How many times does the pyramid fit in the cube of both bases and height are the same?
Answers
If the base is 120×120
120
×
120
units, and the height is 120
120
units, with the summit directly above the center of the base, then each side has a slope of 2
2
: one unit towards the center, the side wall rises by two units.
This means that at height 5
5
above the base, each side is 5×12=2.5
5
×
1
2
=
2.5
inwards, i.e. 115×115
115
×
115
in area, because each of the four sides (north, south, east west) is inwards by that amount. In other words, the bottommost layer of 5×5×5
5
×
5
×
5
blocks covers 115×115
115
×
115
unit area of the base, and thus consists of 23×23
23
×
23
blocks.
The next layer of blocks is similarly smaller, covering a 110×110
110
×
110
area on top of the previous layer of blocks, i.e. one block less in both directions, consisting of 22×22
22
×
22
blocks. (You might note that the center of each block in the upper layer is at the corners of four blocks in the lower layer, although it does not affect the math here at all.)
This continues upwards, with the 23rd layer having just one block. Note that since 23×5=115
23
×
5
=
115
, the summit of the pyramid (a rectangular pyramid itself, of course, with base 5×5
5
×
5
on top of the topmost block, and height another 5
5
) is empty; it does not have enough room to contain even a single block.
If we count the number of blocks in each layer, we get
=23×23+22×22+21×21+…+1
N
=
23
×
23
+
22
×
22
+
21
×
21
+
…
+
1
That is not too hard to do by hand (or, better, calculator; or even with 2×2 Lego bricks), but mathematically we can also say that
=∑=1232
N
=
∑
i
=
1
23
i
2
As it happens, it is already known (in lists of known sums) that
∑=12=16(+1)(2+1)
∑
i
=
1
n
i
2
=
1
6
n
(
n
+
1
)
(
2
n
+
1
)
and therefore
=16×23×24×47=4324
Related Questions
A sales manager wanted to determine if increasing sales commissions by 5% would increase employee satisfaction. Her analyst determined the p-value was 0.04. (Use α = 0.05.)
Based on the above output, what is the correct conclusion for the Wilcoxon Signed Rank Test?
a. We do not have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
b. We do not have evidence that there is a difference in sample median employee satisfaction rating before and after the commission change.
c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
d. We have evidence that there is a difference in sample median employee satisfaction rating before and after the commission change.
Answers
Answer:
c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
Step-by-step explanation:
Pvalue is less than the alpha-level:
If the pvalue is less than the alpha-level, we have that there is sufficient evidence of the hypothesis for the population mean/median/standard deviation we are testing.
In this question:
Pvalue less than the alpha-level, so there is evidence that there is a difference in the population median. This means that the correct answer is given by option C.
The correct conclusion is: c. We have evidence that there is a difference in population median employee satisfaction rating before and after the commission change.
The given parameters are:
[tex]\mathbf{p = 0.04}[/tex] --- the p-value
[tex]\mathbf{\alpha = 0.05}[/tex] --- the significance value or the alpha level
From the options, we understand that the test parameter is the population median
By comparison, the p-value (0.04) is less than the alpha level (0.05)
When the p-value is less than the alpha-level, then it means that there is enough evidence of the hypothesis for the population parameter that is being tested.
Since the p-value is less than the alpha level, then it means that there is enough evidence to show the difference in the population median.
Hence, option (c) is correct
Read more about hypothesis testing at:
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The diagram shows three forces being applied to a crate on a floor. If the crate is to remain stationary, what amount of force must be applied for z?
Answers
Answer:
800 N
Step-by-step explanation:
I don’t know I just submitted it and that was the answer
Someone please help me! Write the equation in standard form!
Answers
Answer:
x^2+y^2=6^2
Step-by-step explanation:
The equation of a circle is (x-h)^2+(y-k)^2=r^2
where h is the x coordinate of the center, k is the y coordinate of the center, and r is the radius of the circle.
