Answer:
a) 71.25 gallons
b) 25 hrs
c) 105 gallons
d) 47.91 hrs
Step-by-step explanation:
Solution:-
- The rate at which the pollution enter the lake is expressed by a function f ( t ) as follows:
[tex]f ( t ) = 10*( 1 - e^-^0^.^5^t )[/tex]
- Where, the rate at which pollution is removed from the lake via a filter is expressed by a function g ( t ):
[tex]g ( t ) = 0.4t[/tex]
- We will denote ( x ) as the amount of population in lake at time ( t ).
- We will set up a linear first order ODE using rate of change of pollution ( x ) in the lake at any instance ( t ):
[tex]\frac{dx}{dt} = ( flow _ i_n ) - ( flow _ o_u_t )[/tex]
- The respective inflow and outflow of pollution from the lake are expressed by the functions f ( t ) and g ( t ). Hence, the ODE becomes:
[tex]\frac{dx}{dt} = f ( t ) - g ( t )\\\\\frac{dx}{dt} = 10*( 1 - e^-^0^.^5^t ) - 0.4t\\\\[/tex]
- Separate the variables and integrate from t = 0 to t = 12 hours.
[tex]x = \int\limits^1^2_0 [{10*( 1 - e^-^0^.^5^t ) - 0.4t} ] \, dt \\\\x ( 12 ) = [ 10 * ( t + 2e^-^0^.^5^t ) - 0.2t^2 ] \limits^1^2_0\\\\x ( 12 ) = [ 10 * ( 12 + 2e^-^6 ) - 0.2(12)^2 ] - [ 10* ( 0 + 1 ) - 0.2(0)^2 ]\\\\x ( 12 ) = 71.25 galls[/tex]
- We will use the graphing calculator to evaluate the time ( t ) at which the rate of inflow of pollution is equal to the rate at which pollution is removed from the lake. In other words solve the following equation:
[tex]f ( t ) = g ( t )\\\\10*( 1 - e^-^0^.^5^t ) = 0.4t[/tex]
- Solving for the above equation the following intersection point was observed:
t = 25 hours
- We will perform integration of the previously expressed ODE from t = 0 to t = 25 hrs.
[tex]x ( 25 ) = [ 10*(t - 2e^0^.^5^t ) - 0.2t^2 ]\limits^2^5 _ 0\\\\x ( 25 ) = [ 10*(25 - 2e^1^2^.^5 ) - 0.2(25)^2 ] - [ 20 ] \\\\x ( 25 ) = 105 galls[/tex]
- We will evaluated result of the integration from time t = 0 to time t = t set the amount of pollution ( x ) equal to zero:
[tex]x ( t ) = [ 10*( t - 2e^-^0^.^5^t ) - 0.2t^2 ]\limits^t_0\\\\x ( t ) = 10 + 20e^-^0^.^5^t - 0.2t^2 - 20[/tex]
- Use the derived result x ( t ) and feed it into the graphing calculator and solve for x ( t ) = 0; hence,
10 + 20e^( -0.5*t ) - 0.2t^2 - 20 = 0
- The answer is evaluated as t = 47.91 hr
What is the probability of drawing a red marble out of the bag without looking?
Answer:
it depends on how many red marbles are there
Step-by-step explanation:
is there any green or orange or yellow?
Answer:1 over 3
Step-by-step explanation:
Suppose you take a random sample from a normal population and you want to determine whether there is sufficient statistical evidence to claim that the population variance differs from a corresponding variance specified in a government contract. Which type of test is appropriate, a test of one variance or a test of two variances?
Answer:
A test óf one variance
Step-by-step explanation:
A test of one variance. In this case, one will be testing against the hypothesized variance that was given.
3. A sphere has a volume of 4,500Tt cubic inches. What is the radius of the
sphere?
