a) Amount of sugar in the tank initially is 0.
b) The amount of sugar in the tank after t minutes is 13.6(1 - [tex]e^{\frac{4t}{1360} }[/tex]).
c) The concentration of sugar in the solution in the tank after 60 minutes is 3.672.
a) Assign the sugar content of the tank for time t to the symbol A(t). Starting with only clean water, the tank
A(0) = 0
b) Sugar flows in at a rate of
(0.02 kg/L) × (2 L/min) = 0.04 kg/min
and flows out at a rate of
(A(t) ÷ 1360 kg/L) × (2 L/min) = (2A(t) ÷ 1360) kg/min
so that the net rate of change of A(t) is governed by the ODE,
dA(t) ÷ dt = (4 ÷ 100) - (2A(t) ÷ 1360)
A'(t) + (2A(t) ÷ 1360) = 2 ÷ 100
Multiply both sides by the integrating factor [tex]e^{\frac{4t}{1360} }[/tex] to condense the left side into the derivative of a product:
[tex]e^{\frac{4t}{1360} }[/tex] A'(t) + (2 [tex]e^{\frac{4t}{1360} }[/tex] A(t) ÷ 1360) = 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100
( [tex]e^{\frac{4t}{1360} }[/tex] A(t))' = 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100
Integrate both sides:
[tex]e^{\frac{4t}{1360} }[/tex] A(t) = ∫ 4 [tex]e^{\frac{4t}{1360} }[/tex] ÷ 100
[tex]e^{\frac{4t}{1360} }[/tex] A(t) = 13.6 [tex]e^{\frac{4t}{1360} }[/tex] + C
Solve A(t);
A(t) = 13.6 + C [tex]e^{\frac{4t}{1360} }[/tex]
A(0) = 0, substitute the value
0 = 13.6 + C [tex]e^{\frac{4t}{1360} }[/tex]
C = -13.6
so that the amount of sugar at any time t is,
A(t) = 13.6 - 13.6[tex]e^{\frac{4t}{1360} }[/tex]
A(t) = 13.6(1 - [tex]e^{\frac{4t}{1360} }[/tex])
c) As t → 60, the exponential term converges to 0 and is left with
[tex]\lim_{t \to \(60}[/tex] A(t) = 13.6 × (1 - 0.73)
[tex]\lim_{t \to \(60}[/tex] A(t) = 3.672 kgs of sugar.
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1/7a + 1/7 = ?
YALL HELP I LOST MY NOTES
Step-by-step:
1)Combine multiplied terms into a single fraction
1/7a+ 1/7
1a/7+1/7
2)Multiply by 1
3)Combine fractions with a common denominator
Solution
a+1/7
Hope That helps!
For her final project, stacy plans on surveying a random sample of students on whether they plan to go to florida for spring break. From past years, she guesses that about % of the class goes. Is it reasonable for her to use a normal model for the sampling distribution of the sample proportion? why or why not?.
Less than 10 attempts were successful in this situation. due to the fact that 5 is less than 10. The data does not satisfy the requirement as a result.
Because the data don't fit the success or failure criteria, it is not appropriate to adopt a normal model for the sampling distribution of the sample.
50 students make up the sample. The likelihood that she assumes 10% of the class will attend is 10%. It will be demonstrated by:
1 - p = 1 - 10%
⇒ 1 - 0.10 = 0.90
np = 50 × 0.1
np = 5
This suggests the number of victories.
In this case, fewer than 10 efforts have been successful. Since 5 is less than 10, this is the situation. The data does not meet the criteria as a result.
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-6n² = -414
Please help me solve this
Answer:
8.31
Step-by-step explanation:
-6n² = -414
[take away negative]
6n² = 414
[divide by 6]
n² = 69
n = 8.3066 (to 5 significant figures)
n = 8.31 (to 3 significant figures)
Determine the next three terms in the following sequence:
2, 3, 5, 8, ____, ____, ____,...
a.
13, 19, 26
b.
12, 17, 23
c.
12, 16, 20
d.
13, 17, 23
Answer:
b. 12, 17, 23
Step-by-step explanation:
Look at the differences between the numbers.
Number Difference
2
3 1
5 2
8 3 The difference increase by 1 at each step. The next 3 increase would be:
4
5
6
The next three numbers are:
12 4
17 5
23 6
Answer:
b.
