what is the lower sum for f(x)=18−x2 on [1,2] using four subintervals? round to the nearest hundredth if necessary.

The sum of the reciprocals of the squares of the odd positive integers is equal to π²/8.

Given that the sum of the reciprocals of the squares of all positive integers (Σk=1 1/k²) is equal to π²/6, you want to determine the sum of the reciprocals of the squares of the odd positive integers.

Let's denote the sum of reciprocals of odd squares as S_odd. We can represent it as:

S_odd = 1/1² + 1/3² + 1/5² + ...

Now, consider the sum of the reciprocals of even squares, which we'll call S_even:

S_even = 1/2² + 1/4² + 1/6² + ...

We know that Σk=1 1/k² = S_odd + S_even = π²/6.

To find S_odd, we can rewrite S_even in terms of S_odd by factoring out 1/4 (since all even numbers are divisible by 2):

S_even = 1/4 (1/1² + 1/2² + 1/3² + …)

Now, we can substitute this back into our original equation:

π²/6 = S_odd + 1/4 (Σk=1 1/k²)

Since Σk=1 1/k² = π²/6, we have:

π²/6 = S_odd + 1/4 (π²/6)

Now, solve for S_odd:

S_odd = π²/6 - 1/4 (π²/6)
S_odd = (3/4) (π²/6)
S_odd = π²/8

Therefore, the sum of the reciprocals of the squares of the odd positive integers is equal to π²/8.

To learn more about integers here:

brainly.com/question/490943#

#SPJ11

Answer:

256 cm^2

Step-by-step explanation:

All of the sides of the square are equal so to calculate the area we do side times side.

16*16 = 256

cm^2 is the unit for this question

Answer:

The missing term is 3x

Step-by-step explanation:

Given

-(x - 1) + 5 = 2(x + 3) - _

Required

Find _

For proper identification of the parameters, represent _ with Z

So, the equation becomes

-(x - 1) + 5 = 2(x + 3) - Z

Open bracket (start from the left hand side)

-x + 1 + 5 = 2(x + 3) - Z

-x + 1 + 5 = 2x + 6 - Z

Solve like terms

-x + 6 = 2x + 6 - Z

Subtract 6 from both sides

-x + 6 - 6 = 2x + 6 - 6 - Z

-x = 2x - Z

Subtract 2x from both sides

-x - 2x = 2x - 2x - Z

-3x = -Z

Multiply both sides by -1

-3x * -1 = -Z * -1

3x = Z

Reorder

Z = 3x

Hence, the missing term is 3x

Answer:

answer is 3x

Step-by-step explanation:

For the period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

According to the specified question-

Rate of change = (final number - initial number)/(final year - initial year)

Rate of change = (12,458 - 968)/(2010 - 2005)

Rate of change = -11490/5

Rate of change = -2298 fishes per year.

Negative sign shows there is a decline in the number.

Thus, for the time period 2005–2010, the drought caused a change in fish population of 2298 fishes each year.

To know more about the rate of change, here

https://brainly.com/question/25184007

#SPJ4

To develop a 95% confidence interval for the proportion of registered voters who are Democrats, we can use the formula for calculating the confidence interval. Based on the given information, the correct answer is option D, .5485 to .6567.

To calculate the confidence interval, we need the sample proportion and the sample size. In this case, the sample proportion is 120/200 = 0.6 (since 120 out of 200 indicated they are Democrats), and the sample size is 200.

Using the formula for the confidence interval:

CI = sample proportion ± z * sqrt[(sample proportion * (1 - sample proportion)) / sample size]

For a 95% confidence interval, the critical z-value is approximately 1.96 (corresponding to a two-tailed test). Plugging in the values, we get:

CI = 0.6 ± 1.96 * sqrt[(0.6 * 0.4) / 200]

Calculating this expression, we obtain:

CI ≈ 0.6 ± 0.0538

Simplifying, we get:

CI ≈ (0.5462, 0.6538)

Therefore, the 95% confidence interval for the proportion of registered voters who are Democrats is approximately 0.5485 to 0.6567.

