The quantity of salt in the tank at period t equivalents A(t) = 200 - 130 e(-t/40).
Initially, the tank has A(0) = 50 g of salt.
The rate of salt entryway is (1 g/L) × (5 L/min) = 5 g/min
And a rate of (A(t) ÷ 200 g/L) × (5 L/min) = (A(t) ÷ 40) g/min,
As an outcome, the quantity of salt in the tank modifications as
A'(t) = (5 - A(t)) ÷ 40.
Solve ODE for A(t):
A'(t) + (A(t) ÷ 40) = 4
[tex]e^{\frac{(t)}{40} }[/tex] A'(t) + ([tex]e^{\frac{(t)}{40} }[/tex] ÷ 40 A(t)) = 4[tex]e^{\frac{(t)}{40} }[/tex]
([tex]e^{\frac{(t)}{40} }[/tex] A(t))' = 4[tex]e^{\frac{(t)}{40} }[/tex]
[tex]e^{\frac{(t)}{40} }[/tex] A(t) = 160[tex]e^{\frac{(t)}{40} }[/tex] + C
A(t) = 160 + C[tex]e^{\frac{(t)}{40} }[/tex]
Given A(0) = 30, conclude that
30 = 160 + C
C = -130,
This denotes that the quantity of salt in the tank at period t equivalents
A(t) = 200 - 130 e(-t ÷ 40).
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2
Select the correct answer.
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x − 8?
A.
It is the graph of y = x where the slope is decreased by 8.
B.
It is the graph of y = x translated 8 units up.
C.
It is the graph of y = x translated 8 units to the left.
D.
It is the graph of y = x translated 8 units down.
Answer:
the answer of a question is option A
3) {(-7, 1), (2, -9), (-9, −4), (-1, -1), (-8, 0) }
Domain:
Range:
2. How much heat in kilojoules has to be removed from 225g of water to lower its temperature from 25.0oC to 10.0oC?
Answer:
-14.1 kJ
Step-by-step explanation:
We need the specific heat of water, which is 4.184 J/g-K. It means that 4.184 Joules of energy will raise 1 gram of water by 1 degree Kelvin. It also means that removing 4.184 Joules of energy will lower the temperature of 1 gram of water by 1 degree Kelvin.
We want to lower the temperature by 15 degrees C (-15C). That is also -15K. We have 225 grams of water.
This can be used in the equation q = mc(T2 - T1),
where q is the heat, or energy, m is the mass, c is the specific heat, and (T2-T1) is the temperature change, in Kelvin.
q = mc(T2 - T1)
q = (225g)(4.184 J/g-K)(10K - 25K)
q = (225g)(4.184 J/g-K)(-15K)
q = -14121 J or -14.1 kJ
It is negative because heat is leaving the system.
Jessica is trying to save money to set aside for emergencies. she already has $75 and she earns $9 per hour at her family job. how many hours will she need to work to earn at least $500?
Answer:
Either 55.56 or 47.222 hours, depending on how the qyuestion is interpreted. The first answer assumes that Jessica's existing savgings of $75 is not available for emergencies.
Step-by-step explanation:
The question is difficult to answer. It doesn't specify that the $75 counts agains the $500. It simply asks how many hours of work does she need to earn $500.
Jessica is paid $9/hr, so her earnings (y, in $) are described by the formula: x hours at :
y = ($9/hr)*x
If we set y = $500:
$500 = ($9/hr)*x
x = $500/($9/hr)
x = 55.56 hours.
However, if we set y = $500 - $75, the Jessica only needs to work:
$425 = ($9/hr)*x
x = $425/($9/hr)
x = 47.222 hours
Which one of these expressions doesn’t have a value less than 1 please help thank you if u do
The fourth option [tex](3^{5)^{2} }[/tex]/[tex](3)^{4}[/tex] does not have value less than 1.
What is Power or Exponent?Power of a number is defined as how many times to use the number in a multiplication. We also call Powers as Exponents or Indices. For example, [tex]8^{2}[/tex] could be called “8 to the power 2” or “8 to the second power”, or simply “8 squared”.
Step-by-step explanation:
In first option, [tex]4^{11}[/tex]/[tex]4^{14[/tex], if we solve this, the answer comes out to be 1/[tex]4^{3}[/tex] which will be 1/64 which is 0.015 that is lesser than 1.
In second option, [tex](5^{4)^{2} }[/tex]×[tex]5^{-11}[/tex],if we solve this, the answer comes out to be 1/[tex]5^{3}[/tex] which will be 1/125 which is 0.008 that is lesser than 1
In third option,[tex](2^{3)^{-2} }[/tex],if we solve this, the answer comes out to be 1/[tex]2^{6}[/tex] which will be 1/64 which is 0.015 that is lesser than 1
in Fourth option ,[tex](3^{5)^{2} }[/tex]/[tex]3^{4}[/tex] , if solve this, the answer comes out to be [tex]3^{6}[/tex] which will be 729 that is larger than 1
∴fourth option will be the answer.
