Answer:
Volume flow rate, Q, into the tank is 12.376 m³
Step-by-step explanation:
Here we have Bernoulli's equation presented as follows
[tex]\frac{P_{1}}{\rho _{1}g}+\frac{v_{1}^{2}}{2g} + z_{1} = \frac{P_{2}}{\rho _{2}g}+\frac{v_{2}^{2}}{2g} + z_{2}[/tex]
Where:
P₁ = Pressure, of the open tank = Atmospheric pressure = 0
P₂ - Pressure at the discharge of the pipe = Atmospheric pressure = 0
ρ₁ = Density of the fluid = ρ₂
v₁ = Velocity of the fluid in the tank
v₂ = Velocity of the fluid in the pipe
d₁ = Diameter of the tank = 1.5 m
d₂ = Diameter of the pipe = 15 cm = 0.15 m
A₁ = Cross sectional area of tank = π×d₁²/4 = 1.767 m²
A₂ = Cross sectional area of pipe= π×d₂²/4 = 0.01767 m²
z₁ = Level of water in the tank = 0 m
z₂ = Level of water in the pipe = 2.5 m
Whereby the level remains constant at 2.5 m, pressure at the base, P₂ = ρ₁×g×2.5
Also
v₁×A₁ = v₂×A₂ which gives;
v₁×1.767 = v₂×0.01767
v₂ = v₁×1.767/0.01767 = 100·v₁
Hence we have;
[tex]\frac{0}{\rho _{1}g}+\frac{v_{1}^{2}}{2g} + z_{1} = \frac{0}{\rho _{1}g}+\frac{(100v_{1})^{2}}{2g} + z_{2}[/tex]
[tex]z_{1} - z_{2} = \frac{(100v_{1})^{2}}{2g}- \frac{v_{1}^{2}}{2g}[/tex]
[tex](2.5)2g = 99v_{1}^{2}}[/tex]
v₁² = 2.5×2×9.81 = 49.05
v₁ = √49.05 = 7.0035 m/s
Therefore, since the rate of discharge = Rate of entry into the tank, we have;
Volume flow rate, Q, into the tank = v₁×A₁ = 7.0035 m/s × 1.767 m² = 12.376 m³.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.5-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.9% or largest 1.9%. a) What is the minimum head breadth that will fit the clientele? b) What is the maximum head breadth that will fit the clientele?
Answer:
a) min = 4.4251
b) max = 8.5743
Step-by-step explanation:
Given:
Mean, u = 6.5
Standard deviation = 1
To get our values, we are to use the inverse of the standard normal table.
a) The minimum head breadth that will fit.
P(Z < z) = 1.9%
P(Z < z) = 0.019
P(Z < -2.0749) = 0.019
z = -2.0749
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = -2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (-2.0749 * 1) + 6.5
x = 4.4251
The minimum head breadth that will fit the clientele is 4.4251
b) The maximum head breadth that will fit.
P(Z > z) = 1.9%
1 - P(Z < z) = 0.019
P(Z < z) = 1 - 0.019 = 0.981
P(Z < 2.0749) = 0.981
From the z-score formula, we have:
[tex] \frac{x - \mu}{\sigma} = Z_0_._0_1_9 [/tex]
Let x be the breath of heads.
Making x the subject of the formula, we have:
[tex] x = z * \sigma + \mu [/tex]
We already have:
z = 2.0749
u = 6.5
s.d = 1
Substituting figures, we have:
x = (2.0749 * 1) + 6.5
x = 4.4251
x = 8.5743
The maximum head breadth that will fit the clientele is 8.5743
Factor as the product of two binomials.
81 +18x +x^2
Answer:
(x + 9)²
Step-by-step explanation:
x² + 18x + 81
(x + 9)(x + 9)
(x + 9)²
A middle school took all of its 6th grade students on a field trip to see a play at a theatre that has 5000 seats. The students filled 4500 of the seats in the theatre. What percentage of the seats in the theatre were filled by the 6th graders on the trip?
Answer:
90%
Step-by-step explanation:
So, in order to get this answer, you must divide the amount of students that filled the theatre, which is 4,500, by the amount of seats at the theatre, which is 5,000. You can eliminate the two zeros at the end of each number, which will leave you with 45/50. 45 divided by 50 equals 0.9. You can then multiply 0.9 by 100, because of the 2 zeros eliminated earlier. This will leave you with 90%.
The spinner below is spun 20 times. It lands on red 6 times, yellow 2 times, green 8 times, and blue 4 times.
