10011 base 2 +P + 11100 base 2+ 101 base 2=1001111 base 2

The volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis is 51π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curve y = 1 - (x - 5)² in the first quadrant about the y-axis, we can use the method of cylindrical shells.

The formula for the volume using cylindrical shells is:

V = 2π ∫ [a, b] x * h(x) dx

Where:

- V is the volume of the solid

- π represents the mathematical constant pi

- [a, b] is the interval over which we are integrating

- x is the variable representing the x-axis

- h(x) is the height of the cylindrical shell at a given x-value

In this case, we need to solve for x in terms of y to express the equation in terms of y.

Rearranging the given equation:

x = 5 ± √(1 - y)

Since we are only interested in the region in the first quadrant, we take the positive square root:

x = 5 + √(1 - y)

Now we can rewrite the volume formula with respect to y:

V = 2π ∫ [c, d] x * h(y) dy

Where:

- [c, d] is the interval of y-values that correspond to the region in the first quadrant

To determine the interval [c, d], we set the equation equal to zero and solve for y:

1 - (x - 5)² = 0

Expanding and rearranging the equation:

(x - 5)² = 1

x - 5 = ±√1

x = 5 ± 1

Since we are only interested in the region in the first quadrant, we take the value x = 6:

x = 6

Now we can evaluate the integral to find the volume:

V = 2π ∫ [0, 1] x * h(y) dy

Where h(y) represents the height of the cylindrical shell at a given y-value.

Integrating the expression:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * h(y) dy

To find h(y), we need to determine the distance between the y-axis and the curve at a given y-value. Since the curve is symmetric, h(y) is simply the x-coordinate at that point:

h(y) = 5 + √(1 - y)

Substituting this expression back into the integral:

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

Now, we can evaluate this integral to find the volume

V = 2π ∫ [0, 1] (5 + √(1 - y)) * (5 + √(1 - y)) dy

To simplify the integral, let's expand the expression:

V = 2π ∫ [0, 1] (25 + 10√(1 - y) + 1 - y) dy

V = 2π ∫ [0, 1] (26 + 10√(1 - y) - y) dy

Now, let's integrate term by term:

\(V = 2\pi [26y + 10/3 * (1 - y)^\frac{3}{2} - 1/2 * y^2]\)] evaluated from 0 to 1

V = \(2\pi [(26 + 10/3 * (1 - 1)^\frac{3}{2} - 1/2 * 1^2) - (26 * 0 + 10/3 * (1 - 0)^\frac{3}{2} - 1/2 * 0^2)]\)

V = 2π [(26 + 0 - 1/2) - (0 + 10/3 - 0)]

V = 2π (25.5)

V = 51π cubic units

Learn more on volume of a solid obtained by rotating curve here;

https://brainly.com/question/32301706

#SPJ1

Answer:

Step-by-step explanation:

10 divided by 2.77 is

3.61010830325.

rounded up is 4 pounds?

Answer:

3

Step-by-step explanation:

If you divide 10 divided by 2.77 you get 3.610108303 but you don't need all the decimals so instead you will just get rid of the decimals in this scenario (not in all) and if you double check yourself by doing 2.77 x 3 you will get 8.31 and thats all you can do because 2.77 x 4 is 11.08 but you have a budget of $10.00 so your answer is:

You can get 3 pounds of blueberries with $10

Answer:

6

Step-by-step explanation:

I just learned this!! :)

Answer:

it has 6 faces

Step-by-step explanation:

The equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

According to the question,

We have the following information:

Slope of the line = 1/3

We know that the slope of the line is denoted by m.

y-intercept of the line = -1

We know that the y-intercept is denoted by b.

We have the following equation for the line in slope-intercept form:

y = mx+b

Putting the above values in this equation:

y = x/3-1

Hence, the equation of the line with slope 1/3 and y-intercept as -1 is y = x/3-1 in slope-intercept form.

