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
A farmer wants to fence off part of a rectangular field to create an area that is 22,500 square feet. He then wants to divide that area in half by creating a fence parallel to one side of the rectangle. Find the dimensions of the area that will minimize the amount of fencing he needs.
Answer:
90 x 125
Step-by-step explanation:
22500÷2 = 11250
factors of 11250 = {1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 625, 750, 1125, 1250, 1875, 2250, 3750, 5625, 11250} (this took me long to type and calculate lol)
well we want the factors as close as possible to minimize the perimeter. In this case, it is 90 and 125. therefore the dimenstions are 90 x 125
Jose is 49 inches tall. His mother is 18 inches taller. How tall is Jose's mother?
67 inches or 5.58 feet.
What is the equation of the graph below?
*A graph shows a parabola that opens down with a vertex at three commas two*
A) y = − (x + 2)² + 2
B) y = − (x − 3)² + 2
C) y = (x − 2)² + 2
D) y = (x + 3)² + 2
Pretty sure it's B, but I'm not sure.
Answer:
B: y = − (x − 3)² + 2
Step-by-step explanation:
You can check this using a graphing calculator, but it has a vertex of (3,2)
Answer:
B
Step-by-step explanation:
The ratio of band students to choir students is 4:6. There are a total of 60 students in the band and choir. How many students are in the band?
Answer:
24
Step-by-step explanation:
Given that:
The ratio of band students to choir students is 4 : 6.
Total number of students in the band and choir combined = 60
To find:
The number of students in the band = ?
Solution:
First of all, let us understand the meaning of the ratio given.
Ratio of 4 : 6 means there are 4 number of band students for every 6 number of choir students.
Also, number of band students will be in the multiples of 4 only and
number of choir students will be in the multiples of 6 only
Let the total number of band students = 4[tex]x[/tex]
Let the total number of choir students = 6[tex]x[/tex]
Total number of students = 60
As per question statement, we can write the following equation:
[tex]\Rightarrow 4x+6x=60\\\Rightarrow 10x = 60\\\Rightarrow x =6[/tex]
Total number of band students = 4 [tex]\times[/tex] 6 = 24
Help me please
Tyler filled a small jar with quarters and dimes and
donated it to his school's charity club. The club member
receiving the jar asked, "Do you happen to know how
much is in the jar?" Tyler said, "I know it's at
least $8.50, but I don't know the exact amount."
Write an inequality to represent the relationship
between the number of dimes, x, and the number of
quarters, y, and the dollar amount of the money in the
jar.
(It will say "CORRECT" when you type in the correct
inequality.)
Answer:
Step-by-step explanation:
X=8.50
y=9.50
The inequality that represents the relationship will be 0.10x + 0.25y ≤ 8.50.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Tyler filled a little container with quarters and dimes and gave it to his school's foundation club. The club party getting the container inquired, "Do you end up realizing how much is in the container?" Tyler said, "I know it's something like $8.50, yet I don't have a clue about the specific sum."
Let x be the number of dimes and y be the number of quarters. Then the inequality is given as,
0.10x + 0.25y ≤ 8.50
The inequality that represents the relationship will be 0.10x + 0.25y ≤ 8.50.
More about the inequality link is given below.
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A number times nine + four gives you fifteen if you have time
Answer:
11 / 9
Step-by-step explanation:
Let number = x
(x * 9) + 4 = 15
9x + 4 = 15
9x = 15 - 4
9x = 11
x = 11 / 9
Hence, the number is 11 /9
Laura is graphing an absolute-value function in the form
f(x) = a|x - h| +k. She determines that the domain
is (-00,00) and that the minimum value is y=-3.
What might be the equation of this function?
