Using separation of variables, it is found that the expression for the mass, M, at any time t, is given by:
[tex]M(t) = 150e^{-kt}[/tex]
What is separation of variables?In separation of variables, supposing a differential equation in the format [tex]\frac{dy}{dx}[/tex], we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
[tex]\frac{dM}{dt} = -kM[/tex]
Then, applying separation of variables:
[tex]\frac{dM}{M} = -k dt[/tex]
[tex]\int \frac{dM}{M} = \int -k dt[/tex]
[tex]\ln{M} = -kt + C[/tex]
[tex]M(t) = M(0)e^{-kt}[/tex]
The initial mass is of M(0) = 150, hence:
[tex]M(t) = 150e^{-kt}[/tex]
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In analysis of variance, then the term factor refers to_______
a) a dependent variable
b) a treatment total
c) an independent variable (or quasi-independent) variable
d) a treatment mean
A company paid $211.00 for an item. The original price was $299.20, but this was marked down 40%. If the operating expenses are 36% of the cost, find the operating loss and the absolute loss.
1. What is the operating loss?
2. What is the absolute loss?
Answer:
If the operating expenses are 36% of the cost, find the operating loss and the absolute loss.
1. An operating loss occurs when a company's operating expenses exceed gross profits (or revenues in the case of a service-oriented company.
2. Mean absolute error (MAE) is a loss function used for regression. The loss is the mean overseen data of the absolute differences between true and predicted values, or writing it a formula.
Step-by-step explanation:
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The Choose is Choose. your options are for the first one is Mean or Median then for the second one is 2 inches, 2.5 inches, 3 inches, or 3.2 inches
.
The best way to describe the center of the data represented in this line plot include the following: the median is 2.5 inches.
What is a median?In Mathematics, a median refers to the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
Since the data set representing the amount of rainfall has an outlier, the median would be best way to describe the center of the data represented in this line plot.
First of all, we would sort the 10 observations from the least to greatest as follows:
1, 1, 2, 2, 2, 3, 3, 5, 6, 7
Median = (2 + 3)/2
Median = 5/2
Median = 2.5 inches.
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The expression below is a sum of cubes.
125x^3 + 144
A. True
B. False
Answer:
False
Step-by-step explanation:
Hey there!
If this is a sum of cubes, this means that both numbers have whole numbers as the cube root of that number
The cube root of 125 is 5
But the cube root for 144 is a decimal meaning this is not a sum of cubes
A spinner is divided into 12 identical sectors and labeled 1 through 12.
How many spins are expected for a multiple of 5 to be spun 8 times?
Select from the drop-down menu to correctly complete the sentence.
The spinner is expected to have to spin approximately
times for a multiple of 5 has been spun 8 times.
Answer: The awnser is 48
Step-by-step explanation: I took the quiz
6.03 Quiz: Use Theoretical Probability to Predict
It is expected to take 48 spins for a multiple of 5 to be spun 8 times.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.
The probability of not landing on a multiple of 5 is 5/6.
We can use the geometric distribution formula to find the expected number of spins:
E(X) = 1/p, where p is the probability of success.
As per the question, the probability of success is 1/6.
Therefore, E(X) = 1/(1/6) = 6.
We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:
6 x 8 = 48.
Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.
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!!!!!!!!!!!!!!!!!!!!!
Answer:
I believe it would be 9.
Step-by-step explanation:
Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9
Use the proof above to answer the question: What reason can be used to prove that the triangles are congruent?
A. AAS B. ASA C. AAA D. SAS E. SSS
Answer:
E. SSS
Step-by-step explanation:
AB=BC (Given)
AD=CD (Midpoint)
BD=BD (common)
Therefore answer is : SSS
Decide whether it would be more convenient to solve the system of equations by substitution or elimination.
{−2x/3−15y=−6, 10x−6y=−4
Select the correct answer below:
elimination
substitution
Answer:
I would use elimination in this scenario. Because in both equations there is a coefficient on both variables, it would be difficult to isolate one variable and would leave the equation as a fraction. Instead, use elimination. Multiply the first equation by -15, which changes it to 10x + 225y = -90, and then subtract the second equation, thus cancelling out the 10x's and letting you solve for Y. Hope this helps!
If (x, 42) is a solution to the equation y = -6 (x – 15) – 3, find x
Put y and find x
y=-6(x-15)-342=-6(x-15)42+3=-6(x-15)45=-6x+90-6x=-45x=45/6x=15/2Marlo uses 252 lb of gravel to cover a garden plot of 36 ft2.
Answer: 7lb
Step-by-step explanation:
The amount of gravel required cover each square feet of the garden obtained by dividing the total amount of gravel used and the total area of the garden is 7 lb
Total area of garden = 36 ft²
Total amount of gravel used = 252 lb
The amount of gravel used to cover each ft² of the garden can be calculated thus :
(Total amount of gravel used) ÷ (Total area of garden)
252 ÷ 36 = 7 lb
Therefore, the amount of gravel required to cover each square feet of the garden is 7 lb
Answer:
See below
Step-by-step explanation:
D o you want pounds / sq foot ?
252 lbs / 36 ft^2 = 7 pounds per square foot
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
For what value of k will the relation R = {(2k+1, 3), (3k−2, −6)} not be a function?
For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).
2k+1= 3k-22k-3k = -2-1-k = -3k = 3Now plugging in the value of k,
(2 x 3+1 ,3) =( 7,3)(3 x 3-2,-6) = (7,-6)hence , the relation won't be function if k would be equal to 3
The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
What is a function?In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.
For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.
We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.
Let's equate the first coordinate of the ordered pairs:
2k+1 = 3k-2
Solving for k, we get:
k = 3
If we substitute k = 3 into the relation, we get:
R = {(2(3)+1, 3), (3(3)−2, −6)}
R = {(7, 3), (7, -6)}
Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.
Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
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39 28. If y = (1 - 3x), find the value of dy! dx at x = -1.
Answer:
the answer to this question is 52.18
solve system of equations can someone show step by step please
2x-6y=-12
x+2y=14
Answer:
x=6 y=4
Step-by-step explanation:
I hope this helps you and please mark me as brainlest!
Good people please don't leave me help!!!
Answer:
I hope it helped you
Step-by-step explanation:
Pls check the given attachment
I hope it helped you
What is the area of the figure?
A. 18 yd
B. 54 yd
C. 72 yd
D. 90 yd
Martinez and grouse swimming pool is finally finished and all this left to do is fill it with water. Martinez family decides to fill their pool using their garden hose to save money even though they know it will take a really long time the swimming pool is 10 m long and 5 m wide and Martinez family wants to the water to be 2 m deep water from the garden holes flows at a rate of 2500 l or 2.5 m³ per hour how long will it take to fill the pool
Answer:
the answer ia true
Step-by-step explanation:
hope this helps
Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )
Answer:
y = -2x + 16
Step-by-step explanation:
Slope-intercept form is:
y = mx + bWhere m = slope
b = y-intercept
To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.
m = (y2 - y1)/ (x2 - x1)= (12 - 2)/(2 - 7) = 10/-5 = -2Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:
y = -2x + blet's use point (7,2) to find b:
2 = -2(7) + b2 = -14 + bb = 16Now, we can find the equation of this line:
y = -2x + 16Answer:
y=-2x+16
Step-by-step explanation:
First we should find the slope.
We can use the formula (y2-y1)/(x2-x1)
(12-2)/(2-7)=10/-5=-2
So, the slope is -2.
From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found
y=-2x+b
12=-2(2)+b
12=-4+b
b=16
So, the slope-intercept equation is y=-2x+16
Given the function f(x) = 4 - 2x, find f(3r - 1).
Answer:
6 - 6r
Step-by-step explanation:
we just plug in 3r - 1 instead of x
f(3r - 1) = 4 - 2(3r - 1)
= 4 - 6r + 2
= 6 - 6r
In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?
Answer:
Step-by-step explanation:
Remark
Using Algebra, this is a proportion question. A proportion is 2 equal ratios
If the of the 2 ratio parts are known, it is possible to solve for the 4th one.
Formula
9_bats/50_grams::81_bats/x grams insects
Solution
Put the three knowns in and solve for the 4th which is not known
9 bats/ 50 insects = 81 bats /x insects. Cross multiply
9 * x = 50 * 81 Combine
9x = 4050 Divide by 9
9x/9 = 4050/9
Answer: x = 450 grams
Can someone help me? I'm pretty bad at math... But what is the number needed?
6 x ? x 3 = 90
What is the range of the function graphed below?
A sample of 36 people yielded the information about their health insurance in the table to the right.
Two people who provided information for the table were selected at random, without replacement. Find the probability that neither had traditional insurance.
The probability that neither of the two people selected have traditional insurance is 0.33.
What is the probability that neither had traditional insurance?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that neither of the two people selected have traditional insurance = (number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed x [(number of people that chose manage care plan + number of people who dont have any insurance) / total number of people surveryed - 1]
21/36 x 20/35 = 0.33
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Which set of angle measures could be the interior angles of a triangle?
Answer:
the three angles inside a triangle need to add up to 180 degrees
Step-by-step explanation:
HELP PLEASE!!
Discuss the steps that you used
to create your tangent line.
What was the most important
step?
Give an example of tangents in
the real world that have not
been presented in this lesson.
Explain how you know the
tangent and the radius are
perpendicular.
Answer:
You need to have both the opposite and adjacent side of the right angled triangle. Tan = Opp/Adj
Step-by-step explanation:
Tangents are pretty much everywhere. A good example is maybe a slide at the playground. You’d need the tangent to figure out the angle of the slide and how it is.
The radius from the center of a circle to the point of tangency point shows that it would be perpendicular to the tangent line considering that anything with a radius is circular and the tangent line is… a line, making it impossible to be parallel.
I need help finding the surface area of this shape
Answer:
1030 [tex]yd^{2}[/tex]
Step-by-step explanation:
split it into 2 different rectangular prisms
first one is 27 yd by 8 yd by 9 yd
second is 10yd by 8 yd by 12 yd
Answer:
1494 [yd²].
Step-by-step explanation:
1) the required area can be calculated as (see the attached picture):
A=A1+A2+A3+A4+A5+A6+2*A7;
2) finally,
A=9*8+17*8+8*12+10*8+(12+9)*8+27*8+2*(27*9+12*10);
A=1494 [yd²].
Note, the suggested solution is not the shortest one.
£ 686 is shared out between David, Steve and Mike. Mike gets twice as much as Steve who gets twice as much as David. How much does Mike get?
Answer:
£ 392
Explanation
Anyone can help me with this? Kinda confusing. Thank you!
Answer:
14
Step-by-step explanation:
you can do 9 x 14 and get 126
For the point P(17,22) and Q(22,27), find the distance d(P,Q) and the coordinates of the midpoint M of the
segment PQ.
Step-by-step explanation:
[tex]x \: component = \frac{17 + 22}{2} \\ = 19.5 \\ y \: component = \frac{22 + 27}{2} \\ = 24.5 \\ (19.5...24.5)[/tex]
I don't know how to do this (don't mind the 21)
Answer:
The definition of alternate interior angles is that those two angles are the same.
Therefore because they are the same you can set them equal to eachother
3x + 24 = 78 is true
3x = 54
x = 18
Just know the definitions, for instance 3 and 4 are the same, 2 and 5 are the same, 1 and 6 are the same