Answer:
Step-by-step explanation:
Let
V
be the number of vertices of a polyhedron,
F
the number of faces of that polyhedron, and
E
be the number of edges. The quantity
χ
=
V
−
E
+
F
is called the Euler characteristic (of a polyhedron). In the case of convex polyhedra,
χ
=
2
.
Consider, for example, a tetrahedron (which is the simplest solid). It has 4 faces,
1
2
(
4
)
(
3
)
=
6
edges, and
1
3
(
4
)
(
3
)
=
4
vertices. Thus we have
V
−
E
+
F
=
4
−
6
+
4
=
2
.
Euler's formula holds for all Platonic solids (tetrahedron, cube, octahedron, dodecahedron, and icosahedron). Since a cube and an octahedron are dual polyhedra (each is formed by connecting the centers of the faces of the other), their
V
and
F
values are equal to the
F
an
V
values of the other. (The same is true for the dodecahedron and icosahedron).
To protect your town from a possible zombie invasion, your city council decides to build a wall. The Waters Proposal suggests building a wall 20 feet tall that the would weigh approximately 43275 tons. A second proposal, the Barrett Proposal, says that 20 feet is too short, and the wall in the Waters Proposal is also not long enough or thick enough to keep out zombies. He suggests scaling up the wall, i.E increasing all the dimensions of the wall by the same percentage. Under this plan, the height of the wall would be 34 feet tall and the new perimeter would be 9809 feet long. What would the perimeter of the wall under the Waters Proposal be? feet.
Answer:
5770 feet
Step-by-step explanation:
The height of the wall under the Waters proposal is 20 feet and the height of the wall under the Barrett proposal is 34 feet and its perimeter is 9809 feet. Since there is an increase in the dimensions of the wall, we find this percentage increase.
So, the percentage increase in the height of the wall is thus (New height - Old height)/Old height × 100%
New height = 34 feet and Old height = 20 feet
So, Percentage increase = (New height - Old height)/Old height × 100% = (34 ft - 20 ft)/20 ft × 100 % = 14/20 × 100% = 7/10 × 100% = 70 % increase.
Since all the dimensions increase by the same amount, the perimeter in the Waters proposal increases by 70% to the perimeter in the Barrett proposal.
Let P = perimeter in the Waters proposal and P' = perimeter in the Barrett proposal.
So, the percentage increase in perimeter is
(P' - P)/P × 100 % = 70 %
We now find P
(P' - P)/P = 70%/100%
(P' - P)/P = 0.7
P' - P = 0.7P
P' = 0.7P + P
P' = 1.7P
P = P'/1.7
So, substituting the value for P' = 9809 feet
P = P'/1.7
= 9809 ft/1.7
= 5770 feet
So, the perimeter of the wall under the Waters Proposal is 5770 feet.
What is: 8% of $450?
Answer:
36$
Step-by-step explanation:
Answer:
36 next time use a calculator
The average cost of tuition and room and board at a small private liberal arts college is reported to be $8,500 per term. A financial administrator believes that the average cost is higher. A study conducted using 350 small liberal arts colleges showed that the average cost per term is $8,745. The population standard deviation is $1,200. Let α
Answer:
D. +3.82
Step-by-step explanation:
The computation of the test static for this test is shown below:
Data provided in the question
[tex]\bar x[/tex]= $8,745
[tex]\mu[/tex] = $8,500
[tex]\sigma[/tex] = $1,200 and n = 350
Now based on the above information, the test static for this test is
[tex]z = \frac{\bar x - \mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
[tex]z = \frac{\$8,745 - \$8,500}{\frac{\$1,200}{\sqrt{350} } } \\[/tex]
= 3.82
= +3.82
Hence, the test static for this test is +3.82
We simply applied the above formula so that the correct value could come
And, the same is to be considered
PLEASE HELP WITH #6 and #8, DUE SOON!!
how do i answer that I don't even know that sorry
Answer:
I would say triangle VQB is congruent to triangle TJE. Not entirely sure about the transformation, try reflecting it over y=x or y = -x,, translate it, and rotate it
(Can't look at it right now fully cause i have my own math hw to do lol)
For 8, FAKE is congruent to CMDI, (Transformations from FAKE to CMDI) then its a reflection over the y axis, and reflect over the x axis.