12, 17, 23
Step-by-step explanation:
Dan uses the equation g left parenthesis x right parenthesis equals 5 x plus 50 to model the balance of his savings account after saving for x weeks. What is the value and meaning of g left parenthesis 60 right parenthesisblank in the context of the problem?
The value is 350.
From the question, we have
Dan uses the equation g(x)=5x+50 to model the balance of his savings account after saving for x weeks.
g(x)=5x+50
substituting the value x = 60, we get
g(60)=5*60+50
=300+50
=350
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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a professor wants to study the effectiveness of a new study tool for a course. there are 150150150 students registered for the course. the professor assigns each student a number from 111 to 150150150 and uses a random number generator to assign the first 757575 students selected to use the new study tool. the remaining 757575 subjects are assigned to use the previous study tool. what type of experiment design is this?
This is a "completely randomized" type of experiment design.
In terms of data analysis as well as accessibility, and simplicity a randomized design is perhaps most likely the shortest experimental study.
The investigator expects that sometimes extraneous influences would affect treatment conditions similarly in general, so that any substantial improvements across conditions may be allocated appropriately towards the individual entity.
Thus the above approach is right.
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Suppose you have 50 blueberry scones and 75 cranberry scones you wanted to make as many identical birds of scones as possible each bread should have an equal number of blueberry scones and an equal number of cranberries called what is the greatest number of bags you can fill explain
He can fill a total of 25 bags.
The values are,
50 blueberry scones total.
75 cranberry scones total.
For each bag to have an equal quantity of blueberry scones & cranberry scones, he must determine the maximum amount of bags he can fill.
H.C.F. of 50 & 75 is thus 25.
As a result, he can fill 25 bags.
There would be scones with blueberries in each bag of
50 ÷ 25 = 2
There would be cranberry scones for each bag, for a total of
75 ÷ 25 = 3
As a result, he may fill a total of 25 bags.
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what is the correct postulate to prove these two triangles congruent?
A. SAS
B. ASA
C. SSS
D. AAS
E. HL
Don't understand problem. Need help solving problem.
Answer:
x = -12
Step-by-step explanation:
x/-3 + 5 - 5 = 9 - 5
x/-3 = 4
x/-3 (-3) = 4(-3)
x = -12
a news poll which estimated that 82% of all voters believe global warming exists had a margin of error of /- 3%. suppose an environmental group planning a follow-up survey on this issue wants to determine a 95% confidence interval with a margin of error of no more than 2%. how large a sample do they need? (for estimate of p use 0.82)
The needed sample size is 1419. Sample Size is defined as the number of observations in the study.
In the question we have ,
estimate value of all voters who believe global warming ( p) = 82% = 0.82
margin of error (M.E) = 2% = 0.02
confidence of interval is calculated by estimate point value and add or subtract margin of error .
here,we have the value of confidence of interval is 95% = 0.95
Margin of error formula is
M.E = Z × √(p(1-p)/n)
where, p --> is estimated value
n---> sample size , which we required
Z ----> is z-value for observation
for the confidence of interval level 95% , the Z-value is 1.96 exist.
put all value in above formula we get,
0.02 = 1.96 × sqrt( ( 0.82)(1-0.82)/n)
=> 0.02 = 1.96× √(0.82×0.18/n)
= 0.02/1.96 = √0.1476/n => 0.000104= 0.1476/n
=> n = 1419
So, sample size is large and it is 1419.
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(1 point) a bit is a 0 or a 1. a bit string of length 5 is a sequence of 5 digits, all of which are either 0 and 1. (a) how many bit strings of length 5 are there?
A bit string of length 5 contains 2^5 = 32 potential values because each bit has two possible values.
The quantity of bits in a bit string determines its length. When the bit string is produced, this precise non-negative integer is fixed. The exact non-negative integers that are smaller than the bit string's length are the valid indexes. Bit strings can have zero bits or more. A series of bits is known as a bit string. Bit strings can be used to modify binary data or represent sets. In right to left order, a bit string's elements are numbered from zero to the number of bits in the string minus one.
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A city doubles its size every 83 years. If the population is currently 88,200, what will the
population be in 249 years?
people
Answer:
264,600
Step-by-step explanation:
249 ÷ 83 = 3
88,200 ×3 = 264,600
on
de)
yi
19 Dados los siguientes pares de medidas, explica en cada caso cuál es más precisa y justifica
tus elecciones.
