The flow rate of the hose calculated mathematically is 0.0127425 m³/s.
What is defined as the flow rate?The amount of water which flows through a pipe per unit time is measured as its flow rate. It is typically calculated by dividing the volume of water by the total time it requires to flow. A pipe's flow rate is typically assessed in meters cubes per second as well as litres per second.The flow rate of a pipe is determined by dividing this same volume of water leaving the pipe in cubic yards by the time in hours.
unit = cubic yard/ hours
The mathematical units are as follows:
1 cubic yard equals 0.764555 cubic meter.
The units in meters cubes per second are calculated as follows:
unit = 0.764555 cubic meter/60 seconds
unit = 0.0127425 cubic meter/ seconds
or, 0.0127425 m³/s
Thus, the flow rate is calculated mathematically is 0.0127425 m³/s.
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The complete question is-
The flow rate of a pipe, found by dividing the volume of water that leaves the pipe in cubic yards during a period of time measured in hours. What are the units mathematically?
An inlet pipe can fill Reynaldo's pool in 5 hours, while an outlet pipe can empty it in 8 hours. In his haste to surf the internet, Reynaldo left both pipes open. If he discovered his error after an hour-long surf and closed the outlet pipe, how much longer would be needed to fill the pool?
Answer:
4.625 hours
Step-by-step explanation:
Since it takes 5 hours for the inlet pipe to fill the pool, just using the inlet pipe alone will fill [tex]\frac{1}{5}[/tex] of pool in 1 hour
Since it takes 8 hours for the outlet pipe to empty the pool, just using the outlet pipe alone will empty [tex]\frac{1}{8}[/tex] of pool in 1 hour
Let us assume the pool capacity is 40 gallons
We choose 40 because it is the LCM of 5 and 8 so we can get integer values
Inflow rate = 40/5 = 8 gal per hour
Outflow rate = 40/8 = 5 gal per hour
Net rate = 8-5 = 3 gal per hour if both pipes are open
In one hour with both pipes open, the pool will have 3 gallons of water. Therefore remaining water to fill the pool is 40-3 = 37 gallons
After 1 hour, the outlet pipe is closed and only inlet pipe is open. Therefore inflow rate is 8 gal/hour and outflow rate is 0 gal/hour
So net inflow rate = 8 - 0 = 8 gal/hour
To fill 37 gallons using this rate would be 37/8 = 4.625 hours
Use the table below to answer questions on the number of TV sets per household in the United States. # TV Sets 0 1 2 3 4 5 or more Prob. 0.092 0.275 0.101 0.194 0.035 0.303 a. Verify that this is a probability model. b. Find (3 4) c. Find ( ) d. Find (4) e. Is (4) an unusual event? Why?
From the given discrete probability distribution, we have that:
a) Because the sum of all probabilities is of 1, we can verify that this is a probability model.
b) P(3 or 4) = 0.229.
c) P(at least one) = 0.908.
d) P(4) = 0.035.
e) Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.
What is the discrete probability distribution?The probability distribution in this problem gives the probability of a household having a number of TV sets, given as follows:
P(X = 0) = 0.092.P(X = 1) = 0.275.P(X = 2) = 0.101.P(X = 3) = 0.194.P(X = 4) = 0.035.P(X = 5) = 0.303.For item a, we have to add all the probabilities, hence:
0.092 + 0.275 + 0.101 + 0.194 + 0.035 + 0.303 = 1.
Because the sum of all probabilities is of 1, we can verify that this is a probability model.
For item b, we take the probabilities from the table as follows:
P(3 or 4) = P(X = 3) + P(X = 4) = 0.194 + 0.035 = 0.229.
For item c, we follow a similar procedure to item b, taking the probabilities from the table as follows:
P(at least one) = 1 - P(X = 0) = 1 - 0.092 = 0.908.
For item d, from the table, we have that:
P(4) = 0.035.
For item e, we have that:
P(X ≥ 4) = 0.338.P(X ≤ 4) = 0.662.Since both P(X ≤ 4) and P(X ≥ 4) > 0.05, 4 is not an unusual event.
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How high is a tree that casts a 24 ft shadow at the same time a 5-ft pole casts a shadow 14 ft-long the tree height
Answer:
60/7 ft
Step-by-step explanation:
Using similar triangles, if we let the height of the tree in ft be x,
[tex]\frac{x}{24}=\frac{5}{14} \\ \\ x=\frac{60}{7}[/tex]
Select the values that are solutions to the inequality x2 + 3x – 4 > 0.
Which expressions are equal to 0 when x=-1? Check all that apply.
Answer:
The answer A,B,C
Indicate type of fraction: 10/9
This fraction is an improper fraction.
In improper fractions, the numerator is greater than the denominator
SAT scores are normally distributed, with a mean of 500 points and a
standard deviation of 100 points. Suppose you take the SAT. Several weeks
later, you receive your results, which show that you reached the 90th
percentile for the math portion.
Recalling that SAT scores are always expressed as multiples of 10, how many
points did you get on the test?
A.600
B.630
C.130
D.590
E.690
Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.
What do you mean by standard deviation?In statistics, Standard deviation is a measure of the variation of a set of values.
σ = standard deviation of population
N = number of observation of population
X = mean
μ = population mean
WE have been given that SAT scores are normally distributed, with a mean of 500 points and a standard deviation of 100 points.
The solution as follows;
Let be X: scores of SAT
P(X ≥ x) = 0.9
P((X - 500)/100 ≥ (x - 500)/100) = 0.9
P(Z ≥ z) = 0.9
z = 1.28
1.28 = (x - 500)/100
128 + 500 = x
x = 628
Recalling that SAT scores are always expressed as multiples of 10, then the points we get on the test will be 628.
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Solve the inequality: r divided by negative 3.5 is greater than 9.1 for r.
A: r < −31.85
B: r > −31.85
C: r < −2.6
D: r > 2.6
The solution to the inequality, r/-3.5 > 9.1 is: A: r < −31.85.
How to Solve an Inequality?Just like a normal algebraic equation is being solved, so is an inequality. An inequality is solved by finding the value of the variable that makes the inequality true.
Given the inequality, r/-3.5 > 9.1, follow the steps below to find the possible values of r in the inequality:
r/-3.5 > 9.1
Multiply both sides by -3.5, then change the inequality sign ">" to "<" since we are dividing by a negative number:
r/-3.5(3.5) < 9.1(-3.5) (multiplication property of equality)
r < −31.85
Therefore, the solution to the inequality, r/-3.5 > 9.1 is: A: r < −31.85.
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Answer:
a
Step-by-step explanation:
Round the number to the nearest thousandth.
0.3244
Answer:
.324
Step-by-step explanation:
.3244 if underlined digit >= 5 round the thousandth digit up o/w leave it as is
Jay rides his bike 634 miles in 13 hour.
What is his average speed?
Answer:
49 mile per hour
Step-by-step explanation:
Divide 634 miles by 13 hours to get 48.7, which we can round to the nearest mile (49) to match the significant digits in the problem.
20(1/2x-2)+40(3/4y-4)
Find 3 ratios that are equivalent to the given ratio 12:16
Answer:
answer.3.4,6.8,9.12
Step-by-step explanation:
get 12+16=28.
12/28=6/14=3/7
16/28=8/14=4/7.
now get 3/7and 4/7.
subtruct 3 from 12 and also subtract 4 from 16 to get 9.12
a raindrop falls at the rate of 4/50 mile in 1/20 hour. at this rate how far will the raindrop travel in 1 hour
Answer:
Step-by-step explanation:
4/50 * 20 = 8/5 miles
URGENT PLEASE HELP!!!!! WILL GIVE BRAINLIEST!!!
The coordinates of parallelogram ABCD are A(0, 0), B(a, 0), C(
,
), and D(0, b).
The coordinates of the midpoint of AC¯¯¯¯¯ are (
,b2).
The coordinates of the midpoint of BD¯¯¯¯¯ are (a2,
).
The midpoints of the diagonals have the same coordinates.
Therefore, AC¯¯¯¯¯ and BD¯¯¯¯¯ bisect each other.
Answer:
a, b, a/2, b/2
Step-by-step explanation:
The coordinates of C are (a,b).
You find the midpoint by taking the averages of the coordinates.
The third blank is a/2.The fourth blank is b/2.The diagram shows a circle inside a square work out the area of this circle
16cm is the square
The area of the circle inscribed inside the square is 64π cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The circle inside the square as shown in the diagram have a diameter of 16 cm. Hence:
Radius = diameter / 2 = 16/2 = 8 cm
Area of circle = π * radius² = π * 8² = 64π cm²
The area of the circle inscribed inside the square is 64π cm²
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how to find percentage
Answer:
The easiest way to find percentage is to multiply the number by 100. Like if you were required to find the percentage of 0.87 you multiply it by 100 and get 87 there for 0.87 is equal to 87%.
Step-by-step explanation:
Hope it helps! =D
Find the general expression for the slope of a line tangent to the curve of y=x2+2x at the point P(x,y). Then find the slopes for x=−3 and x=0.5. Sketch the curve and the tangent lines.
The general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.
A line that only touches a curve once is said to be tangent to it. The point (x₀ , y₀) where a line with the equation of a tangent to a curve
y = f ( x ) is given by:
T' (x) = f'(x) (x ₋ x₀) ₊ y₀
The slope of the tangent line to a curve at a point is computed by getting the first derivative of the curve.
y(x)=2x²y
y'(x) = (2)2x²⁻¹ ₊ (1)2x¹⁻¹
y'(x) = 4x¹ ₊ 2x°
y'(x) = 4x ₊ 2(1)
y'(x) = 4x ₊ 2
The slope at a point
P (x, y) is computed by substituting the x-coordinate of the point to the first derivative. This is the general expression for the slope:
m = y'(x) = 4x + 2
For x = - 3
m = 4 (- 3) + 2
m = - 12 + 2
m = - 10
For x = 0.5
m = 4 (0.5) + 2
m = 2 + 2
m = 4
Therefore, the general expression for the slope of the tangent line is m = y'(x) = 4x + 2. the value of m is - 10 for x = - 3 and is 4 for x = 0.5.
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Find an equation of the circle that satisfies the given conditions. Center (−1, 8); passes through (−3, −5)
Answer:
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
Step-by-step explanation:
[tex]\textsf{The standard form of the equation of a circle is }\\\\ \sf (x -h)^2 + (y-k)^2 = r^2 \;where\; (h, k) \textsf{ are the coordinates of the center of the circle and \;r\; is the radius}[/tex]
Here h = -1, k = 8
So we get
[tex](x - (-1)) ^2 + (y - 8)^2 = r^2[/tex]
[tex](x + 1)^2 + (y - 8)^2= r^2\\\\[/tex]
Since the circle passes through the point (-3, -5) we can plug in these values of x = -3 and y = -5 to get r squared
[tex](-3 + 1)^2 + (-5 -8)^2 = r^2\\\\(-2)^2 + (-13)^2 = r^2\\\\4 + 169 = r^2\\\\r^2 = 173\\\\\\[/tex]
So the equation of the circle is
[tex](x + 1)^2 + (y-8)^2 = 173[/tex]
8 There are 3 horses in a field.
Each horse has 4 legs. Write
an addition equation and a
multiplication equation to find
the number of legs on 3 horses.
Add:
Multiply:
Let a = any rational number. Is the absolute difference if a is a positive or a negative number? Explain
Answer: Is the absolute difference if a is a positive number, when a = any rational number.
Step-by-step explanation:
Define Positive numbers:
Positive numbers are the numbers which are greater than zero that lies on the right side of the number line.
Example: 0, 1, 2, 3, 4…
Define Negative numbers:
Negative numbers are the numbers which are less than zero that lies on the left side of the number line.
Example: … -5, -4, -3, -2, -1, 0.
Given data,
Let a = any rational number. Is the absolute difference if a is a positive number.
Because,
Let us take, a = any rational number
We have to know → Is the absolute value of a different if a is a positive number or negative number.
Define Modulus (|x|) of a number :
The modulus or absolute value of a number means the distance that goes from the number to its origin, this is, to the point 0 (zero) that makes part of the real straight line. For instance, the distance from point 6 to its origins is 6, but the distance from point -6 to its origins is also 6.