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high school seniors in a small town are asked a series of questions to measure the frequency of their drinking and driving. the students give consistent answers to the series of questions, but police records indicate that drinking and driving is much more common than indicated by the students' responses. this suggests that the measure of frequency of drinking and driving is:
When a study's findings are highly valid, it means that they accurately reflect the genuine features, traits, and variations in the physical or social reality. The measure of frequency of drinking and driving is: reliable but not valid.
What are the measure of frequency of drinking and driving?This option contends that although the survey's measure was not valid, it was dependable. This happens when research is constructed in a consistent but ineffective manner. In this instance, a sample of young people from a small town was taken into account; however, despite its consistency and reliability, it does not accurately reflect the findings of data from police records.
How well a method measures what it is supposed to measure is known as its validity. When a study's findings exists highly valid, it indicates that they accurately reflect the genuine features, traits, and variations in the physical or social reality. High dependability exists one sign of a valid measurement.
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find h from this help please
The variable h, as the subject of the given formula is h = 3 / (G.V + 1)
Making a variable the subject of the formulaFrom the question, we are to make h the subject in the given formula
The given equation is
(3 - h) / V = G . h
Multiply both sides of the equation by V
V × (3 - h) / V = G . h × V
3 - h = G . h . V
Add h to both sides
3 - h + h = GhV + h
3 = GhV + h
Factorize h
3 = h(G.V + 1)
Now,
Divide both sides of the equation by (G.V + 1)
That is,
3 / (G.V + 1) = h
∴ h = 3 / (G.V + 1)
Hence, the value of h is 3 / (G.V + 1)
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Find the value of X
What is the value of x?
Answer:
5
Step-by-step explanation:
X - 2 = 3.5 A: 1.5 B: 5.5 C: 5 1/2 D: 5 3/6
To solve this expression we have to add 2 to both sides of the equation:
[tex]x-2+2=3.5+2[/tex][tex]x=5.5[/tex]So, the correct option is: B: 5.5
A rectangular prism is 9 inches long, 3 inches wide, and _____ inches high.
The volume of the box is 324 in.
What is the height of the box?
Answer:
height = 12
Step-by-step explanation:
try and use the formula to plug it in and solve for x.
x+3/5 + x-2/5
as a single fraction
Answer:
x+3/5 + x-2/5
simply add variable
x+x +3/5-2/5
2x+3/5-2/5
taking L.C.M
5*2x+3-2/5
10x+1/5
How is a number squared?Select one:a. Multiplying a number by 4. b. Multiplying a number by itself. c. Dividing a number by 4. d. Dividing a number by itself.
A number is squared when it is multiplied by itself.
Hence, the correct option is Option B
A 16 oz pack of green salad costs $2. Find the price of salad per ounce. Also, find the cost of 8 oz, 12 oz, 18oz, and 28 oz packs of salad.
step 1
Find out the unit price
Divide the total cost by the total ounces
so
2/16=$0.125 per ounce
step 2
Find the cost of 8 oz
Multiply the number of ounces by the unit price
so
0.125*8=$1
Find the cost of 12 oz
0.125*12=$1.5
Find the cost of 18 oz
0.125*18=$2.25
Find the cost of 28 oz
0.125*28=$3.5
10 miles per hour equal feet per second
Let's recalll that:
• 1 mile per hour = 1.46667 feet per second
Therefore:
• 10 miles per hour = 1.46667 * 10 feet per second
,• 10 miles per hour = 14.6667 feet per second, Khalil!
Alexa buys an oil painting online for $941.20. If shipping and handling are an additional 20% of the price, how much shipping and handling will Alexa pay?
What is 102 divided by 105?
Answer:
102 / 105 = 0.971428571
Step-by-step explanation:
i used a calculator c:
(10-x)+(12-x) HELPPPPPPPPPPPPPPPPPP
Answer:
x=-11
Step-by-step explanation:
Steps are in the attachment, but I couldn't include the last step.
The last step is to divide by -2 on both sides.
The final answer then will be x=-11
Using the formula °F = 1.8°C +32°, find the temperature in
Degrees Celsius of an oven that is 500°F.
Using the formula °F = 1.8°C +32°, The temperature in Degrees Celsius of an oven that is 500°F is 260°C.
What is Fahrenheit?For everyday purposes, Fahrenheit is used in the United States, its territories, and related states (all of which are covered by the U.S. National Weather Service), as well as in Liberia, the Cayman Islands, and other places. For instance, temperatures for freezing, cooking, and other conditions are typically given in degrees Fahrenheit in the United States.
What is Celsius?On the Celsius scale, one of the two temperature scales used in the International System of Units along with the Kelvin scale, the unit of temperature is the degree Celsius. The term "degree Celsius" can be used to describe either a specific temperature on the Celsius scale or a measurement of the difference between two temperatures.
Here,
°F=1.8°C+32°
500°F=1.8°C+32°
1.8°C=468°F
°C=468/1.8
°C=260°C
The temperature in Degrees Celsius of an oven that is 500°F is 260°C by using the formula °F = 1.8°C +32°.
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What is 420÷6 hellllll,lllllllllllllllpppppp I n ee d it now
Answer:
70
Step-by-step explanation:
Given m ||n, find the value of x and y.