We can see the center is on 0,0, and the radius is 6, so our equation is
(x-0)^2+(y-0)^2=6^2
or
x^2+y^2=6^2
Answer:
[tex] x ^2 + y^2 = 36 [/tex]
Step-by-step explanation:
Center of the circle (h, k) =(0, 0)
Radius of the circle (r) = 6 units
Equation of circle in center radius form is given as:
[tex] (x-h) ^2 + (y-k) ^2 = r^2 [/tex]
[tex] (x-0) ^2 + (y-0) ^2 = (6)^2 [/tex]
[tex] x ^2 + y^2 = 36 [/tex]
PLEASE HELp ME U GET ALOT OF POINTS 97points
circumference and Area of circles
7. Demi measured the wheels on her brother's wagon. The diameter of each
wheel is 15 inches. To the nearest inch, how far will the wagon travel each
time the wheels make a complete turn?
8.The radius of circle A is 6 ft. The diameter of circle B is 6 ft. To the nearest
foot, how much greater is the circumference of circle A as compared to the circumference of circle B?
9. The larger circle in the design at the right has a radius of 40 in.
What is the area of the shaded part of the design?
30 in.
10. Max knows that the circumference of a circular pool is 12 ft.
He estimates that the diameter of the pool is between 3 ft and 4 ft. Is this reasonable? Explain.
Answers
Answer:
#7
C = πd = 3.14*15 in = 47 in (rounded)#8
C₁ = 2πr = 2*3..14*6 ft = 37.68 ftC₂ = πd = 3.14*6 ft = 18.84 ftThe difference:
C₁ - C₂ = 37.68 - 18.84 = 19 ft (rounded)#9
No picture attached#10
C = 12 ftd = C/πd = 12/3.14 = 3.82 ft3 ft < 3.82 ft < 4 ftMax is right
Need work to be shown as well
Answers
Answer: [tex]40yd^{2}[/tex]
Step-by-step explanation:
area for square
4(4)=16
area for triangle (1/2bh)
(8)(6)/2
48/2
24
now adding
[tex]24+16=[/tex] [tex]40 yd^{2}[/tex]
X 3.5.PS-12
Question Help
A department store buys 400 shirts at a cost of $9,600 and sells them at a selling price of $30 each.
Find the percent markup.
The percent markup is
%. (Round to the nearest whole number as needed.)
Answers
Answer:
The percent markup is 25%.
Step-by-step explanation:
Percent markup:
The percent markup is given by the difference in selling price and buying price multiplied by 100% and divided by the buying price.
A department store buys 400 shirts at a cost of $9,600
This means that the buying price is:
$9600/400 = $24
Find the percent markup.
Buying price: $24
Selling price: $30
30 - 24 = 6
6*100%/24 = 25%
The percent markup is 25%.
20, 10, 40, 10, 60, 20, 80, 60,
100, 240, 120, ______,_____
Answers
Answer:
1200, 140
Step-by-step explanation:
for easier: (20), 10, (40), 10, (60), 20, (80), 60, (100), 240, (120), 1200, (140)
numbers already (), add 20 per number
=== so (20, 40, 60, 80, 100, 120, answer 140)
numbers that are not turned () are 10x1x2x3x4x5
=== so 10, 10, 20, 60, 240, 1200
Answer:
2400, 140
Step-by-step explanation:
Hope it helps :)
Alexandra invested $610 in an account paying an interest rate of 7 3/8% compounded
daily. Madeline invested $610 in an account paying an interest rate of 7 7/8%
compounded continuously. After 16 years, how much more money would Madeline
have in her account than Alexandra, to the nearest dollar?
Answers
Exact answer: 165.5754
Rounded to the nearest dollar: 166
Find the volume (in cubic feet) of a rectangular moving van with length 12 feet, width 6 feet, and height 6 feet.
Answers
Answer:
Step-by-step explanation:
V = L * W * H
L = 12
W = 6
H = 6
Volume = 12 * 6 * 6
Volume = 432 cubic feet
Answer:
432 cubic feet
Step-by-step explanation:
To find the volume of a retangular prism or a rectangle you use L x W x H so that would be 12 x 6 x 6 which is 432. So the volume is 432 cubic feet
Lu is graphing the ordered pair (3, 5). Starting at the origin, what does she need to do?
Answers
Answer:
Lu needs to move the right 3 units and up 5 units.
Step-by-step explanation:
Someone please answer this corectly!!
Answers
Answer:
I think the answer would be
8 < Rad 70 < 9
Step-by-step explanation:
Hope it was correct & helpful ^__^ .
find the missing length?
Answers
Answer:
16
Step-by-step explanation:
If triangle GFE is similar to triangle RST, using the similarity theorem
RS/RT = GF/EF
Using pythagoras theorem;
RT² = 10² - 6²
RT² =100 - 36
RT² = 64
RT = √64
RT = 8
Recall that RS/RT = GF/EF
10/8 = 20/EF
Cross multiply
10EF = 8 * 20
10EF = 160
EF = 160/10
EF = 16
Hence the missing length is 16
Maryam has a coupon for 33% off her entire meal of 232.88 what is the discount.
help!
Answers
Answer:
$156.03
Step-by-step explanation:
33% = 33/100 = 0.33
First, multiply the total cost with 0.33:
232.88 x 0.33 = ~76.85 (round).
Subtract 76.85 from the original cost ($232.88):
232.88 - 76.85 = 156.03
Maryam's meal will cost $156.03 after the discount.
~
At a casino, people line up to pay $20 each to be a contestant in the follow- ing game: The contestant flips a fair coin repeatedly. If she flips heads 20 times in 20 mil a row, she walks away with lion dollars; otherwise she walks away with R 0 dollars
(a) Find the PMF of R, the reward earned by the contestant.
(b) The casino counts "losing contestants who fail to win the 20 million dollar prize. Let L equal the number of los- ing contestants before the first winning contestant. What is the PMF of L?
(c) Why does the casino offer this game?
Answers
Answer:
a)
P ( R = 20 million ) = 0.00000095367
P ( R = 0 million ) i.e. not winning = 0.99999904633
b) P ( L ) = ( 1 - p )^l * p
C)The casino offer the game because the expected revenue exceeds the winning
Step-by-step explanation:
P( winning ) = P ( getting 20heads in a row ) = 0.5^20 = 0.00000095367
a) PMF of R
P ( R = 20 million ) = 0.00000095367
P ( R = 0 million ) i.e. not winning = 0.99999904633
b) what is the PMF of L
L = number of loosing clients before winning
P( L = 0 ) = P i.e. if first contestant wins, if the second contestant win, L=1 repeat same process continuously
P ( L = 2 ) = ( 1 - p)^2 p
Hence the PMF of L
P ( L ) = ( 1 - p )^l * p where p = 0.5^20
C) The casino offer the game because the expected revenue exceeds the winning
we can prove this using the relation below
E( L ) = ( 1 - P ) / 1 - ( 1 - P )
= 1 / P - 1
where p = 0.00000095367 ( probability of winning )
Hence E ( L ) = 1048575
hence expected revenue before someone wins
= (1048575 + 1 ) * 20 = $20,971,520
Answer al 4 question and I’ll give your Brainly
Answers
Answer:
C-C-B-D
Step-by-step explanation:
Hope this helps and look out for people trying to take your points!
Will give brainliest for correct answer
Answers
Answer:
4 = function
5 = function
6 = not a function
Step-by-step explanation:
The first two pass the vertical line test
while the last ne doesn't
This sphere has a radius of 3 cm. What is the surface area of the sphere?
Answers
The required surface area of the sphere is given as 113.1 cm².
Given that,
This sphere has a radius of 3 cm. The surface area of the sphere is to be determined.
Surface area is defined as the measure of a region or surface is called as surface area.
Here,
The surface area of the sphere is given as,
The surface area of the sphere = 4πr²
= 4 × 3.14 × 3²
≈ 113.1
Thus, the required surface area of the sphere is given as 113.1 cm².
Learn more about surface area here: https://brainly.com/question/2835293
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Which equation shows y = (x − 4)2− 3 written in standard form?
Answers
Answer:
2 x − y = 11
Step-by-step explanation:
Corresponding Angles are congruent.
Which angle corresponds with <3?
Answers
Answer: Angle 8 corresponds with Angle 3
Which of the following scenarios is best represented by the scatter plot above?
Answers
Answer: B
Step-by-step explanation:
negative correlation so as x increases y decreases,
as population rises houses should rise, not A
as buildings rise, need more space and less trees, B is the answer
as cars rise population should rise, not C
no correlation, not D
You bought a magazine for $3 and some
candy bars for $5 each. You spent a total
of $28. How many candy bars did you
buy
Answers
Answer: you bought 5 candy bars
Step-by-step explanation:
total is 28 you subtract 3 for the magazine you bought & end up with 25 dollars & each candy bar is 5 so you divide the 25 by 5 & end up with 5
If the initial point of a vector is (6, −5) and the terminal point is (2, −3), find the components of the vector. A) <−4, −8> B) <−4, 2> C) <4, −2> D) <4, 2>
Answers
Answer:
i honestly dont know this but im guessing its about 12th grade work.
Which of the following scenarios shows a value of 0.4? Select all that apply.
A.
Jesse sold 40 out of 60 items at a garage sale.
B.
Jesse rode 4 out of 10 miles on his bike.
C.
Jesse finished 40 out of 100 math problems.
D.
Jesse ate 4 out of 100 jellybeans.
E.
Jesse returned 4 out of 8 library books.
Answers
Answer:
D and B
Step-by-step explanation:
The scenarios which gives a value of 0.4 is depicted by the equations B and C
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
a)
Jesse rode 4 out of 10 miles on his bike.
So , the fraction is A = 4/10 = 0.4
b)
Jesse finished 40 out of 100 math problems.
So , the fraction is A = 40/100 = 0.4
Hence , the equation is A = 0.4
To learn more about equations click :
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THE TOPIC IS: AREA OF CIRCLES!! PLEASE HELP ME WITH THIS QUESTION!!! WHATS THE ANSWER?? I WILL GIVE YOU BRAINLIEST AND A THANKS!!! THANK YOUUU!!! <33
Answers
Answer:
50.24in²
Step-by-step explanation:
Formula: πr²
Given: π = 3.14, r = 4
Sub: 3.14(4)²
SImplify: 3.14(16)
Solve: 50.24
Select the values that are solutions of the inequality X 3<4.
X=4
X=8
X= 12
X= 16
X= 20
X= 24
Answers
Answer:
x=12 if you divide you'll get 4
What is the value of log625^5?
О-4
O -1/4
O1/4
O4
Answers
Answer:
3rd option, 1/4
Step-by-step explanation:
decimal form is 0.25
I really need help with this stadistic problem
Answers
Answer:
the mean is 5.8 and the median is 6
Step-by-step explanation:
if you multiply the test scores by their frequencies and then add up all those values, and then divide by the number of test scores, you get 5.8
for the median, you write out all the test scores in order from least to greatest and how many times they appear. then if you go to the middle of that number line, youll find the median
what is more 7921 ft or 3 / 2 miles
Answers
Answer:
7,921
Step-by-step explanation:
If you get a calculator and put in 3 divided by 2, you will get 1.5 which is less than 7,921, by 7,919.5.
Question: Explain the Difference between an equation and an expression
Answers
Answer:
An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
An equation is made up of two expressions connected by an equal sign.
Step-by-step explanation:
expand and simplify 2(3a-5b)+4(a+2b)
Answers
Answer:
[tex]10a - 2b[/tex]
That is the answer