A. 3,375 inches
B. 15 inches
C. 30 inches
D. 225 inches
Answer:
10.24 in
Step-by-step explanation:
Formula for volume of a sphere
= 4/3πr³
This sphere has a volume of
4,500cubic inches= 4500in³
The radius will be equall to
4/3πr³= 4500in³
r³ =( 4500 * 3)/(4π)
r³ = 1074.296
r = 3√1074 296
r = 10.24 in
Determine if the triangles below are similar and explain.
Answer:
The answer would be C the triangles are not similar
Step-by-step explanation:
A cube has sides that are 3 in. long. What is the surface area of the cube?
OA) 72 in2
OB) 54 in 2
OC) 36 in2
OD) 61 in 2
Answer:
B 54in
Step-by-step explanation:
In the xy-plane, point E has coordinates (4,5) and point O has coordinates (0,0). Which of the following is an equation of the line that contains points O and E?
a)y=x-1
b)y=x+1
c)y=4/5x
d)y=5/4x
Answer:
D
Step-by-step explanation:
You can plug in the given x and y values into the equations and see which one works for both of them.
D works for both of them:
5 = 5/4(4)
0 = 5/4(0)
Answer:
y=5/4x
Step-by-step explanation:
I just took the TSI2 and it says its correct
The weight of an object on a particular scale is 145,2 lbs. The measured
weight may vary from the actual weight by at most 0.3 lbs. What is the range
of actual weights of the object?
Answer:
145.2 + .3 = 145.5
145.2 - .3 = 144.9
C. 144.9 <= x <= 145.5
Step-by-step explanation:
H is directly proportional to the square root of p h=5.4 when p=1.44 find h when p=2.89
Answer:
h=7.65
Step-by-step explanation:
h=k√p
k=h/√p
k=5.4/√1.44
k=4.5
h=4.5√p
when p=2.89
h=4.5√2.89
h=7.65
Answer:
H = 7.65
I hope it helps
[tex]h \: = \sqrt{p} \\ h \: = k \sqrt{p} .....(1) \\ when \: h \: = 5.4 \: p = 1.44 \\ 5.4 = k \: \sqrt{1.44} [/tex]
[tex]5.4 = 1.2k \\ divide \: both \: sides \: by \: 1.2 \\ k \: = 4.5[/tex]
[tex]h \: = 4.5 \sqrt{p} = \: formula \: connecting \: h \: and \: p \\ from \: equation \: .....(1) \\ when \: p \: = 2.89 \: h = \\ when \: p \: = 2.89 \: h \: = \\ h \: = 4.5 \sqrt{2.89} \\ h = [/tex]
[tex]h \: = 4.5 \sqrt{2.89} \\ h = 4.5 \times 1.7 \\ h \: = 7.65[/tex]
Write the equation of a line that is perpendicular to the given line and that passes through the given point. y = 3/4x -9; (-8, 18)
Answer: y=-4/3x+22/3
Step-by-step explanation:
the slope of a perpendicular line is the "negative reciprocal" of the slope of the original line
y=-4/3x+b
if you put in the x and y values
18=-4/3*-8+b
18-32/3=b
b=22/3
y=-4/3x+22/3
Which expressions are equivalent to 30 - 3y - 9?
3(17-y)
3(20-y-3)
17(3-y)
Or 20(3-3y)-9
Answer:
3(20 - y - 3)
Explanation:
If you expand it:
3 · 20 = 30
3 · -y = -3y
3 · -3 = -9
Combine them altogether to get:
30 - 3y - 9
(3 1/2 - 9 3/4) ÷ (-2.5)
exact form
5/2
decimal form
2.5
mixed number form
2 1/2
what is the solution to -4[2×+6]=-24
Answer:
x=0
Step-by-step explanation:
-4(2x+6) = -24
distribute the -4 to the parentheses
-8x-24 = -24
add the 24 over
-8x=0
divide both sides by -8
x=0
PLEASE HELP WILL MARK BRAINLIEST !!!
Answer:
work is shown and pictured
You are painting a door with a diamond shape shaped window as shown you have to put a tape around the edge of the window to keep the paint off find the length of tape you need to to the nearest inch
Answer:
104 inches
Step-by-step explanation:
No window dimensions are given. We might assume that the shape of the window can be defined by these coordinates:
(18,64), (28,40), (18,16), (8,40)
A graph of the points reveals the window to be a rhombus, so we can figure the length of one side to determine the lengths of all sides.