Answer: The correct answer is x=18 and y=59
Step-by-step explanation:
Opposite angles are congruent:
(6x+13) = (7x-5)
Solve for x:
6x+13−7x=7x−5−7x
−x+13−13=−5−13
−x=−18
x=18
Plug x value in for y:
Y=180-(7x-5)
Y=180-(126-5)
Y=180-121
Y=59
which pair of equations is a set of parallel lines ? a. y = x + 2 and y = 2 b. x = 2 and y = 4
Neither of the pairs of linear equations has the same slope in both lines, so we don't have parallel lines.
Which pair of equations is a set of parallel lines?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Two linear equations are parallel only if both lines have the same slope and a different y-intercept.
In this case, the lines given are:
y = x + 2 and y = 2.
x = 2 and y = 4
Neither of these are particularly parallel lines (because in both pairs we have different slopes), so we conclude that there is no correct option.
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[tex]x^{2} + 2x _5=0[/tex]
Step-by-step explanation:
Substitute the values
a
=
1
,
b
=
−
2
, and
c
=
−
5
into the quadratic formula and solve for
x
.
2
±
√
(
−
2
)
2
−
4
⋅
(
1
⋅
−
5
)
2
⋅
1
Simplify.
x
=
1
±
√
6
Simplify the expression to solve for the
+
portion of the
±
.
x
=
1
+
√
6
Simplify the expression to solve for the
−
portion of the
±
.
Which points are solutions to the system of inequalities shown below?
Check all that apply.
y2 x + 3
y< 2x
X>6
A. (8, 12)
B. (6, 11)
C. (7,10)
D. (5, 10)
E. (8, 10)
F. (9,12)
Solution for the given Inequality
x > 6 : (6 , 11), (5 , 10)
y < 2x: (8, 12), (6, 11), (7,10), (5, 10), (8, 10), (9,12)
What is Inequality?
Inequality of wealth in major cities Economic inequality comes in many forms, most notably wealth inequality measured by the distribution of wealth and income inequality measured by the distribution of income.
Let us study each inequality and find the right solutions
∵ x > 6
∴ The x-coordinates of the points are 7,8,9
- That means answer A and D is out because its x-coordinate not greater
than 6 ⇒ (6 , 11), (5 , 10),
∵ y < 2x
∴ The y-coordinates of the points are 10,11,12
- That means all are answers because y-coordinates is
not greater than 2x ⇒ (8, 12), (6, 11), (7,10), (5, 10), (8, 10), (9,12)
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I don’t understand can someone help me? Create a linear equation for the following data:
Given the data shown in the table, you can identify that these two points are on the line:
[tex](-1,7)(2,-2)[/tex]By definition, the Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
You can find the slope of the line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where these two points are on the line:
what is the first step that contains an error
7+8x=0
first step -Subtract 7 from both sides.
7+8x-7=0-7
Step 2
8x=-7
Step 3
Divide both side by 8
[tex]\frac{8x}{8}=\frac{-7}{8}[/tex]Instead of dividing the right hand side of equation in step 2 by 8, the right hand side is multiplied by 8 in step 3.
So, the error is in step 3.
Use the diagram and the given angle measure to find the other three measures
The measures of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created. The vertex of an angle is the location where two points come together. The Latin word "angulus," which means "corner," is where the term "angle" originates. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.So, ∠2 = 34°:
Now calculate other angles as follows:
(1) ∠1:
We can easily tell that ∠1 and ∠2 together make a straight angle which makes 180°. Then,
∠1 + ∠2 = 180∠1 + 34 = 180∠1 = 180 - 34∠1 = 146°(2) ∠3:
∠1 and ∠3 are a pair of vertically opposite angles and thus are equal.
∠1 = ∠3 = 146°∠3 = 146°(3) ∠4:
∠2 and ∠4 are a pair of vertically opposite angles and thus are equal.
∠2 = ∠4 = 34°∠4 = 34°Therefore, the measure of angles ∠1, ∠3, and ∠4 is 146°, 146°, and 34°.
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Solve for X round to nearest tenth
Answer:
the answer for this question is 35.0
Josiah skateboards from his house to school 3 miles away. It takes him 36 minutes. If Josiah's speed, in miles per minute, is constant, what is the constant of proportionality? Type the number that represents the constant of proportionality in the box below.
13
Step-by-step explanation:
i said 36 divide by 3 is 13
5x+3=53
I don’t know pls help
Answer:
x10
Step-by-step explanation:
How to solve your problem
5x+3=53
Subtract 3 from both sides
5x+3=53
5x+3-3=53-3
Simplify
Subtract the numbers
5x+3-3=53-3
5x=53-3
Subtract the numbers again
5x=53-3
5x50
Divide both sides by the same factor
5x=50
5x=50\
[tex]\frac{50x}{5}[/tex][tex]\frac{50}{5}[/tex]
Simplify
Cancel terms that are in both the numerator and denominator
[tex]\frac{5x}{5}[/tex]=[tex]\frac{50}{5}[/tex]
x=[tex]\frac{50}{5}[/tex]
Divide the numbers
x=[tex]\frac{50}{5}[/tex]
x=10
answer is 10