Mathematics High School

a drainage pipe 66 in. tall measures 25.12 in. around.

Using the formula for the volume of a cylinder, what is the volume of the drainage pipe rounded to the nearest hundredth of a cubic inch?

(Pi = 3.14)

Answers

Answer 1
in order to solve this using V= B(h) (The B is area of the base) you need a radius it doesn't give us that but it does give us the circumference. 
C= 3.14(2r)
25.12=2r divide each by 2 
12.56=r
now use this in the volume formula:
V= 12.56^2(3.14)(66)
V=32,692.86 cubic inches 

Related Questions

How many radii does a circle have? Explain.

Answers

Radii is defined as the line joining the centre of the circle to a point on the circumference
as there are infinite points on a circle
therefore there are infinite number of radii and hence there is no fixed number.

Answer:

one because the distance stay the same and infinite because the are infinite positions that the radii could be in

Step-by-step explanation:

The mass of a grain of sand is about 10^-3 gram. About how many grains of sand are in a 10kg bag of sand?

Answers

10000000

Divide the mass of the bag by the mass of sand. First you need to convert kg to g
The mass of a grain of sand is about 10 to the -3 power gram. 
About how many grains of sand are in the bag of sand

Answer

10 kg* (1000 g/ 1 kg)* (1 grain of sand/ 10^(-3) g)= 10^7 grains of sand. 
(Note that the units cancel out so you get the answer) 
The final answer is 10^7 grains of sand. 
Hope this helps~

Which of the following has 8.012 in written form?A.eight and twelve hundredthsB.eight and twelve thousandthsC.eight and twelve thousandsD.none of the above

Answers

the correct answer to this problem is letter choice B
the answer is B wala 

In a factory, a parabolic mirror to be used in a searchlight was placed on the floor. It measured 40 cm tall and 90 cm wide. Find an equation of the parabola with its vertex at the origin.

Answers

Equation of a parabola that opens up with vertex at it's origin: x^2=4py
point on the parabola:(45,40)
equation:
45^2=4p(40)
4p=45^2/40=40.625
thus
x^2=(50.625)y

Answer: x^2=(50.625)y

40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?

Answers

Using pythagoras length of the other leg  = sqrt ( 8^2 - 4^2) = sqrt 48 = 4 sqrt3

the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3   so this is a 
30-60-90 degree triangle

Please help with geometry

Answers


[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]
It's a equilateral triangle. The area of the white region is the area of a sector minus the area of a triangle.
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex] 
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
 The formula of an area of the circle: [tex]A_O=\pi r^2[/tex] 
 The area of the sector: 
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
 The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
 [tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]  

The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
  The area of the shaded region: 
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]

2,400 principal earning 2%, compounded annually, after 7 years. Find the balance in the account

Answers

A = P (1 + r/n) ^nt
P = 2400
r = .02
n = 1
t = 7

Answer: $2756.86

The balance in the account after 7 years will be approximately $2,747.70.

How did we get the value?

To calculate the balance in the account after 7 years with a principal of $2,400 earning 2% interest compounded annually, you can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future balance

P = the principal amount ($2,400)

r = the annual interest rate (2% or 0.02 as a decimal)

n = the number of times the interest is compounded per year (annually, so n = 1)

t = the number of years (7 years)

Plug these values into the formula:

A = 2400(1 + 0.02/1)^(1*7)

A = 2400(1 + 0.02)⁷

A = 2400(1.02)⁷

A = 2400(1.144877)

A ≈ $2,747.70

So, the balance in the account after 7 years will be approximately $2,747.70.

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For a recent project, a teacher purchased 250 pieces of red construction paper and 114 pieces of blue construction paper. what is the ratio of red to blue? select one:
a. 57:125
b. 125:57
c. 125:182
d. 182:125

Answers

well start buy putting R=250 and B=114 for the color and amount. 250:114 simplified is 125:57. To simplify it find the greatest common factor, in this case is 2, then divide each number by 2. So your answer is B.

points J and K lie on the same line, as shown on the coordinate plane below. What is the slope of the line passing through points J and K?

Answers

The slope is 1/2.

The slope is given by the formula
m = (y₂-y₁)/(x₂-x₁)

Using our two points, we have
m = (5-3.5)/(6-3) = 1.5/3 = 0.5 = 1/2

In ΔPQR, what is sin Q written as a decimal?

Answers

sin Q = oppo. / hypo
sin Q = 9/15
sin Q = 0.6
Hi there!