On edge of the window will have a length determined by the distance formula:
d = √((x2 -x1)^2 +(y2 -y1)^2)
For (x1, y1) and (x2, y2) as (8, 40) and (18, 64), the edge length is ...
d = √((18 -8)^2 +(64 -40)^2) = √(10^2 +24^2) = √676
d = 26 . . . . . the length of one of the four edges
The total length of the four window edges is ...
4 × 26 = 104
104 inches of tape are needed.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
p(x)=19x+15
Step-by-step explanation:
Distribution property
Take the values of r and x- you should end up with p(x)=(25x-6x+15)(x)
- 25x minus 6x equals 19x
- form there you distribute the (x) and it will square 19x and multiply with 15
- end answer should be p(x)=19x²+15x
- simply by factoring the ² and 15x and you should get 19x+15
comment if you need clearer step by stepAnswer:
A. p(x) = 19x - 15
Step-by-step explanation:
→Set it up, like so:
[tex](25x)-(6x+15)[/tex]
[tex]25x - 6x-15[/tex]
→Add like terms (25x and -6x):
[tex]19x - 15[/tex]
Alan made a small four sided table for his office .Two sides of the table are 27 inches long and 36 inches long .If the diagonal of the table is 40 inches ,does the table have a right angle at the corners
Answer:
does NOT have right angles at the corners
Step-by-step explanation:
we are given that the sides of a table are 27" and 36" long.
If we assume the table to be rectangular, then by Pythagorean formula, we can find the diagonal and compare it to the 40" that we are given.
(refer to attached)
diagonal² = 27² + 36²
diagonal² = 27² + 36²
diagonal² = 2025
diagonal = √2025
diagonal = 45 inches
because the diagonal that we found is not the same as the 40" that was given, we can conclude that the table is not a rectangle (i.e does not have right angles at the corners)
Evaluate the function at the given values of the independent variable. Simplify the results.
[tex]answers \\ a. \: \: 0 \\ b. \: \: \frac{ - 63}{8} \\ c. \: \: {c}^{3} - {5c}^{2} \\ d. \: \: {t}^{3} + 25t + {10t}^{2} \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
Find the area of the triangle QRS, R(6, 10) Q(-9, 5) S(2, -10)
Answer:
[tex]Area = 140[/tex]
Step-by-step explanation:
Given
R(6, 10)
Q(-9, 5)
S(2, -10)
Required
Area of triangle RQS
The are of RQS is calculated using the following formula;
[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]
Where x and y represent the axis of the given coordinates;
Given that R(6, 10);
[tex]R_x = 6 ; R_y = 10[/tex]
Given that Q(-9, 5);
[tex]Q_x = -9 ; Q_y = 5[/tex]
Given that S(2, -10);
[tex]S_x = 2 ; S_y = -10[/tex]
By Substituting these values in the given formula;
[tex]Area = \frac{1}{2} [R_x(S_y - Q_y) + Q_x(R_y - S_y) + S_x(Q_y - R_y)][/tex]
[tex]Area = \frac{1}{2} [6(-10 -5) + -9(10 - (-10)) + 2(5 - 10)][/tex]
[tex]Area = \frac{1}{2} [6(-15) + -9(10 + 10)) + 2(-5)][/tex]
[tex]Area = \frac{1}{2} [-90 + -9(20)) - 10][/tex]
[tex]Area = \frac{1}{2} [-90 -180 - 10][/tex]
[tex]Area = \frac{1}{2} [-280][/tex]
The expression |-280| means absolute value of -280 and the value is 280
[tex]Area = \frac{1}{2} [-280][/tex]
[tex]Area = \frac{1}{2}* 280[/tex]
[tex]Area = 140[/tex]
Hence, the area of the triangle is 140
Bugs Bunny was
42
4242 meters below ground, digging his way toward Albuquerque, when he realized he wanted to be above ground. He turned and dug through the dirt diagonally for
100
100100 meters until he was above ground.