To know more about equation of the line here

https://brainly.com/question/402319

#SPJ1

Answer:

The original price of the television before the 20% discount was applied, is $300

Step-by-step explanation:

Whenever you decrease a value by a certain percentage, let's say "x"%, all you're doing is calculating (100 - x)% of the item. So in this case when a 20% discount is applied, the value is decreasing by 20%, and the new value is (100-20) or 80% it's original value.

So we have one unknown we are solving for, which is the original price before reduction, and let's just represent this with: "P". After applying a 20% discount by calculating 80% the value, we get the value 240.

To calculate 80% of a value, you simply multiply it by the decimal form, which is calculated by dividing a percentage by 100, so 80% = 0.80

So we can derive the following equation: \(0.8(P) = 240\) and from here it's just one step to solve this equation... divide by 0.80 to isolate the "P" which gets us: \(P = \frac{240}{0.8} = 300\)

The original price of the television before the 20% discount was applied, is $300

Answer:

m<GHI = 17°

Step-by-step explanation:

m<GHI = (2x - 3)°

m<IGH = (2x + 15)°

m<HIJ = (7x - 18)°

<HIJ is an exterior angle of ∆GHI

<GHI and <HIJ are both interior angles of ∆GHI that are opposite to the exterior angle.

Therefore, based on the exterior angle theorem of a triangle, we would have the following equation:

m<GHI + m<IGH = m<HIJ

(2x - 3)° + (2x + 15)° = (7x - 18)° (substitution)

Solve for x

2x - 3 + 2x + 15 = 7x - 18

Add like terms

4x + 12 = 7x - 18

4x - 7x = -12 - 18

-3x = -30

Divide both sides by -3

x = 10

✔️m<GHI = (2x - 3)°

Plug in the value of x

m<GHI = 2(10) - 3 = 20 - 3

m<GHI = 17°

Answer:

Step-by-step explanation:

5 pts = $1

$43 × (5 pts)/$1 = 43×5 pts = 215 pts

Answer:

16x^4

Step-by-step explanation:

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[see below]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(\boxed{\text{Simplifying the Expression:}}\\\\(2x)^4\\----------------\\\rightarrow (2x)^4 \text{ is 2x multiplied 4 times.}\\\\\rightarrow (2x)^4 = \boxed{2x * 2x * 2x * 2x}\\\\\rightarrow 2x * 2x * 2x * 2x = \boxed{16*x^4}\\\\\rightarrow 16*x^4 = \boxed{16 * x * x * x * x}\\\\\text{The boxed answers with exception to the second one could be possible answers.}\)

»»————-　★　————-««

⸻⸻⸻⸻

Hope this helps you. I apologize if it’s incorrect.  

Hence, if i > j, then (AB)ij is a sum of products of zeros, and is therefore zero. This means that all the entries below the main diagonal in the matrix AB are zero. Therefore, AB is also an upper triangular matrix.

To show that if a and b are square, upper triangular matrices, then so is ab, we need to prove that all the entries below the main diagonal in the matrix ab are zero.

Let A and B be square, upper triangular matrices of size n x n.

Then the (i,j)th entry of AB is given by:

(AB)ij = Σk=1n AikBkj

For i > j, we have:

(AB)ij = Σk=1n AikBkj = Σk=1j AikBkj + Σk=j+1n AikBkj

Since A is upper triangular, we have Aik = 0 for k > i.

Therefore, the first sum above is non-zero only for k ≤ i. Since B is also upper triangular, we have Bkj = 0 for k > j.

Therefore, the second sum above is non-zero only for k > j.

For more questions on upper triangular matrix

https://brainly.com/question/14413614

#SPJ4

The discount price is $3009.3.

It is the amount of money spends on the creation or production of goods or services.

The cost price of the bicycle is $3000.

The marked price is given by

3000+(0.433 * 3000) = 4299

The marked price is $4299.

The discount rate is 30%.

The discount price of the cycle is given by

4299 - (0.3 * 4299) = 4299 - 1289.7 = 3009.3

Hence, the discount price of the bicycle is $3009.3.

To learn more about cost, use the link given below:

https://brainly.com/question/15135554

#SPJ1

Answer:

Mean :31.66

Median:35.5

Mode:35.5

Step-by-step explanation:

(hope this helps can i plz have brainlist :D hehe)

Hello

1.1 Formula

triangle's area = b * h

1.2 Application

4.25ft * 6.54ft = 27.795ft²

2.1 Formula

Just multiply the area of the triangle by 10 (there are 10 triangles)!

2.2 Application

27.795ft² * 10 = 277950ft²

The rug's area is 277950 feet.

Answer:

69

Step-by-step explanation:

Answer:

$7.00

Step-by-step explanation:

there is a total of $35,000 worth of prizes being given out for 5,000 tickets.  We can find the expected value for each ticket by dividing 35,000/5,000.  This equals $7.00.

The correct equation is

Expected value for a ticket = 29980 (1/5000) + 80 x 5(5/5000) - 20(4994/5000)

A charity event is any gathering whose main goal is to raise money for a nonprofit, cause, or organisation.

We have,

Car is the gift offered and the car is worth 30000

Tickets sold = 5000

Out of 500 tickets, one ticket would fetch the car worth 30000 dollars and five gift cards will bring 100 dollars

So, the Expected value for a ticket

= 29980 (1/5000) + 80 x 5(5/5000) - 20(4994/5000)

=5.996+0.4-19.976

=-13.58

Learn more about Charity here:

https://brainly.com/question/2819165

#SPJ7

$120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.

Two or more expressions with an equal sign is called equation.

Given that Jane spends $15 each time she travels the toll roads..

Jane started the month with $240 in her toll road account.

The amount, A (in dollars), that she has left in the account after r trips on the toll roads is given by the following function

A(r)=240-15r.

Now for 8 trips the amount she left is

A(8)=240-15(8)

=240-120

=120

So $120 money does Jane have left in the account after 8 trips on the toll roads.

$240/15

=16.

She has to make 16 trips to make her account empty.

Hence $120 money does Jane have left in the account after 8 trips on the toll roads and She has to make 16 trips to make her account empty.

To learn more on equations click:

https://brainly.com/question/10413253

#SPJ1

The correlation coefficient between X and Y is Corr(X, Y) = 0.

To calculate the marginal distribution of X and Y, we need to integrate the joint probability density function (PDF) over the appropriate ranges.

a. Marginal distribution of X:

To find the marginal distribution of X, we integrate the joint PDF over the range of Y:

∫[0, 1] J(x, y) dy

Since the joint PDF is defined as J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1 and J(x, y) = 0 otherwise, the integral becomes:

∫[0, x] 1 dy = x, for 0 ≤ x ≤ 1

So, the marginal distribution of X is simply X(x) = x for 0 ≤ x ≤ 1.

b. Expectation of X:

The expectation (mean) of X can be calculated as the integral of x times the marginal PDF of X:

\(E(X) = ∫[0, 1] x * X(x) dx = ∫[0, 1] x^2 dx = [x^3/3] from 0 to 1 = 1/3\)

Therefore, the expectation of X is E(X) = 1/3.

c. Variance of X:

The variance of X can be calculated using the formula:

\(Var(X) = E(X^2) - (E(X))^2E(X^2) = ∫[0, 1] x^2 * X(x) dx = ∫[0, 1] x^3 dx = [x^4/4] from 0 to 1 = 1/4Var(X) = 1/4 - (1/3)^2 = 1/4 - 1/9 = 5/36\)

Therefore, the variance of X is Var(X) = 5/36.

d. Covariance of X and Y:

The covariance of X and Y can be calculated as:

Cov(X, Y) = E(XY) - E(X)E(Y)

Since the joint PDF J(x, y) = 1 for 0 ≤ y ≤ x ≤ 1, the integral becomes:

\(E(XY) = ∫[0, 1] ∫[0, x] xy dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

\(E(X) = 1/3 (from part b)E(Y) = ∫[0, 1] ∫[0, x] y J(x, y) dy dx = ∫[0, 1] [(x^2)/2] dx = [(x^3)/6] from 0 to 1 = 1/6\)

Cov(X, Y) = 1/6 - (1/3)(1/6) = 0

Therefore, the covariance of X and Y is Cov(X, Y) = 0.

e. Correlation coefficient between X and Y:

The correlation coefficient can be calculated using the formula:

Corr(X, Y) = Cov(X, Y) / √(Var(X) * Var(Y))

Since the covariance of X and Y is 0, the correlation coefficient will also be 0.