The sine of an angle is opposite over hypotenuse. Looking at angle Q, we know the opposite side is 9 and the hypotenuse is 15. These numbers give us this equation: sin Q = 9/15. Upon solving this equation, the result is approximately 56.5.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

y varies directly as x and y = 18 when x= 1/2. write an equation that relates y and x

Answers

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=18\\ x=\frac{1}{2} \end{cases}\implies 18=k\cfrac{1}{2}\implies 18=\cfrac{k}{2} \\\\\\ 36=k\qquad therefore\qquad \boxed{y=36x}[/tex]

Use logarithms to solve each equation
2x 9/8=111
A. 18.9561
B.25.8961
C. 10.2587
D. 35.5208

Answers

We have this equation:

[tex]2x^{\frac{9}{8}} = 111[/tex]

and we need to find the value of x.

First of all, we multiply the whole equation for 1/2, so our goal is to isolate x, therefore:

[tex]x^{\frac{9}{8}}=\frac{111}{2}[/tex]
 
Next step we must do is to apply logarithms:

[tex]logx^{\frac{9}{8}} = log(\frac{111}{2})[/tex]

Next, we have to apply identities and then to solve the equation:

[tex] \frac{9}{8}logx = log(\frac{111}{2})[/tex]
[tex]logx = \frac{8}{9}log(\frac{111}{2})[/tex]
[tex]logx = 1.5504[/tex]
[tex]10^{logx} = 10^{1.5504}[/tex]

Finally, we have the value of x which was our goal. This is the answer for the question above:

[tex]x= 35.5140[/tex]

The answer is D.

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin.

r = 5 + 4 cos θ

Answers

Explaining how to determine the symmetry of a polar graph based on the given equation r = 5 + 4 cos θ.

To determine the symmetry of the graph r = 5 + 4 cos θ, we can substitute (-θ) for θ in the equation and check if the resulting polar equation remains the same, indicating symmetry about the origin.

If replacing (-θ) gives us the same equation, the graph is symmetric about the y-axis. If replacing (π - θ) gives the same equation, then the graph is symmetric about the x-axis.

In this case, replacing (-θ) in r = 5 + 4 cos θ gives r = 5 + 4 cos(-θ), which simplifies to r = 5 + 4 cos θ, indicating symmetry about the y-axis.

Find the number if the square root of another number that is 6 greater than this number is equal to the number itself.

Answers

Answer:

The number is 3 and the another number is 9

Step-by-step explanation:

Let

x-------> the number

y-----> another number

we know that

[tex]y=x+6[/tex] ----> equation A

[tex]\sqrt{y}=x[/tex] ----> equation B

Substitute equation A in equation B

[tex]\sqrt{x+6}=x[/tex]

squared both sides

[tex]x+6=x^{2} \\x^{2}-x-6=0[/tex]

Using a graphing tool

solve the quadratic equation

see the attached figure

The solution is  x=3

Find the value of y

[tex]y=x+6[/tex] -------> [tex]y=3+6=9[/tex]

Sina played basketball on a rectangular court that was 74 feet by 42 feet. after the game, she walked across the court diagonally from one corner to the opposite corner. approximately what distance did sina walk in feet?

Answers

Distance walked = 85.088 feet


The distance Sina walked would be equal to the length of the diagonal of rectangle.

As every angle in a rectangle is 90 degree. So, we can apply Pythagoras theorem in right triangle formed by sides,

Base- 74 feet, Altitude-  42 feet and Hypotenuse- Diagonal

Base^2 + Altitude ^ 2 = Hypotenuse ^2

74^2 + 42 ^ 2 = Diagonal ^2

On solving,

Diagonal = 85.088 feet

To calculate the distance Sina walked diagonally across the basketball court, we utilize the Pythagorean theorem using the court's length and width. The calculation gives us a diagonal distance of approximately 85 feet.

To calculate the distance Sina walked across the rectangular basketball court diagonally, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since the court is 74 feet long and 42 feet wide, these dimensions can be considered the two shorter sides of a right triangle, with the diagonal Sina walked being the hypotenuse.

The Pythagorean theorem formula is:

[tex]c^2 = a^2 + b^2[/tex]

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides. Substituting the known values:

[tex]c^2 = 742 + 422\\c^2 = 5476 + 1764\\c^2 = 7240[/tex]

To find c, we take the square root of 7240:

c ≈ 85.09 feet

Therefore, Sina walked approximately 85 feet diagonally across the basketball court.

what is the complete factorization of the polynomial below
x^3-4x^2+x-4?

