Answer:
a) C(2000)=1915
C(2014)=1915
b) [tex]C'(2000)=-\frac{275}{14}[/tex]
[tex]C'(2014)=-\frac{275}{14}[/tex]
c) [tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]
d) t=2021
e) too early
Step-by-step explanation:
a)
Since C(t) is the concentration of CFCs in ppt in year t, all we need to do to solve this part is determine what the concentration of CFCs is in years 2000 and 2014. Luckily for us, the problem already gives us those values, so:
C(2000)=1915 concentration in year 2000
C(2014)=1915 concentration in year 2014
b)
By definition, the derivative of a function at a given point is interpreted as the slope of the tangent line to the point of interest, so in order to find this answer, we need to find the slope of the line. Since the problem specifies that the behavior is linear, this means that the slope will always be the same no matter the year, so we get:
[tex]m=C'(t)=\frac{C'(t_{2})-C'(t_{1})}{t_2-t_1}[/tex]
so:
[tex]C'(t)=\frac{1640-1915}{2014-2000}=-\frac{275}{14}\approx -19.64[/tex]
therefore:
[tex]C'(2000)=-\frac{275}{14}[/tex]
[tex]C'(2014)=-\frac{275}{14}[/tex]
c)
Since the behavior is linear, we can calculate it with the point-slope form of the line which is:
[tex]y-y_{1}=m(x-x_{1})[/tex]
in this case:
[tex]C(t)-C(t_1)=C'(t)(t-t_{1})[/tex]
so we get:
[tex]C(t)-1915=-\frac{275}{14}(t-2000)[/tex]
and we can now solve for C(t) so we get:
[tex]C(t)=-\frac{275}{14}t+\frac{275000}{t}+1915[/tex]
for a final answer of:
[tex]C(t)=-\frac{275}{14}t+\frac{288405}{7}[/tex]
d)
So next we solve the equation for C(t)=1500 so we get:
[tex]1500=-\frac{275}{14}t+\frac{288405}{7}[/tex]
[tex]1500-\frac{288405}{7}=-\frac{275}{14}t[/tex]
[tex]-\frac{277905}{7}=-\frac{275}{14}t[/tex]
[tex]t=2021 \frac{7}{55}[/tex]
so we will reach that concentration level at the year 2021 approximately.
e)
Since the second derivative of the concentration function is greater than zero, this means that the original function might be a function in the form: .
This means that the decrease of the concentration levels is slower than that of a linear equation. So the projected date will be too early than the real date.
The angle represents the phase shift, determined by the initial conditions of the experiment or the position of the weight at t = 0. If the weight is at its maximum positive position (weight is above equilibrium) at t = 0, then = 0. If the weight is at its maximum negative position (spring is stretched and weight is below equilibrium) at t = 0, then . If the weight is traveling in the negative direction and passing through equilibrium at t = 0, then . In the response box, describe the initial condition of our experiment; specifically, describe the position of the weight and the direction in which it was traveling.
Answer:
the weight was approaching the equilibrium position from the positive direction. The weight was on its way down, with the spring stretching
Step-by-step explanation:
This is the word for word answer but be careful and don´t copy it exactly!! paraphrase the answer using your own words
A school principal plans to form teams from 126 third-graders, 180 fourth-graders, and 198 fifth-graders so that there is the same number of students from each grade level on each team. If all students participate, what is the largest possible number of teams and how many students will there be on each team?
Answer:
There are 9 teams possible each having 14 third-graders, 20 Fourth-graders, 22 Fifth-graders
Step-by-step explanation:
126 third-graders
180 fourth-graders
198 fifth-graders
Find the highest common factor of 126, 180, 198
Factors of 126: 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126.
Factors of 180 : 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
Factors of 198: 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198.
