3. The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made one sixth of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank?
Using the information from #3, answer the following question by filling in the blank: The volume of the original main show tank is ____% of the mock-up of the tank.
Answer:
1. Volume = 5128.67 ft³
The volume if sphere is given by:
V = (4/3)πr³
If the tank is cut into half vertically, then the volume of sphere becomes.
V = (4/3)πr³ / 2
If the tank is cut into half again horizontally, then the volume of the sphere becomes.
V = (4/3)πr³ / 4
Hence, as the main tank forms a quarter sphere, its Volume is given by:
V = (4/3)πr³ / 4
It is given in the question that the radius is 70 ft.
Substitute that in the given formula:
V = (4/3)π(70)³ / 4
V = 5128.67 ft³
2. Volume of tank = 461,814 ft³
Step-by-step explanation:
Congruent tanks implies that both tanks are of identifical shape, form & dimensions. Congruent means that the tanks have the same radius as well as height. Hence, the heights and radii of tanks #1 and #2 are equal and the same.
Let's list out the information given us:
radius(tank #1) = 35 ft ⇒ radius(tank #2) = 35 ft, height(tank #2) = 120 ft ⇒ height(tank #2) = 120 ft
Volume of cylinder = πr²h
The tanks have been cut into half, as such:
Volume of tank = ½πr²h
Volume of tank = Volume(tank #1) + Volume(tank #2)
Since the tanks are congruent (same dimensions), we have:
⇒ ½πr²h + ½πr²h ⇒ πr²h
Volume of tank = π * 35² * 120 = 147,000 π
Volume of tank = 461,814 ft³
3. 1047.2 ft³
Step-by-step explanation:
The following information is missing:
The main show tank has a radius of 60 feet and forms a quarter sphere where the bottom of the pool is spherical and the top of the pool is flat. (Imagine cutting a sphere in half vertically and then cutting it in half horizontally)
The only dimension needed for the main show tank is its radius. Then the model radius will be 1/6 * 60 = 10 feet
The volume of a sphere is:
V = 4/3 * π * r³
For a quarter sphere it is:
V = 4/3 * π * r³ * 1/4
V = 1/3 * π * r³
For the smaller mock-up tank:
V = 1/3 * π * 10³
V = 1047.2 ft³
The total cost of Dara's purchases was $38.07. Upon subtracting this amount from her initial $50, she is left with $11.93 change.
To solve the problem, you need to add up how much Dara spends and subtract that from $50. First, add the cost of the sandals, shorts, and hat together:
When you add these three amounts together, you get $38.07. So, Dara has spent $38.07 in total. Now, subtract that amount from $50:
$50.00 - $38.07 = $11.93
This means Dara should get back $11.93 in change.
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2k(7-5k)+11=6k+3(k^2-1)
with work please.
Answer:
Step-by-step explanation:
2k(7-5k)+11=6k+3(k^2-1)
We move all terms to the left:
2k(7-5k)+11-(6k+3(k^2-1))=0
We add all the numbers together, and all the variables
2k(-5k+7)-(6k+3(k^2-1))+11=0
We multiply parentheses
-10k^2+14k-(6k+3(k^2-1))+11=0
We calculate terms in parentheses: -(6k+3(k^2-1)), so:
6k+3(k^2-1)
We multiply parentheses
3k^2+6k-3
Back to the equation:
-(3k^2+6k-3)
We get rid of parentheses
-10k^2-3k^2+14k-6k+3+11=0
We add all the numbers together, and all the variables
-13k^2+8k+14=0
a = -13; b = 8; c = +14;
Δ = b2-4ac
Δ = 82-4·(-13)·14
Δ = 792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
k1=−b−Δ√2ak2=−b+Δ√2a
The end solution:
Δ−−√=792−−−√=36∗22−−−−−−√=36−−√∗22−−√=622−−√
k1=−b−Δ√2a=−(8)−622√2∗−13=−8−622√−26
k2=−b+Δ√2a=−(8)+622√2∗−13=−8+622√−26
of 70 inches? Is this usual or unusual?
A. Z-score is 2.56 and is usual. B. Z-score is 2.56 and is unusual
C. Z-score is -2.56 and is usual D. Z-score is -2.56 and is unusual
The corresponding z-score for a height of 70 inches is 2.56, which is considered unusual based on the standard threshold.
Use the concept of statistics defined as:
Statistics is a discipline of mathematics that deals with all aspects of data. Statistical knowledge aids in the selection of the appropriate technique of data collection and the use of those samples in the appropriate analysis process in order to effectively create the results. In short, statistics is an important procedure that assists in making data-driven decisions.
Given that,
The mean height of women: 63.6 inches
The standard deviation of women's heights: 2.5 inches
Height in question: 70 inches
Z-score formula: Z = (X - μ) / σ
The Z-score calculation for a height of 70 inches: Z = 2.56
Z-score interpretation: Unusual (greater than 2)
To find the z-score,
Use the formula:
Z = (X - μ) / σ
Where,
X is the value (in this case, 70 inches),
μ is the mean (63.6 inches),
σ is the standarddeviation (2.5 inches).
Calculating the z-score for a height of 70 inches:
Z = (70 - 63.6) / 2.5
Z = 6.4 / 2.5
Z = 2.56
So, the z-score corresponding to a woman with a height of 70 inches is 2.56.
Now, to determine if this z-score is usual or unusual,
Use the standard z-score table.
Usually, z-scores greater than 2 or less than -2 are considered unusual.
In this case,
The z-score is 2.56, which is greater than 2.
Hence,
The correct answer is B. The z-score is 2.56 which is unusual.
To learn more about statistics visit:
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Answer:
A
Step-by-step explanation:
Hopefully this helps
2y = 1
12y = 17
5y = 17
Answer:
2y=1
Step-by-step explanation:
7y + 8 = 9 + 3y + 2y
WE need to simplify it, try to get variable on one side and constant on the other side
7y + 8 = 9 + 3y + 2y
first we combine like terms
3y+2y is 5y
7y + 8 = 9 + 5y
Now to get y terms on one side we subtract 5y from both sides
7y -5y + 8 = 9 + 5y-5y
2y +8 = 9
Now we subtract 8 from both sides
2y +8 -8 = 9-8
2y= 1