A. (x-4)(x+i)(x-1)
B. (x+4)(x+i)(x-i)
C. (x+4)(x-i)(x-i)
D. (x-4)(x-i)(x-i)

Answers

Answer:

B. (x+4)(x+i)(x-i)

Step-by-step explanation:

Let [tex]P(x)=x^3-4x^2+x-4[/tex]

We can factor this polynomial by grouping:

[tex]P(x)=x^2(x-4)+1(x-4)[/tex]

We factor further to obtain:

[tex]P(x)=(x^2+1)(x-4)[/tex]

[tex]P(x)=(x^2-\sqrt{-1}^2)(x-4)[/tex]

We apply difference of two squares to get:

[tex]P(x)=(x-i)(x+i)(x-4)[/tex]

Answer:

(x+1)(x-1)(x+4)

Step-by-step explanation:

What's the probability a number is odd given that it's an integer between 0 and 11?

Answers

A odd number lie between 0 and 11(0 and 11 not included), it means that total of ten numbers, starting from {1,2,3........,10} form our sample space.

sample space=s={1,2,3....,10}=total 10 numbers
So,
m=total no. of odd numbers{1,3,5,7,9} in our sample space=5 numbers
 
probability that number is odd=p=m/s
p=5/10=0.5
  

Please help!!! Mark is learning to snowboard. The club charges $10 per hour for snowboard lessons and $40 for the lift ticket and a snowboard rental. Which value represents the rate of change for this scenario?

Answers

h represents the number of hours:
10h + 40
(40 represents, well $40)
the answer is 40 + 10h

How many solutions does 15x+11=8x

Answers

Hello there!

How many solutions does 15x + 11 = 8x


Answer: 1 solution
-------------------------------------------------------------------------------------------------------

Explanation:


To solve this, we must isolate the x.

15x + 11 = 8x

We will subtract 15x from each side to isolate the x.

15x + 11 = 8x
- 15x         -15x

11 = -7x

Finally, we must simplify this by dividing each side by -7

11 = -7x
---    ----
-7     -7


Our answer is: -11/7 = x

Ths means that this equation only has one solution.


I hope I helped!

Let me know if you need anything else!

~ Zoe


Hi there,

To get the number of solutions that the equation is giving, we are going to need to solve the equation. Here’s how to find the solution...

15x+11= 8x

If we collect it sorta like terms we are going to get:

11=8x-15x

11=-7x dividing both of the sides by -7 we get:

x=-7/11


The number of solutions you have is 1. So your answer would be one.

what is the fifth term of the arithmetic sequence 7,3,-1....

Answers

The formula is a1+d(n-1). 7+ -4(5-1). a5 = -9.

What is the equivalent decimal? Drag the answer into the box to match the fraction. ​ 5/45 ​

Answers

the decimal for is .1 the one is repeating 
what you do is divide 5 into 45 to make it a decimal

Jamal is 167 cm tall. Which expression finds Jamal’s height in dekameters? Use the metric table to help answer the question.

Answers

we know that
1 cm is equal to -----------> 0.001 dekameters
so
167 cm------------------> X
x=167*0.001------> x=0.167 dekameters

Expression to finds Jamal’s height in dekameters
[Jamal’s height in cm]*0.001  or [Jamal’s height in cm]/1000

Answer:

It is D

Step-by-step explanation:

What are the similarities and differences between these data sets in terms of their centers and their variability?

Data Set A: 14, 21, 24, 28, 28, 35

Data Set B: 18, 19, 21, 25, 29, 32



Select from the drop-down menus to correctly complete the statements.

Comparing the centers of the data sets, the median for Data Set A is (less than, greater than, equal to) the median for Data Set B. The mean for Data Set A is (less than, greater than, equal to) the mean for Data Set B.

Answers

the median for data A is greater.
the mean for data A is greater.

Answer:

a

Step-by-step explanation:

It costs $5.75 to enter an arcade and $0.50 to play an arcade game. You have $7.25. Write an equation that represents the number g of games you can play.

Answers

5.75+3(.50) because it’s 5.75 and then add .50 3 times to get 7.75. Meaning you can play 3 games...
Hope that helps
You'll need probably
About 11 games

An earthquake strikes and an isolated area is without food or water. three crews arrive. one can dispense needed supplies in 4545 ​hours, a second in 9090 ​hours, and a third in 6060 hours. how long will it take all three crews working together to dispense food and​ water?

Answers

It'll take 10 hours for the crew to finish the work.

1 person takes 20h, the second would hake 30h, third 60h. 
 1/20+1/30+1/60=1/10

Use the graph below to answer the question that follows:
cosine graph with points at 0, negative 1 and pi over 3, 0 and pi, 3 and 5 pi over 3, 0 and 2 pi, negative 1

What are the amplitude, period, and midline of the function?