What is the angle of elevation, in degrees, of Bugs Bunny's climb?
Answer:
24.83 degrees.
Step-by-step explanation:
In the diagram, Bugs Bunny was initially at point A 42 meters below ground and dug diagonally 100 meters to point B.
We are to determine the angle of elevation, [tex]\angle BAX[/tex] of his climb.
Now, [tex]\angle BAX=\angle ABC$ (Alternate Angles)[/tex]
Using Trigonometric ratios
[tex]\sin B=\dfrac{AC}{AB} \\\sin B= \dfrac{42}{100}\\\\B=\arcsin \dfrac{42}{100}\\\\B=24.83^\circ[/tex]
The angle of elevation of Bugs Bunny's climb is 24.83 degrees. (correct to 2 decimal places).
WHICH TWO CHOICES ARE EQUIVALENT TO THE FRACTION BELOW?
Answer:
option B, and D
Step-by-step explanation:
coz when u multiply 2/3 by 2/2, u wud get 4/6,
and when u divide 8/12 by 2/2, u wud agn get 4/6
Answer: 2/3 and 8/12
Step-by-step explanation: When we multiply or divide the numerator and denominator of a fraction by the same number, we get an equivalent fraction.
First write 4/6 in lowest terms by dividing both the numerator and the denominator by 2 to get the equivalent fraction 2/3.
Starting at 4/6 again, if we multiply the numerator and the denominator by 2, we get the equivalent fraction 8/12.
So our two equivalent fractions are 2/3 and 8/12.
It's important to remember the following rule: Whatever you do to the numerator of a fraction, you must also do to the denominator because if you don't, you're changing the value of the fraction.
A sculpture is in the shape of a square pyramid. The sculpture has a height of 36 feet and a volume of 19,200 cubic feet. Find the side length of the square base
Answer:
40ft
Step-by-step explanation:
The volume of a square pyramid is given by:
[tex]V=\frac{l^2h}{3}[/tex]
where V is the volume, l is the length of the square base, and h is the height.
Since we need to find the length, we solve for [tex]l[/tex] in the last equation:
[tex]l^2h=3V\\\\l^2=\frac{3V}{h} \\\\l=\sqrt{\frac{3V}{h} }[/tex]
and now, we substitute the known values:
[tex]V=19,200ft^3\\h=36ft[/tex]
and we get the following:
[tex]l=\sqrt{\frac{3(19,200ft^3)}{36ft} }\\ \\l=40ft[/tex]
the length of the square base is 40ft
A 80 kg patient needs a medication x in the amount of 0.25 mg/kg/day. The medication comes in a liquid solution of 50 mg for every 10mg. How many ml of this solution will this patient need in a day
Answer:
v = 100ml
Step-by-step explanation:
0,25mg/kg
-----------> 0,25 * 80 = 20mg
50ml for every 10mg
'v"ml for 20mg
10 * v = 50 * 20
v = 100ml
5TH GRADE MATH!!!! PLEASE HELP BRAINLEIST AND 5 STARS!!!!!!!!!!!!!!!!!!!!
Answer with Step-by-step explanation:
1. V= 17*24*32= 13056
2. V=Same as above
3. V= 50*24*22=26400
4. Add them up and total
V= 13056*2+26400
V= 52510 yds
Answer:
So the volume is 52,512 cubic yards or 52,512 yd³
Step-by-step explanation:
1. V = 17 × 24 × 32
V = 13,056
2. Exact same thing as 1 (13,056)
3. V = 50 × 24 × 22
V = 26,400
4. 13,056 + 13,056 + 26,400 = 52,512
Hope that helped :)
la suma de la longitud de una semicircunferencia y su diametro es 4(pi+2)cm . determine el arrea del circulo
Answer: [tex]16\pi \;cm^2[/tex]
Step-by-step explanation:
La longitud de una semicircunferencia es [tex]l=\pi r[/tex]
[tex]\pi r+2r=4(\pi+2)\\r(\pi+2)=4(\pi+2)\\r = 4\frac{\pi+2}{\pi+2} \\r=4[/tex]
[tex]A = \pi r^2 = \pi (4)^2=16\pi[/tex]
What is the value of X?
