The base of a solid right pyramid is a square with an
edge length of n units. The height of the pyramid is n
1 units
Which expression represents the volume of the
pyramid?
VA
on(n-1) units
on(n-1)2 units
or’n - 1) units
on*(n − 1) units
(n-1)
n
Answers
Answer:
C
Step-by-step explanation:
Base area = n^2
V = (base area * height)/3 = (n^2 *(n-1)/3 = 1/3n^2(n-1)
The expression for the volume of pyramid is V = ( 1/3 )n² ( n - 1 ) units³
What is the volume of a pyramid?The volume of a pyramid, is the product of the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V = ( 1/3) ×B×h, where B is the area of the base of the pyramid, and h is its height.
Volume of Pyramid = ( 1/3 )a²H
Given data ,
Let the base edge length of the solid pyramid be = n units
So , the base area of the pyramid = n² units²
Let the height of the pyramid be = ( n - 1 ) units
And , Volume of Pyramid = ( 1/3 )a²H
On simplifying , we get
V = ( 1/3 ) n² ( n - 1 ) units³
Hence , the expression is V = ( 1/3 ) n² ( n - 1 ) units³
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Related Questions
Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 ft high? (Round your answer to two decimal places.)
Answers
Answer:
0.42ft/mn
Step-by-step explanation:
we have the following information to answer this question
dv/dt = 40 feet
height = 11 ft
volume = 1/3πr²h
= 1/3π(h/2)²h
= 1/3πh³/4
= πh³/12
dv/dt = π3h²/12
= πh²/4
dh/dt = 4/πh²dv/dt
= 4(40)÷22/7(11)²
= 160/380.29
= 0.42 ft/min
The height of the pile is therefore increasing by 0.42ft/min at a height of 11 feets
33. Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5
b. The constant is 2
C. The power is 10
d. The constant is 5
Answers
Answer:
Given the following algebraic expression 5x² + 10 Which statement is true?
a. The coefficient is 5. ( true)
b. The constant is 2
C. The power is 10
d. The constant is 5
hope this helps
Find the area
10
7
12
4
5
5
Answers
Answer:
[tex]{ \tt{area = (7 \times 10) + (12 \times 4) + (5 \times 5)}} \\ { \tt{ = 70 + 48 + 25}} \\ { \tt{ = 143 \: {in}^{2} }}[/tex]
Answer: break into 2 rect and 1 sqr the sum areas of each
Step-by-step explanation: square = 5x5
Rectangle 1 = 10x7
Rectangle 2 = 12x4
Sum each shape area = total area
If ∠1 = 3x, ∠2 = 5x + 18, and s ⊥ r, find m∠1.
Answers
I hope it will help you.
Answer:
x = 9
Step-by-step explanation:
angle <1 and angle <2 is complementary and their sum is 90 degrees
3x + 5x + 18 = 90 add like terms
8x + 18 = 90 subtract 18 from both sides
8x = 72 divide both sides by 8
x = 9 to find the measure of angle <1 replace x with the value we found
write a rational number between root2 and root3
Answers
Answer:
prational number between root2
At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answers
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
Three different design configurations are being considered for a particular component. There are two possible failure modes for the component. An engineer obtained the following data on the number of failures in each mode for each of the three configurations. Is there evidence to conclude that the configuration has an effect on the type of failure?
Failure Mode
1 2 3 4
Configuration 1 20 44 17 9
2 4 17 7 12
3 10 31 14 5
Answers
Answer:
No evidence .because the configurations factors and failure mode are independent
Step-by-step explanation:
Determine if there is sufficient evidence to conclude that configuration affects the type of failure
Number of configurations = 3
Number of failures = 4
assuming Pij represents proportion of items in pop i of the category j
H0 : Pij = Pi * Pj, I = 1,2,-- I, j = 1,2,---J
Hence the expected frequencies will be
16.10 , 43.58 , 18, 12.31
7.5, 19.37, 8 , 5.47
10.73, 29.05, 12, 8.21
x^2 = 13.25
test statistic = 14.44. Hence the significance level where Null hypothesis will be acceptable will be = 2.5%
x2 + 5x + 9.
Find the equation of the axis of symmetry for the parabola y =
Answers
Answer:
x = -5/2
Step-by-step explanation:
From the quadratic equation
the axis of symmetry for quadratics of the form
y = ax² + bx + c is
x = -b/2a
x² + 5x + 9
x = -5/2
In the school chorus,
5/25 of the students are fourth-graders.
In simplest form, what fraction of the students in the school chorus are fourth graders?