To learn more about proportion click here, brainly.com/question/31548894

#SPJ11

Answer:

$1.25

Step-by-step explanation:

4 pounds= $10

1 pound= $10/4

1/2 pound= $10/8

$1.25

Answer:

1/10 10% of 1

Step-by-step explanation:

3/4 0.75

0.2 20% of 1

15/10 150% of 1

14/10 1.4

Fraction: 1/10, 3/4, 3/2, 4/5

Decimal: 0.75, 0.2, 1.4

Percentage: 10%, 20%, 150%

(The answer is in the same order as the column, I did not include the boxes that were already filled in)

Answer:

(√6x√20) / √3 = 2√10

Step-by-step explanation:

hello :

(√6x√20) / √3 =√2x√3 x√4x√5 / √3

because : √6 = √2x√3 and √20= √4x√5 = 2x√5

now simplify by √3 :(√6x√20) / √3 =√2x2x√5

(√6x√20) / √3 = 2√10 so : a =2 and b =10

The value of the given integral, ∬_R arctan(y/x) dA, when changing to polar coordinates, is π/8.

To evaluate the given integral using polar coordinates, we need to express the region R in terms of polar coordinates. The region R is defined by the inequalities 1 ≤ \(x^{2}\) + \(y^{2}\) ≤ 4 and 0 ≤ y ≤ x.

In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r is the distance from the origin and θ is the angle.

Converting the inequalities for R into polar form, we have 1 ≤ \(r^{2}\) ≤ 4 and 0 ≤ rsin(θ) ≤ rcos(θ). Simplifying the second inequality, we get 0 ≤ sin(θ) ≤ cos(θ), which corresponds to the region where the angle θ satisfies 0 ≤ θ ≤ π/4.

The integral becomes ∬_R arctan(y/x) dA = ∫∫_R arctan(rsin(θ)/rcos(θ)) r dr dθ.

Simplifying further, the integral becomes ∫∫_R arctan(tan(θ)) r dr dθ = ∫∫_R θ r dr dθ.

learn more about polar coordinates here:

https://brainly.com/question/31904915

#SPJ11

The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;

A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;

Solving the above inequality, we have;

2•x + 3 ≤ -3

2•x ≤ -3 - 3 = -6

2•x ≤ -6

Therefore;

x ≤ -6 ÷ 2 = -3

x ≤ -3

Which gives;

-∞ < x ≤ -3 in interval notation is (-∞, -3]

The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;

Learn more about inequalities here:

https://brainly.com/question/11613554

#SPJ1

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

x + y = 420; y = 6x

Thus, 420 fish were ultimately caught, with 6x standing in for "6 times as much."

The smallest and largest fish range in size from 1 cm to 18 m. 18 m then equals 18 x 100 or 1800 cm. ∴ The length of large fish exceeds that of little fish by 1800 times.

The number of parrotfish Carlos purchased is represented by the variable y, whereas the number of angelfish Carlos purchased is represented by the variable x.

To know more about Fish visit:-

brainly.com/question/29657983

#SPJ4

Given

A chemist wishes to mix a solution that is 8% acid.

She has on hand 8 liters of a 2% acid solution and wishes to add some 12% acid solution to obtain the desired 8% acid solution.

To find: How much 12% acid solution should she add?

Explanation:

It is given that,

A chemist wishes to mix a solution that is 8% acid.

She has on hand 8 liters of a 2% acid solution and wishes to add some 12% acid solution to obtain the desired 8% acid solution.

Now, Let x be the liters of acid added to obtain the desired 8% acid solution.

Then,

Hence, 12liters of acid is added to 12% acid solution.

To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

Learn more about assets on:

https://brainly.com/question/25746199

#SPJ1

The P-value in this case is approximately 0.1131.

In the given problem, we are given a test statistic t = 1.212, a sample size n = 6, and an alternative hypothesis H1: μ > μ0.

To calculate the P-value, we need to find the area to the right of the test statistic t in the t-distribution with n - 1 degree of freedom (df), assuming the null hypothesis is true.

Using a t-table or calculator, we can find that the area to the right of t = 1.212 with 5 degrees of freedom is approximately 0.1131. This means that if the null hypothesis were true (i.e., if the population mean were equal to the hypothesized value μ0), we would expect to observe a test statistic as extreme as t = 1.212 or more extreme in about 11.31% of random samples of size 6.

Since the P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample data, assuming that the null hypothesis is true, we can conclude that the P-value in this case is approximately 0.1131.

To learn more about the hypothesis;

brainly.com/question/29519577

#SPJ1

Answer:

20b - 16

=> 4 (5b - 4)

or

20b - 16

=> 20b/16 - 16/16

=> 1.25b - 1

Answer:

4(5b-4)

Step-by-step explanation:

To factor this you need to find a number, that 20 and 16 are divisible by. You can divide 4 from both of these.

It becomes 4(5b-4)

What is the importance of geometric figures in one’s life?

