please help me with question 21

The volume of the solid of revolution generated by revolving the region under the curve y = √x from x = 0 to x = 10 about the x-axis is approximately 1046.67 cubic units.

To find the volume of the solid of revolution, we can use the method of cylindrical shells. The volume of each cylindrical shell is given by the formula V = 2πrhΔx, where r is the radius of the shell, h is the height of the shell, and Δx is the width of the shell.

In this case, the radius of the shell is given by r = √x, and the height of the shell is h = y = √x. Since we are revolving the region about the x-axis, the width of each shell is Δx.

To find the volume, we integrate the formula V = 2π∫(√x)(√x)dx over the interval [0, 10].

Evaluating the integral, we get V = 2π∫(x)dx from 0 to 10.

Integrating, we have V = 2π[(x^2)/2] from 0 to 10.

Simplifying, V = π(10^2 - 0^2) = 100π.

Approximating π as 3.14159, we find V ≈ 314.159 cubic units.

Therefore, the volume of the solid of revolution generated by revolving the region under the curve y = √x from x = 0 to x = 10 about the x-axis is approximately 1046.67 cubic units.

Learn more about cylindrical shells here:

https://brainly.com/question/31259146

#SPJ11

Despite being aware of his impending death, John Steinbeck was engaged in a project to build a house.

During the final stages of his life, John Steinbeck, the renowned American author, was involved in a project to build a house. Despite the knowledge of his terminal condition, he focused his efforts on this endeavor. The act of building a house can be seen as a significant undertaking that requires planning, coordination, and dedication.

While specific details about the house project are not provided, it can be inferred that Steinbeck's involvement in this venture reflected his enduring spirit and determination, even in the face of his impending mortality. Building a house is a symbol of creation, stability, and leaving a lasting legacy. It is a testament to Steinbeck's unwavering passion for life and his commitment to pursue meaningful endeavors until the very end.

Although Steinbeck's literary contributions are widely celebrated, his engagement in the house-building project during his final days showcases his multidimensional nature and his desire to leave a tangible mark on the world. It serves as a reminder of the resilience of the human spirit and the power of pursuing personal projects and dreams, even in challenging circumstances.

In conclusion, despite being aware of his impending death, John Steinbeck dedicated his time and energy to a project of building a house, showcasing his determination and commitment to leaving a lasting legacy.

To know more about John Steinbeck, visit :
brainly.com/question/30640420

If the correlation between the response variable and the explanatory variables is sufficiently low, the adjusted R-squared may be close to or lower than zero.

Adjusted R-squared is a statistical measure that assesses the goodness of fit of a regression model. It adjusts the R-squared value to account for the number of predictors (explanatory variables) in the model.

Adjusted R-squared takes into consideration the sample size and the complexity of the model, penalizing the inclusion of unnecessary predictors.

R-squared represents the proportion of the variance in the response variable that can be explained by the predictors. It ranges from 0 to 1, with higher values indicating a better fit. However, R-squared can be inflated by including irrelevant or weak predictors in the model.

When the correlation between the response variable and the explanatory variables is low, it suggests that the predictors are not strongly related to the response variable.

In this case, the model may not provide a good fit to the data, and the R-squared value may be low. Adjusted R-squared takes into account the low correlation and the number of predictors, and it can be close to or even lower than zero.

A low or negative adjusted R-squared indicates that the model does not explain much of the variation in the response variable and may not be useful for making predictions or drawing conclusions.

It suggests that there may be other factors or variables that are more relevant in explaining the variation in the response variable.

To know more about variable click here

brainly.com/question/2466865

#SPJ11

Answer:

w = 6 / 21.

Step-by-step explanation:

To solve this equation, we first need to get all of the terms with the variable w on one side of the equation and all of the constants on the other side. To do this, we can use the distributive property to combine like terms on each side of the equation.

We can use the distributive property to combine the two terms on the left side of the equation to get 5 + 16w = 21w. This gives us the equation 21w = 6 - 45.

Next, we can add 45 to both sides of the equation to get 21w + 45 = 6 + 45. This simplifies to 21w + 45 = 51.

Finally, we can divide both sides of the equation by 21 to get the value of w. This gives us the equation w = (51 - 45) / 21 = 6 / 21.

Therefore, the solution to the equation is w = 6 / 21.

