Answers
To work out this you need to do the change in y/ the change in x.
So we take 2 points you are given in the table- e.g (1,5) and (2,1)
So the change in y is from 5 to 1 so it is -4 and the change in x is from 1 to 2 so is 1.
Then you have -4/1 which is just -4.
Let me know if you have any questions!
Related Questions
Use the slope formula to determine the slope of the line.
(6,7) (9,9)
Answers
Answer:
2/3
Step-by-step explanation:
y2-y1/x2-x1
9-7/9-6
2/3
Chlorofluorocarbons (CFCs) were used as propellants in spray cans until their buildup in the atmosphere started destroying the ozone, which protects us from ultraviolet rays. Since the 1987 Montreal Protocol (an agreement to curb CFCs), the CFCs in the atmosphere above the US have been reduced from a high of 1915 parts per trillion (ppt) in 2000 to 1640 ppt in 2014.23 The reduction has been approximately linear. Let C(t) be the concentration of CFCs in ppt in year t.
(a) Find C(2000) and C(2014).
(b) Estimate C′(2000) and C′(2014).
(c) Assuming C(t) is linear, find a formula for C(t).
(d) When is C(t) expected to reach 1500 ppt, the level before CFCs were introduced?
(e) If you were told that in the future, C(t) would not be exactly linear, and that C″(t) > 0, would your answer to part (d) be too early or too late?
Answers
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.
Solve the simple equation.
5(2d+2) = 3 (8d-5)
Answers
Answer:
d = 25/14
Step-by-step explanation:
5(2d+2) = 3 (8d-5)
10d + 10 = 24d - 15 | +15
10d + 25 = 24d | - 10d
25 = 14 d | :14
d = 25/14
A tractor trailer has maximum capacity of 8,000 pounds. The equipment needed to load
and unload the tractor trailer must travel with the trailer and weighs a combined 1,500
pounds. The trailer will be loaded with x containers, each of which weighs 300 pounds.
What is the largest value of x such that the trailer's capacity is not exceeded?
Answers
Answer:
subtract from the maximum load the 1500 of the loading equipment and you have 6500 pounds of capacity for the containers you divide this by 300 which is what each of the containers weighs gives you 21,666 which tells us that the maximum of containers is 21
8000-1500 = 6500
6500/300 = 21.66
Step-by-step explanation:
find the mean of the data set 0.2 0.4 1 0.25
Answers
Answer:
.4625
Step-by-step explanation:
To find the mean, add up all the numbers, then divide by the number of terms
(0.2 +0.4+ 1+ 0.25) /4
1.85/4
.4625
Solve equation:7t-48=113
Answers
Answer:
The answer is 23
Answer:
t = 23
Step-by-step explanation:
A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is, a fish that really weighed 26 g was reported to weigh 24 g. What is the mean and standard deviation after correcting for the error in the scale
Answers
Answer:
Correct mean = 32 grams
Correct Standard deviation = observed S.D = 2 grams
Step-by-step explanation:
We are told in the question above :
A scientist is weighing each of 30 fish. She obtains a mean of 30 g and a standard deviation of 2 g. After completing the weighing, she finds that the scale was misaligned and always under reported every weight by 2 g that is
The mean after correcting the error in the scale is :
= observed mean + 2g
= 30g + 2g = 32g
The standard deviation after correcting the error in the scale remains the same as the difference of 2g has no significant effect on the Standard deviation.
This standard deviation = 2g
A group of students were discussing whether the relationship on the graph
is a function.
Answers
Answer:
A function is a relationship that maps the elements of a set, the domain, into elements of another set, the range.
The restriction that we have for functions is: The elements on the domain can be mapped into only one element in the range.
Then if:
f(x1) = y1
and
f(x1) = y2
where y1 is different than y2
f(x) is not a function.
Now, in the graph you can see a region where both lines overlap, then for some values of x we have two possible values of y, this means that the graph does not represent a function.
Then:
Ed: He is incorrect because we can have different values in the domain mapped into the same value in the range (like in the case of a line y = b, where we have all the elements in the domain mapped into the same element in the range, b)
Debra: There is something called piecewise functions, that are functions of this type, formed by different pieces.
Alejandro: He is correct.
Antoine: Not because you can write an equation means that the relation is a function. You can write an equation for a circle, but it will not be a function.
Use the figure at the right. If JK = 2x + 12 and NO = 14, what is the value of x?
Answers
Answer:
X=8
Step-by-step explanation:
JK would equal 28, since it basically is double the side of that triangle. So now we have the equation, 2x+12=28. Now we solve using inverse operation. 28-12=16 and then 16 divided by 2 is 8, so x=8.
The required simplified value of x is 8, for the given triangle.
What is the midpoint?A midpoint is a point on the line whose distance from both ends of the line is equal.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The property of a triangle states that the line joining the midpoints of the two adjacent sides is equal to half of the third side.
So,
JK = 2NO
2x + 12 = 24
x = 16 / 2
x = 8
Thus, the required simplified value of x is 8, for the given triangle.
Learn more about triangles here:
https://brainly.com/question/2773823
#SPJ2
Becky and claire went trick or treating.At the end of the night ,they combined their candy and found they each had four large candy bars.Becky ate two candy bars and clair ate one
Answers
Answer:
Well, You possibly did all the math depending on the question. But if it was subtraction that means there's one candy bar left
step-by-step explanation:
I hope this helped in any way!
The ratio of boys to girls in a classroom is 7 to 11. If there are a total of 49 boys in the classroom, then how many boys and girls are there all together?
Answers
Answer: 65
Step 1: Multiply and add until you get 49.
11 x 4 = 44.
44 + 5 = 49.
Step 2: Multiply and add until you get 26, because 7:11 to 49 boys is 26, 26 : 49.
7 x 3 = 21.
21 + 5 = 26.
Step 3: Add 26 and 49.
26 + 49 = 65
Answer:
126 students
Step-by-step explanation:
Boys : Girls
7 : 11
How do you get from 7 to 49?
49 ÷ 7 = 7
Therefore, you should multiply the number of boys by 7.
Multiply:
7 : 11
7 × 7 = 49
49 : 11
Remember that whatever we do to the left, do to the right.
Multiply:
49 : 11
11 × 7 = 77
49 : 77
Now, let's add the number of boys and girls in the class to find the total number of students.
Add:
49 + 77 = 126
Therefore, there are 126 students in all.
Of the following statements, which are equivalent?
I. 0
II. x(x−3)<0
III. −5
(A) I and II
(B) I and III
(C) II and III
(D) I, II, and III
(E) none of the above
Answers
Answer:
i think its C
Step-by-step explanation:
sorry if i get it wrong
Select all the expressions that have a value of 180 when b=4
Answers
Can you tell me if there are a word bank of answers and I can tell there are more then one answer so ima need more information
What is the point slope form of (8,5) and (3,4)?
Answers
Answer:
(-2,-4) or (2,4) depending on which one you start on.
Step-by-step explanation:
if you start from the highest point it is (-2,-4)
And if you start from the lowest point (2,4)
Add.
0.125 + 0.25 + 0.33
Answers
Answer:
0.705
Step-by-step explanation:
Answer: the answer is .705
Step-by-step explanation:
the numbers 0.25 and 0.33 are technically 0.250 and 0.330
so just line them up and add. 0.250+0.125+0.330=0.705
What is one other way to write 10x7 ?
A:10+7
B:(10)(7)
C:10-7
D:10/7
Answers
Answer
B
Step-by-step explanation:
What are the Factors of 8?
Answers
2 and 4 (2 x 4 = 8)
1 and 8 (1 x 8 = 8)
the factors of 8 are 2, 4, 1, and 8
Answer:
1,2,4,8
Step-by-step explanation:
Try 1x8=8, put on factor list.
Take 2.
Take 3 next.
Since there's no more, iss done.
What is the solution to the inequality? 14x - 14 > -7x + 7
Answers
Answer:
X<1 or X>3/2
Step-by-step explanation:
22 – 2(12 = 4+2*3) 3+7
Answers
Which fraction is equivalent to 20
Answers
Answer:
4/16
Step-by-step explanation:
An investment of $9,875 earns 4.8% interest
Answers
Answer:
474$
Step-by-step explanation:
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
Answers
Answer:
2.4x - 4.4
Step-by-step explanation:
0.3(4x – 8) – 0.5(–2.4x + 4)
1.2x - 2.4 + 1.2x -2
2.4x - 4.4
Which diagram best shows how fraction bars can be used to evaluate 1/2 divided by 1/4
Answers
Answer:
first one
Step-by-step explanation:
it is what is it
hello please help will give brainliest!
Answers
Answer:
The Answer is D
Step-by-step explanation:
Do what answer D tells you to do. Obviously.
if you do 280 ÷8, you get 35.
Name the relationship: complementary, linear pair, vertical, adjacent, alternative interior, corresponding, or alternate exterior.
Answers
Answer:
Step-by-step explanation:
9. Alternative exterior
10. Alternate interior
11. Complementary
12. Corresponding
13. Corresponding
14. Alternate exterior
15. Vertical
16. Linear Pair
Leti has just received a $15.00 gift card to Late, Late, Coffee for her birthday. Leti buys a small coffee each day. The total cost of the coffee is $1.50 including tax. The relationship between the coffee that Leti buys and the gift card can be modeled by a linear function y=15-1.50x. What is the initial value and what does it represent in the context of this problem?
Answers
Answer:
the initial value is 15 and it represents the y-intersect in the context of this problem
Step-by-step explanation:
The sum of two numbers is 43, the difference is 7. Find the numbers
Answers
Answer:
25 and 18
Step-by-step explanation:
Find a pair of numbers with
1. a sum of 40 and a product of 400
2. a sum of 15 and a product of 54
Answers
1. Those numbers would be, 20 and 20
20 + 20 = 40
20 x 20 = 400
2. Those numbers would be:
9 + 6 = 15
9 x 6 = 54
I hope this helps!!
how do you factor 450 a2 +242c2 + 660ac
Answers
Find each product mentally using the distributive property show the steps that you used.
1.8x71
2.6x83
Answers
Answer:
1.8 x 71 = 127.8, just 18 x 71 = 1278, then count the the decimal place from the right, i.e 127.8
same for 2.6 x 83 = 215.8
.......ok try 5.52 x 5
Answer:
27,579.24 OR 343.6
Step-by-step explanation:
I don't know if this is what you mean but 1.8x71x2.6x83=27,579.24
Also, (if that was not what you meant), 1.8x71=127.8, 2.6x83=215.8, 127.8+215.8=343.6