Therefore, the correlation coefficient between X and Y is Corr(X, Y) = 0.

f. Conclusion based on the correlation coefficient:

The correlation coefficient of 0 indicates that there is no linear relationship between X and Y. In this case, the fraction of male runners (X) and the

for more such question on correlation visit

https://brainly.com/question/13879362

#SPJ8

Answer:

-17.8+1.7

Step-by-step explanation:

When there are double negatives, it's a positive

Answer:

\( 2^{2x + 2} = 2^{4x - 4} \)

Step-by-step explanation:

\( 4^{x + 1} = 16^{x - 1} \)

\( 2^{2(x + 1)} = 2^{4(x - 1)} \)

\( 2^{2x + 2} = 2^{4x - 4} \)

Answer:

Step-by-step explanation:

360 people can fit in 8 buses.

First we need to find how many people fit in 1 bus, so we can divide 495, the total number of people, by 11, the number of buses.

495/11=45

Now we know 45 people can go on 1 bus, and we have 8 of them, so we multiply these 2 numbers.

45*8=360

360 people.

Answer:
8 buses can carry 360 passengers

If this help please set brainliest.

Step-by-step explanation:

To find out how many people can fit in 8 buses, you need to multiply the number of people that can fit in one bus by the number of buses. Since 11 buses can carry 495 passengers and each bus can carry the same number of passengers, one bus can carry 495/11=45 45 passengers.

Therefore, 8 buses can carry 360 passengers.

Answer:

D. \(3^3 - 4^2\)

Step-by-step explanation:

Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2

The total number of minutes that Anaya rides her bike on Monday and Tuesday is 18 minutes.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that on Monday, Anaya rides her bike for 9 minutes. On Tuesday, she rides her bike times as many minutes as on Monday.

Total number of minutes = Monday time + Tuesday time

Total number of minutes  = 9 + 9

Total number of minutes  = 18 minutes

Therefore, the total number of minutes that Anaya rides her bike on Monday and Tuesday is 18 minutes.

To know more about an expression follow

https://brainly.com/question/20444244

#SPJ1

Answer:

Step-by-step explanation:To calculate the savings percentage, we first need to find out the cost of the cardboard required for each box.

For the larger box:

Total Surface Area = 2 * (1926 + 1934.5 + 26*34.5) = 2 * (494 + 655.5 + 897) = 4093 cm²

Cost of cardboard for larger box = 0.502 * 4093 = 2055.986 cents = 20.55986 dollars (rounded to 5 decimal places)

For the smaller box:

Total Surface Area = 2 * (2517 + 2526 + 1726) + 6 * (25-21)* (17-2*1) = 3034 cm²

Note that the additional term in the equation is the surface area of the six sides of the lid and base of the box.

Cost of cardboard for smaller box = 0.502 * 3034 = 1522.268 cents = 15.22268 dollars (rounded to 5 decimal places)

The difference in cost between the larger and smaller boxes is:

20.55986 - 15.22268 = 5.33718 dollars (rounded to 5 decimal places)

The percentage savings can be calculated as follows:

Percentage savings = (difference in cost / cost of larger box) * 100%

= (5.33718 / 20.55986) * 100%

= 25.98%

Therefore, using the smaller box will result in a savings of approximately 26% on cardboard costs for Bathu Sneakers compared to using the normal larger box.

Answer:

D

Step-by-step explanation:

If it was 2/4, percent is 50% greater than 0, but less than 100

2/4 decimal 0.5 between 0 and 1

Answer:

all sides have different lengths

and the third angle measures 90⁰

Answer:

Step-by-step explanation:

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

Learn more about coordinates at:

https://brainly.com/question/17206319

#SPJ1

Answer:

8

Step-by-step explanation:

The diagonals of a parallelogram divide each other into two equal parts.

Answer: the vertex is 157x4

Step-by-step explanation: