The figure has 60 edges and 30 vertices. Use Euler’s formula to find the number of faces in the given polyhedron.

Answers

Answer 1

Let the number of faces ⇒⇒⇒ F
Number of Vertices        ⇒⇒⇒ V
Number of Edges          ⇒⇒⇒ E

Euler's Formula ⇒⇒⇒⇒⇒ F + V − E = 2

given:⇒⇒⇒ 60 edges and 30 vertices
∴ E = 60    and    V = 30
∴ F + 30 - 60 = 2
∴ F = 2 + 60 - 30 = 32

Number of faces = 32

Related Questions

Please answer ASAP!!! How many vertical asymptotes does the graph of this function have ?

Answers

Answer:

The answer is 1.

Got it from Apex

Step-by-step explanation:

Write a quadratic equation whose solutions are 2i and -2i.

Answers

are there any answer choices

Answer:

answer= 2i

Step-by-step explanation:

Anyone know the answer?

Answers

i think it is 3=4 i could be wrong though

How many distinct permutations are there of the letters of the word BOOKKEEPER?
There are __[blank]__ distinct permutations of the letters of the word BOOKKEEPER.

A group of 3 English majors, 2 anthropology majors, and 5
history majors are going out to dinner, where they will sit at a circular table. If students with the same major need to sit together, how many different ways can the students be seated around the table?

Answers

The letters of the word BOOKKEEPER can be arranged in 151,200 ways.

The group can be arranged in 8640 ways with all students of the same major together.

Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
[tex]\frac{n!}{n_1!\times n_2!\times ... \times n_k!} \\ \\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200[/tex]

Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.

Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.

This gives us 6(6*2*120) = 8640

Final answer:

The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.

Explanation:

The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.

In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.

Learn more about Permutations and Circular Arrangements here:

https://brainly.com/question/1216161

#SPJ3

The sum of three numbers is 62. The second number is equal to the first number diminished by 4. The third number is four times the first. What are the numbers?

Answers

Hey there!

Let: 1st number = x
2nd number = x - 4
3rd number = 4x

x + (x-4) + 4x = 62
6x - 4 = 62
6x = 62 + 4
6x = 66

x = 11 ---> 1st number

x - 4 = 11 - 4
= 7 ---> 2nd number

4x = 4(11)
= 44 ---> 3rd number

Please help with geometry

Answers

[tex]A=240\\\\A=a\cdot h\\\\New:a'=\dfrac{1}{4}a\ and\ h'=2h\\\\A'=a'h'=\dfrac{1}{4}a\cdot2h=\dfrac{1}{2}ah=\dfrac{1}{2}A=\dfrac{1}{2}\cdot240=\boxed{120}[/tex]

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, f(t), in feet, at different times, t, in seconds: f(t) = −16t2 + 48t + 160 The average rate of change of f(t) from t = 3 seconds to t = 5 seconds is _____ feet per second.

Answers

The Average rate of change of f(t) from t = 3 seconds to t = 5 seconds is - [tex]v_{avg} = -80\;ft/s[/tex]

We have a equation -

[tex]f(t) = -16t^{2} +48t+160[/tex]

that calculates the height of the ball from sea level in feet at different times.

We have to find the average rate of change of f(t) from t = 3 seconds to t = 5 seconds.

What is Average velocity?

The rate of change of displacement per unit time is called average velocity. Mathematically -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

We have -

[tex]f(t) = -16t^{2} +48t+160[/tex]

For time t = 3 seconds, f(t) is -

[tex]f(3) = -16(3)^{2} + 48(3) + 160\\f(3) = -144 +144 +160\\f(3) = 160\; feets\\[/tex]

For time t = 5 seconds, f(t) is -

[tex]f(5) = -16(5)^{2} + 48(5) + 160\\f(5) = -400+240+160\\f(5) = -400 + 400\\f(5) = 0 feet[/tex]

The formula for average velocity is -

[tex]v_{avg} = \frac{d_{2} - d_{1} }{t_{2} - t_{1} }[/tex]

According to question -

[tex]t_{2} = 5s[/tex] and [tex]t_{1} = 3s[/tex]

[tex]d_{2} = f(5) = 0 feet[/tex] and [tex]d_{1} = f(3)=160[/tex]

Substituting the values in the formula of average velocity, we get -

[tex]v_{avg} = \frac{0 - 160}{5 - 3} \\v_{avg} = \frac{-160}{2\\} \\v_{avg} = -80\;ft/s[/tex]

Hence, average rate of change of f(t) from t = 3 seconds to t = 5 seconds is [tex]v_{avg} = -80\;ft/s[/tex].