34 cm ± 0.10 cm
14
14.8 cm
22.8 +0.1 cm
34 cm ± 0.12 cm
14.85 cm
6.2 + 0.1 cm
Answer: no clue
Step-by-step explanation: i don't know Spanish lol
A train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. How far is the train from the station?
Answer
23
45
65
89
If a train leaves a station heading east. after traveling east for 33 miles, the train leaves 56 miles south. The distance of the train from the station is C. 65.
How to find the distance?Using Pythagoreans theorem formula to find the distance
d² = a² + b²
Where:
d = distance =?
a= east for 33 miles
b = 56 miles south
Let plug in the formula
d = √33² + 56²
d = √ 1089 + 3136
d = √4225
d = 65 miles
Therefore the correct option is C.
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6y^2 + 7y - 20= 0
solve this quadratic equation using a multiplication frame.
y= -4/3=-1.333
y= 5/2=2.500
Find the range of values which satisfy the following:
8x-11>5 and 15(6x+2)>-150
x>
Answer: ______
The range of values that satisfy the given inequalities, 8x - 11 > 5 and 15(6x+2) > -150, is x > -2 OR x > 2
Solving Linear Inequalities: Determining range of valuesFrom the question, we are to determine the range of values which satisfy the given inequalities.
The given inequalities are
8x - 11 > 5 and 15(6x+2) > -150
To determine the range of values that satisfy the inequalities, we will solve each of the inequalities separately
Solving 8x - 11 > 5
Add 11 to both sides
8x - 11 + 11 > 5 + 11
8x > 16
Divide both sides by 8
8x/8 > 16/8
x > 2
Solving 15(6x+2) > -150
Divide both sides by 15
15(6x+2)/15 > -150/15
6x + 2 > -10
Subtract 2 from both sides
6x + 2 - 2 > -10 - 2
6x > -12
Divide both sides by 6
6x/6 > -12/6
x > -2
Putting the two solutions together,
x > -2 OR x > 2
Hence, the solution is x > -2 OR x > 2
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Evaluate if x³ if x = 6
This is a quiz but I was sick so I do now to do this pls show work
Answer:
Step-by-step explanation:
Answer: 108
Step-by-step explanation:
6 x 6 x 6=10
Which factor most likely results in the loss of genetic variation from a small population?.
The factor most likely results in the loss of genetic variation from a small population is called genetic drift.
Small populations tend to lose genetic variation at a faster rate than large populations due to genetic drift (stochastic sampling error). Genetic drift refers to the change in an existing gene variant frequency in the population due to random chance. Genetic drift may result in the disappearance of gene variants completely and thus decreases genetic variation. Furthermore, it could initially cause rare alleles to become much more frequent, and even fixed. The loss of some versions of a gene due to random chance is more likely to happen when populations are small.
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ABCD, BEG and CEF are straight lines. Find a and b
Answer:A=72
B=108
Step-by-step explanation:
The solution is, angle a = 72 & b = 108
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
from the given figure we get,
∠ABC = 180
∠BCD = 180
so, we have,
∠ABC + ∠BCD = 180 + 180
ABE + EBC + a + b = 360
again, we know that,
EBC + a = 180 - 38 = 142
[we know, from property of triangle's angle]
now, we get,
ABE + 142 + b = 360
or, 110 + 142 + b = 360
or, b = 108
so, we get,
a = 180 - 108 = 72
Hence, The solution is, angle a = 72 & b = 108.
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Carter bought p packs of baseball cards. There are 12 cards in each pack. Write an expression that shows how many baseball cards Carter bought.
The expression that shows the number of baseball cards is 12n
How make an expression that shows how many baseball cards?An algebraic expression in mathematics is an expression that is made up of letters and numbers, along with algebraic operations (addition, subtraction, multiplication, etc). Expressions are made up of terms
Given that: Carter bought p packs of baseball cards and there are 12 cards in each pack
To know the number of baseball cards, we have to multiply the number of packs by the number of cards in each pack:
Since the number of packs = n and the number of cards in each pack = 12.
Thus, total number of baseball cards = 12 x n = 12n
Therefore, the expression that shows how many baseball cards Carter bought is 12n
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a sample of student opinion at a big ten university selects an srs of 200 of the 30,000 undergraduate students and a separate srs of 100 of the 5,000 graduate students. what is the term for this kind of sample?
The term for this kind of sample is cluster sampling
Given
that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.
What is cluster sampling ?
Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.
Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.
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What is the solution to the following equation?
x² + 3x + 7 = 0
A. x= 3+-√25/2
B. x= -3+-√37/2
C. x= -3+-√²7/2
D. x= -3+-√-19/2
Answer: D
Step-by-step explanation:
Answer: Choice D
[tex]x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
==================================================
Explanation:
Compare the given equation x² + 3x + 7 = 0 to ax² + bx + c = 0 to find that,
a = 1b = 3c = 7Those values are plugged into the quadratic formula to get the following:
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-3\pm\sqrt{(3)^2-4(1)(7)}}{2(1)}\\\\x = \frac{-3\pm\sqrt{-19}}{2}\\\\[/tex]
which points us to choice D being the final answer.
--------------
Side note:
The discriminant [tex]d = b^2 - 4ac = (3)^2-4(1)(7) = -19[/tex] is negative, so there are no real solutions. Instead, the two solutions are non-real complex numbers.
I need help like asap !!!
only numbers and decimal points
Answer:
b = 8 ft
Step-by-step explanation:
Formula we use,
→ (AC)² = (BC)² + (AB)²
Now the value of a will be,
→ (10)² = b² + (6)²
→ 100 = b² + 36
→ b² = 100 - 36
→ b = √64
→ [ b = 8 ft ]
Hence, value of b is 8 ft.
In the figure below, a pole has two wires attached to it, one on each side, forming two right triangles.
Based on the given information, answer the questions below. Round each answer to the nearest tenth.
Part A: How tall is the pole? Show your work.
Part B: How far from the base of the pole does Wire 2 attach to the ground? Show your work.
Part C: How long is Wire 1? Show your work.
The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled.
Given is a figure, of two wires 1 and 2 attached to a pole and ground
Using trigonometric ratios, we have,
a) tan41° = Height of pole/34
Height of pole = tan41°x34
Height of pole = 29.55 ft
b) tan38° = (distance of wire 2 from the base of pole)/29.55
Distance of wire 2 from the base of pole = tan38°x29.55 = 23.08 feet
c) cos41° = 34/length of wire 1
Length of wire 1 = 34/cos41°
Length of wire 1 = 45.05 feet
Hence, The answers are a) 29.55 ft, b) 23.08 feet and c) 45.05 feet
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HURRYYYY DUE IN 10!!!!
Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).
Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).
What is a coordinate system?
In geometry, a coordinate system is a system that uses one or more numbers or coordinates to uniquely determine the location of points or other geometric elements on a manifold, such as Euclidean space.
In the original figure, we can plot the coordinates, and we get
For dark blue dot = (-2, 2)
For red dot = (-2, 0)
For light blue dot = (2, 2)
After applying a scale factor of '2', we get the new coordinates as
For dark blue dot = (-4, 4)
For red dot = (-4, 2)
For light blue dot = (4, 4)
Hence,
Coordinates of the original figure: (-2, 2), (-2, 0), and (2, 2).
Coordinates of the final transformed figure: (-4, 4), (-4, 2), and (4, 4).
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A particular car is 16 ft long. A model of it was built with a scale of 1 in: 2 ft. How long is the model car?
The car that is 16 feet long has a length of 8 inches on the scale.
How to find the length of the modelled car?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
Therefore, the particular car is 16 feet long. A model of it was built with a scale of 1 in: 2 ft. The length of the car can be found as follows:
2 feet = 1 inches
16 feet = ?
cross multiply
length of the model car = 16 / 2
Therefore,
length of the model car = 8 inches
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Write the equation of the line that is parallel to the line 14x - 2y = 51 and goes through the point(3, -11)
what is the correct postulate to prove these two triangles congruent?
A. SAS
B. ASA
C. SSS
D. AAS
E. HL
Answer:
SAS
Step-by-step explanation:
By applying the Side Angle Side Postulate (SAS), you can be sure that your two triangles are congruent.
A 8 oz jar of peanut butter costs $1.32 – what is the price per ounce?
Answer:
the price per once is $0.165
Step-by-step explanation:
[tex]8 \: jar \: of \: peanut \: cost \: 1.32 \\ 1jar \: cost \: what \: \\ now \: to \: get \: price \: of \: each \: jar\\ 1.32 \div 8 \\ = .0165[/tex]
III. Write each quadratic equation in standard form
1. 3x-2x² = 7
2.5-2x² = 6x
3.(x+3)(x+4)=0
4.(2x + 7)(x-1)=0
5,2x(x-3) = 15
ax²+bx+c=0
Answers are attached