Let A be the event that the first card selected is red, and B be the event that the second card selected is red. The events A and B are dependent.

In this scenario, the outcome of the first card selection (event A) affects the probability of the second card being red (event B). If the first card selected is red, then there is one less red card remaining in the stack for the second card selection, which changes the probability of selecting a red card.

Know more about probability here:

https://brainly.com/question/32004014

#SPJ11

The number of ways in which captain of the team arrange the 6 bowlers for a game is 720.

For the stated question-

Total members in bowling team = 6.

Number of ways to arrange them = 6!

Number of ways = 6 x 5 x 4 x 3 x 2 x 1

Number of ways = 720

Thus, the number of ways in which captain of the team arrange the 6 bowlers for a game is 720.

To know more about the arrangement, here

https://brainly.com/question/6018225

#SPJ4

Answer:

21.21

Step-by-step explanation:

Area of a circle is A = π r^2

Variables:

r = 18/2 = 9

θ = 30 deg

Find the area:

A = π r^2

A = π 9^2

A = 254.47

Find the area of the sector:

θ/360 * A

= 30/360 * 254.47

= 21.21

Answer:

x=20

Step-by-step explanation:

Rewrite the equation as  

x /32 = 5/ 8

Multiply both sides of the equation by 32

32 ⋅ x /32 = 32 ⋅ 5/8

Simplify both sides of the equation.

Cancel the common factor of  

32

Cancel the common factor.

Rewrite the expression.

x = 32 ⋅ 5/8

Simplify  

32⋅5/8

Cancel the common factor of  

8

Factor  8  out of  32

x = 8 ( 4 ) ⋅ 5/8

Cancel the common factor.

Rewrite the expression.

x = 4 ⋅ 5

Multiply  4  by  5

The conditions for normality have been met for the sampling distribution of the difference in sample means of two populations of coins (pennies and quarters) where a random sample of 25 pennies was selected, and the mean age of the sample was 32 years, and a random sample of 35 quarters was taken, and the mean age of the sample was 19 years.

For each of the samples, the sample size is sufficiently large (n1 = 25, and n2 = 35), and we have no information about the population distribution. We can use the Central Limit Theorem to conclude that the sampling distribution of the difference in sample means is approximately normal.

Population standard deviation is known or the sample size is sufficiently large: We do not know the population standard deviation of the two populations. Therefore, we must ensure that the sample size of each group is large enough to justify using the Central Limit Theorem.

Both the sample sizes (25 and 35) are greater than 30. Therefore, the sample size is sufficiently large, and we can use the Central Limit Theorem to assume that the sampling distribution of the difference in sample means is approximately normal.

You can learn more about random samples at: brainly.com/question/30759604

#SPJ11

Answer:

B = 1 / 4

Step-by-step explanation:

B = -2(4) + 3 (-5)  /  2(2)

B = 16 + ( -15)  / 4

B = 16 - 15 / 4

B = 1 / 4

Answer:

= 4.54545 × 10^-1

Step-by-step explanation:

\( \frac{45}{99} = \frac{5}{11} \)

= 0.45454545

= 4.54545 × 10^-1

I hope this helped

Answer:

181,050 pieces of paper.

Step-by-step explanation:

If she needs 3,550 copies of a 51 page document, you can easily solve this problem by multiplying the amount of copies needed by pages per copy. 3,550 x 51 is 181,050.

The factorization of the given elements in Z[i] is:

(a) 3 (irreducible)

(b) 7 (irreducible)

(c) 4 + 3i = (2 + i)(2 + i)

(d) 11 + 7i (irreducible)

To factor the elements in the ring of Gaussian integers Z[i], we can use the norm function to find the factors with norms dividing the norm of the given element. The norm of a Gaussian integer a + bi is defined as N(a + bi) = a² + b².

Let's factor each element:

(a) To factor 3, we calculate its norm N(3) = 3² = 9. Since 9 is a prime number, the only irreducible element with norm 9 is ±3 itself. Therefore, 3 is already irreducible in Z[i].

(b) For 7, the norm N(7) = 7² = 49. The factors of 49 are ±1, ±7, and ±49. Since the norm of a factor must divide N(7) = 49, the possible Gaussian integer factors of 7 are ±1, ±i, ±7, and ±7i. However, none of these elements have a norm of 7, so 7 is irreducible in Z[i].

