A water storage tank is in the shape of a hemisphere​ (half a​ sphere). If the radius is 20 ​ft, approximate the volume of the tank in cubic feet.

Answer:

The right answer is figure B

Step-by-step explanation:

* Lets talk about the complex number

- The complex number z = a + bi consists of two part:

# a is the real part and represented graphically by the x-axis

# b is the imaginary part and represented graphically by the y-axis

- We can add and subtract them by adding or subtracting the real parts

 together and the imaginary parts together

# Ex: if z1 = 2 + 3i and z2 = -1 - i

∴ z1 + z2 = (2 + -1) + (3 + -1)i = 1 + 2i

∴ z1 - z2 = (2 - -1) + (3 - -1)i = (2 + 1) + (3 + 1)i = 3 + 4i

* Now lets solve the problem

- Let find from the graph z1 , z2 and point A

- Look to the any graph and find z1 through the axes

- We moved 6 units on the x-axis (real part) and 7 units up

 (imaginary part)

∴ z1 = 6 + 7i

- Similarly find z2 through the axes

- We moved 5 units on the x-axis (real part) and 2 units down

 (imaginary part)

∴ z2 = 5 - 2i

* Now lets solve z1 - z2

∵ z1 = 6 + 7i and z2 = 5 - 2i

∴ z1 - z2 = (6 + 7i) - (5 - 2i) = (6 - 5) + (7 - -2)i = 1 + 9i

* Lets find in which figure the coordinates of A are (1 , 9)

∵ In figure A point A is (1 , 6)

∵ In figure B point A is (1 , 9)

∵ In figure C point A is (11 , 5)

∵ In figure D point A is (11 , 9)

∴ The right answer is figure B

Lol ok where’s the question is this just for fun?

Answer:

{x = 3 , y = -3 thus the answer is A

Step-by-step explanation:

Solve the following system:

{5 x + 2 y = 9 | (equation 1)

{2 x - 3 y = 15 | (equation 2)

Subtract 2/5 × (equation 1) from equation 2:

{5 x + 2 y = 9 | (equation 1)

{0 x - (19 y)/5 = 57/5 | (equation 2)

Multiply equation 2 by 5/19:

{5 x + 2 y = 9 | (equation 1)

{0 x - y = 3 | (equation 2)

Multiply equation 2 by -1:

{5 x + 2 y = 9 | (equation 1)

{0 x+y = -3 | (equation 2)

Subtract 2 × (equation 2) from equation 1:

{5 x+0 y = 15 | (equation 1)

{0 x+y = -3 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 3 | (equation 1)

{0 x+y = -3 | (equation 2)

Collect results:

Answer:  {x = 3 , y = -3

Answer:

A) 5x+2y=9

B) 2x-3y=15

Multiply A) by 1.5

A) 7.5x +3y = 13.5  then add it to B)

B) 2x-3y=15

9.5x = 28.5

x = 3

5*3 + 2y=9

2y = -6

y = -3

answer is A

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

∠4 and ∠5 are congruent and alternate angles, hence

A and B  are parallel lines

Answer:

x = -2 and y = -3

Step-by-step explanation:

It is given that,

-8x + 3y =7    ----(1)

13x - 3y =-17   -----(2)

To find the value of x and y

eq(1) + eq(2) ⇒

-8x + 3y = 7    ----(1)

13x -  3y = -17   -----(2)

 5x +    = -10

x = -10/5 = -2

Substitute value of x in eq (1)

-8x + 3y =7    ----(1)

-8 * -2  + 3y = 7

16 + 3y = 7

3y = 7 - 16 = -9

y = -9/3 = -3

Therefore x = -2 and y = -3

For this case we must solve the following system of equations:

[tex]-8x + 3y = 7\\13x-3y = -17[/tex]

If we add both equations we have:

[tex]-8x + 13x + 3y-3y = 7-17\\5x = -10\\x = \frac {-10} {5}\\x = -2[/tex]