What is the theoretical probability of landing on red? Select all that apply
Group of answer choices
0.42
1/2
5/12
50%
42%
Answer:
I think the answer is 42%
given g (x) = -x -2, find g (-5)
Answer:
g(-5)=3
Step-by-step explanation:
g(-5)=-(-5)-2=5-2=3
Substitute x with -5.
g(-5) = -(-5) - 2
g(-5) = 5 - 2
g(-5) = 3
Best of Luck!
What is the solution to this equation?
-8x + 4 = 36
A. x= -5
B. x= 4
C. x = 5
D. x= -4.
Answer:
D. x= -4
Step-by-step explanation:
-8x × -4 = 32 + 4 = 36
you can subtract 4 from 36, which leaves you with -8x = 32. you then divide 32 by -8 to (1) cancel out -8 which will leave you with x, and (2) give you your answer. 32 / -8 = -4.
x is -4
which graph represents the linear function y=1/4x-3
Answer:
The graph with a y-intersect of (0, -3) and x-intercept of (12, 0)
Step-by-step explanation:
So the graph goes 1 unit up every 4 units to the right
The graph which represents the linear function y = 1/4x – 3 is A. A line on a graph passes through the (-4, -4), (0, -3), and (4, -2).
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Given linear function is,
y = 1/4x – 3
Substitute x = 0.
y = 0 - 3 = -3
So the graph passes through (0, -3).
Let x = 4.
y = (1/4 × 4) - 3 = -2
So the graph passes through (4, -2).
Let x = -4,
y = (1/4 × -4) - 3 = -4
So the graph passes through (-4, -4).
Hence the graph passes through (-4, -4), (0, -3), and (4, -2).
Learn more about Linear Functions here :
https://brainly.com/question/20106471
#SPJ3
The complete question is given as follows.
Which graph represents the linear function y = 1/4x – 3?
A. A line on a graph passes through the (-4, -4), (0, -3), and (4, -2).
B. A line on a graph passes through the (-4, -2), (0, -3), (4, -4).
C. A line on a graph passes through the points (0, -3), (1, 1), (2, 5).
D. A line on a graph passes through the points (-4, 2), (0, 3), (4, 4).
| 2p -1 | =45, what are the values of p?
Answer:
p = 23 and p = -22
Step-by-step explanation:
| 2p -1 | =45
Absolute value equations have 2 solutions, one positive value and one negative
2p-1 = 45 and 2p-1 = -45
Add 1 to all sides
2p-1+1 = 45+1 and 2p-1+1 = -45+1
2p = 46 2p = -44
Divide by 2
2p/2 = 46/2 and 2p/2 = -44/2
p = 23 and p = -22
PLEASE ANSWER THIS QUESTION,ILL MARK YOU AS THE BRAINLIEST IF UR ANSWER IS CORRECT.
Answer:
I WILL SAY THE 2 ONE
Step-by-step explanation:
joy and Peter were each walking along a straight road. joy walked 1800 meters in 1/3 hour. Peter walked 1/2 of joys distance in 1/5 hour.
the 1/3, 1/2, and 1/5 are fractions
Answer:
what is it asking to find then i can help
Step-by-step explanation:
Answer:
B: It travels for 2 hours, then stops for 1 hour, and finally travels again for 2 hours.
Fill in the blank
The equation *blank* describes the relationship
( simplify your answer )
Answer:
y=2/3x
Step-by-step explanation:
PLEASE HELP!!
g(r)=25−3r
G(4)=
Answer:
13
Step-by-step explanation:
g(r)=25−3r
Let r=4
G(4)= 25 - 3(4)
= 25 -12
= 13
Answer:
13
Step-by-step explanation:
7x^2-2x+1-(9x^2+2x-1)
Answer:
[tex]-2x^2-4x+2[/tex]
Step-by-step explanation:
[tex](7x^2-2x+1)-(9x^2+2x-1)=\\(7x^2-9x^2)+(-2x-2x)+(1+1)=\\-2x^2-4x+2[/tex]
Hope this helps!
1) Use the factor theorem to determine if 3x-4 is a factor of f(x)=3x^2+2x-8
2) Find the value of K so that x+6 is a factor of 6x^3+kx^2-7x-6
Step-by-step explanation:
put f(4/3)= 3(4/3)^(2) +2(4/3)-8 =0
so 3x-4 is a factor
similarly, k=35
find the smallest 4 digit number that is a perfect square and perfect cube
Answer:
1024 is the smallest four digit number which is a perfect square.
Step-by-step explanation:
So the least number to be added to 1000 is 24. Therefore, 1000+24 = 1024 is the smallest four digit number which is a perfect square.
Answer:
1024
Step-by-step explanation:
So the least number to be added to 1000 is 24. Therefore, 1000+24 = 1024 is the smallest four digit number which is a perfect square.
PLZ MARK ME BRAINLIEST
Factor completely: x^2-y^2-1.5(x-y)
Answer:
(x-y)(x+y-1.5)
Step-by-step explanation:
At a pizza resturant they have a choice of 20 toppings. If a customer choosea two topping pizza find the probability that they ordered a pepperoni and sausage
Answer: The probability is 1/190 = 0.005
Step-by-step explanation:
The probability of ordering two specific toppings out of 20 is:
For the first selection he can order 2 of them, peperoni or sausage, so the probability for the first selection is 2/20 = 1/10 (the number of correct options divided by the total number of options)
For the second selection we have only one option, because we assume that the other one was selected previously, here we also had a total of 19 toppings because one already was selected, the probability in this selection is 1/19.
The joint probability is equal to the product of those two probabilities:
P = (1/19)*(1/10) = 1/190 = 0.005
what is m/2=12? plz helps
Answer:
Its 6
Step-by-step explanation:
6 times 2 equals 12
so m=6
Answer:
m=24
Step-by-step explanation:
12x2=24
24/2=12
quanto fa 2 +2??? grazie
Answer:
4
Step-by-step explanation:
2+2=4
A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to the height of 7 centimeters. Find the volume of empty space in the cylinder.
Answer:
volume of empty space = 141.3 cm³
Step-by-step explanation:
volume of empty space = volume of the cylinder - volume of water
First, we need to calculate the volume of the container
volume of a cylinder = πr²h
where r = radius of the container and h is the height of the container
r = 3cm and h = 12 cm π is a constant which is ≈ 3.14
volume of a cylinder = πr²h
=3.14 × 3²×12
=3.14×9×12
=339.12 cm³
We will proceed to find the volume of water
since liquid will take the shape of its container,
then volume of water = πr²h
r is the radius of the container and h is the height of the water
r = 3cm and h = 7cm
volume of water = πr²h
= 3.14 ×3²×7
=3.14×9×7
=197.82 cm³
volume of empty space = volume of the cylinder - volume of water
=339.12 cm³ - 197.82 cm³
= 141.3 cm³
OR
WE CAN SOLVE DIRECTLY
height of empty space = height of container - height of water
= 12 - 7
=5 cm
volume of empty space = πr²h
=3.14×3²×5
=3.14×9×5
=141.3 cm³
volume of empty space = 141.3 cm³
The volume of the empty space in the cylinder is equal to the difference between the volume of the cylinder and the volume of water in the cylinder.
The volume of the cylinder can be calculated using the formula:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Substituting the given values, we get:
V = π(3 cm)^2(12 cm)
V ≈ 339.3 cubic centimeters
The volume of water in the cylinder can be calculated by multiplying the cross-sectional area of the cylinder by the height of the water:
V_water = πr^2h_water
where V_water is the volume of water and h_water is the height of the water.
Substituting the given values, we get:
V_water = π(3 cm)^2(7 cm)
V_water ≈ 197.9 cubic centimeters
Therefore, the volume of empty space in the cylinder is:
V_empty = V - V_water
V_empty ≈ 339.3 - 197.9
V_empty ≈ 141.4 cubic centimeters
So, the volume of empty space in the cylinder is approximately 141.4 cubic centimeters.
Fill in the Blank 6:15=8:_
Answer:
20
Step-by-step explanation:
What proportion of... help me please
Answer:
Below in bold.
Step-by-step explanation:
I won't do all these but you should get the idea of how to do them from the following. Be careful with the units if they are given . You must convert both values to the same unit before working out the percentages.
a. What proportion of 15 is 5:
As a fraction it is 5/15 = 1/3.
Now convert to a percentage by multiplying by 100:
1/3 * 100 = 33.33%
b. 20 and 10
= 10/20 = 1/2
1/2 * 100 = 50%.
e. £30 and £12
= 12/30
= 2/5
= 2/5 * 100 = 40%.
h. 6.4 is 0.4
= 0.4 / 6.4
= 4/64
= 1/16
= 1/16 * 100 = 6.25%
i. £144 is 12p
Here we convert the 2 values to pence:
£144 = 144 * 100 = 14,400p
The fraction is 12/14,400
= 1/1200
= 1/1200 * 100 = 0.083%
j. 1.2 m is 30 cm
Convert 1.2 m to cm
= 1.2 * 100 = 120
The fraction is 30/120 = 1/4
= 1/4 100 = 25%.
Which number line shows the solution set to this inequality? -2x + 9 < x − 9
Answer:
see below
Step-by-step explanation:
-2x + 9 < x − 9
Add 2x to each side
2x-2x + 9 < 2x+x − 9
9 < 3x-9
Add 9 to each side
9+9 < 3x
18 < 3x
Divide each side by 3
18/3 < 3x/3
6 < x
Open circle at 6 line going to the right
Answer:6 to the right of the number line
Step-by-step explanation:I just did this quiz
If r = 10 and s = 31, find R. Round to the nearest tenth
Answer: c 17.9°
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
I took the test
$ The polynomial 3x3 + 10x2 - x - 12 has a factor of x + 3. Find the remaining factors,
Answer:
(3 x + 4) (x - 1) (x + 3)
Step-by-step explanation:
Factor the following:
3 x^3 + 10 x^2 - x - 12
The possible rational roots of 3 x^3 + 10 x^2 - x - 12 are x = ± 1/3, x = ± 2/3, x = ± 4/3, x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = -4/3, x = 1 and x = -3 are roots. This gives 3 x + 4, x - 1 and x + 3 as all factors:
Answer: (3 x + 4) (x - 1) (x + 3)
4X minus 5X +9 equals 5X -9
A sundae requires 2 ice-cream scoops and 4 raspberries, and a milkshake requires 3 ice-cream scoops and 5 raspberries. Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 blueberries. Let S denote the number of sundaes she makes and M the number of milkshakes she makes. Write an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS).
This question is incomplete because it was a details in the question was not written correctly.
Complete Question:
A sundae requires 2 ice-cream scoops and 4 raspberries, and a milkshake requires 3 ice-cream scoops and 5 raspberries. Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries. Let S denote the number of sundaes she makes and M the number of milkshakes she makes. Write an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS).
Answer:
An inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:
2S + 3M ≤ 80
Step-by-step explanation:
From the above question, we are told that:
Let S denote the number of sundaes Laila makes
M the number of milkshakes
a) A sundae requires 2 ice-cream scoops and 4 raspberries
A sundae = 2S and 4S
b) A milkshake requires 3 ice-cream scoops and 5 raspberries.
A milk shake = 3M and 5M
Laila wants to sell sundaes and milkshakes with at most 80 ice-cream scoops and 150 raspberries .
Therefore, an inequality that represents the condition based on the number of (ICE-CREAM SCOOPS) is given as:
2 ice cream scoops + 3 ice cream scoops ≤ 80
2S + 3M ≤ 80
In the diagram, which pair of angles are alternate interior angles?
5/6
1 2
43
8/ 7
22 and 25
21 and 27
25 and 23
27 and 24
I needs halp
What are the roots of y = x2 – 3x – 10?
Answer: y =x2 (squared)−3x−10
Step-by-step explanation:
Answer:
What are the roots of y [tex]y=x^{2}-3x-10[/tex]?
[tex]x=5[/tex] [tex]and[/tex] [tex]=-2[/tex] .
Step-by-step explanation:
The given equation in two variables is [tex]y=x^{2}-3x 10 y = x 2 - 3 x - 10[/tex] .
We are asked to find the roots. We will now apply the zero factor property
by equating each factor to zero. Thus, the roots of the equation are
[tex]x=5[/tex] and [tex]x=-2[/tex] .
SOLVE USING ELIMINATION *20 POINTS*
1. 3x - y = 28
3x - y = 14
a. (8,-4)
b. (-7,7)
c. (7,-7)
d. (-4,8)
2. x+ 4y 13
2x + 3y 6
a. (3,5)
b. (-3,4)
C. (4,5)
d. (4,4)
3. 12r-9y 30
6x + 15y = 54
A. x = 4 and y 2
B. x = 2 and y = 4
C. x = 14 and y 2
D. x = 37/7 and y =26/7
4. x + 3/2 y = -3
6/7x + 7y = -8
A. (27/8, -1/4)
B. (9/2, -5)
C. (-3/11, -10/11)
D. (-63 / 40, -19/20)
1. No answer ( may be due to incorrect question)
2. x = -3
y = 4
3. x= 4
y = 2
4.x = -63/40
y= -19/20
Step 1
Multiply equation 1 by the coefficient of x in equation 2
Multiply equation 2 by the coefficient of x I'm equation 1
(after completing this step you will derive equation 3 and 4 )
Step 2
Subtract equation 4 from equation 3
Step 3
Divide both sides of the equation by the coefficient of y
Step 4
substitute your value for y in equation 1 or 2
(after this you will derive the values of x)
Note : This method is for the Elimination of x
I hope it helps
Answer: A. X = 11
Step-by-step explanation:
x - 7 = 4
11 - 7 = 4