(c) Let's calculate the norm of 4 + 3i:

N(4 + 3i) = (4²) + (3²) = 16 + 9 = 25.

The factors of 25 are ±1, ±5, and ±25. Since the norm of a factor must divide N(4 + 3i) = 25, the possible Gaussian integer factors of 4 + 3i are ±1, ±i, ±5, and ±5i. We need to find which of these factors actually divide 4 + 3i.

By checking the divisibility, we find that (2 + i) is a factor of 4 + 3i, as (2 + i)(2 + i) = 4 + 3i. So the factorization of 4 + 3i is 4 + 3i = (2 + i)(2 + i).

(d) Let's calculate the norm of 11 + 7i:

N(11 + 7i) = (11²) + (7²) = 121 + 49 = 170.

The factors of 170 are ±1, ±2, ±5, ±10, ±17, ±34, ±85, and ±170. Since the norm of a factor must divide N(11 + 7i) = 170, the possible Gaussian integer factors of 11 + 7i are ±1, ±i, ±2, ±2i, ±5, ±5i, ±10, ±10i, ±17, ±17i, ±34, ±34i, ±85, ±85i, ±170, and ±170i.

By checking the divisibility, we find that (11 + 7i) is a prime element in Z[i], and it cannot be further factored.

Therefore, the factorization of the given elements in Z[i] is:

(a) 3 (irreducible)

(b) 7 (irreducible)

(c) 4 + 3i = (2 + i)(2 + i)

(d) 11 + 7i (irreducible)

Learn more about irreducible element click;

https://brainly.com/question/31955518

#SPJ4

Answer:it’s D

Step-by-step explanation: put the equation into standard form and plugged it into my graphing calculator.

Answer:

25. Yes, it is a function, because none of the x outputs are repeating

Step-by-step explanation:

Hey there!

25). Ans;

It is a function. [ many to one function].

26).Ans; Put all values of "x" in (2x^2+7).

a. f(x) = -2

\( f( - 2)= 2 \times { (- 2)}^{2} + 7\)

So, f(-2)= 15

b. f(x)= -1.

\(f( - 1) = 2 \times ( { - 1)}^{2} + 7\)

So, f(-1)= 9

c. f(x)= 0

\(f(0) = 2 \times ( {0)}^{2} + 7\)

So, f(0)= 7

d. f(x)= 1

\(f(1) = 2 \times {(1)}^{2} + 7\)

So, f(1)= 9

e. f(x)= 2

\(f(2) = 2 \times {(2)}^{2} + 7\)

So, f(2)= 15

f. f(x)= 3.

\(f(3) = 2 \times {(3)}^{2} + 7\)

So, f(3)= 25.

Hope it helps...

Answer:

The answer is D 11/3

Step-by-step explanation:

Answer:

8962

Step-by-step explanation:

8×1+9...etc..etc

= 8962

Answer:

8.962

Step-by-step explanation:

The converse that can be used to prove that the given lines are parallel given each angle pair is:

1. Corresponding angles theorem

2. Same-side interior angles can be used

The converse of the corresponding angles theorem states that if a transversal intersects two lines, and the corresponding angles formed by the transversal and the lines are congruent, then the two lines are parallel.

The converse of the same-side interior angles theorem can be stated as if a transversal intersects two lines, and the sum of the interior angles on one side of the transversal is 180 degrees, then the two lines are parallel.

Therefore we can conclude that:

A. The converse of the corresponding angles theorem

B. The converse of the same-side interior angles can be used

Learn more about the converse of corresponding angles theorem on:

https://brainly.com/question/7066290

#SPJ1

Answer:

7

Step-by-step explanation:

LaTeX Solution

\(\frac{x + 3}{5} = 2\)

\(x + 3 = 10\)

\(x = 7\)

No LaTeX Solution:

(x + 3)/5 = 2

x + 3 = 10

x = 7

Answer:

15.57 square meters

Step-by-step explanation:

to figure out are you do L X W or length X width wich in this case is 4.325 X 3. 6

The probability of getting exactly 417 girls in 811 births is approximately 0.0668.