We find the value of the variable "y":

[tex]3y = 7 + 8x\\y = \frac {7 + 8x} {3}\\y = \frac {7 + 8 (-2)} {3}\\y = \frac {7-16} {3}\\y = \frac {-9} {3}\\y = -3[/tex]

Thus, the solution of the system is (-2, -3)

ANswer:

(-2, -3)

Answer:

it is 1/6 because there is 6 colors and the probability of getting 3 which is 1 number is 1 out of 6

Step-by-step explanation:

Answer:

Sum of the interior angles = (n-2) x 180°

where

n is the number of sides of the polygon

Step-by-step explanation:

The formula for the sum of the interior angles of a polygon is:

[tex]sum=(n-2)*180[/tex]

where

[tex]sum[/tex] is the sum of the interior angle of the polygon

[tex]n[/tex] is the number of polygons

Let's check the formula using an example:

We want to find the sum of the interior angles of a square, we know that a square has 4 sides, so [tex]n=4[/tex].

Replacing values

[tex]sum=(4-2)*180[/tex]

[tex]sum=(2)*180[/tex]

[tex]sum=360[/tex]

We can apply the same procedure to any convex polygon with n sides.

Answer:

         Sum of the interior angles = (n - 2) × 180°.

         Where n is the number of sides of the polygon.

Explanation:

The formula (n - 2) × 180° is valid for any convex polygon.

A convex polygon is one whose interior angles (every interior angle) measure less than 180°.

You can prove and remember that formula following this reasoning:

For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.

P and Q are endpoints, so the center of the circle would be the midway point.

A. The midpoint is found using:

(x1 + x2 /2 , y1 +y2 /2)

-10 + 4 = -6 /2 = -3

-2 + 6 = 4 /2 = 2

The center of the circle is at (-3,2)

B) The radius would be the distance from the midpoint to an end point.

Using the distance formula:

√((x2-x1)^2 + (y2-y1)^2)

√(4 - -3^2 + 6-2^2)

√(7^2 + 4^2)

√(49+16)

√65

C) Using the circle equation form of (x-h)^2 + (y-k)^2 = r^2

H,K is the center point found in part A and r is the radius found in part B.

The equation becomes (x-(-3))^2 + (y -2)^2 = √65^2

Which simplifies to: (x+3)^2 + (y-2)^2 = 65

We want (x - h)^2 + (y - k)^2 = r^2.

This circle is not centered at the origin.

The point we want is in the form

(h, k).

We are given that h = -4 and k = 2.

We also know that the radius is 9.

Let r = 9 leading to (9)^2 or 81.

We know substitute in the form given above for circles not centered at the origin.

(x - (-4)^2 + (y - 2)^2 = 81

(x + 4)^2 + (y - 2)^2 = 81

Answer: Choice C

20 is the correct answer

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}) = (- 6, -8)\\(x_ {2}, y_ {2}) = (6,8)[/tex]

Substituting:

[tex]d = \sqrt {(6 - (- 6)) ^ 2+ (8 - (- 8)) ^ 2}\\d =\sqrt {(6 + 6) ^ 2 + (8 + 8) ^ 2}\\d = \sqrt {(12) ^ 2 + (16) ^ 2}\\d = \sqrt {144 + 256}\\d = \sqrt {400}\\d = 20[/tex]

ANswer:

20

Answer:

C

Step-by-step explanation:

Plotting the points in a sketch quickly shows that the vertices are not at right angles to each other, thus excluding rectangle and square whose vertices are at right angles.

The best selection is a rhombus

Answer:

x = 36

Step-by-step explanation:

The angles 3x - y and 2x + y form a straight angle and are supplementary, so

3x - y + 2x + y = 180

5x = 180 ( divide both sides by 5 )

x = 36

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

5y and 3x - y are vertical angles and congruent, hence

5y = 3x - y ( add y to both sides )

6y = 3x ← substitute x = 36

6y = 3 × 36 = 108 ( divide both sides by 6 )

y = 18

Area = length times width

Length = x + 4

Width = 4_2/5, which we can write as the improper fraction 22/5.