Step-by-step explanation:
:)
#teamtrees #WAP (Water and Plant)
ok so i rlly need help with number 8 and 9. as a class the teacher did 10 and ik she went up by 3’s but why like i just need help (i will make u brainliest)
Step-by-step explanation:
y = 2x + 6 means that the letter Y equals 2x plus 6. So add 2 and 6 which gives you 8 and you are with this: 8x or 8(x). If your teacher gave you the value of X multiply 8 by x since the eight is outside its parenthesis. Once you have that answer or just 8X put the result of 8x in the y box and the 8x in the x box (skip count from ther of which the value ur teacher gave u)
Use the same context with the next problem. Hope this helps.
If 5 pounds of avacodo cost $9 how much will 1 pound of avocados be?
Answer:
1.8
Step-by-step explanation:
5 divided by 5 is 1, 9 divided by 5 is 1.8
Answer:
Step-by-step explanation:
5 pounds of avacodo=$9. 1 pound of avacodo= $(9 divided by 5). so 1 pound of avocado = $1.8
A 2-column table with 5 rows. Column 1 has entries x, x, x, x, Total 100 percent. Column 2 has entries 5 dollars, 5 dollars, 5 dollars, 5 dollars, Total 20 dollars. Mia bought a poster that was discounted $5 from an original price of $20. Which equation models how Mia can find the percent of discount? $5 = x ?- $20 $5($20) = x $5 = $20(x) $5(x) = $20
Answer:
c
Step-by-step explanation:
A
If the contractor cuts the tile along one of its diagonals, what figures result?
A. two triangles that are similar but not congruent
B. two congruent triangles
C. two quadrilaterals that are similar but not congruent
D. two congruent quadrilaterals
Plz help and explain
Answer:
p(x) = (x-a)(x-b)(x-7) - a and b can be whatever you want, any real numbers
Step-by-step explanation:
If you plug in 7, you need to multiply the other two numbers by 0, which will result in 0. There are 3 factors since it must be a 3rd degree polynomial
Hope this helps! Please give brainliest!
solve each equation by substitution
1, y=6x+14
6x+5y=-2
2 y=-2x-2
y=-4x+4
3, x-5y=-20
7x+3y=12
i need the equation too
Step-by-step explanation:
here it is.Hope it helps
Combine like terms:
12a + 3b - 4a + 19 - b
Answer: 8a + 2b + 19 is the answer
Answer:
= 8a +2b + 19
Step-by-step explanation:
Combine Like Terms:
(12a + −4a) + (3b + −b) + (19)
=8a + 2b + 19
Find the range of the function y =-x^2-3x when the domain {-5, 0, 2}
Answer:
Range: [−94,∞),{y∣y≥−94}
Answer:
5
Step-by-step explanation:
Leo learns to perform 2 vocal pieces during each week of lessons. After 16 weeks of voice lessons, how many pieces will Leo be able to sing,in total? pls answer
Step-by-step explanation:
I. A Child’s Voice
One common mistake that adults make when singing with children is that they tend to “pitch” the songs, (or sing them in a key), that is comfortable for themselves, but unfortunately, out of a comfortable singing range for the children. Adults sing in much lower range than children, therefore pitching a song too low causes children to be unsuccessful at reaching some of the lower notes.
Pitching a song in the wrong range can have significant negative consequences on a child’s musical self-esteem. An incorrect key can take away the child’s ability to sing the song well or sing the song at all. Singing in a key that is out of a child’s range would be analogous to an art teacher giving a creative assignment to students and then placing all of the art materials up on a shelf out of reach for most of them. While a few might be tall enough, most won’t be. After a while, they will give up trying to reach the material altogether. Similarly, these are the students who start to believe that they can’t sing at all, and give up on music.
Good Singing
Although we are used to hearing and singing pop music, a child’s voice is not yet ready to sing songs either with such a wide vocal range or with the sophisticated vocal stylings or timbre that he or she might try to imitate from pop singers. As children’s voices are very light, they should not be pushed out of their vocal ranges too soon. Using a clear, clean, straight head voice rather than chest voice will help to avoid this, and will strengthen a child’s vocal musculature for a lifetime of excellent singing.
One good habit to help children sing well is to ask them sing in their head voice rather than their chest voice. Although most songs children hear are pop songs that are placed in the chest, a child’s voice is not yet developed, and should not be belting out or pushing from the lower range or chest voice. Head voice requires placing the sound higher up in the “vocal mask” or the face, as if singing from the eyes. Chest voice feels like the sound is emanating from the chest, which tends to create a lot of tension in the throat, particularly in younger singers. The head voice is lighter, more tension-free, and more natural and therefore more beautiful sounding.
Children’s Vocal Ranges
Below are the general ranges of a child’s voice.
Find the measure of angle a and b?