The highest common factor of 126, 180, 198 is 9
The largest possible number of teams that can be formed is 9
Each team has
third-graders = 126 / 9
= 14
Fourth-graders = 180 / 9
= 20
Fifth-graders = 198 divided by 9
= 22
There are 9 teams possible each having 14 third-graders, 20 Fourth-graders, 22 Fifth-graders
Having trouble with finding the rise over run and simplifying the fraction
A system of equation is shown: 2x = -y + 6 -4x + 3y =8 what is the solution tonthis system of equations? (-1, -4) (1, 4) (4, 4) (-4, -1)
Answer:
(1 , 4)
Step-by-step explanation:
2x = -y + 6
-4x + 3y = 8
2x = -y + 6
2x - 6 = -y
-2x + 6 = y
-4x + 3y = 8
-4x + 3(-2x + 6) = 8
-4x - 6x + 18 = 8
-10x + 18 = 8
-10x = -10
x = 1
-2x + 6 = y
-2(1) + 6 = y
-2 + 6 = y
4 = y
A washer and a dryer cost $796 combined. The washer cost $54 less than the dryer. What is the cost of the dryer?
Answer:
The cost of the dryer would be 425$
Step-by-step explanation:
796 - 54 = 742
742 ÷ 2 = 371
371 = washer cost
371 + 54 = 425
425 = dryer price
======================================================
Explanation:
w = cost of washer
d = cost of dryer
costs are in dollars
w+d = 796 since the two costs combine to get a total cost of $796
w = d-54 because the washer is $54 cheaper
-------------------------
Let's start with the first equation and plug in the second equation
w+d = 796
(w) + d = 796
(d-54)+d = 796 ... replace w with d-54
d-54+d = 796
2d-54 = 796
2d = 796+54 ... adding 54 to both sides
2d = 850
d = 850/2 ... dividing both sides by 2
d = 425
The dryer costs $425
We can stop here.
-------------
If you want to find the cost of the washer, then,
w = d-54
w = 425-54 .... plug in d = 425
w = 371
The washer costs $371
Note that
w+d = 371+425 = 796
which matches with the total cost we were given. This confirms our answer.
What is fo)?
12 only
2 and 3 only
-2, -1, 1, and 2 only
-2, -1, 1, 2 and 12
9514 1404 393
Answer:
f(0) = 12 . . . only
Step-by-step explanation:
We don't know your intended meaning of "fo)". If it is supposed to be f(0), that is the value of the function at x=0, in other words, the y-intercept.
The graph of f(x) crosses the y-axis at y=12, so ...
f(0) = 12
Answer: 4,12
Step-by-step explanation: Gimme points I counted the lines where the f(x) is located at then found 4 same for y ( I started with X then Y)
what is the answer to this question?
Answer:
1st box
3rd box
5th Box
Step-by-step explanation:
For the first equation, you have to move the decimal place 11 places to the right.
For the second equation, you have to move the decimal 13 places to the right.
-tell me if I'm wrong
The sum of 7 and Chau's height is 48.
Answer:
7+c=48
Step-by-step explanation:
Please help me with this question?
Answer:
Step-by-step explanation:
The answer is A
If it's not then i'm sorry
Answer:
None of the above
Step-by-step explanation:
A. b ≠ 0
B. Solve for b:
-7/(2 b) = (2 b)/7
Cross multiply:
-49 = 4 b^2
-49 = 4 b^2 is equivalent to 4 b^2 = -49:
4 b^2 = -49
Divide both sides by 4:
b^2 = -49/4
Take the square root of both sides:
Answer: b = (7 i)/2 or b = -(7 i)/2
Identify next three numbers in this sequence: 2, 6, 3, 9, 6, 18, 15…
Answer:
10000000000000000000000,
the next number: 1-934028049747284
that's all
pls report
thanks!))))
Step-by-step explanation:
need help not sure
Answer:
6
Step-by-step explanation:
You add 3 and 5 to get 8 and then you will subtract 2 from 8 to get 6
Suppose that two balanced dice are tossed repeatedly and the sum of the two uppermost faces is determined on each toss. a) What is the probability that we obtain a sum of 3 before we obtain a sum of 7? Hint: Let A denote the event of a sum of 3. Let B denote the event of no sum of 3 or 7. Now, begin to list the out the sample space in terms of A and B - it should be recognizable in the lecture notes. Hint: A useful infinite series result when |z| < 1: 1 + z + z 2 + z 3 + z 4 + . . . = 1 1 − z
The price of a stock steadily decreased by a total of $123 over the past 14 months.
What happened when the stock decreased by $123?
What is the opposite of 4:3?
Answer:
3:4???
Step-by-step explanation:
Answer:
3:4
3/4
Step-by-step explanation:
reciprocal
A researcher predicts that listening to music while solving math problems willmake a particular brain area more active. To test this, a research participant hasher brain scanned while listening to music and solving math problems, and thebrain area of interest has a percentage signal change of 58. From many previousstudies with this same math problems procedure (but not listening to music), it isknown that the signal change in this brain area is normally distributed with amean of 35 and a standard deviation of 10.
(a) Using the .01 level, what shouldthe researcher conclude? Solve this problem explicitly using all five steps of hypothesistesting, and illustrate your answer with a sketch showing the comparisondistribution, the cutoff (or cutoffs), and the score of the sample on this distribution.(b) Then explain your answer to someone who has never had a course in statistics(but who is familiar with mean, standard deviation, and Z scores).
Answer:
one equal to 5
Step-by-step explanation:
5x x 66
If g is the midpoint of AB, classify each triangle by its angles and sides
Each triangle can be classified by its angles and sides in the following ways :
triangle CFE = triangle CFE is a right angle triangle ( as one of its interior angle measures 90° ) . Triangle CFE is also a scalene triangle ( as none of its sides are equal ) .triangle BEC = Triangle BEC is a right angle triangle . It is also a scalene triangle ( as none of its sides or angle are equal ) .triangle BFG = triangle BFG is an equilateral triangle ( all of its sides are equal ) and it is also an acute angle triangle ( all of its angle will be equal to 60° , which is acute ) .triangle GAF = Triangle GAF is an isosceles triangle ( two of its sides - GF and GA are equal ) . It is also an obtuse angled triangle ( one of its angle measures 120° ) .Mai's new bedroom has a walk-in closet with a floor that measures 20 square
feet. Her closet ceiling is 9 feet from the floor.
What is the volume of her closet?
Answer:
The volume of he bedroom is about 180 feet :)
The manufacturer of a soccer ball claims that only 3% of the soccer balls produced are faulty. An employee of this company examines the long-run relative frequency of faulty soccer balls produced as shown in the graph.
A graph titled Faulty Soccer Balls has frequency on the x-axis, and probability on the y-axis. The graph levels out around y = 0.06.
Which conclusion can be drawn from this graph?
The company’s claim seems to be true because the graph shows that when 50 soccer balls were tested, only about 3% of them were faulty.
We should not believe the company’s claim that only 3% of their soccer balls are faulty because this graph shows a continuous increase in probability.
Because the graph shows that the probability of producing a faulty soccer ball is 0.03, we can believe the company’s claim that only 3% of the produced soccer balls are faulty
The graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company’s claim that only 3% of the produced soccer balls are faulty.
Answer:
The answer is D
Step-by-step explanation:
Answer:
D. The graph shows that the probability of producing a faulty soccer ball is about 0.06; therefore, we should not believe the company’s claim that only 3% of the produced soccer balls are faulty.
Step-by-step explanation:
What is the value of 3/4 divided by 3/8
Answer:
2
Step by Step Explanation
Keep Change Flip
3/4x8/3=24/12=2
Answer:
2
Step-by-step explanation:
3/4 divided by 3/8
3/4 x 8/3
cross simplify to get
1/4 x 8/1
cross simplify again to get
1 x 2 = 2
1/2 mi = 880 yd
True
O False
Answer:
True.
Step-by-step explanation:
If you multiply the length value, you'd get 880 yd. Which basically answers it, the answer is true.
Answer:
True
Step-by-step explanation:
I did this before it kind of complicated but trust me it true
The surface area of a right square pyramid is given by A=b2+2bh where b is the length of a side of the base and h is the slant height.solve the formula for h if b=3
Answer:
[tex] h = \dfrac{A - 9}{6} [/tex]
Step-by-step explanation:
A=b^2+2bh
b = 3
A = 3^2 + 2(3)h
A = 9 + 6h
6h = A - 9
[tex] h = \dfrac{A - 9}{6} [/tex]
The required expression for the slant height is h = [A - 9] / 6 .
Given that,
The surface area of a right square pyramid is given by A=b2+2bh where b is the length of a side of the base and h is the slant height.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
A=b²+2bh
According to the condition,
put b = 3
A = 3² + 2 * 3 h
A = 9 + 6h
h = [A - 9] / 6
Thus, the required expression for the slant height is h = [A - 9] / 6 .
Learn more about simplification here:
https://brainly.com/question/12501526
#SPJ2
Order these in descending order (greatest to least). 3/20, 0.15%, 0.015
Answer:
3/20, 0.015, 0.15%
Step-by-step explanation:
Write an algebraic expression for the difference of 5 from b .
Answer:
b-5
Step-by-step explanation:
Write as a product:
25a^2−0.01b^10
Answer:
(5a + 0.1b^5)(5a + 0.1b^5)
Step-by-step explanation:
25a^2 − 0.01b^10 =
This follows the pattern: x^2 - y^2 = (x + y)(x - y)
= (5a + 0.1b^5)(5a + 0.1b^5)
Help plz asap I really need help with this
Answer:
the only solution is -7
Step-by-step explanation:
i am 95% sure that im right
Answer:
3rd
C
The only solution is -7
Step-by-step explanation:
I need help with this problem (THIS IS NOT FROM A TEST)
Answer:
44.5 degrees.
Step-by-step explanation:
Since these triangles are congruent, their angles are the same.
Therefore, we can set an equation with the 2 labeled angles (which are angles C and F):
2.5x+8=3.5x-7
8=x-7
x=15
We can plug 15 back into one of the equations:
2.5(15)+8 = 45.5
This means angle F is 45.5.
To find out the measure of angle E, recall the fact that the angles in a triangle add up to 180. Since this is a right triangle, and F = 45.5, we can set up an equation and solve for x:
90 + 45.5 + x = 180
135.5 + x = 180
x = 44.5
Therefore, the angle E is 44.5 degrees.
Answer:
44.5
Step-by-step explanation:
These triangles are the same so we know that
2.5x + 8 = 3.5x - 7
Subtract 2.5 x from both sides
8 = x - 7
Add 7 to both sides
15 = x
Substitute x
37.5 +8
45.5
There is a right angle so we must add 45.5 + 90 to get 135.5
Subtract 135.5 from 180 to get
44.5
3. The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean of 9.1 picomoles per liter and a standard deviation of 3.5 picomoles per liter. Find the probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter.
Answer: 0.8956
Step-by-step explanation:
Given: The daily surface concentration of carbonyl sulfide on the Indian Ocean is normally distributed, with a mean [tex]\mu=100[/tex] picomoles per liter and standard deviation of [tex]\sigma=3.5[/tex] picomoles per liter.
Let X be the daily surface concentration of carbonyl sulfide.
The probability that on a randomly selected day, the surface concentration of carbonyl sulfide on the Indian Ocean is less than 13.5 picomoles per liter [tex]= P(X<13.5)[/tex]
[tex]=P(\dfrac{X-\mu}{\sigma}>\dfrac{13.5-9.1}{3.5})\\\\=P(Z<1.257)\\\\= 0.8956\ \ \ [\text{By p-value table}][/tex]
Hence, the required probability = 0.8956
what is the value of 2.5x+17+21x-25=180
Answer:
x=8
Step-by-step explanation:
2.5x+17+21x−25=180
Simplify 2.5x+17+21x−25
23.5x−8=180
Move all terms not containing x to the right side of the equation.
23.5x=188
Divide each term by 23.5 and simplify.
x=8
Hope this helps! :) Plz mark as brainliest
write an equation to solve for x 8x+2 14x-76 will give brainiest
Answer:
8x + 2 = 14x - 76Step-by-step explanation:
just add both corresponding angles
When given a system of equations in slope-intercept form, is graphing or substitution the most efficient method to solve?