Answer:
20
Step-by-step explanation:
When we use Pythagorean Theorem we get x² + 21² = 29² which means x = 20.
Answer:
B: 20
Step-by-step explanation:
By the pythagorean thereom, x^2+21^2=29^2. Solving gives X^2=29^2-21^2=400, so X=20.
Ali wraps a birthday present in a tube that has a length of 14 inches and a diameter of 6 inches.
a. a. How much space can the gift hold?
Answer:
395.84
Step-by-step explanation:
The radius squared is nine. 9 times pi then 14, is 395.84
What is the volume of a hemisphere with a radius of 4.8 ft, rounded to the nearest
tenth of a cubic foot?
Answer: 231.6
Step-by-step explanation:
Answer:
231.6 ft³
Step-by-step explanation:
volume of sphere:
V=[tex]\frac{4}{3} \pi r^{3}[/tex]
radius=4.8
plug in:
[tex]\frac{4}{3} \pi (4.8)^{3}[/tex]
463.246686328
Volume of Hemisphere HALF of Volume of Sphere:
[tex]\frac{463.246686328}{2}[/tex] =231.623343164
≈231.6 ft³
Write the word sentence as an equation. Then solve.
The difference between a number c and 13 is −2.
Answer: C-13 = -2 C = 11
Step-by-step explanation:
difference means subtraction.
the wording "is" implies the answer to the equation = -2
let C be a variable
C - 13 = -2
C = -2 + 13 solve for C by getting C by itself
C = 11
The word sentence as an equation will be as C - 13 = -2, then the solution is 11.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given that difference between a number c and 13 is −2.
Here the difference means subtraction.
Assume C be a variable;
C - 13 = -2
C = -2 + 13
Now solve for C by getting C by itself;
C = 11
Therefore, the word sentence as an equation will be as C - 13 = -2, then the solution is 11.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
The score below represents Akilahs science exam score 20 90 25 100 85 30 what is the MAD of her test
Answer:
The mean absolute deviation (MAD) of the dataset is 33.333.
Step-by-step explanation:
The mean absolute deviation (MAD) of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.
These are the steps to calculate the mean absolute deviation.
Step 1: Calculate the mean.
[tex]Mean = \frac{20+90+25+100+85+30}{6} =\frac{175}{3}\approx58.333[/tex]
Step 2: Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.
[tex]|20-\frac{175}{3} |=\frac{115}{3}\\\\|90-\frac{175}{3} |=\frac{95}{3}\\\\|25-\frac{175}{3} |=\frac{100}{3}\\\\|100-\frac{175}{3} |=\frac{125}{3}\\\\|85-\frac{175}{3} |=\frac{80}{3}\\\\|30-\frac{175}{3} |=\frac{85}{3}[/tex]
Step 3: Add those deviations together.
[tex]\frac{115}{3}+\frac{95}{3}+\frac{100}{3}+\frac{125}{3}+\frac{80}{3}+\frac{85}{3}=\frac{600}{3}=200[/tex]
Step 4: Divide the sum by the number of data points.
[tex]MAD=\frac{200}{6} =33.333[/tex]
The duration of telephone calls directed by a local telephone company: σ = 3.6 minutes, n = 560, 90% confidence. Round your answer to the nearest thousandth
Answer:
The margin of error for the confidence interval is of 0.25 minutes.
Step-by-step explanation:
With what we are given, the only thing that this question can be asked is the margin of error for the confidence interval of the mean duration of telephone calls directed by a local telephone company.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Using what we are given:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.645*\frac{3.6}{\sqrt{560}}[/tex]
[tex]M = 0.25[/tex]
The margin of error for the confidence interval is of 0.25 minutes.