Area is given to be 28_3/5, which can be written as 143/5.

Here is the set up:

(143/5) = (x + 4)(22/5)

Take it from here.

Answer:

360

Step-by-step explanation:

Answer:

360

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

62 percent of 500 is 310

Hope this helps :)

Answer:

Option D, 310

Step-by-step explanation:

In the given graph 500 people were surveyed.

Now we have to calculate the number of individuals who have a college degree or some college.

Now from the given pie chart.

College degree individuals = 25% of 500

                                             = 0.25 × 500

                                            = 175

Individual with some college = 27% of 500

                                                = 0.27 × 500

                                               = 135

So the total of college dgree + some college = 135 + 175 = 310

Option D 310 is the answer.

Answer: OPTION B

Step-by-step explanation:

Let be "x" the acceptable lengths for the rod.

You know that the ideal length of the metal rod is 30.5 centimeters and the measured length may vary from the ideal length by at most 0.015 centimeters.

Therefore, knowing this, you can say that the acceptable lengths must be:

[tex]30.5cm-0.015cm\leq x\\\\30.485\leq x[/tex]

[tex]x \leq 30.5cm+0.015cm\\\\x\leq 30.515[/tex]

Therefore, the range of acceptable lengths for the rod is the following:

[tex]30.485\leq x\leq 30.515[/tex]

This range matches with the one shown in the option B.

if you shift it down 7, the new equation would be

g(x)=x-7

hope this helps

Answer:

B

Step-by-step explanation:

An upward shift or a downward shift is reflected in the +k or -k (k being some real number).  If there is a number "stuck" to the x, that reflects the steepness (slope) of the line.  The slope of this line is 1, and the y-intercept (where it goes through the y-axis) is down 7 from the origin. B is your answer.

Answer:

The equation that represents the instantaneous velocity at any given time, t is:

[tex]v (t) = 8t -2[/tex]

Step-by-step explanation:

In physics, the equation that describes the instantaneous velocity of an object is the derivative of the position of this object as a function of time.

In this problem we have the function that describes the position of the object at a time t.

[tex]f (t) = 4t ^ 2-2t[/tex]

Therefore to obtain the instantaneous velocity we derive f (t) with respect to time

[tex]\frac{df(t)}{dt} = 2(4)t-2\\\\\frac{df(t)}{dt} = 8t-2 = v (t)[/tex]

Finally the equation of velocity is:

[tex]v (t) = 8t -2[/tex]

Answer:

A. how much of the students time is spent on social media during school hours.

B. By using some kind of selection technique Like Having students draw number from a hat, who ever have the specific numbers will take her survey.

C. The population for Sofies research would be a rate of 5/2. For every 5 people who take the survey only 2 turned it in.

D. She would conclude that 1 out of every 2 or 50 percent of students use social media while doing school work.

Step-by-step explanation:

The percent of all high school students who use social media while doing schoolwork, if Sofie uses only the completed surveys, is 50%.

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

For a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork.

Sofie can use the question as, how many times a student look at social media while doing schoolwork?

Sofie can use a simple random sampling technique to select a simple random sample of students to take her survey.

As Sofie gives out 80 surveys but receives only 32 completed surveys. Thus, the sample is data of 32 completed surveys and the population is total 80 surveys.

Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. Thus, the percentage is,

[tex]P=\dfrac{16}{32}\times100\\P=50\%[/tex]

Hence, the percent of all high school students who use social media while doing schoolwork if Sofie uses only the completed surveys, is 50%.

Learn more about the random sample here;

https://brainly.com/question/17831271

By the law of sines,

[tex]\dfrac{\sin m\angle A}a=\dfrac{\sin m\angle B}b\implies\sin m\angle B=\dfrac{33.7\sin75^\circ}{51.2}[/tex]

We get one solution by taking the inverse sine:

[tex]m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\approx39^\circ[/tex]

In this case there is no other solution!

To check: suppose there was. The other solution is obtained by recalling that [tex]\sin(180-x)^\circ=\sin x^\circ[/tex] for all [tex]x[/tex], so that

[tex]180^\circ-m\angle B=\sin^{-1}\dfrac{33.7\sin75^\circ}{51.2}\implies m\angle B\approx141^\circ[/tex]

But remember that the angles in any triangle must sum to 180 degrees in measure. This second "solution" violates this rule, since two of the known angles exceed 180: 75 + 141 = 216 > 180. So you're done.

This triangle is not a right triangle. How do we solve this then? You will use the law of sine with is shown below:

[tex]\frac{sin A}{a} =\frac{sin B}{b} = \frac{sinC}{c}[/tex]

What we know is shown in the image attached below:

Plug what you know into the law of sine

[tex]\frac{sin75}{51.2} =\frac{sinB}{33.7}[/tex]

To solve for sinB cross multiply

sin75*33.7 = sinB * 51.2

32.55 = sinB*51.2

Divide 51.2 to both sides to isolate sinB

32.55 / 51.2 = sinB / 51.2

0.63577 = sinB

To find B you must use arcsin:

[tex]sin^{-1} 0.63577[/tex]

39.477

^^^This is your rough estimate but you can simply keep it to 39 degrees

This means that your answer is correct!

Hope this helped!

Answer:

1.2 cm

Step-by-step explanation:

Quadrilateral circumscribing a circle is a quadrangle whose sides are tangent to a circle inside it (see attached diagram).

The area of circumscribed quadrilateral is

[tex]A=p\cdot r,[/tex]

where [tex]p=\dfrac{a+b+c+d}{2}[/tex] is semi-perimeter and r is radius of inscribed circle.

In your case, [tex]A=12\ cm^2[/tex]

If a quadrilateral is circumscribed over the circle, then the sum of opposite sides is equal, so

[tex]a+c=b+d=10\ cm,[/tex]

so

[tex]P=10+10=20\ cm\\ \\p=\dfrac{20}{2}=10\ cm[/tex]

Now

[tex]12=10\cdot r\Rightarrow r=\dfrac{12}{10}=1.2\ cm[/tex]

For this case we have that the volume of the figure is composed of the volume of a prism and the volume of a pyramid:

The volume of the prism is given by:

[tex]V = A_ {b} * h[/tex]

Where:

[tex]A_ {b}[/tex]: It is the area of the base

h: It's the height

Substituting:[tex]V = 6 * 6 * 6\\V = 216 \ units ^ 3[/tex]

The volume of the pyramid is given by:

[tex]V = \frac {1} {3} * L ^ 2 * h[/tex]

Where:

[tex]L ^ 2:[/tex]It is the area of the base

h: It's the height

Substituting:

[tex]V = \frac {1} {3} * 6 ^ 2 * 5\\V = \frac {1} {3} * 36 * 5\\V = 60units ^ 3[/tex]

We add and we have:

[tex]V = 276 \ units ^ 3[/tex]

ANswer:

Option D

Answer:

g(x)=7x-3

Step-by-step explanation:

the y axis becomes -3 because 6-9=-3

The equation that has (-2, -1) as a solution is, C. 4x - y = -7.

To determine if an ordered pair is a solution to an equation, plug in the values of the coordinates of the pair into the equation to check if it will make it true

If it makes it true, it is a solution, otherwise, it is not if it does not make the equation true.

Given the ordered pair, (-2, -1) substitute the values to check which will be true:

-4(-2) - (-1) = 7

9 = 7 [not true].

4x + y = -7

4(-2) + (-1) = -7

-9 = -7 [not true]

4x - y = -7

4(-2) - (-1) = -7

-7 = -7

Therefore, the equation is: C. 4x - y = -7.