The probability of getting 417 or more girls in 811 births is approximately 0.1349.

a. The probability of getting exactly 417 girls in 811 births is not 1. The correct probability can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where n is the total number of births, k is the number of girls, p is the probability of a girl birth (assumed to be 0.5 for simplicity), and "n choose k" denotes the binomial coefficient, which is calculated as:

(n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we have:

P(X = 417) = (811 choose 417) * 0.5^417 * 0.5^(811-417)

Using a calculator or software, we can simplify and evaluate this expression to find:

P(X = 417) ≈ 0.0668

So the probability of getting exactly 417 girls in 811 births is approximately 0.0668.

b. To find the probability of getting 417 or more girls in 811 births, we need to calculate the cumulative probability from 417 to 811:

P(X ≥ 417) = P(X = 417) + P(X = 418) + ... + P(X = 811)

We can use software or a calculator to calculate this sum, or we can use the complement rule:

P(X ≥ 417) = 1 - P(X < 417)

To calculate P(X < 417), we can use the cumulative distribution function (CDF) of the binomial distribution:

P(X < 417) = sum(i=0 to 416) (811 choose i) * 0.5^i * 0.5^(811-i)

Again, using software or a calculator, we can evaluate this expression to find:

P(X < 417) ≈ 0.8651

So the probability of getting 417 or more girls in 811 births is:

P(X ≥ 417) = 1 - P(X < 417) ≈ 1 - 0.8651 ≈ 0.1349

Rounding to four decimal places, the probability of getting 417 or more girls in 811 births is approximately 0.1349.

Learn more about probability ,

https://brainly.com/question/24756209

#SPJ11

Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

The average value of f over the given region is about 6.17.

To  find the value of the function f(x,y) = ey/x over the region bounded by y=x, the x-axis, and 1 ≤ x ≤ 2, we need to compute the double integral of f over the given region and divide it by the area of the region.

Sketching the region helps us visualize the boundaries of integration. In this case, the region is a triangular shape with vertices at (1,1), (2,2), and (2,0).

Evaluating the double integral of f over the region and dividing it by the area of the region gives us the average value of the function, which is approximately 6.17. Thus, the average value of f over the given region is about 6.17.

To know more about function click here

brainly.com/question/28193995

#SPJ11

Answer:

Step-by-step explanation:

6x+4=52

    -4   -4

6x/6=48/6

x=8

Answer:

-4 -4

6x=48

Explanation

Answer:

Yes

Step-by-step explanation:

Replace x with -7 and y with 1 in the original inequality and solve

1 < -7/2 + 9

1 < -3.5 +9

1 < 5.5 (Since this statement is true, the point (-7, 1) is a solution)

Yes, irrational numbers such as π are included in the domain of the function f(x) = 7.

The domain of a function is the set of all possible input values (x) for which the function is defined. In the case of the function f(x) = 7, the output value (y) is always equal to 7, regardless of the input value.

Since every real number, including irrational numbers like π, can be an input value for f(x) = 7, the domain of this function is the set of all real numbers, which includes both rational and irrational numbers. Therefore, π is included in the domain of the function f(x) = 7.

To know more about  irrational numbers here

https://brainly.com/question/26862717

#SPJ4

Answer:

The circumference of the circle is 28.26 m.

The area of the circle is 63.585 \(m^{2}\).

Step-by-step explanation:

To solve for the circumference of the circle, start by using the circumference formula of a circle, which is \(C= 2\pi r\). However, 3.14 will be used instead of \((\pi)\) for this formula.

First, the radius of the circle needs to be found. To find the radius of the circle, divide the diameter by 2 because the radius equals half of the diameter. The radius is 9 m divided by 2, which equals 4.5 m.

Next, plug in the radius into the formula, and the formula will look like \(C=(2)(\pi )(4.5 m)\). Then, solve the equation, and the answer will be 28.26 m.

To solve for the area of the circle, start by using the area formula of a circle, which is \(A=\pi r^{2}\). However, 3.14 will be used instead of \((\pi)\) for this formula.

For the area, plug the radius into the formula, and the formula will look like \(A= (3.14)(4.5m)^{2}\). Then, solve the equation, and the answer will be 63.585 \(m^{2}\).

Answer:

C

Step-by-step explanation:

parallel means no matter how far you stretch it the 2 lines will never touch and these 2 lines won’t EF and CD

Hopes this helps please mark brainliest

Answer: 57.8

Step-by-step explanation:48.7 seconds + 49.3 seconds.= 57.8