Amplitude: 4; period: π; midline: y = 2
Amplitude: 2; period: 2π; midline: y = 1
Amplitude: 4; period: 2π; midline: y = 1
Amplitude: 2; period: π; midline: y = 2

Answers

For this case the amplitude is given by:
 A = (l-1l + 3) / 2
 A = 4/2
 A = 2
 The middle line is given by:
 y = 1
 The period of the function is given by:
 T = l x2 - x1 l
 T = l 0 - 2pi l
 T = l - 2pi l
 T = 2pi
 Answer:
 Amplitude: 2; period: 2π; midline: y = 1

Answer:

For this case the amplitude is given by:

A = (l-1l + 3) / 2

A = 4/2

A = 2

The middle line is given by:

y = 1

The period of the function is given by:

T = l x2 - x1 l

T = l 0 - 2pi l

T = l - 2pi l

T = 2pi

Answer:

Amplitude: 2; period: 2π; midline: y = 1

Step-by-step explanation:

PLEASE HELP 20 POINTS

Answers

Hello!

A sample of Bromine-82 begins at 80 mL. We are given that this value will decrease by half of its current amount every 35 hours. First, we'll determine the number of times that 35 goes into 140. This will reveal the number of times we should divide the sample by 2:

140 ÷ 35 = 4

We have now proven that there are 4 periods of 35 hours in 140 hours. This means that we will divide the sample in half a total of 4 times, as follows:

1. 80 ÷ 2 = 40
2. 40 ÷ 2 = 20
3. 20 ÷ 2 = 10
4. 10 ÷ 2 = 5

We have now proven that an 80 mL sample of Bromine-82 will be reduced to only 5 mL after 140 hours. Therefore, the correct answer is 5 mL.

I hope this helps!
To solve this problem, we have to use the half-life formula, where A represents the remaining amount, P is the initial amount, t is the time that has passed, and h is the substance's half-life:

[tex]A = P( \frac{1}{2} )^{\frac{t}{h} } [/tex]

This is what it looks like with the values from this scenario plugged in:

[tex]A = 80( \frac{1}{2} )^{\frac{140}{35} } \\ A = 5[/tex]

There are 5 mL of the 80 mL Bromine sample left after 140 hours.

Ginger makes pies and sells them for $14 each. Write an equation that represents the situation, if y represents the money that Ginger earns and x represents the number of pies sold.

Answers

y = 14x is the equation you should use! Hope this helped.
can u help me im just asking

Can somone help me with this 1 problem? QRST is a parallelogram. Determine the measure of ∠Q
Q (4x+10) bottom left
R (9x+1) top left
S (5x-3) top right
T bottom left


Answers

(In the picture, QRST looks like a rhombus, so I will assume that it is a rhombus.)

In a rhombus, opposite angles are congruent based on the alternate interior angle theorem. In other words, R and T along with Q and S are both alternate interior angle pairs.
(You can actually test this by printing out a rhombus, cutting out the angles, and matching up the opposite ones.) 

We know that Q is equal to 4x + 10, but we need to solve for x. Since Q and S are congruent, we can set them equal to each other:
1) 4x + 10 = 5x - 3
2) 4x + 13 = 5x
3) 5x = 4x + 13
4) x = 13
Now let's plug 13 in for Q:
5) 4(13) + 10 = 52+10 = 62

I got m<Q = 62 degrees. Hope this helps!

In the parallelogram QRST then measure of  ∠Q is 62 degrees.

What is Quadrilateral?

A quadrilateral is a four-sided polygon, having four edges and four corners.

Given that  QRST is a parallelogram.

We have to find the measure of ∠Q.

Both pairs of opposite sides are parallel, quadrilateral QRST is a parallelogram.

∠Q= ∠S

4x+10=5x-3

We have to find the value of to find ∠Q measure.

10+3=5x-4x

13=x

Now let us plug in the value of x in ∠Q measure.

∠Q = 4x+10

Now plug in x value in ∠Q

∠Q = 4(13)+10

=52+10

=62 degrees

Hence, in the parallelogram QRST then measure of  ∠Q is 62 degrees.

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PLEASE HELP :( i'm stuck

What are the amplitude and midline?

Amplitude: 1; midline: y = 1
Amplitude: 0; midline: y = 0
Amplitude: 2; midline: y = 1
Amplitude: 2; midline: y = 0

Answers

Amplituide is and midline is y = 1.

