answer:

the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 15000.

Step-by-step explanation:

The function g(x) is a dilation of the parent function f(x) = 0.98^x.

Specifically, g(x) = 15000(0.98)^x is a vertical dilation of f(x) = 0.98^x by a factor of 15000.

This means that the graph of g(x) is the same shape as the graph of f(x), but it is vertically stretched by a factor of 15000.

In other words, the values of g(x) are 15000 times greater than the values of f(x) for any given value of x.

For example, when x = 1, f(1) = 0.98 and g(1) = 15000(0.98) = 14700. This means that the number of visitors to the water park in the second month (x = 1) is 15000 times greater than the number of visitors in the first month.

Overall, the dilation in g(x) as it relates to the parent function f(x) is a vertical dilation by a factor of 15000.