The correct answer of this question is;
A=(2x+4)
=2×37+4
=78
B=(2x-9)
=2×37-9
=65
Step-by-step explanation:
(2x+4)+(2x-9)+x=180(The sum of all angle of a triangle is 180°)
or,5x-5=180
or,5x=185
or,x=185/5
Therefore the value of x=37.
At the end of the summer, lawn furniture
selling at a market price of $482 is on sale
for 20% off. What is the discount?
Answer:
Final Price = $385.60
You save = $96.40
Step-by-step explanation:
Discount = Original Price x Discount %/100
Discount = 482 × 20/100
Discount = 482 x 0.2
You save = $96.40
Final Price = Original Price - Discount
Final Price = 482 - 96.4
Final Price = $385.60
Answer: $385.60
Step-by-step explanation:
1. 20% x 482
= 0.2 x 482
= $96.40
2. 482 - 96.4
= 385.6
= $385.60
The lawn furniture now costs $385.60.
MONEY Sadie has $22.75 in her school lunch account. If she wants the money to last for this 5-day week of school, determine the appropriate
amount she should spend each day. $________?
I’m confused
Answer:
The most she can use in a day is $4.55.
Step-by-step explanation:
The explanation is simple.
22.75 divided by 5 = 4.55
Mark as Brainliest!
Answer:
$4.55
Step-by-step explanation:
All you do is take the total amount Sadie has right now and divide it by how many days it needs to last.
$22.75/5=$4.55
So Sadie can only spend $$.55 a day for the 5 days.
Suppose the diameter of a circle is \color{green}{4}4start color green, 4, end color green units. What is its circumference?
Answer: 12.56 units
Step-by-step explanation:
Malique wants to take four of his friends to a movie. He knows it is $7.50 for
a ticket and $3.25 for popcorn. How much will it cost if he pays for the
movie and a popcorn for all five people? Explain your answer.
Answer:
$16.25
Step-by-step explanation:
7.50
+7.50
+7.50
+7.50
+7.50
36.50
then you have to do 3.25 *5=16.25
Part B
Notice that two line segments are formed on each transversal between the central parallel line and the outer parallel
lines. Measure the lengths of the four line segments.
ANSWER. Part b
Line segment PM = 2.2 length
ML = 2.2
ON = 2
NK = 2
Answer:60
Step-by-step explanation:
Can somebody please help me with this math question
Dc=ac
Step-by-step explanation:
A blueprint for a building includes a rectangular room that measures 3 inches long and 5.5 inches wide. The scale for the blueprint says that 1 inch on the blueprint is equivalent to 10 feet in the actual building. What are the dimensions of this rectangular room in the actual building? (Hint; dimensions means both how long and how wide)
Answer:
30 ft. x 55ft
Step-by-step explanation:
3 x 5.5
1 inch = 10 ft
3 * 10 = 30
5.5 = 55
30' x 55'
Hi pls help me on this!
What is TR(453) - TR(450)?
Answer:
1356
Step-by-step explanation:
453*454 divided by 2 then 450*451 divided by two then minus both
Can someone please help me with this last one. I am totally lost and don’t understand
Answer:
g(-4) = -1
g(-1) = -1
g(1) = 3
Explanation:
If you are given a function that is defined by a system of equations associated with certain intervals of x, just find which interval makes x true, and then substitute x into the equation of that interval.
For example, given g(-4), this is an expression which is asking for the value of the equation when x = -4. So -4 is not ≥ 2, so ¼x - 1 will not be used. -4 is also not ≤ -1 and ≤ 2, so -(x - 1)² + 3 will not be used either. So in turn, we will just use -1 which is always -1 so g(-4) will just be -1, right because there is no x variable in -1 so it will always be the same.
Using the same idea as before g(-1) is g(x) when x = -1 so -1 will not be a solution because -1 is not less than -1 (< -1). -1 is not ≥ 2 either so we will be using the second equation because -1 is part of the interval -1≤x≤2 (it is a solution to this inequality), therefore -(x - 1)² + 3 will be used.
As x = -1, -(x - 1)² + 3 = -(-1 - 1)² + 3 = -(-2)² + 3 = -4 + 3 = -1.
It is a coincidence that g(-1) = -1.
Now for g(1), where g(x) has an input of 1 or the value of the function where x = 1, we will not use the first equation because x = 1 → x < -1 → 1 < -1 [this is false because 1 is never less than -1], so we will not use -1.