Answers
Answer:
1/5 of the students are 4th graders
The probability that a person has blue eyes is 16%. Three unrelated people are selected at random. a. Find the probability that all three have blue eyes b. Find the probability that none of the three have blue eyes c. Find the probability that one of the three has blue eyes
Answers
Answer:
Step-by-step explanation:
All three have blue eyes.
P(1 has blue eyes) = 16/100 = 4/25
P(3 have blue eyes) = 4/25 * 4/25 * 4/25
P(3 have blue eyes ) = 64/15625
If you need the decimal answer, it is .004096
No one has blue eyes out of three
The probability for this is very large.
P(no blues) = 1 - 64/15625
P(no blues) = 15561/15625
If you need the decimal answer, it is 0.996
One has blue eyes (the other two do not).
P(1 has blue eyes) = 16/100 * 84/100*84/100
P(1 has blue eyes) = 112896/1000000
P(1 has blue eyes) = 0.112896
Split 294x306, which identity is used to solve it?
Answers
Answer:
identity :- ( a + b ) ( a - b ) = a² - b ²
Answer :- 89,694
Step-by-step explanation:
Given : 294 × 306
split 294 × 306
294 × 306 = ( 300 - 6 ) × ( 300 + 6 )
Using Identity, ( a + b ) ( a - b ) = a² - b ² :
= ( 300 )² - ( 6 )²
= 90000 - 36
= 89,964
Hence, 294 × 306 = 89,694
Bianca recently bought a rope that is 25 yards long. Find the length in feet
Answers
Answer:
25 yards is equal to 75 ft
Answer:
75 feet
Step-by-step explanation:
1 yard=3ft
so 25 times 3 equals 75 feet :)
A line goes through the points (1, -19), (-4,1), (0, -15), (2, -23). What is the slope and y-
intercept of the line
Answers
Answer:
Step-by-step explanation:
The y-intercept is super easy. The y-intercept exists when x = 0; therefore, the point given where x = 0 is found in (0, -15). That means that the y-intercept is -15. Easy enough. Now, the slope.
Since all these points are on the same line, using any 2 of them in the slope formula will get us the slope. I picked the first 2 points (1, -19) and (-4, 1):
[tex]m=\frac{1-(-19)}{-4-1}=\frac{1+19}{-5}=\frac{20}{-5}= -4[/tex]
The y-intercept is -15 and the slope is -4
critical observations thinking is the best deomstrated by which of the following action
Answers
Answer: spotting trends in data
Step-by-step explanation:
Which of the following expressions could be used to represent "three less than half a number"?
• 1/2 - 3n
• 3 - 1/2n
• 3n - 1/2
• 1/2n - 3
Answers
Answer:
the answer is
[tex]3 - \frac{1}{2}n [/tex]
Help me out please???
Answers
9514 1404 393
Answer:
x = 5
Step-by-step explanation:
DE being a midsegment means that D is a midpoint. Then BD = DA, or x = 5.
Find the median of the following data 9,15,17,18,6,20,8,5,18,18,10,5,14,12,10,7
Answers
Answer:
11
Step-by-step explanation:
first, sort the numbers from lowest to highest.
5,5,6,7,8,9,10,*10,12*,14,15,17,18,18,18,20
the median is the number in the middle of the data
average if you need to (10+12 and divide by 2)
Mark is hosting a "Who Dunnit?" party at his house. He plans on taping off a triangular section of his backyard to represent the crime scene. If the sides measure 23 feet, 15 feet, and 32 feet, how much tape will be needed? DO NOT ANSWER JUST TO STEAL MY POINTS!! AND NO CHICKEN NUGGETS!!!!
Answers
Answer:
70 feet
Step-by-step explanation:
as perimeter of triangle =
23+15+32= 70 feet
Answer:
Solution given:
side 1=23ft.
side 2=15ft
side 3=32ft
we have
perimeter=sum of all sides
=23+15+32=70ft
70ft tape will be needed.
Gavin was thinking of a number. Gavin doubles it and adds 6.6 to get an answer of 9. Form an equation with
x
from the information.
Answers
Answer:
(9-6.6)÷2=x
Step-by-step explanation:
Do it in reverse from 9 all the way to x.
Answer:
(9-6.6)÷2=x
Step-by-step explanation: since you had 9 as the answer, start there. Then subtract 6.6. You then divide that number by 2 to get x
Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long. What is the travel time to work that separates the top 12% of people with the longest travel times and the lower 88%
Answers
Answer:
22.3 minutes
Step-by-step explanation:
The computation of the travel time is as follows:
Given that
[tex]\mu[/tex] = 17
And, the standard deviation is 4.5
P(X≤C) = 0.88
P( x - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] ≤ (C - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] = 0.88
(C - [tex]\mu[/tex]) ÷ [tex]\sigma[/tex] = 1.175
c = [tex]\mu[/tex] + 1.175 × [tex]\sigma[/tex]
= 17 + 1.175 × 4.5
= 22.3 minutes
Hence, the travel time is 22.3 minutes
The average car depreciates at a rate of 14% per year.