Answer:

Amplitude: 1; midline: y = 1

Step-by-step explanation:

From the graph we can conclude that it is a sine or cosine function. In their standard form, these functions are given by the following equations:

[tex]y(t)=Acos(\omega t +\phi)\\\\or\\\\y(t)=Asin(\omega t+ \phi)[/tex]

Where:

[tex]A=Amplitude=\frac{|A_m_i_n-A_m_a_x|}{2}\\\omega=Angular\hspace{3}frequency\\\phi=Initial \hspace{3}phase[/tex]

And:

[tex]A_m_a_x=Maximum\hspace{3}amplitude\\A_m_i_n=Minimum\hspace{3}amplitude[/tex]

On the other hand, we can define the midline of these kind of functions as the halfway between the maximum and minimum amplitude of the function, Therefore:

[tex]Midline=M_l=\frac{A_m_a_x+A_m_i_n}{2}[/tex]

From the graph you can see that the maximum value of the function(maximum amplitude) is 2 and the minimum value of the function (minimum amplitude) is 0, thus:

[tex]A=\frac{|A_m_i_n-A_m_a_x|}{2} =\frac{|0-2|}{2} =\frac{|-2|}{2} =\frac{2}{2} =1[/tex]

And:

[tex]M_l=\frac{A_m_a_x+A_m_i_n}{2}=\frac{2+0}{2} =\frac{2}{2} =1[/tex]

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Spring is like a perhaps hand (which comes carefully out of nowhere) arranging a window, into which people look(while people stare) Which of these poetic devices does this poem most represent?A. MetaphorB. End-stopped linesC. EnjambmentD Iambic pentameter can somebodyhelp me please this is my last question i need to submit this!! help!! I sing jingles when I read their persistence is extreme! 9 I find ignoring messages to be a rough routine. 10 According to line 9, persistence means A)silliness. B)rowdiness. Eliminate C)reservation. D)determination. can someone tell me where to place commas? I forgot because i never used to put it what's the answer to this? Which sentence would a writer use to best appeal yo the readers sense of smell PLEASE HELP AND FAST, 15 POINTS! In the coordinate plane shown, how far apart are points B and D? Explain how you can use the Pythagorean theorem to determine this. I need help on these problems PLZ HELP LIKE IN THE NEXT 5 MINS!Read the excerpt from Fast Food Nation. Instead of relying upon a small, stable, well-paid, and well-trained workforce, the fast food industry seeks out part-time, unskilled workers who are willing to accept low pay. Teenagers have been the perfect candidates for these jobs, not only because they are less expensive to hire than adults, but also because their youthful inexperience makes them easier to control.In this excerpt, Schlosser claims that fast food restaurants areA. taking advantage of people to save money.B. helping society by hiring unskilled workers.C. providing valuable training for teenagers.D. using highly skilled workers in low-paying jobs. "why was it important for women to enter the workforce during the war?" The tube that connects the oral cavity to the stomach is called the ________ List three uses of bacteria in food production and industry. Transitions provide _____ from one sentence to the next or from one paragraph to the next.empty wordsconnectionsthesis statementscommas In the conclusion of her speech on cyber bullying, rooney told a story about an 18 year old girl who committed suicide as a result of being cyber bullied by her peers. rooney said, "megan mara was a sensitive soul. she was a talented artist and those who were close to her said she would have accomplished great things in Given the following sets: A={ 2, 4, 6, 8, 10} B={ 3, 5, 7, 9} C={ 2, 3, 5, 7}N={ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}Match the following Unions and intersections to the correct set.1.What is A U C? 2.What is A B?3.What is A N?4.What is B N?5.What is B U C?{2, 3, 4, 5, 6, 7, 8, 10}{2, 3, 5, 7, 9}{ }{3, 5, 7, 9}{2, 4, 6, 8, 10} QUESTION 1 Which of the following was a problem for the British army at the beginning of the American Revolution? financial support age of the equipment familiarity with the terrain experience of the officers PLEASE HELP MEEEEE (using 98 points to post)Given that the molal freezing point depression constant (kf) for methyl alcohol (CH3OH) is -0.83 oC/molal, how much will the freezing point of methyl alcohol be lowered if 46.0 g of glycerine (C3H8O3) is added to 1.00 kg of methyl alcohol? (must show work, correct unit and correct answer) Part 1: Solve the system by graphing. Draw the graphs on paper and indicate their intersection point. Type the ordered pair solution here as your answer to Part 1. Part 2: Solve the system using the substitution method. Show all work here and indicate the solution for the system as an ordered pair. Part 3: Solve the system using the addition method. Show all work here and indicate the solution for the system as an ordered pair. 2x+3y=6 x-2y=10 Identify whether each circumstance provided will promote an increase or decrease in blood pressure watts,volts and amps are used to measure electricity. there is a formula that shows the relationship between watts,volts and amps. volts times amps = watts . if the volts are 120 and the amps are 5 how many watts are there?