We will use -(x - 1)² + 3 again because 1 is not ≥ 2, 1≥2 [this is also false]. And -1 ≤ 1 < 2 [This is a true statement]. Therefore g(1) = -(1 - 1)² + 3 = -(0)² + 3 = 3
Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning." These words begin a report on a statistical study of the effects of logging in Borneo. Here are data on the number of tree species in 12 unlogged forest plots and 9 similar plots logged 8 years earlier:
Col1 Unlogged 2218 222015121 13 13 1913 19 15
Col2 Logged 17 4 181418151510 12 Use the data to give a 90% confidence interval for the difference in mean number of species between unlogged and logged plots. Compute degrees of freedom using the conservative methoo. Interval: ________to__________.
Answer: -8.16 to 15.84
Step-by-step explanation: Confidence Interval is an interval in which we are a percentage sure the true mean is in the interval.
A confidence interval for a difference between two means and since sample 1 and sample 2 are under 30, will be
[tex]x_{1}-x_{2}[/tex] ± [tex]t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }[/tex]
where
x₁ and x₂ are sample means
t is t-score
[tex]S_{p}[/tex] is estimate of standard deviation
n₁ and n₂ are the sample numbers
The estimate of standard deviation is calculated as
[tex]S_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2} }[/tex]
where
s₁ and s₂ are sample standard deviation of each sample
Degrees of freedom is:
[tex]df=n_{1}+n_{2}-2[/tex]
df = 12 + 9 - 2
df = 19
Checking t-table, with 90% Confidence Interval and df = 19, t = 1.729.
The mean and standard deviation for 12 unlogged forest plots are 17.5 and 3.53, respectively.
The mean and standard deviation for 9 logged plots are 13.66 and 4.5, respectively.
Calculating estimate of standard deviaton:
[tex]S_{p}=\sqrt{\frac{(12-1)(3.53)^{2}+(9-1)(4.5)^{2}}{12+9-2} }[/tex]
[tex]S_{p}=\sqrt{\frac{299.07}{19} }[/tex]
[tex]S_{p}=[/tex] 15.74
The difference between means is
[tex]x_{1}-x_{2}[/tex] = 17.5 - 13.66 = 3.84
Calculating the interval:
[tex]t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }[/tex] = [tex]1.729.15.74.\sqrt{\frac{1}{12} +\frac{1}{9} }[/tex]
[tex]t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }[/tex] = [tex]27.21\sqrt{\frac{21}{108} }[/tex]
[tex]t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }[/tex] = [tex]27.21\sqrt{0.194}[/tex]
[tex]t.S_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}} }[/tex] = 12
Then, interval for the difference in mean is 3.84 ± 12, which means the interval is between:
lower limit: 3.84 - 12 = -8.16
upper limit: 3.84 + 12 = 15.84
The interval is from -8.16 to 15.84.
What is the slope of the line?
y - 4= -7(2 – 6)
Answer:
-7
General Formulas and Concepts:
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate
y₁ - y coordinate
m - slope
Step-by-step explanation:
Step 1: Define function
y - 4 = -7(x - 6)
Step 2: Break function
Point (4, 6)
Slope m = -7
For which equation is m = 10 a solution?
Answer:
incomplete question
Step-by-step explanation:
Find the missing side length of the triangle.
b
0.3 cm
0.5 cm
Answer:
0.8
Step-by-step explanation:
because you just had to add
Answer: 0.4
Step-by-step explanation: picture below
Use the function g(x)=5x−2 to complete the table. please help
Answer:
g = 5x-2
Step-by-step explanation:
GUYS PLZ HELP MATH CLASS THIS QUESTION IS WORTH 15 #)
Answer:
option b is the correct answer
225 feet for 3 minutes
for 1 minute, 225/3
=75
At a school fete, Nicole buys 5 books and 2 CDs for $50, and Sharyn buys 2 books and 3 CDs for $31. Find the price of
i. A book
ii. A CD
Answer:
Book = $8 each
CD = $5 each
8 x 5 = 40
2 x 5 = 10
= 50
8 x 2 = 16
5 x 3 = 15
= 31
Please mark as brainliest.
Answer:
One book equals $8 and one CD equals $5
Step-by-step explanation:
Let books be denoted as 'x' and CDs as 'y'
5x + 2y = 50 ...1
2x + 3y = 31 ...2
I usually eliminate the y variable, and to do this, you multiply the first equation by 3 and the second equation by 2, because the lowest common multiple between 2 and 3 is 6.
...1*3 and ...2*2
15x + 6y + 150 ...3
4x + 6y = 62 ...4
Eliminate y by taking ...4 away from ...3
15x - 4x = 150 - 62
11x = 88
x = 8
Sub this value into ...1
5(8) + 2y = 50
40 + 2y = 50
Rearrange
2y = 50 - 40
2y = 10
y = 5
This means that one book is $8 and one CD equals $5