Learn more about the solution of an equation on:

#SPJ1

Complete Question:

The ordered pair (-2,-1) is a solution to which

of the following equations?

A.-4x - y = 7

B. 4x+y=-7

C. 4x - y = -7

D. -4x + y = -7

22/3 or 7.3333333333333333333333333333 or 7 1/3 feet

Answer:

The equation of the parabola is (x - 4)² = 8(y - 4)

Step-by-step explanation:

* Lets revise the equation of a parabola

- If the equation is in the form (x − h)² = 4p(y − k), then:  

• Use the given equation to identify h and k for the vertex, (h , k)

• Use the value of h to determine the axis of symmetry, x = h

• Use h , k and p to find the coordinates of the focus, (h , k + p)  

• Use k and p to find the equation of the directrix, y = k − p

* Now lets solve the problem

∵ The directrix is y = 2

∴ The equation is (x - h)² = 4p(y - k)

∴ The focus is (h , k + p)

∵ The focus is (4 , 6)

∴ h = 4

∵ k + p = 6 ⇒ (1)

∵ The directrix is y = k - p

∴ k - p = 2 ⇒ (2)

* Add (1) and(2) to find k

∴ 2k = 8 ⇒ ÷ 2 for both sides

∴ k = 4

* Substitute the value of k in (1) to find p

∵ 4 + p = 6 ⇒ subtract 4 from both sides

∴ p = 2

* Now lets write the equation

∴ (x - 4)² = 4(2)(y - 4) ⇒ simplify

∴ (x - 4)² = 8(y - 4)

* The equation of the parabola is (x - 4)² = 8(y - 4)

Answer:

In conclusion, dreams are the driving theme and characterization in the novel. They help explain each character's motivation for the actions they take and the way they feel. All of the characters have a obstacles in their life stopping them from reaching their goal. Authors use dreams to give their characters something to live for and strive for. Without the character's dreams and goals for the future, the characters would have nothing to work towards and they would be much less complex  

A conclusion for an essay on dreams in 'Of Mice and Men' should discuss the portrayal of the elusive American Dream, the use of dreams as a literary device, and the reflection of societal constraints and collective unconscious.

When crafting a conclusion for an essay about the theme of dreams in Of Mice and Men, you must strive to encapsulate the essence of the theme and its impact on the characters and the reader's understanding of the novel's message. The unattainable nature of the American Dream is vividly portrayed through the characters' struggles, symbolizing the universal experience of aspiration and loss. While each character harbors personal ambitions, the novel ultimately reveals the harsh reality of shattered dreams and the perseverance of hope, despite life's unpredictable and often tragic course. Understanding the role of dreams as a literary tool employed by John Steinbeck deepens one’s appreciation for his exploration of the human psyche and the societal constraints of the time period. Dreams in Steinbeck’s work reflect a combination of the characters' inner desires and the collective unconscious that connects them to the broader human experience, as Carl Jung would suggest.

Answer:

Step-by-step explanation:

This is the pre-calculus version of the arc length problem.  The formula we need for this is:

[tex]s=r\theta[/tex]

where s is the arc length (here, the distance she has to travel to get the gum off the tire), r is the radius, and theta is the angle given (the angle here always always has to be in radians!!!)  Filling in accordingly, we get

[tex]s=(6.5)(\frac{37\pi }{90})[/tex]

Do the math.  You need the answer rounded to the nearest inch, so that means you have to multiply in the pi (I used 3.1415):

s = 8 inches

Answer:

8

Step-by-step explanation:

Answer:

[tex]\large\boxed{D.\ D(0,\ -4)}[/tex]

Step-by-step explanation:

The formula of a midpoint of the segment"

[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]

We have the points X(3, -4) and Y(-3 -4).

Substitute:

[tex]x=\dfrac{3+(-3)}{2}=\dfrac{0}{2}=0\\\\y=\dfrac{-4+(-4)}{2}=\dfrac{-8}{2}=-4[/tex]