A water tank holds 18,000 gallons. How long will it take for the water level to reach 6000 gallons if the water is used at an average rate of 450 gallons per day?
Circle P has a diameter of 20 feet. Circle Q has a diameter of 30 feet. What is the ratio of the circumference?
Answer:
The ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
Explanation:
The circumference of a circle is given by the formula \(C = \pi \times d\), where [tex]\(d\)[/tex] is the diameter.
For Circle P with a diameter of 20 feet, the circumference is:
[tex]\[ C_P = \pi \times 20 \][/tex]
For Circle Q with a diameter of 30 feet, the circumference is:
[tex]\[ C_Q = \pi \times 30 \][/tex]
To find the ratio of the circumferences of Circle P to Circle Q, we divide the circumference of Circle P by the circumference of Circle Q:
[tex]\[ \text{Ratio} = \frac{C_P}{C_Q} = \frac{\pi \times 20}{\pi \times 30} \][/tex]
[tex]\[ \text{Ratio} = \frac{20}{30} = \frac{2}{3} \][/tex]
So, the ratio of the circumferences of Circle P to Circle Q is [tex]\( \frac{2}{3} \).[/tex]
Cindy has 26 nickels. She is getting rolls of nickels from the bank. She has enough money to get up to 10 rolls of nickels and each roll contains 40 nickels. The bank will not give partial rolls. The function that models the number of nickels Cindy will have after leaving the bank is f(r)=40r+26, where r is the number of rolls of nickels she gets. What is the practical domain of the function?
A) all real numbers
B) r>1
C) {66, 106, 146, 186, 226, 266, 306, 346, 386, 426}
D) all integers from 1 to 10, inclusive
Answer: Option D is the right answer. The practical domain of the function=all integers from 1 to 10, inclusive.
Step-by-step explanation:
Given function f(r)=40r+26, where r is the number of rolls of nickels she gets.
as it is already mentioned that she can get up to 10 rolls of nickels.
Therefore domain of function contains r ≤10,such that r is a natural number.
i.e.Domain of f(r)=all integers from 1 to 10, inclusive.
Domain of a f(x) is a set of values of x which make function f(x) well defined.
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder.
Answer:
The radius of cylinder is 8 inches.
Step-by-step explanation:
We have given,
Volume of cylinder = 320π cubic inches
Height of cylinder = 5 inches
We know, Formula for volume of cylinder as : V =πr²h
where r is radius of cylinder and h is the height of cylinder.
So, We can plug values for V and h to get radius of cylinder.
i.e V = πr²h
320π = πr²* 5
Solving for r.
We get,
320 = r² * 5
320/5 = r²
64 = r²
or r = ±8 , Since radius of cylinder can not a negative number so we neglect -8.
Hence the radius of cylinder is 8 inches.
Which equation is a point slope form equation for line AB ?
A.y−2=34(x−1)
B.y−1=34(x−2)
C.y−5=34(x−6)
D.y−6=34(x−5)
The required equation is C.) y−5 = 3/4(x−6)
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
Here, we have to points (6,5) and, (-2,-1)
So, by using the formula of equation of straight line of two-point form, we get,
(y-y_1)/(x-x_1 )=(y_2-y_1)/(x_2-x_1 )
=>(y-5)/(x-6)=(-1-5)/(-2-6)
=>4y-20=3x-18
=>y-5=3/4(x-6)
Hence, the required equation is, C.) y−5 = 3/4(x−6)
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Write each number in standard form 600 + 90 + 3
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