➪ Geometry plays an important role in our day to day life because it helps us in deciding material, design etc.. of an object. It also plays a vital role in construction process itself. Different types of houses and buildings are built using geometric shapes to give them a modern look.

The importance of geometric figures in one's life can be used for architectural drawings and design, astronomy work, or construction purposes.

Geometric figures are mathematical shapes that are used for construction by combining points, straight lines, or planes.

The importance of geometric figures in one's life has large importance depending on the intended purpose it's required to carry out. Geometric figures can be used:

Learn more about geometric figures here:

https://brainly.com/question/24370439

#SPJ5

Answer:

0.5

Step-by-step explanation:

1/2=0.5

Answer:

0.5

Step-by-step explanation:

1/2 is half and half is 50 and in decimal form you can put it as 0.5 or 0.50 or as much zeros as u want unless u put it in front of the 5 id does not the change the value.

The slope of the line in the simplest form is 1 / 2.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

The slope is rise over run.

The slope of the line can be found as follows:

m = slope = y₂ - y₁ / x₂ - x₁

Therefore, using (7, 0) and (3, -2)

Hence,

x₁ = 7

x₂ = 3

y₁ = 0

y₂ = -2

Therefore,

slope = - 2 - 0 / 3 - 7

slope = - 2 / -4

slope = 1 / 2

learn more on slope here: https://brainly.com/question/23087740

#SPJ1

There are 30 of 1/10's in the number 3

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

How many 1/10's are in 3?​

The above statement is a quotient expression that has the following features

Dividend = 3

Divisor = 1/10

So, we have

Quotient = Dividend /Divisor

Substitute the known values in the above equation, so, we have the following representation

Quotient = 3/(1/10)

Evaluate

Quotient = 30

Hence, there are 30 1/10's

Read more about fractions at

https://brainly.com/question/17220365

#SPJ1

Answer:

7 Hope that works?

Step-by-step explanation:

11 1/2 divided by 1 5/6 equals  

But, 6.27272727273 you can round it to 7

The test statistic is 2.02, and the P-value is 0.022. As the P-value is less than the significance level of 0.10, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 20% of users develop nausea. The correct option is C.

The null and alternative hypotheses for this test are

H0: p ≤ 0.20 (the proportion of users who develop nausea is less than or equal to 20%)

H1: p > 0.20 (the proportion of users who develop nausea is greater than 20%)

The test statistic for this hypothesis test is z = (P - p0) / √(p0*(1-p0)/n) = (0.266 - 0.20) / √(0.20*(1-0.20)/203) = 2.02 (rounded to two decimals).

The P-value for this hypothesis test is P(z > 2.02) = 0.022 (rounded to three decimals).

Since the P-value is less than the significance level of 0.10, we reject the null hypothesis. The conclusion for this hypothesis test is therefore: C. Reject H0. There is sufficient evidence to warrant support of the claim that more than 20% of users develop nausea.

To know more about null and alternative hypotheses:

https://brainly.com/question/28331914

#SPJ4

The cubic polynomial interpolation function for the given data using different methods is as follows:

Polynomial Coefficient Interpolation Method: p(x) = -1x³ + 4x² - 2x - 8

Newton Interpolation Method: p(x) = -8 + 6(x+1) - 4(x+1)(x-0) + 2(x+1)(x-0)(x-2)

Lagrange Interpolation Method: p(x) = -4((x-0)(x-2)(x-3))/((-1-0)(-1-2)(-1-3)) - 8((x+1)(x-2)(x-3))/((0-(-1))(0-2)(0-3)) + 2((x+1)(x-0)(x-3))/((2-(-1))(2-0)(2-3)) + 28((x+1)(x-0)(x-2))/((3-(-1))(3-0)(3-2))

Polynomial Coefficient Interpolation Method: In this method, we find the coefficients of the polynomial directly. By substituting the given data points into the polynomial equation, we can solve for the coefficients. Using this method, the cubic polynomial interpolation function is p(x) = -1x³ + 4x² - 2x - 8.

Newton Interpolation Method: This method involves constructing a divided difference table to determine the coefficients of the polynomial. The divided differences are calculated based on the given data points. Using this method, the cubic polynomial interpolation function is p(x) = -8 + 6(x+1) - 4(x+1)(x-0) + 2(x+1)(x-0)(x-2).

Lagrange Interpolation Method: This method uses the Lagrange basis polynomials to construct the interpolation function. Each basis polynomial is multiplied by its corresponding function value and summed to obtain the final interpolation function. The Lagrange basis polynomials are calculated based on the given data points. Using this method, the cubic polynomial interpolation function is p(x) = -4((x-0)(x-2)(x-3))/((-1-0)(-1-2)(-1-3)) - 8((x+1)(x-2)(x-3))/((0-(-1))(0-2)(0-3)) + 2((x+1)(x-0)(x-3))/((2-(-1))(2-0)(2-3)) + 28((x+1)(x-0)(x-2))/((3-(-1))(3-0)(3-2)).

These interpolation methods provide different ways to approximate a function based on a limited set of data points. The resulting polynomial functions can be used to estimate function values at intermediate points within the given data range.

Learn more about cubic polynomial interpolation here:

https://brainly.com/question/31494775

#SPJ11

Answer:

8

Step-by-step explanation:

We can start by subtracting 3 from both sides of the equation:

7(x+2) + 3 - 3 = 73 - 3

We will get:

7(x+2) = 70

Now we have to figure out what times seven gives us 70:

70/7 = 10

We get the answer 10. Now we know that:

x+2 = 10

We can now subtract two from both sides of the equation:

x+2-2 = 10-2

We will get:

x = 8

Answer:

Step-by-step explanation:

7x + 14 + 3 = 73

7x + 17 = 73

7x = 56

x = 8

A hippopotamus had a mass of 32.7 kg at birth. the hippopotamus's mass increased by approximately 167.1% over the two-month period.

To calculate the percentage increase in the hippopotamus's mass over the two-month period, we can use the following formula:

Percentage increase = ((New mass - Original mass) / Original mass) * 100

Given that the original mass (birth weight) was 32.7 kg and the new mass (after two months) was 87.4 kg, we can substitute these values into the formula:

Percentage increase = ((87.4 - 32.7) / 32.7) * 100

Calculating this expression:

Percentage increase = (54.7 / 32.7) * 100 ≈ 167.1%

Therefore, the hippopotamus's mass increased by approximately 167.1% over the two-month period. Rounding to the nearest 1%, the percentage increase is 167%.

For more details regarding Percentage increase, visit:

https://brainly.com/question/20818421

#SPJ1

The proportion of cranberries required for the muffins is 4 pounds x 16 ounces/pound = 64 ounces of cranberries. Therefore, to make the muffins for the party, you will need 64 ounces of cranberries.

To calculate the amount of cranberries needed for the muffins at a party of 12 people, making 11/2-ounce muffins and assuming each person will have three muffins, we need to convert the measurements and quantities.

Given that each muffin weighs 11/2 ounces, and each person will have three muffins, we can calculate the total weight of muffins needed. 11/2 ounces is equivalent to 1.5 ounces, so each person will consume 1.5 ounces x 3 muffins = 4.5 ounces of muffins.

For a party of 12 people, the total amount of muffins required is 4.5 ounces/person x 12 people = 54 ounces of muffins.

Now, to determine the amount of cranberries needed for the muffins, we need to consider the recipe's proportion. The recipe makes 15 pounds of dough and calls for 4 pounds of cranberries. To convert pounds to ounces, we know that 1 pound is equal to 16 ounces.

Learn more about pounds and ounce coversions here:

https://brainly.com/question/29091346

#SPJ11

Answer:

y - 8

Step-by-step explanation:

She is 8 years younger so you'd subtract eight from her sister's age.

Using the given differential equation with the solution \(x^4\) and reduction order, we can substitute \(y^2 = ux^4\) to obtain the new equation \(2x^2u'' + 12xu' - 16u = 0\).

Given the differential equation \(x^2(d^2y/dx^2) - 7x(dy/dx) + 16y = 0\), with \(x^4\) as a solution, we can apply reduction order to obtain a simpler differential equation.

Reduction order involves substituting \(y^n = ux^i\), where i is the lowest positive integer for which the equation becomes simpler.

We can substitute \(y^n = ux^4\) into the given equation, which yields:

\(y^2 = ux^4\)

⇒\(2y(dy/dx) = 4x^3u + x^4u'\)

⇒\((d/dx)(y^2) = (d/dx)(x^4u)\)

⇒\(2y(dy/dx) + y^2(d^2y/dx^2) = 4x^3u' + 4x^4u''\)

Substituting this into the original equation and simplifying gives:

\(2x^2u'' + 12xu' - 16u = 0\), which is a second-order linear homogeneous differential equation that can be solved by substitution or other methods.

Learn more about differential equation here:

https://brainly.com/question/32538700

#SPJ11

Answer:

c

Step-by-step explanation: