If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?

Answers

Answer 1

There is a formula for finding the number of faces, edges, and vertices of any convex polyhedron. So if you don't know the shape you can use the formula.
V + F - E = 2
12 + F - 18 = 2
F - 6 = 2
add 6 to both sides
F = 8

CHECK:12 + 8 - 18 ??=?? 2
20 - 18 = 2 checks

Related Questions

At 2:00 Tony rented a mountain bike from the slick rock cyclery. He returned the bike at 5:00 after cycling 18 mi.Tony paid 24 for the rental. Find the rental rate in dollars per mile. Take the number of dollars and divide by the number rate mile

Answers

he paid 24 for the rental......he rode 18 miles...
24/18 = 1.33 per mile

that time that he rented it and returned it is just extra info that is not needed

A blue billiard ball with mass m crashes into a red billiard ball with the same mass that is at rest. The collision results in the blue billiard ball traveling with a velocity of v and the red billiard ball travelling with a velocity of 3v. In terms of v and m, determine the blue billiard ball’s velocity before the collision...

Answers

Draw a diagram to illustrate the problem as shown below.
Each ball has mass = m.
The initial velocity of the blue ball = u.
The initial velocity of the red ball = 0.

Initial total momentum is
P1 = m*u + m*0 = mu
Final momentum is
P2 = mv + 3mv = 4mv

Because momentum is conserved,
mu = 4mv
u = 4v

Answer:
The velocity of the blue ball before the collision is 4v.

Look at the figure. What is the next step in this construction of a line parallel to AC passing through point B.

A. use a protractor to measure ∠BAC

B. Draw a line through point B that intersects arc 2.

C. Measure the distance between AB and AC along arc 1 with a ruler.

D. Measure the distance between AB and AC along arc 1 with a compass.

Answers

B. Draw a line through point B that intersects arc 2

Answer:

Option A is correct

Step-by-step explanation:

In the given figure to draw the parallel line to AC passing through B we have to tell the next step.

As lines AC and AB given and we know if lines are parallel then alternate angles are equal.

Hence, if line through B parallel to AC drawn then alternate angles ∠BAC and ∠ABD equal.

∴ To draw parallel lines our next step is to use a protractor to measure ∠BAC so that the same angle through B is drawn results in equal alternate interior angles.

Hence, Option A is correct.

Jones is the chairman of a committee. in how many ways can a committee of 5 be chosen from 10 people given that jones must be one of them?

Answers

Since Jones is mandatory, you have 9 people to choose from for the second seat, then 8 for the third, 7 for the fourth, and finally 6 for the fifth.

So your equation is
1(Jones) • 9( possibilities left) •8( possibilities left)• 7( possibilities left)• 6( possibilities left)
Or

1 • 9 • 8 • 7 • 6
=
3,024 possible ways in which a committee of 5 can be chosen from 20 people given that Jones must be one of them.

Final answer:

A committee of 5 can be chosen in 126 different ways from 10 people if Jones must be one of them, by using the combination formula C(9, 4) to choose the remaining four committee members from the other nine people.

Explanation:

To determine in how many ways a committee of 5 can be chosen from 10 people given that Jones must be one of them, we need to apply the concept of combinations in probability and combinatorics. Since Jones must be on the committee, we are actually choosing the remaining 4 members from the remaining 9 people.

The number of ways to choose 4 people out of 9 is calculated using the combination formula, which is:

C(n, k) = n! / (k!(n - k)!), where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.

Applying this to our scenario:

C(9, 4) = 9! / (4! * (9 - 4)!) = 126

Therefore, there are 126 different ways to form the committee if Jones is already chosen as one member.

If the average price of four pairs of shoes is $50, and three of those pairs of shoes are priced at $35, $40 and $55, what is the price of the fourth pair of shoes?

Answers

The average price is calculated by dividing the sum of all prices with the number of items.
average price= price1+price2+...priceN/N
In our case , we have four pairs of shoes.So, N=4.
We also know the average price. average price=$50
We also know the price of the first pair of shoes (price1), of the second (price2) and the third (price3). We need to find out Price4:
$50=$35+$40+$55+Price4/4
50*4=$35+$40+$55+Price4
$200=$130+Price4
Price4=200-130
Price4=$70

PLEASE HELP ME FIGURE THIS OUT if i have 6 questions on a test, how many would i get wrong to get a score of 48%

Answers

if you get a score of 48% from 6, that means you've got 48% right, so the remainder is wrong, namely 100 - 48, or 52%.

now, how much is 52% of 6?

whatever% of anything is just (whatever/100) * anything.

thus 52% of 6 is just (52/100) * 6, that many.

In triangle KLM LM = 7 and angle k equals 45 Find KL.

Answers

Final answer:

In this problem, the student can use the properties of a 45°-45°-90° triangle to determine that the hypotenuse KL is 7 * √2 which is approximately equal to 9.9.

Explanation:

In a triangle where you know one angle (45°) and one side (7 units) across from the right angle, it is a typical example of a situation where trigonometry can be used. In this case, you're dealing with a 45°-45°-90° triangle, also known as an isosceles right triangle. In such a triangle, the sides are in a specific ratio. The sides opposite the 45° angles are the same length (let's call it 'a'), and the hypotenuse is a√2.

Given that LM = 7 and angle K is 45°, triangle KLM is therefore an isosceles right triangle and KL (the hypotenuse) is equal to LM multiplied by √2. So, KL = 7 * √2 which approximately equals to 9.9.

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A principal of $2600 is invested at 7.5% interest, compounded annually. How much will the investment be worth after 8 years?

Answers

To add 7.5% to a number you simply multiply the number by 1.075. To compound that amount year after year, you raise 1.075 to an exponent that corresponds to the number of years. 2600*(1.075^8)=4637.04234646

Give the number of significant figures in this number 34.20

Answers

Significant figures are important in reporting values especially in mathematics and chemistry. This is for the purposes of consistency and precision. When doing calculations, we sometimes round off numbers which affects the quality of our measurements. As a convention, significant figures are to be followed. There are three rules for significant figures.

1. All nonzero numbers are significant.
2. All zeros between nonzero numbers are significant.
3. All zeros after the decimal point are significant.

Following the rules, I think all of the numbers in 34.20 are significant. Thus, there are a total of 4 significant figures.

Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 – 25?
(x – 5)(x – 5)

(x + 5)(x + 5)

(x – 20)(x + 5)

(x – 5)(x + 5)

Answers

That is D
positive sign in one bracket and negative in the other

Answer:

its D

Step-by-step explanation:

Write the standard equation for the circle center (10,-6), r=6

Answers

The standard form of a circle is (x-h)²+(y-k)²=r², where h is the x-value of the center coordinate and k is the y-value.

Therefore, since the center is (10,-6), h=10 and k=-6. The radius is 6 which means r=6.

Substitute these values into the standard form equation.

(x-(10))²+(y-(-6))²=(6)²
(x-10)²+(y+6)²=36

Therefore, the standard equation for the circle centered at (10,-6) where r=6 is (x-10)²+(y+6)²=36.

Mr. Chavez spent $199.99 for a new smart phone, 3

Answers

Mr. Chavez spent $299.97 altogether. The estimated total matches approximately with the calculated total, confirming the accuracy of our answer.

To find the total amount Mr. Chavez spent, we need to add the costs of the smartphone, carrying case, and accessories.

Total amount = |-199.99| + |-39.99| + |-59.99|

Now, let's evaluate each absolute value:

|-199.99| = 199.99

|-39.99| = 39.99

|-59.99| = 59.99

Now, let's add them together:

Total amount = 199.99 + 39.99 + 59.99

Total amount = 299.97

So, Mr. Chavez spent $299.97 altogether.