The modulus operator formula is :
|x| = { x if x ≥ 0 and -x if x ≤ 0
Given question,
Assume any rational number x/y
Using the Modulus property :
|x| = { x/y if x/y ≥ 0 and -x/y if x/y ≤ 0
Therefore, if the rational number is less then zero (say -2).
Then the absolute value will be = - (- 2) = 2
and for any rational number greater than 0 (say 2)
Then its absolute value will be = 2 only.
Hence,
Is the absolute difference if a is a positive number, when a = any rational number.
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chapter 8
1.Find the surface area of each figure. Round your answers to the nearest hundredth, if necessary.
The surface area of the sphere is approximately equal to 615.752 square miles.
How to determine the surface area of a solid
The surface area of a solid is the area comprised by all faces of a solid, in the case of a sphere, there is only one face whose extension is determined by the following formula:
A = 4π · r²
Where:
A - Area of the sphere, in square miles.r - Radius of the sphere, in miles.If we know that r = 7 miles, then the surface area of the sphere is:
A = 4π · (7 mi)²
A ≈ 615.752 mi²
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Round 2,159 to the nearest hundred
Answer: 2200
Hope it helps!
Change
69
7
to a mixed number
Answer:
9 6/7
This is the answer
What is the range equation
34. La información nutrimental de
cierto pan dulce señala que una
porción equivale a 7 g. ¿A cuánto
equivale "peso neto", en onzas?
Considera 1 onza (oz) = 28.3 g
Answer:
7 gramos = 0,247 onzas
Explanation
Fórmula
para obtener un resultado aproximado, divida el valor de la masa por 28,35
7 ÷ 28,35
= 0.247 onzas
The coordinates of M are(_,_)and the perimeter of Triangle MOl is__
units. For the perimeter, round your solution to the nearest tenth of the exact value.
Distance between the two (x₁, y₁) and (x₂, y₂) coordinates are-
d = √[(x₁ - x₂)² + (y₁ - y₂)²]
The coordinates of M taken from the graph are -
M = (1.5, 3)
Now, for calculating the perimeter of triangle MOI is-
First find the distance between points O and I.
O = (0, 0) and I = (3, 0)
OI = √[(3 - 0)² + (0 - 0)²]
OI = 3 units.
The distance between MI;
MI = √[(3 - 1.5)² + (0 - 3)²]
MI = √[(1.5)² + (-3)²]
MI = √(2.25 + 9)
MI = 3.35 units
Now, find distance between OM
MO = √[(1.5 - 0)² + (3 - 0)²]
MO = √[(1.5)² + (3)²]
MO = √(2.25 + 9)
MO = 3.35 units
Thus, the perimeter of the triangle MOI is;
Perimeter = OI + MO + MI
= 3 + 3.35 + 3.35
Perimeter = 9.7 units.
Thus, the perimeter of the Triangle MOI is 9.7 units.
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A marching band uses a grid to determine the members positions. Juan starts at (2,2). Every 15 seconds, he moves 4 yards east and 3 yards north.
After 15 seconds Juan moves (6, 5).
In the given question,
given that,
A marching band uses a grid to determine the members’ positions.
Juan starts at (2, 2).
Every 15 seconds, he moves 4 yards east and 3 yards north.
2 + 4 = 6.
2 + 3 = 5.
so after 15 seconds Juan moves (6, 5).
Hence we get the (6,5) as the main answer.
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Amir buys a car for £13155 which depreciates in value at a rate of 1.5% per year.
How much Amir's car will be worth in 9 years.
Answer: $11,379 i believe
Step-by-step explanation: Multiplying 9 times the percentage value at which the cars value depreciates it gives you, 13.5%. Dividing 13155 by that 13.5% will give you the absolute value of $11379.075 in which would be $11,379.
Hope this helps!
1=1cm x 1\2 cm x 2cm
There isn't a ton of info provided in your question, however, I believe the solution is 1 = 1.
-4 + 8[tex]\frac{3} {8}\frac{6} {7}[/tex]
It should be noted that the value of -4 + 8 36/87 will be 4 12/29.
How to calculate the fraction?It should be noted that based on the information illustrated, the fraction given is illustrated as:
= -4 + 8 36/87
= -4 + 8 12/29
= 4 12/29
Therefore, it should be noted that the value of -4 + 8 36/87 will be 4 12/29.
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