To solve more questions on calculating the average rate of change of height with time, visit the following link -

https://brainly.com/question/22257105

#SPJ2

the equation 3sinx+cos^2x=2 is solved below
Please help! Thanks!

Answers

we have that
3sin x+cos²x=2
3sin x+(1-sin²x)=2
-sin²x +3sin x=1
sin²x -3 sin x+1=0---------> up to here the procedure is correct
let
A=sin x
then
A²-3A+1=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

(A²-3A)=-1

Complete the square. Remember to balance the equation by adding the same constants to each side.

(A²-3A+2.25)=-1+2.25

Rewrite as perfect squares

(A-1.5)²=1.25

(+/-)(A-1.5)=1.12

first solution

(A-1.5)=1.12--------> A=1.12+1.5-----> A=2.62-----> sin x=2.62

second solution

-(A-1.5)=1.12----> -A+1.5=1.12----> A=1.5-1.12----> A=0.38---> sin x=0.38

the answer is

the equation was factored incorrectly

Its is b. hope this halps

brainly The point (−4, 2) is on the terminal side of angle Θ, in standard position. What are the values of sine, cosine, and tangent of Θ? Make sure to show all work. (10 points)

Answers

The tangent = -2/4 = -1/2
The length of the hypotenuse = sqrt20 = 2 sqrt5
sine = 2 / 2 sqrt5 = 1 / sqrt5
cosine = -4 / 2 sqrt5 = -2/sqrt5

PLEASE SOMEONE I AM SO DESPERATE like actually crying
1. The equation of a parabola is given. y=−1/6x2+7x−80 What is the equation of the directrix of the parabola?
2. (y+2)^2= 129X-5)
What is the equation of the directrix of the parabola?

Answers

Part 1)
we have that
y=−1/6x2+7x−80

y= (−1/6)x^2+7x−80 multiply both sides by -6

-6y = x^2 - 42x + 480 subtract 480 from both sides

-6y - 480 = x^2 - 42x take (1/2) of 42 = 21.....square this = 441 and add to both sides

-6y - 480 + 441 = x^2 - 42x + 441 simplify the left, factor the right

-6y - 39 = (x - 21)^2 factor the left side as

-6 (y + 39/6) = ( x - 21)^2 (1)

Using the form

4p (y - k) = ( x - h)^2 we can write (1) as

4 (-3/2)(y - (-39/6) ) = ( x - 21)^2

The vertex = ( h, k) = ( 21, -39/6) and p = -3/2

And the directrix is given by

y = k - p → y = -39/6 - (-3/2) = -39/6 + 3/2 = -39/6 + 9/6 =

-30/6 = - 5-------> y=-5

the answer Part 1) is

y=-5

Part 2) (y+2)^2= 129X-5

What is the equation of the directrix of the parabola?
(y+2)²= 129X-5 -----> 129*(x-5/129)=(y+2)² (1)

Using the form

4p (x - h) = ( y - k)^2 we can write (1) as

4*(129/4)*(x-5/129)=(y+2)²

The vertex = ( h, k) = ( 5/129, -2) and p = 129/4

And the directrix is given by

x = h - p → x = 5/129 - (129/4) = (20-16641)/516-----> -16621/516

x=-32.21

the answer part 2) is

x=-32.21

Find the domain of the function :

Can you show the steps

Answers

a rational function must not have a denominator of 0, since that means the divisor is a 0 and there's no number whatsoever you can multiply it with 0 to get the dividend, the short version of all that is, the fraction is "undefined".

a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.

so, what values "x" cannot take on safely? well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,

[tex]\bf 5x+2=0\implies 5x=-2\implies x=-\cfrac{2}{5}[/tex]

so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.

so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}

For a circle with a radius of 6 feet, find the arc length of a central angle of 45 degrees

Answers

The arc length formula is given below.

Arc Length, s = radius*theta where theta is in radians. First we need to convert theta from degrees to radians.

theta (radians) = 45 degrees * π radians / 180 degrees = 0.785 radians

radius = 6 ft
theta = 0.785 radians

s = arc length = 6 ft * 0.785 radians = 4.712 ft

15 is 10 % of what number

Answers

15*10=150

15 is 10% of 150

PLEASE ANSWER QUICKLY! Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?

A. n may cause p.

B. p must cause n.

C. n must cause p.

D. n must not cause p.

Answers

The correct answer will be option A.

Correlation does not imply Causation.
This means if two variables are strongly related, it is not a must thing that one is causing any occurrence or change in the other variable. For example, before and during an occasion or an event people buy new clothes and celebrate by having different drinks. So there will be a strong correlation between buying new clothes and having drinks.
Thus this mean, having different drinks is causing people to buy new clothes? The answer is NO.

However, it is possible that if two variables are correlated on might be causing the other. For example, more hours of work will help the worker to earn more. So more work is causing the salary to grow. So more work is Causing an increase in salary? The answer is YES

Therefore, the answer to this question will be option A

Item 11 Solve y=4x+8x for x.

Answers

Final answer:

To solve the equation y = 4x + 8x for x, isolate x by combining like terms on the right side and dividing both sides by 12. The solution is x = y/12.

Explanation:

To solve the equation y = 4x + 8x for x, we need to isolate x on one side of the equation.

We can start by combining the like terms on the right side:

12x = y

To find the value of x, divide both sides of the equation by 12:

x = y/12

So the solution to the equation is x = y/12.

Final answer:

To solve the equation y = 4x + 8x for x, combine like terms to get y = 12x and then divide both sides by 12 to find x = y/12.

Explanation:

The student's question requires us to solve the given equation for x. The original equation provided is y = 4x + 8x. To solve for x, we first combine like terms on the right side of the equation.

Combine like terms: y = 4x + 8x becomes y = 12x.Divide both sides of the equation by 12 to isolate x: x = y/12.

The solution for x is x = y/12. This is a straightforward algebraic manipulation that involves combining like terms and using division to solve for the unknown variable.

quando o Ângulo de elevação do sol e de 70 a sombra de um edifício medes 20 cm calcule a altura do edifício
dados : sen 70=0,93 cos 70=0,3 e tg70=2,74?

Answers

Use x para a altura.

tg 70 = x/(20 cm)

x = 20 cm * tg 70

x = 20 cm * 2,74

x = 54,8 cm

Resposta: A altura do edifício é 54,8 cm.

A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?

Answers

For this case we have the following function:
P (x) = - 3 (x-5) ^ 2 + 12
We derive the function to obtain the maximum.
We have then:
P (x) = - 6 (x-5)
We match zero:
-6 (x-5) = 0
We clear x:
x-5 = 0
x = 5
Answer:
the company should set a sock price of 5 $ to earn a maximum profit

Final answer:

To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.

Explanation:

The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.

In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.

This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.

Learn more about Profit Maximization here:

https://brainly.com/question/33809682

#SPJ3

The Nichols family consists of 8 children and 2 adults. The family minivan can safely transport a total of 7 family members, including an adult driver.

Which number line illustrates the capacity of the Nichols minivan as an inequality?

Answers

For this case, the first thing we must do is define a variable:
x: number of people who will use the family minivan.
We have then:
"The family minivan can safely transport a total of 7 family members, including an adult driver":
x <= 7
Answer:
x <= 7
A number line that illustrates the capacity of the Nichols minivan as an inequality is:
option C)

The depreciating value of a semi-truck can be modeled by y = Ao(0.87)x, where y is the remaining value of the semi, x is the time in years, and it depreciates at 13% per year.

An exponential function comes down from the positive infinity and passes through the points zero comma eighty-seven thousand. The graph is approaching the x-axis.

What is the value of the truck initially, Ao, and how would the graph change if the initial value was only $67,000?

$90,000, and the graph would have a y-intercept at 20,000
$87,000, and the graph would have a y-intercept at 67,000
$87,000, and the graph would fall at a slower rate to the right
$87,000, and the graph would fall at a faster rate to the right

Answers

The initial value of the truck is the value of y when x = 0. Since the graph passes (0, 87000), this means that the value of the truck initially was $87,000. If the initial value was only $67,000, then the y-intercept would have been (0, 67000). This is the second choice.

Answer:

I just took the test the answer is

Step-by-step explanation:

B. 87,000, and the graph would have a y-intercept at 67,000.

Choose the example that correctly shows the mean population density of a region.

A. 678 people per cubic meter

B. 678 cubic meter per number of people

C. 678 people per square mile

D. 678 square mile per people

Answers

678 people per cubic meter - lol!! That would be a SQUash!!!

The answer is C

- 678 per square mile

What is the area of the parallelogram?

Answers

Area of the parallelogram is given by:

Area = Base x Height

Base = 8 cm

Height is the perpendicular distance between the base. 6 cm is not the height, but we can use 6 cm and the angle 60 to find the height. See the picture attached with.

The height x is the perpendicular side of the triangle as shown in figure and 6 is the hypotenuse.

So,we can write

cos 60 = x/6
⇒
x = 6 * cos 60 = 3 cm

So, now we can write:

Area of parallelogram = 8 x 3 = 24 cm²

The area of a parallelogram is base*height

or A = base*lateral side /cos(theta)

A = 8 * 6 / cos(60) = 96cm^2

The area of the parallelogram is 96 sq.cm

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Answers

I find short work can be made of many limit problems simply by graphing them. Your limits appear to be:
1. 1
2. -1
3. 0
4. 1
5. 1 (x has been replaced by 1/x and the limiting value of x changed to 0)

What is the answer for this equation?

36^-x+3=(1/216)^x+1

Answers

x=-9
also photomath is a good app to use for math ☺️
hoped this helped

Three added to eight times a number is the same as three times the value of two times the number minus one

Answers

im sorry do not now i will try and help

I need to answer three questions about y = x^(-2) on the interval [-4, -1/2]. I have attached my questions and my answers as screenshots:

Part 1 - ANSWER C
Part 2 - ANSWER A
Part 3 - ANSWER B

I am referring to each part in the order that I uploaded the screenshots. You will see that my answers are highlighted in blue. I like second opinions!

Answers

I wasn't sure how to order things, so I decided to write directly on top of your screenshots. Have a look at the three attachments. Two of which are correct. There is one incorrect answer though you're fairly close.

please help asap 48 pts

Answers

The correct answer is B.

The correct answer is B

-2y multiplied by -2y = 4y^2
3x Times 5x = 15x^2
3x Times -2y = -6xy
-2y times 5x = -10xy
-6xy plus -10xy = -16xy

If an airplane travels 15 miles in 2 minutes what is the speed in miles per hour

Answers

15 miles = 2 minutes

1 hour = 60 minutes

60 ÷ 2 = 30

30 × 15 = 450

Answer = 450 miles in 1 hour

Hope this helped :)

Jack and Jane are married and both work. However, due to their responsibilities at home, they have decided that they do not want to work over 65 hours per week combined. Jane is paid $14 per hour at her job, and Jack is paid $7 per hour at his. Neither of them are paid extra for overtime, but they are allowed to determine the number of hours per week that they wish to work. If they need to make a minimum of $770 per week before taxes, what is the maximum amount of hours that Jack can work per week according to these limits?

Answers

By setting up a system of equations we can easily solve this problem. Let's denote Jane's working hours with x and Jack's working hours with y. Since they don't want to work more than 65 hours, the first equation is x+y=65. The second equation is 14x+7y=770. By solving this system of equation [tex] \left \{ {{x+y=65} \atop {14x+7y=770}} \right. [/tex], we find that y=20 hours, which is Jack's maximum working hours.

Answer:

Step-by-step explanation:

How do I convert 2.4 x 10^21 formula units of magnesium hydroxide to grams?

Answers

Are you taking chemistry at the same time? If not, this is a pretty hard question.

Facts

1. As a formula unit, Magnesium Hydroxide has a chemical formula of Mg(OH)2
2. That means for every Magnesium, there are 2 oxygens and 2 hydrogens
3. The weights of these components are found on a periodic table. Since every periodic table is different, I'm going to approximate the results.

Mg = 24
O = 16
H = 1

4. One mole of anything has 6.02 * 10^23 (in this case) formula units associated with it.

Step One
Find the number of grams in 1 formula unit using the numbers from the periodic table.