Now, let's check the answer using estimation:

Round each amount to the nearest ten:

- $199.99 is approximately $200.00

- $39.99 is approximately $40.00

- $59.99 is approximately $60.00

Now, let's add them together:

Total estimation = $200.00 + $40.00 + $60.00

Total estimation = $300.00

The estimated total matches closely with the calculated total, confirming the accuracy of our answer.

The complete question is:

Mr. Chavez spent $199.99 for a new smart phone,$39 .99 on a carrying case, and $59.99 on accessories. The expression |-199.99|+|-39.99|+|-59.99| represents the total amount that Mr. Chavez spent. How much did Mr. Chavez spend altogether? Check your answer using estimation.

For what values of x is the rational expression below undefined?
Check all that apply.
x-4/3x^2-75
A. -3
B. -4
C. 3
D. -5
E. 4
F. 5

Answers

(x-4)/(3)(x+5)(x-5)

In order for the rational expression to be undefined, the denominator must be equal to 0.

Thus, set 3(x+5)9(x-5)=0

x=5 and -5

Joe and Mary each pay the same price for a T-shirt. Before they buy it, Mary has $\$ 2$ more than Joe. To buy the T-shirt, Joe spends $ \$1 $ less than $\frac{2}{5}$ of his money, and Mary spends $\frac{1}{3}$ of her money. What was the total amount of money Joe and Mary originally had altogether?

Answers

Let Joe initially have J dollars, and Mary have M dollars. Let the price of the T-shirt be T dollars.

i) "Before they buy it, Mary has 2$ more than Joe":

means M=J+2

ii)

"To buy the T-shirt, Joe spends 1 $ less than \frac{2}{5} of his money"

so [tex]T= \frac{2}{5}J-1 [/tex]

iii)

"Mary spends \frac{1}{3} of her money"

means [tex]T= \frac{1}{3}M [/tex]

equalize equations ii) and iii):

[tex]\frac{2}{5}J-1= \frac{1}{3}M[/tex] (they are both equal to T)

substitute M=J+2 from equation i:

[tex]\frac{2}{5}J-1= \frac{1}{3}(J+2)[/tex]

[tex]\frac{2J-5}{5}= \frac{J+2}{3}[/tex]

[tex]3(2J-5)=5(J+2)[/tex]

6J-15=5J+10
J=25

so M=25+2=27 (dollars)

Together Mary and Joe had 27+25=52 (dollars)

Answer: 52 $

Answer:

Step-by-step explanation:

Suppose Joe had $J$ dollars to start with. Then Mary had $J + 2$ dollars. Since they both spent the same amount on their shirts, $\frac{2}{5} J - 1 = \frac{1}{3} (J + 2)$. Distributing, we get $\frac{2}{5} J - 1 = \frac{1}{3}J + \frac{2}{3}$. Isolating $J$ on the left side, $\frac{1}{15}J = \frac{5}{3}$. Therefore, $J = 25$. Thus, their original total amount of money was $J + (J + 2) = \boxed{52}$ dollars.

Evaluate | 4t+n | if t=-2 and n=5

Answers

| 4t+n |

= | 4(-2) + 5 |
= | -8 + 5 |
= | -3 |
= 3

Please Help!! Find the measure of angle 2. Image Attached

Answers

opposite angles have to equal 180

so 180-111 = 69

angle 2 is 69 degrees

What is the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2?

Answers

[tex]\bf \qquad \qquad \textit{sum of a finite geometric sequence}\\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=3\\ r=\frac{1}{2}\\ n=8 \end{cases}[/tex]

[tex]\bf S_8=3\left( \cfrac{1-\left( \frac{1}{2} \right)^8}{1-\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{1-\frac{1^8}{2^8}}{1-\frac{1}{2}} \right) \\\\\\ S_8=3\left( \cfrac{1-\frac{1}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{\frac{255}{256}}{\frac{1}{2}} \right)\implies S_8=3\left( \cfrac{255}{256}\cdot \cfrac{2}{1} \right) \\\\\\ S_8=3\left( \cfrac{255}{128} \right)\implies S_8=\cfrac{765}{128}[/tex]

The sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625

Sum of geometric series

Series are the sum of sequences. The sum of geometric series is expressed as:

Sn = a(1-r^n)/1-r

Given the following

n = 8

a = 3

r = 1/2

Substitute

S8 = 3(1-(1/2)^8)/0.5
S8 = 3(1-1/256)/0.5
S8 = 3(255/256)/0.5
S8 = 5.9765625

Hence the sum of the first eight terms of a geometric series whose first term is 3 and whose common ratio is 1/2 is 5.9765625

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Your computer monitor has a width of 13.93 inches and a height of 10.45 inches. what is the area of the monitor display in square meters

Answers

The answer is: " 0.09391 m² " .
__________________________________________________
Explanation:
__________________________________________________
First, calculate the area in square inches:

(13.93 in) * (10.45 in) = 145.5685 in² .

Now, convert this value into "square meters" (or: " m² ") .
__________________________________________________
Note: 0.00064516 square meters = 1 square inch .

So: 145.5685 in² * (0.00064516 square meters / 1 in²) =
___________________________________________________
         = [ (145.5685) * (0.00064516) ] m² ;

         = 0.09391497346 m² ; round to: " 0.09391 m² " .
___________________________________________________

Final answer:

The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.

Explanation:

To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.

Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.

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Thomas buys a cardboard sheet that is 8 by 12 inches. Let x be the side length of each cutout. Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.

Answers

Volume of the box = area of the base * height

Side of each cutout = x

Length of the base = 12 - x - x = 12 - 2x

width of the base = 8 - x - x = 8 - 2x

area of the base = (12 - 2x) (8 - 2x) = 12*8 - 12*2x - 8*2x + 4x^2 = 96 - 40x + 4x^2

height = x

Volume = (96 - 40x + 4x^2) x = 96x - 40x^2 + 4x^3

Equation of the volume of the box = 96x - 40x^2 + 4x^3

Zeros of the function: use the factored form:

x (12 - 2x) (8 -2x) = 0

=> x = 0, x = 6 and x = 4

Sketch of the graph:

The graph comes growing from (- infinity, -infinity), crosses the origin (0,0), grows until a local maximum before 2, starts to decrease, intercepts the x axis at x = 4, continues decreasing until a local minium before 6, starts to increase again, crosses the x axis at x = 6, and continues increasing toward infinity. If you are using derivatives, you can find the local minimum and maximum.

Answer:

Step-by-step explanation:

Any equation that is equivalent to V = x(12 - 2x)(8 - 2x) is accepted. Any graph that is similar to the graph of the function is accepted.

Sample Student Response:

The box is a cube, so the volume is the length × width × height. The height is the side length of the cardboard, which is x.

The length is the original length minus two side lengths of the cutout, so the length is 12 - 2x.

Similarly, the width is the original width minus two side lengths of the cutout, so the width is 8 - 2x.

HELP! What is the volume of the regular pyramid below????

Answers

B. 3408 units cubed
hope this helped!

Use the drop-down menus to complete each statement to show why √21 is between 4 and 5.

Answers

Answer:

To show: [tex]\sqrt{21}[/tex] is between 4 and 5

We know:

21 is lies between two consecutive integer i.e, 16 and 25

We can write this as:

[tex]16 < 21 < 25[/tex]

[tex]\sqrt{16} <\sqrt{21}<\sqrt{25}[/tex]

Simplify:

[tex]4 < \sqrt{21} < 5[/tex]

⇒[tex]\sqrt{21}[/tex] lies between 4 and 5.

Therefore, [tex]\sqrt{21}[/tex] is between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] this means [tex]\sqrt{21}[/tex] lies between 4 and 5.

Answer:

We know that

[tex]16<21<25[/tex]

Because, 16 is less than 21 and 25 is more than 21.

