A rectangular aquarium is 2/3 filled with water and then is tilted on its side until the water level coincides with one edge of the bottom. During the process, 6 quarts of water are poured out. What is the volume of the tank in quarts?
Answer:
36 Quarts
Step-by-step explanation:
Let the volume of the Aquarium be x quarts.
Hence amount of water filled in it will be
[tex]\frac{2x}{3}[/tex] quarts
Also problem says that the tank is tilted until water level coincides with one edge of the bottom. At this position , the amount of water filled in the tank will be half of the total volume , as the slant water level will be the diagonal of the tank and a diagonal divides the tank in two halves.
Hence current volume of water in the tank will be
[tex]\frac{x}{2}[/tex]
And in this process the amount of water poured out is 6 quarts. It will the difference between the amount of water earlier in the tank and the amount of water in the tank now. Hence
[tex]\frac{2x}{3}-\frac{x}{2}=6[/tex]
[tex]\frac{4x-3x}{6}=6[/tex]
[tex]x=36[/tex]
Hence the volume of the tank is 36 quarts.
while his bank account balance was -$45 Dylan made 6 withdrawals of 9$ what was his new bank account balance?
A cylinder has its height doubled and its radius cut to one third. What is the ratio of the volumes of the modified cylinder to the original cylinder?
Final answer:
The ratio of the volumes of the modified cylinder (height doubled and radius cut to one third) to the original cylinder is 2:9.
Explanation:
To find the ratio of the volumes of the modified cylinder to the original cylinder, we need to use the formula V = πr²h.
Let the original radius be 'r' and the original height be 'h'. The volume of the original cylinder V1 is given by:
V1 = πr²h
After doubling the height and cutting the radius to one third, the new radius is 'r/3' and the new height is '2h'. The volume of the modified cylinder V2 is:
V2 = π(r/3)²(2h) = π(r²/9)(2h) = (2/9)πr²h
The ratio of the volumes is then:
Volume Ratio (V2/V1) = (2/9)πr²h / πr²h = 2/9
So, the ratio of the volumes of the modified cylinder to the original cylinder is 2:9.
find the obtuse angle the line y-2x=7 makes with the x- axis
Jason and Jenny are out on a lunch date. Jason gives Jenny a bouquet that has 4 roses, 3 carnations, and 4 orchids. They decide that Jenny gets to choose their lunch order if the flower she randomly picks from the bouquet is a carnation or a rose. What is the probability that Jenny gets to choose lunch?
estimate 17.5×8.4 need help
Side GH = 3, side IG = 5, side JK = 3, and side LJ = 5. What side corresponds to side HI and can be used to show that ΔGHI ≅ ΔJKL by SSS? (Enter your answer using letters only)
Since it says enter with only letters, you would put KL as the answer
Larry has taken out a $600 loan with a 12 percent interest rate to buy a laptop computer. He needs to repay the loan by the end of two years. He will be paying $28.24 every month for two years. What kind of interest rate is Larry being charged? Explain the reasons for your answer.
Answer:
Larry is paying the same amount every month for the duration of the loan. So he is being charged a fixed interest rate.
Step-by-step explanation:
plato answer
What fraction of a minute is 42 seconds
What is the simplified form of 20 times x to the fifth power over 15 times y to the sixth power times the fraction 5 times y to the fourth power over 6 times x squared?
f(x) = –5x – 4 and g(x) = –3x – 2, find (f – g)(x).
Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. The shape of the backyard is rectangular, with the length twice as long as the width. What are the dimensions of the backyard? A(w) = 2w2 512 = 2w2 The width of the backyard is feet. The length of the backyard is feet.
Answer:
16ft by 32ft
Step-by-step explanation:
Answer:
The answer is 512 = 2w2 or C
Step-by-step explanation:
I just did the assignment
Decide if the problems are parallel,perpendicular or neithet and why
1).12x-4y=8
2).3y=-x+5
3).y=1/3x-5
4).12x-10=4y
5).2/3×+2y=8
Given the expression 5a2b – 13ab + 7a3 – 4b, do the following as instructed below:
1. Write the polynomial in descending order.
2. Classify the polynomial by the number of terms.
3. State the degree of the polynomial.
Thank you !!
A large planetarium in the shape of a dome is being built. When it is complete, the base of the dome will have a circumference of 87 kilometers. What area of land was required for this planetarium?
Answer:
602.32 km²
Step-by-step explanation:
First, find the radius of the circle using the circumference formula
C = 2π*r
87 = 2π*r
∴ r = 13.8465 km
Second, using the radius, calculate the area:
A = π * r²
A = π * 13.8465²
A = 602.32 km ²
What is equivalent to this statement:4 is 80% of x
An equivalent statement to '4 is 80% of x' is 'x is 5'.
Explanation:The statement '4 is 80% of x' can be written as the equation 4 = 0.8x. To find an equivalent statement, we can solve this equation for x.
To solve for x, divide both sides of the equation by 0.8: x = 4 / 0.8 = 5.
Therefore, an equivalent statement is: x is 5.
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Your friend's height is close to 180 centimeters. What is your friend's height close to in meters?
Answer:
The friend's height close to 1.8 meters.
Step-by-step explanation:
As given in the question
Your friend's height is close to 180 centimeters.
As
1 meter = 100 centimeter
[tex]1\ centimeter = \frac{1}{100}\ meters[/tex]
Now convert 180 centimeters into meters .
[tex]180\ centimeter = \frac{180}{100}\ meters[/tex]
[tex]180\ centimeter = 1.8 meters[/tex]
Therefore the friend's height close to 1.8 meters.
i need help with this problem. thank you so much who ever answer this
-36/8 = -4.5
-4.5 = -4.5
Please help! find the solution of this system of equations -6x + 2y=38 6x - 8y= -44
Solve it by using the elimination method.
-6x and 6x eliminate each other.
You have -6y=-6
Y=1
Plug this in into another equation and you have
-6x+2(1)=38
solve for x to get
X= -6
Please Help!
1. Define an example of a function – this could be distance traveled vs. time, the cost
of a turkey vs. weight, ect.
2. Show this relation as a set of correctly determined ordered pairs -- you will need
at least 5 ordered pairs in set notation -- remember that set notation will look
like: {(1, 2)(3, 4)(5, 6)(7, 8)(9, 10)} with the { } around the ordered pairs.
Can you please explain how you did it. I want to understand. (30pts)
NEED HELP FAST!
1.
(08.05 LC)
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6
Equation Q: 8y + 7z = 1
Which of the following is a possible step used in eliminating the y-term? (1 point)
(y + z = 6) • –8
(y + z = 6) • 7
(8y + 7z = 1) • 7
(8y + 7z = 1) • 8
Answer:
(y + z = 6) • –8
Step-by-step explanation:
Because in order to eliminate 8 you will need to multiply by a negative number so that you can eliminate a positive number.
Hope this helped!
what is a constant interval and how does it appear on a graph?
A function is said to have a constant interval if, for any input, the output is the same. The graph of a function with a constant interval is parallel to the axis of the range, i.e., a horizontal line.
A constant interval refers to a specific type of interval that remains the same or constant over its entire length. In other words, the difference between any two consecutive points or numbers in a constant interval is always the same.
Let's assume that f(x) = c is a function with a constant interval.
Then,
for any [tex]x_1\leq x_2[/tex] or [tex]x_1\geq x_2[/tex],
[tex]f(x_1) = f(x_2)[/tex].
Thus, a function whose output remains constant for every input is called a function with constant intervals.
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Want brainliest answer this
12 x 11 = 132
3*12=36
132+36 = 168 square feet
Only false statements have counterexamples. true or false
The statement 'Only false statements have counterexamples' is false.
A counterexample is an instance that disproves a statement by providing an example where the premises are true, but the conclusion is false. Thus, only false statements have counterexamples can be considered false. A true statement cannot have a counterexample because that would contradict its truth.
For example, consider the statement 'All swans are white.' A single observation of a black swan would be a counterexample that disproves this statement, showing it is false.
What is b-r-3,when b=9 and r=2
Max has more than 5 carrots (number of carrots Max has = c
An Octagon has the radius of 56 and an area of 10,391.9 square millimeters.
a1) What is the approximate perimeter of the octagon? Round to the nearest whole number.
A) 93
B) 186
C) 371
D) 1299
a2) What is the approximate length of one side of the octagon? Round to the nearest whole number.
A) 23
B) 46
C) 371
D) 1299
Answer:
Step-by-step explanation:
Alright, lets get started.
The area of octagon is given [tex]= 10391.9[/tex]
The formula for area of octagon with side a is = [tex]2(1+\sqrt{2} )a^2[/tex]
[tex]10391.9 = 2(1+\sqrt{2} )a^2[/tex]
hence ,
[tex]a^2 = \frac{10391.9}{2(1+\sqrt{2} )}[/tex]
[tex]a^2 = 2152.2329[/tex]
[tex]a = 46.39[/tex]
Hence the length of the side of the octagon is 46 : Answer
Now perimeter of the octagon will be = [tex]8*side length[/tex]
Hence the perimeter = [tex]8*46.39 =371.1[/tex]
hence the perimeter of the octagon is 371 : Answer
Hope it will help :)
How do i solve
3(x+3)=18
A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation?
a)x+y=3 and x-3y=-27
b)x+y=3 and x-3y=-9
c)x-y=3 and x-3y=-27
d)x-y=3 and x-3y=-9
Answer: x + y = 3 and x - 3 = -9
Step-by-step explanation:
A drawer contains 4 red socks, 8 white socks, and 6 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is white and the second sock is red?