Mr. Wixted wants to buy a new sports car for $30,048.
At this rate of depreciation, what will the car be worth in 5 years?
Round your answer to the nearest hundredth.
Answers
A fair six-sided die is rolled 54 times. Theoretically, how many times should a roll of "5" occur?
-14
-9
There is no way to tell
-5
Answers
Answer:
9 times
Step-by-step explanation:
P("5") = 1/6
n("5") = 1/6 × 54 = 9
Answer:
9
Step-by-step explanation:
(the number of different possible outcomes) 1/6 * 54 = 9
Hope that this helps!
Please help i need it
Answers
A company that manufactures vehicle trailers estimates that the monthly profit for selling its midsize trailer is represented by function p, where t is the number of trailers sold. p(t)= -25t^3+625t^2-2500t Use the key features of function p to complete these statements. The company makes a profit when it sells _____trailers. The maximum profit of approximately $____ occurs when it sells approximately____ trailers.
Answers
Answer:
The answer is below
Step-by-step explanation:
The profit equation is given by:
p(t)= -25t³+625t²-2500t
The maximum profit is the maximum profit that can be gotten from selling t trailers. The maximum profit is at point p'(t) = 0. Hence:
p'(t) = -75t² + 1250t - 2500
-75t² + 1250t - 2500 = 0
t = 2.3 and t = 14.3
Therefore t = 3 trailers and t = 15 trailers
p(15) = -25(15³) + 625(15²) - 2500(15) = 18750
Therefore the company makes a maximum profit of approximately $18750 when it sells approximately 15 trailers.
Answer:
See below
Step-by-step explanation:
Since t is number of trailers, the domain includes only those values greater than 0.
On the relevant domain, the graph crosses the x-axis at the points (5,0) and (20,0). Between these points, the value of p(t) is positive. So the company makes a profit when it sells between 5 and 20 trailers.
On the positive interval between these points, the graph reaches a relative maximum when t roughly equals 14 and p(t) roughly equals $19,000.
So the maximum profit of approximately $19,000 occurs when it sells approximately 14 trailers.
Prob and stats question help
Answers
Answer:
It is C
Step-by-step explanation:
Trust me, i got it right
Answer:
C
Step-by-step explanation:
have a great rest of your day!! btw Ill view ur profile!! :)
Suppose we want to choose 5 objects,without replacement from 16 distinct objects
Answers
Answer:
4368 ways
Step-by-step explanation:
We want to choose 5 objects,without replacement from 16 distinct objects.
We can use combination in this case. The formula for the combination is given by :
[tex]_{n}C_r=\dfrac{n!}{r!(n-r)!}[/tex]
We have, n = 16 and r = 5
So,
[tex]_{16}C_5=\dfrac{16!}{5!(16-5)!}\\\\_{16}C_5=\dfrac{16!}{5!11!}\\\\=4368[/tex]
So, there are 4368 ways in which we want to choose 5 objects,without replacement from 16 distinct objects.
Pythagorean theorem
Answers
Answer:
hello
Step-by-step explanation:
a²+b²=c²
16²+b²=65²
256+b²=4225
b²=4225-256
b²=3969
[tex]b = \sqrt{3969}[/tex]
b=63
b=63 mi
have a nice day
Answer:
b = 63
Step-by-step explanation:
In a right angled triangle, hypotenuse squared is equal to the sum of the square of the other sides.
c² = a² + b² (where c is the hypotenuse, and a and b are the other two sides)
c = 65 , a = 16 b = ?
65² = 16² + b²
4225 = 256 + b²
4225 - 256 = b²
b² = 3969
b = [tex]\sqrt{3969}[/tex]
b = 63
check
c² = 16 ² + 63²
= 256 + 3969
= 4225
c = √4225
c = 65
Help pls I need help
Answers
Answer:
From the origin , move 3 units to the right and 2 units up. B
This is the graph of y= x2 + 4x + 7 what is the range of this function?
Answers
Answer:
C
Step-by-step explanation:
Answer:c
Step-by-step explanation:the answers we’ll change we careful
What is the coefficient of x4 in the expansion of (3x + 1)??
O 315
O 945
O 105
35
O 2,835