Kinsley can illustrate 9 story book pages in 3 hours. How many pages can she
illustrate per hour?
Hint: Make a W.O.N. table to solve.
o A) 27 pages
B) 9 pages
o C) 1 page
D) 3 pages

1. Find the volume of the solid obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis.

The region enclosed by the curves y=21−x,y=9x+11 and x=−1 is as follows:

Solid is obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis is as follows:Let us express y=21−x and y=9x+11 in terms of x, to calculate the volume as follows:

y=21−xy=9x+11

∴ x=21−yx−1119−y94−y

Now, we can write as below:

VolumeV=∫−111π[R(y)]2dy,where R(y) is the radius of the cross-section at a distance y from the axis of rotation.Now, let us consider y=0 as the axis of rotation. Then we have, y=0 to y=10. The radius of the cross-section R(y) is the distance between the axis of rotation and the curve (solid region). So, we can write R(y)=21−x−(9x+11)=10−10x−1.Therefore, the volume of the solid is as follows:

V=∫0^10π[10−10x−1]2dy

=π∫0^10100−40xy+x2dy

=π[100y−20y2+13y3]0^10

=π[0]=0

Volume of the solid obtained by rotating the region enclosed by the curves y=21−x,y=9x+11 and x=−1 about the x-axis is 0 cubic units.

Then we have, x=2 to x=6, as the radius of the cross-section R(x) is the distance between the line x=6 and the curve (solid region). So, we can write R(x)=6−x.

The volume of the solid generated by revolving the region bounded by the graphs of the equations y=6−x, y=0, and x=2 about the line x=6 is as follows:

VolumeV=∫26π[6−x]2dx

=π∫26(x2−12x+36)dx

=π[1/3x3−6x2+36x]26

=π[128/3]=40π/3 cubic units.

To know more about obtained visit :

https://brainly.com/question/26761555

#SPJ11

The code efficiently identifies prime numbers using the ancient Greek algorithm. It initializes an array, marks the multiples of each prime number as non-prime, and then prints the prime numbers.

This algorithm demonstrates a straightforward and efficient method for finding prime numbers within a given range.The ancient Greek algorithm for finding prime numbers less than or equal to a given number is implemented in the provided Python code. The algorithm follows a simple approach of marking numbers as prime or non-prime.

It starts by assuming all numbers as prime and then proceeds to mark the multiples of each prime number as non-prime. The code initializes an array where each element represents a number and marks them all as prime initially. Then, it iterates over each number from 2 to the given number, checking if it is marked as prime. If it is, the algorithm crosses out all its multiples as non-prime. Finally, it prints the numbers that remain marked as prime.

Learn more about prime here: https://brainly.com/question/9315685

#SPJ11

The prediction of the amount of gasoline that is present on the Jet after it has been in flight for 18 hours without stopping to refuel is given as follows:

-52,750 gallons.

(as the estimate is negative, it means that the plane has to stop to refuel before that).

The linear function for this problem is defined in slope-intercept format, as follows:

y = mx + b.

The coefficients of the function are given as follows:

The graph touches the y-axis at y = 422,000, hence the intercept b of the function is given as follows:

b = 422000.

When x = 2, y = 369250, hence the slope m is calculated as follows:

m = (369250 - 422000)/2 = -26375.

Then the linear function giving the amount of gasoline present after x hours is of:

y = -26375x + 422000.

After 18 hours, the estimate of the amount of gasoline in the tank is given as follows:

y = -26375(18) + 422000 = -52,750 gallons.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The seismograph reading of the earthquake is approximately 1.99526.To determine the seismograph reading of the earthquake with a magnitude of 3.3 on the Richter scale, we can use the formula M(I) = log(I/0.001), where M(I) represents the magnitude and I represents the intensity of the earthquake.

In this case, we are given the magnitude of 3.3. Let's substitute this value into the formula and solve for I:

3.3 = log(I/0.001)

To isolate I, we need to convert the equation into exponential form:

10^(3.3) = I/0.001

Simplifying the equation, we have:

I = 10^(3.3) * 0.001

Using a calculator, we find that 10^(3.3) is approximately 1995.26.

So, the seismograph reading of the earthquake is:

I = 1995.26 * 0.001

≈ 1.99526.

For such more questions on Seismograph:

https://brainly.com/question/29200802

#SPJ11

Answer:

28x-4

Step-by-step explanation:

Given

length (l)= 9x-4

Breadth (b) = 5x+2

Now

Perimeter (P) = 2(l+b)

=2(9x-4+5x+2)

=2(14x-2)

=28x-4

Answer: they dont have the same numbers

Step-by-step explanation:

Answer:

Function A is 2

Function B is 5

Difference is -3

Step-by-step explanation:

The y intercept is the rate of change or the value of zero

Answer:

549

Step-by-step explanation:

The order of operations is a sequence in which operations should be performed to evaluate a mathematical expression correctly. A common way to remember is PEMDAS:

To simplify the expression 19×33−2(16+23) using the order of operations, first solve the operations inside the parentheses:

Now we multiply:

The expression now looks like this:

Perform the multiplication before the subtraction:

Now that we have done the multiplication, we can subtract:

Therefore, the expression simplified is 549.

Answer:

b

Step-by-step explanation:

Answer:

x = -2, y = -5, z = 3

Step-by-step explanation:

You have to substitute the letter with its real  value;

3x = -6

Divide both sides by 3;

x = -2

So now we have to replace x with -2;

x + 3y = -7

-2 + 3y = -17

Add 2 to both sides;

3y = -15

Divide both sides by 3;

y = -5

For the last equation you have to replace x and y since we have the values;

4(-2) - 3(-5) + 6z = 25

-8 + 15 + 6z = 25

7 + 6z = 25

Subtract 7 from both sides;

6z = 18

Divide both sides by 6;

z = 3

Check:

4(-2) - 3(-5) + 6(3) = 25

-8 + 15 + 18

7 + 18 = 25

25 = 25

This mean the values are correct.

Answer:

x=-2

y=-5

z=3

Step-by-step explanation:

Ok so first you have to solve for x because its the easiest equation 3x=-6.

Divide by 3 on both sides and you get x=-2. Now that you have your x value you can plug that in to the second equation x+3y=-17. Making it -2+3y=-17. Solve for y by adding 2 to both sides making it 3y=-15 and then divide by 3 making it y=-5. Since you have your x and y value, you can plug that in to the top equation which is 4x-3y+6z=25 and making it 4(-2)-3(-5)+6z=25,

4(-2)-3(-5) equals 7 making your equation 7+6z=25. Take away 7 from both sides and you are left with 6z=18. 18/6 is 3 so you get z=3. Making your final answer: x=-2 y=-5 and z=3

Hope this helped.

Answer:

0 to 5

Step-by-step explanation:

i took it on edg

Answer:

I know it was 0 to 5 but I didn't get to this question fast enough so it look's like I copied it.

By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided below, we have the following equation of a circle:

x² - 4x + y² + 8y = -4

x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²

x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16

(x - 2)² + (y + 4)² = 16

(x - 2)² + (y + 4)² = 4²

Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.

Read more on equation of a circle here: brainly.com/question/15626679

#SPJ4

Complete Question:

Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.

Answer:

35 miles

Step-by-step explanation:

Answer:

35 miles

Step-by-step explanation:

2.5 x 14

The price at which the total quantity supplied is 250 is $11.58.

In order to find the price at which the total quantity supplied is 250, we need to equate the total quantity supplied by both producers (Supply 1 and Supply 2) and solve for the price.

Supply 1: P = 6 + 0.7Q

Supply 2: P = 16 + 0.6Q

To find the equilibrium price, we set the total quantity supplied equal to 250:

0.7Q + 0.6Q = 250

1.3Q = 250

Q = 250 / 1.3 ≈ 192.31

Now that we have the quantity, we can substitute it back into either supply function to find the price. Let's use Supply 1:

P = 6 + 0.7Q

P = 6 + 0.7 * 192.31

P ≈ 6 + 134.62

P ≈ 140.62

Therefore, the price at which the total quantity supplied is 250 is approximately $11.58.

Learn more about Equilibrium price

brainly.com/question/29099220

#SPJ11

All elements x in Dn such that x^2 = f are the same reflection f, and all elements x in Dn such that x^3 = f are the identity element of the dihedral group Dn.

Let f be a reflection in the dihedral group Dn.

For all elements x in Dn such that x^2 = f, these elements would be the same reflection f.

For all elements x in Dn such that x^3 = f, these elements would be the identity element of the dihedral group Dn.

All elements x in Dn such that x^2 = f are the same reflection f, and all elements x in Dn such that x^3 = f are the identity element of the dihedral group Dn.

learn more about group here

https://brainly.com/question/19595591

#SPJ4

This is the same as y = 2.5x+10 since 5/2 = 2.5

============================================

Explanation:

Let's find the slope of the line through those given points

m = (y2-y1)/(x2-x1)

m = (7-3)/(-9-1)

m = 4/(-10)

m = -2/5

To find the perpendicular slope, we flip the fraction and flip the sign

flip the fraction: -2/5 turns into -5/2

flip the sign: -5/2 turns into 5/2

The perpendicular slope is 5/2

Side note: The original slope (-2/5) and the perpendicular slope (5/2) multiply to -1.

-------------------------

Now find the midpoint

We add the x coordinates of the original points to get 1+(-9) = -8, which cuts in half to -8/2 = -4. This is the x coordinate of the midpoint.

Do the same for the y coordinates. First add: 3+7 = 10, then cut in half: 10/2 = 5. The y coordinate of the midpoint is 5.

The midpoint is (-4,5)

-------------------------

The perpendicular bisector will go through this midpoint. It has a slope of m = 5/2

Turn to point slope form to find the equation we need

y - y1 = m(x - x1)

y - 5 = (5/2)(x - (-4))

y - 5 = (5/2)(x + 4)

y - 5 = (5/2)x + (5/2)*4

y - 5 = (5/2)x + 10

y = (5/2)x + 10 + 5

y = (5/2)x + 15

y = 2.5x + 15 ... since 5/2 = 2.5

Answer:

9 inches

Step-by-step explanation:

The population is within 6 standard deviations of the mean with a confidence of 99.7 percent, 3 above and 3 below

The standard deviation of the sample mean is equal to the population standard deviation divided by the square root of the sample size

population standard deviation = 36

sample size = 144

standard deviation of the sample mean = 36/ sqrt(144)

                                      =36/12

                                        =3

The margin of error is  the number of standard deviations above  the mean * the standard deviations

margin of error  = 3 * 3

                         = 9 inches

Given:

\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)

Express 16 as \(4^{2}\): \(x^2+y^2=16\)

\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)

Trignometry,

\(\cos ^2(t)+\sin ^2(t)=1\)

Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:

\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)

Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)

Taking positive square roots as follows:

\(x=4 \cos (t), y=4 \sin (t)\)

Recall that, z = xy.

Now, we have:

\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)

Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)

So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)

Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)

Know more about vector functions here:

https://brainly.com/question/14895420

#SPJ4

Answer:

28

Step-by-step explanation:

similar triangles are proportional

and add all the sides of the bigger triangle

Difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Review the following subtraction rules and properties:

Given: Ahab pays dollars for one year's tuition fees and his sister pays dollars fees in tuition for the first year

To find: Difference in tuition fees paid by Ahab and his sister?

Solution:

To find the difference in their fees we have to perform simply normal subtraction

Subtract the fees of his sister from Ahab's fees which is as follows:

\(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Hence the difference between the fees of Ahab and his sister is \(2.8*10^{3} -1.15*10^{3}=1.65*10^{3}\)

Learn more about Subtraction here:

https://brainly.com/question/1927340

#SPJ4

Answer:

distance = 7.07 units

Step-by-step explanation:

x difference = 7

y difference = -1

using the Pythagorean theorem:

7² + -1² = d²

d² = 49 + 1 = 50

d = 7.07

Answer:

7.1

Step-by-step explanation:

distance between the x is 7 and y is 1

And to find the hypotenuse, you use the quadratic formula, 7^2 + 1^2 = c^2

c=50

and take the square root, which is 7.071, rounds to 7.1

Answer:

-4

Step-by-step explanation:

Find the rate of change for f(x) = x² - 8x + 15 from x = 0 to x = 4

The rate of change is the rate at which a variable changes over a specific period of time.

Averate rate of change: \(\frac{f(b)-f(a)}{b-a}\)

First, we need to find the functions for when x = 0 and when x = 4:

For x = 0

f(x) = x² - 8x + 15

f(0) = 0² - 8(0) + 15

f(0) = 0 - 0 + 15

f(0) = 15

For x = 4

f(x) = x² - 8x + 15

f(4) = (4)² - 8(4) + 15

f(4) = 16 - 32 + 15

f(4) = -16 + 15

f(4) = -1

Averate rate of change: \(\frac{f(b)-f(a)}{b-a}\)

A = \(\frac{f(4)-f(0)}{4-0}\)

A = \(\frac{-1-15}{4-0}\)

A = \(\frac{-16}{4}\)

A = \(-4\)

Therefore, the rate of change from x = 0 to x = 4 is -4.

Hope this helps!

The substitution that has been applied to B(x, y) is dt B(x, y) = √(1+t) (1+t)x+y tx-1.

The substitution that has been applied to B(x, y) is t = tan² 0

The substitution for x and y using the trigonometric identities is given by,

x = sin² 0 / cos² 0 = tan² 0   …(1)

y = sin² 0   …(2)

Differentiating both sides of equation (1) with respect to θ, we get

dx / dθ = 2tan 0 sec² 0

Putting the values of x and y in B(x, y), we get

B(x, y) = I 25 (sin 0)² (sin² 0 / cos² 0)-1 (cos 0)² (sin² 0)-1 dθ

= I 25 (sin 0)² / cos² 0 * cos² 0 / sin² 0 dθ

= I 25 tan² 0 dθ

= 25

∫ t dt √1+t

Now, we need to find the value of dt B(x, y) in terms of t.

To find dt B(x, y), we use the chain rule of differentiation and get

dt B(x, y) = ∂B/∂x dx/dt + ∂B/∂y dy/dt

= 25(2 sin 0 cos 0 sin² 0 / cos³ 0) * 2 sin 0 cos 0 sin 0 cos 0 dθ

= 100 (sin 0)³ (cos 0)³ / cos⁴ 0 dθ

= 100 (sin 0)³ / cos 0 dθ

Now, putting the values of x, y, and t, we get

dt B(x, y) = 100 sin³ 0 / cos 0 dθ

= 100 sin³ θ / cos θ dθ

Using the identity 1+t = sec² 0 or cos² 0 = 1 / (1+t), we can rewrite the above integral as

∫ 100 sin³ θ / cos θ dθ

= ∫ (1+t) (1+t)½ dt

Substituting the limits, we get

∫ 100 sin³ θ / cos θ dθ

= ∫ √(1+t) (1+t)x+y tx-1 dt

Answer: dt B(x, y) = √(1+t) (1+t)x+y tx-1.

To know more about substitution visit:

https://brainly.com/question/29383142

#SPJ11

Answer:

B, .92V

Step-by-step explanation:

1 -- 0.08 = 0.92

8% = .08

The divergence of the vector field F is positive for y > -1/3 and negative for y <  -1/3.

To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.

Here is a sample grid of points and their corresponding vectors:

(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)

(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)

(x, y) = (0, -2) -> F(0, -2) = (0, 2)

(x, y) = (1, -2) -> F(1, -2) = (0, 2)

(x, y) = (2, -2) -> F(2, -2) = (4, 2)

(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)

(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)

(x, y) = (0, -1) -> F(0, -1) = (0, 1)

(x, y) = (1, -1) -> F(1, -1) = (0, 1)

(x, y) = (2, -1) -> F(2, -1) = (2, 1)

... and so on for other values of y and for positive values of y.

To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.

F(x, y) = (xy, x + y^2)

∂F/∂x = y

∂F/∂y = 1 + 2y

divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1

Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).

For divF > 0:

If y > -1/3, then divF > 0.

For divF < 0:

If y < -1/3, then divF < 0.

Know more about vector field here;

https://brainly.com/question/102477

#SPJ11

Hexadecimal and binary are two numbering systems that are commonly used in computing. Binary is a base-2 numbering system, which means it uses only two digits, 0 and 1, to represent all numbers. Hexadecimal, on the other hand, is a base-16 numbering system, which means it uses 16 digits, from 0 to 9 and A to F, to represent numbers.

One hexadecimal digit can represent 16 different values, while one binary digit can represent only two values (0 or 1). This means that one hexadecimal digit can represent 16 times as many values as one binary digit.

To understand this better, let's consider an example. The binary number 1111 is equivalent to the hexadecimal number F. In binary, 1111 can represent only one value, which is 15 in decimal. However, in hexadecimal, the digit F can represent 16 different values, from 0 to 15 in decimal.

Therefore, using hexadecimal notation can be more efficient and compact than using binary notation, especially when dealing with large numbers. In addition, hexadecimal is often used in computing to represent memory addresses, color codes, and other values that need to be represented in a compact and easily readable format.

To know more about Hexadecimal , visit:

https://brainly.com/question/31478130

#SPJ11

Answer:

= 3m2 + 2m - 4m

= 3m2 - 2m

Step-by-step explanation:

you can only subtract similar products

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

To learn more about variance click :

https://brainly.com/question/13041243

#SPJ1