1 Mg = 1 * 24 = 24
2 O = 2 * 16 = 32
2 H = 2 * 1 = 2
Total = 58 grams

So
1 mole of Mg(OH)2 = 58 grams

1 mole / 6.02 * 10 ^23 formula units = x mole / 2.4 * 10 ^ 21 formula units
Cross multiply

1 mole * 2.4 * 10^21 formula units = x mole * 6.02 * 10^23 formula units.
Divide both sides by 6.02 * 10^23

1 * 2.4 * 10^21 / 6.02 * 10 ^ 23 = x
x = 0.003987 moles

Now do this again for grams
1 mole / 58 grams = 0.003987 mole / x grams Cross multiply
1 mole * x = 0.003987 * 58 grams
x = 0.2232 grams <<<<< Answer

A rectangular wall has a length of 12ft and a width of 8ft. The wall has two rectangular windows. Each window has a width of 3ft and a height of 5ft. Andrea chooses a point on the wall at random to test a new paint color. What is the probability she could choose a point on a window

Answers

The probability would be about 31%

Other Questions

Without wildfires, forest ecosystems would be more likely to suffer from outbreaks of plant disease. please select the best answer from the choices provided t f Public education and roads are produced by How do you solve 6 What are 4 specific things you can do to improve your memory for course material based on the 2 lectures we recently had on ltm retrieval? Many species of roundworms are parasites of plants and animals. How is a roundworms body plan related to its function as a parasite? Read the excerpt from Hamlet. Gertrude: O Hamlet! speak no more; Thou turnst mine eyes into my very soul; And there I see such black and grained spots As will not leave their tinct. Hamlet: Nay, but to live In the rank sweat of an enseamed bed, Stewd in corruption, honeying and making love Over the nasty sty, Gertrude: O! speak to me no more; These words like daggers enter in mine ears; No more, sweet Hamlet! The excerpt supports the conclusion that Gertrude ignores what Hamlet says because she thinks hes crazy. cant bear listening to Hamlet because she knows hes right. has difficulty understanding Hamlet because hes yelling so loud. doesnt really pay attention to Hamlet because hes ranting. Will mark as Brainliest.Which of the following [H+] values describes the most acidic solution?10^- 1 M10^-7 M10^-12 M The coefficient of linear expansion of iron is 1.0 105 per C . The surface area of an iron cube, with an edge length of 5.0 cm, will increase by what amount if it is heated from 10 C to 60 C? The Lusiads is a Portuguese epic written by Luis De Camoes in the 16th century. It is a mythical account of the expansion of the Portuguese empire. The Portuguese have had a written language since the ninth century. Which poem does The Lusiads most resemble?The AeneidThe Odyssey What must occur after the president negotiates a treaty? In response to a set of ambiguous pictures, rita writes several stories in which the main characters desire to compete with some standard of excellence and surpass their own previous performances. psychologists in the tradition of henry murray, david mcclelland, and christiana morgan would be likely to characterize rita as rating high in Mayas bedroom is in the shape of a rectangular prism 15 feet long 12 feet wide and 10 feet high it has no windows Maya once to P allfour walls including the door in your ceiling where is the service area she will paint Which of the following bases can be ingested safely? aluminum hydroxide sodium hydroxide calcium hydroxide ammonia Diagnostic criteria for autism spectrum disorder do not includea. impairment in communication.b. restricted, repetitive, stereotyped behaviors.c. deficits in visual acuity.d. deficits in social relatedness. What statement best summarizes the relationship between photosynthesis and cellular respiration? Some penguins were playing on the ice. Ten of them dove in the water. A few seconds later, 6 of those penguins jumped back onto the ice. Now there are 12 penguins on the ice. How many penguins were on the ice to start? Use numbers, pictures,or words to show how you got the answer. A rectangularbroom has an area of 131 1/4 square feet. The length of the room is 12 1/2 feet. What is the width, in feet, of the room? Which terms describes a distributed data protection technology that leverages deep analysis, context evaluation, and rules configured from a central console to ensure confidential information remains secure while in use, in transit, and at rest? anti-forensics information technology infrastructure library (itil) digital forensic techniques data leakage prevention (dlp)? The larger square garden at Volterra Hall has sides twice as long as the smaller square garden. Together the gardens cover 18,000 square feet. Find the dimensions of each garden. Which excerpts from the passage provide strong evidence that Hrothgars hall is famous throughout the lands? Check all that apply.