Now, if we apply a square root to each part, we would have

[tex]\sqrt{16} < \sqrt{21}<\sqrt{25}[/tex]

Then, we solve each square root, except the square root of 21, because it doesn't have an exact result

[tex]4<\sqrt{21}<5[/tex], because [tex]\sqrt{16}=4[/tex] and [tex]\sqrt{25}=5[/tex]

So, basically, the reason why [tex]\sqrt{21}[/tex] is between 4 and 5 is beacuse 21 is between 16 and 25. Then, when you apply square roots to each part, you would find that the square root of 21 is between 4 and 5. That's the reason, the position.

X+y=13and x-y=2 what is the value of x^2-y^2

Answers

x+y=13
x-y=2

Add the equations (elimination method)

x+y+x-y=13+2
2x=15
x=7.5

Plug in this y value

7.5-y=2
-y=-5.5
y=5.5

Plug in both the x and y values into the equation asked for

(7.5)^2-(5.5)^2
56.25-30.25

Final answer: 26

just a quick sidenote.

[tex]\bf \textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b)\\\\ -------------------------------\\\\ x+y=13\qquad x-y=2 \\\\\\ x^2-y^2\implies (x+y)(x-y)\implies (13)(2)[/tex]

Solve the inequality. Graph the solution set. 26+6b (>=) 2(3b+4 A. All real numbers b. b> or less than 1/2 c. no solutions

Answers

i got c because when you solve theres no solution

B no solutions is incorrect.

To take a taxi, it costs $3.00 point plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel?

Answers

You would have traveled 4.2 miles.

A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 200 pounds requires 250 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?

Answers

It should be 176, hope this helps!

How many hours are in 2 weeks?

Answers

24 hours in a day* 14 days in two weeks= 336 hours total

Final answer: 336 hours

First, to find how many hours are in a week, we need to break a week into hours. We can break a week down into days, which is seven. And, since there are 24 hours in a day, we can find how many hours there are in a week by multiplying the hours by days, 24*7 = 168. So, now that we know there are 168 hours in one week, and we need to know two weeks, we just need to multiply the one week (168 hours) by two: 168*2 = 336. So, there are 336 hours in two weeks, hope this helps and don't forget to drop a like.

In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080% confidence interval for the population mean muμ. what is the margin of error of muμ? interpret the results.

Answers

The margin of error can be calculated using the t statistic. The formula for margin of error is given as:

Margin of error = t * s / sqrt (n) ---> 1

Where,

t = the t score based on the given confidence level and degrees of freedom

n = number of samples = 21

s = standard deviation = 7.1

Degrees of freedom = n – 1 = 21 – 1 = 20

Based on the standard probability tables for t, the t score is:

t = 0.860

Substituting into equation 1:

margin of error = 0.860 * 7.1 / sqrt (21)

margin of error = 1.33

The range is:

range = 30.1 ± 1.33

range = 28.77, 31.43

Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.

For her phone service, Kala pays a monthly fee of $13 , and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $63.15 . What are the possible numbers of minutes she has used her phone in a month? Use m for the number of minutes, and solve your inequality for m .

Answers

The inequality would be 0.05m + 13 >= 63.15. Solving:
0.05m >= 50.15

m >= 1003 minutes

Therefore at least 1003 minutes were consumed to be billed $63.15 or more.

Hope this helps.

Need help on 4.9.2 project: performance task: the subway stop

Answers

Final answer:

The subject of this question is Mathematics.

Explanation:

The subject of this question is Mathematics.

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The roots of the equation are 3 + 8i and 3 – 8i.

What is the value of c?

x2 – 6x + c = 0

c = [1]

Answers

Given that the roots of the equation x^2-6x+c=0 are 3+8i and 3-8i, the value of c can be obtained as follows;
taking x=3+8i and substituting it in our equation we get:
(3+8i)^2-6(3+8i)+c=0
-55+48i-18-48i+c=0
collecting the like terms we get:
-55-18+48i-48i+c=0
-73+c=0
c=73
the answer is c=73

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