A. f(x) = \x + 3) + 3
B.f(x) = -3\x+31 - 3
C.f(x) = (x – 31 - 3
D.f(x) = 3|x – 3] + 3
Answer:
The equation of the function is;
y = |x-3| -3
Step-by-step explanation:
Here, we want to give the absolute-value function
For the minimum value to be -3, it means that k is negative
since the domain is the set of all real numbers, then we do not have any undefined value for the range y
So, the equation is ;
y = |x-3| - 3
11r - 14r - 3 + 16 what is the answer
Answer:
-3r + 13
Step-by-step explanation:
11r - 14r - 3 + 16
add like terms
-3r + 13
A 6 foot tall tent standing next to a cardboard box casts a 9 foot shadow. If a cardboard box cast a shadow that is 6 feet long then how tall is
Answer:
It is 4 feet tall
Step-by-step explanation:
Filler
Which equation can be used to solve for c? Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c. c = (5)cos(35o) c = Start Fraction 5 Over cosine (35 degrees) End Fraction c = (5)sin(35o) c = Start Fraction 5 Over sine (35 degrees) End Fraction
Answer:
it is B because the teacher gave me the answer hope y'all enjoy
Step-by-step explanation:
PLEASE HELP MEE, IM STUCK
Answer:
im pretty sure its c
if this helped please consider giving brainliest
Given the measures of the sides of a triangle below, which set could form a right
triangle?
A. 6, 7, 8
B. 9, 12, 15
C. 12, 15, 20
D. 20, 25, 30
(give a brief explanation please)
3/4 =w/6 simplify as much as possible HELP plzzz
Answer:
9/2
Step-by-step explanation:
3/4 = w/6
w = 3/4 *6
w = 9/2
5x + 24 + 5(x + 5)
HELP FAST
5x+24+5(x+5)
Distribute:
=5x+24+(5)(x)+(5)(5)
=5x+24+5x+25
Combine Like Terms:
=5x+24+5x+25
=(5x+5x)+(24+25)
=10x+49
Answer:= 10x+49
solve for x
10x =-49
10/10x -49/10
x= -4.9
Hope this helps
Tell whether the sequence is arithmetic. If it is, identify the common difference. 4, 8, 16, 32, …
Answer:
it's geometric
8/4=2 16/8=2
d=2
Andrews sandwich consists of a 20 g piece of cheese is 60 g piece of turkey into 30 g slices of bread what is the total weight of Andrews sandwich in kilograms
Answer:
0.11 kilos
Step-by-step explanation:
expand and simplify (x+1)(x+7)
Answer:
Factored?
x^2 + 8x +7
Step-by-step explanation:
x times x = x^2, with 7 times x = 7x and x times 1 = 1x. Add those two common terms together to get 8x. Then lastly 7 times 1 =7 so add that.
Simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
What is simplification?
"Simplification in mathematics means to write the given expression in such a way that it is easy to understand."
According to the question,
Simplify the given equation by opening the brackets we get,
(x + 1)(x + 7)
= x² + 1x +7x +7
= x² + 8x + 7
Hence, simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
Learn more about simplification here
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100 points explaination
Answer: bro I'm sorry I don't know how to help you please give me points
Step-by-step explanation:
Don't know how to help you sorry
Answer: okay, this brother.
Step-by-step explanation:
There are 25 town homes in the Alief Community subdivision.
•Company A provides water to 1/5 of the town homes.
•Company B provides water to 9/15 of the town homes.
•Company C provides water to the remaining town homes.
In this subdivision, company C provides water to how many houses?
Answer:
5
Step-by-step explanation:
Fist, you would see that company a Provides water to 5 people, since 1/5 of 25 is 5. 25/15X9=15. 15+5=20. So, 25-20=5.
Find the measure of the indicated side. Round to the nearest tenth.
Answer:
x=23.5
Step-by-step explanation:
[tex]cos59.3=\frac{12}{x}\\x(cos59.3)=12\\x=\frac{12}{cos59.3}\\x=23.5[/tex]
What is the ratio of the number of beaks to the number of legs the chickens and the sheep have on this farm?
Number of Chickens Number of Sheep
8 14
1 to 9
because 1 chicken has 1 beak so the ratio of beaks is 8
1 sheep has 4 legs while 1 chicken has 2 legs
therefore multiply 4legs by 14 =56 then multiply 2 legs by 8=16
Beaks Legs
8. 72
1. 9
th ratio is therefore 1 : 9
a store has 5 cans of soup for 15 dollars.How much is per can
Answer:
3 dollars
Step-by-step explanation:
5 cans= 15 dollars
1 can = 15/5= 3
3 dollars
A meteorologist finds that the temperature at the 6000-foot level of a mountain is 76°F and the temperature at the 12,000-foot level of
the mountain is 49°F. Write a linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet.
Answer:
T=x/78
height/78=76
Step-by-step explanation:
Please help with geometry question!!!! will give brainliest
Answer:
so pretty much what your doing is 4x3
Step-by-step explanation:
Answer:
x = 32
Angle B = 120°
Step-by-step explanation:
3 (4x - 8) = 360°
4x - 8 = 120
4x = 128
x = 32
Suppose the newspaper states that the probability of rain today is 50%. What is the complement of the event "rain today"?
Answer:
50%
Step-by-step explanation:
Given that :
Let Probability of rain today = P(rain today) = 50% = 0.5
The complement of an event A denoted as A' means the opposite of event A is obtained by subtracting event a from 1.
P(rain today) = 0.5
The complement of P(rain today) ; means the probability that it will NOT rain today;
Hence, P(raintoday') = 1 - 0.5 = 0.5 = 50%
Help....i don't remember even going over this at all.
Answer: Choice A)
Set A is an exponential function and the values increase at a faster rate than Set B.
======================================================
Explanation:
Focus on Set A. Each time x goes up by 1, y goes up by a factor of 10. In other words, the y value is being multiplied by 10.
10*10 = 100100*10 = 1,0001,000*10 = 10,00010,000*10 = 100,000etc
This strongly implies that we're dealing with an exponential function. The equation for this function is y = 10^x.
Plug in x = 1 and you should get y = 10. Repeat for x = 2 and it should lead to y = 100. This helps confirm we have the correct function.
On the other hand, Set B deals with a linear equation which is y = 50x+950. The slope 50 is the amount we're increasing y each time x goes up by 1. If you plug x = 1 into this, you should get y = 1000. Plug in x = 2 and it leads to y = 1050, and so on.
When comparing exponential growth rates versus linear growth rates, the exponential will be faster. This is true even if you have a very small exponential growth rate. At some point, the exponential will overtake the linear. The linear growth rate is some constant value that never changes. The exponential growth rate increases over time. Think about simple interest versus compound interest and that may be a good example to go over.
Name the corresponding angle with angle 2
Answer
3 it cant be 6 because lines L and M are not parallel
Step-by-step explanation:
Plz help me on this
What is the solution to the inequality x(x - 3) > 0?
OA) xs O and x > 3
OB) xs O or x3
OC) 0
OD) x<0 or x> 3
Answer:
D) x<0 or x>3
Step-by-step explanation:
x(x-3)>0
either x>0 and x-3>0 .... positive-positive=positive so x>3
or x<0 and x-3<0 ..... negative-negative=positive so x<0
if x=0 then x(x-3)=0
The solution to the inequality is x < 0 or x > 3
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To solve the inequality x(x - 3) > 0, we can use a sign chart.
First, we can find the critical points of the inequality, which are the values of x that make the expression x(x - 3) equal to zero. These values are x = 0 and x = 3.
Then, we can create a sign chart with these critical points and test intervals between them to determine the sign of the expression x(x - 3) in each interval.
Interval Test Value x(x - 3)
x < 0 -1 Positive
0 < x < 3 1 Negative
x > 3 4 Positive
From the sign chart, we see that x(x - 3) is positive when x < 0 and when x > 3, and negative when 0 < x < 3.
Hence , the solution to the inequality x(x - 3) > 0 is x < 0 or x > 3
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Which point is not on the graph of the function y=×+5
Answer:
your gonna need to start from the point 5 and move up
Step-by-step explanation: