Answer:
The answer is
[tex] \huge \frac{5}{2} \\ [/tex]
Step-by-step explanation:
The slope of a line given two points can be found by using the formula
[tex]m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\[/tex]
From the question the points are
(-9, 2) and (1, 27)
We have
[tex]m = \frac{27 - 2}{1 - - 9} = \frac{25}{1 + 9} = \frac{25}{10} = \frac{5}{2} \\ [/tex]
We have the final answer as
[tex] \frac{5}{2} \\ [/tex]
Hope this helps you
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?
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.
giving 70 points please help I only have 20 minutes to get It.......
Answer: 8
Step-by-step explanation:
Allison and her classmates planted bean seeds at the same time as Yuki and her classmates in Tokyo did. Allison is video-chatting with Yuki about their class seedlings. Who should expect to have the taller plant at the end of the school year?
Answer:
probably yuki
Step-by-step explanation:
real fact
A customer purchased a lawn mower for a total purchase price of $318.75. If the state has a sales tax rate of 7.75%, what was the selling price of the lawn mower
Answer:
$343.45
Step-by-step explanation:
$318.75 x 1.0775 = $343.45
or
$318.75 x 0.0775 = $24.70
$318.75 + $24.70 = $343.45
The selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.
What is percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
We have a customer purchased a lawn mower for a total purchase price of $318.75.
Sales tax rate = 7.75%
Sales tax amount = 7.75% of $318.75
Sales tax amount = $24.64 ≈ $24.70
Original price = 318.75 + $24.70 = $343.45
Thus, the selling price of the lawn mower is $343.45 if the customer purchased a lawn mower for a total purchase price of $318.75.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
what is greater 0 or 2x-6?
Answer:
It's 0
Step-by-step explanation:
0 is a greater number than the answer for 2 times -6, which is -12
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 8 hours. How long will it take the pipe to fill the pool if the drain is left open? Express your answer as a reduced fraction.
Answer:
24 hours
Step-by-step explanation:
Let x represent the time required to fill both pipes if they are left open
1/6 + (-1/8)= 1/x
1/6 - 1/8= 1/x
Divide through by 48
48(1/6) -48(1/8) = 48(1/x)
8 - 6 = 48 x
2= 48/x
2x= 48
x= 48/2
x= 24
Hence it will take 24 hours to fill the pipe if the drain is left open
The quotient of fifty and five more than a number is ten
Answer:
This number would be straight out zero .
Step-by-step explanation:
First it said the quotient of fifty and five MORE than a number is 10, so we first need to focus on the line five MORE than a number is 10, so we know this number is less than the value used in the equation then we focus on the quotient of fifty and, So we know this unknown number lets just say the variable for it is n, then we know that fifty/ n+5=10. So Lets use the associative property to turn this into and some algebra to fifty/10 = n+5, so 50/10 equals to 5, so we know that, 5= n+5, so that would be... n = 0. Hope this helps you answer your question! :)
Find the equation of the graphed line.
The answer I put in was incorrect and I’m not sure why
Answer:
-3x + 2 = y
As the y-intercept is y = 3
And the rise/run = 3/-1
PLEASE HELP THIS IS DUE TODAY!
Justify each step of the solution by stating the property that was used to get to each step.
Given: 4.5(8-x)+36=102-2.5(3x+24)
Step 1: 36-4.5x+36=102-7.5x-60
Step 2: 72-4.5x=42-7.5x
Step 3: 72+3x=42
Step 4: 3x=-30
Step 5: x=-10
Answer:
_1+5+0+8=65
Step-by-step explanation:
Col-ledge math solution hope you dont get confused
Hope this helps :)
Brainest pls?
Answer:
x= -10
Step-by-step explanation:
simplify 36 - 4.5x + 36 to -4.5x + 72
simplify 102 - 7.5x - 60 to -7.5x + 42
add 7.5x to both sides
simplify -4.5x + 72 + 7.5x to 3x + 72
subtract 72 from both sides
simplify 42 - 72 to -30
divide both sides by 3
simplify 30/3 to 10
Answer: x = -10
PLEASE HELP ME I WILL GIVE BRAINLIEST!!!!!!
Consider the relationship between the words pine and tree Which answer choice contains a pair of words with the same relationship? A. book: title B. hook: instrument C. badger: animal D. head: scarf
Answer:
Maybe it's C.
Step-by-step explanation:
Answer:
ti is A BOOK TITLE
Step-by-step explanation:
what value for x makes this equation true? 0.6x-5=0.1x+7
Calculate the Social Security and Medicare tax that would be applied to an annual salary of $235,430. Use $106,800 for
maximum taxable earnings.
a. Social Security tax: $1,459.67, Medicare tax: $341.37
b. Social Security tax: $14,596.66, Medicare tax: $3,413.70
c. Social Security tax: $662.16, Medicare tax: $341.37
d. Social Security tax: $6,621.60, Medicare tax: $3,413.70
Answer:
D Social Security tax: $6,621.60, Medicare tax: $3,413.70
Step-by-step explanation:
Following are the calculation to the Social Security and Medicare tax value:
This Social Security tax is a percent to which both workers and employers must pay [tex]6.2\%[/tex] of employee wages, for a total of [tex]12.4\%[/tex].The state pension, which would be applied to a [tex]\$235,430[/tex] annual wage with a maximum tax liability:[tex]\to \$106,800\ is\ 12.4\%\ of\ \$106,800 = 0.124 \times \$106,800 = \$13,243.20[/tex]
Its payroll tax for Medicare is [tex]2.9\%[/tex].This only applies to earned income, which includes salaries and tips from an employer. We are liable for [tex]1.45\%[/tex] of a tax, which would be immediately withheld from your paycheck. The other [tex]1.45\%[/tex] is paid by your company. This Medicare tax would be charged to a [tex]\$235,430[/tex] annual salary with a maximum taxable income:[tex]\to \$106,800\ is\ 2.9\%\ of\ \$106,800 = 0.029 \times \$106,800 = \$3,097.20[/tex]
Therefore, the final answer is "$13,243.20 and $3,097.20".
Learn more:
brainly.com/question/1899088
In other words, which one doesn't belong?
x>-2
3< x
x < 4
5>6
Please help!!
Answer:
5>6
Step-by-step explanation:
What is the rule of the rotation. Did it rotate clockwise or counterclockwise? How many degrees did it rotate?
Find the 2nd term in the expansion of (1+3y)5
Step-by-step explanation:
Using pascal's triangle;
Then second term of the expansion (1+3y)5
is given as:
5(1)^4(3y) = 15y
Answer:
15y
Step-by-step explanation:
Is there a proportional relationship between x and y?
5
10
6
9
2
Cans of Paint (x)
Bird Houses Painted (y)
15
30
18
27
6
Yes, k =2
Yes, k=3
No
Answer:
Unnnnnnnnnnnnnnnnnnnnnnnnbnbnnnn
The variable y is directly proportional to the variable x. If y = 32 when x = 20, what is the value of x when y = 40?
Answer
25
Step-by-step explanation:
20/32 = 0.625
40 x 0.625 = 25
You can check by doing 25/40 and see if you get the same proportion (x/y)
25 is the correct answer 32/20 is 1.6 and 40/25 is also 1.6
Find the value of x.
Pls explain to me I’m lost
Answer:
idk but i can tell you another site if you still need help,
QUIZLET
Step-by-step explanation:
Answer:
x=17 degrees
Explanation:
Its the same angle as 17 degrees
A DJ is preparing a playlist of 23 songs. How many different ways can the DJ arrange the first four songs on the playlist?
Answer:
Sample Response: The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.
DJ can arrange 88,55 times the first four songs on the playlist.
What is permutation and combination?Permutation and combination are ways to arrange values in a set. In permutation the order of arrangement matters, but in combination the order of arrangement does not matter,
Given that,
DJ prepares a playlist of 23 songs.
Since, DJ arranges the first four songs on the playlist,
The ways to arrange the song on the playlist,
= [tex]^{23}C_4[/tex]
= 23 ! / (4! x (23 - 4)! )
= 23 ! / (4! x 19!)
= (23 x 22 x 21 x 20 x 19!) / (4 x 3 x 2 x 1 x 19!)
= 23 x 11 x 7 x 5
= 8855
There are 8,855 ways to arrange first 4 songs.
To know more about Permutation and Combination on:
https://brainly.com/question/13387529
#SPJ2
a
domain: {0, 2, 4), range: (2,6, 10}
b. domain: {0}, range: {2}
domain: (2, 6, 107, range: {0, 2, 4}
d.
domain: {2}, range: {0}
C.
Answer:
A
Step-by-step explanation:
Jake, Utah, renting with a friend
Hourly rate: $8.75/hour
Hours worked: 40/40
Commission rate: 2.75%
Sales amount: $7500
Expenses: everything.
Y
CO20
Answer:
What is the question?
Step-by-step explanation:
I will change my answer if you put a clear question up...
A dice is rolled twice.
What is the probability of getting a 2 AND a 5?
In 1902, the yearly attendance at a major league baseball park was 3.4 × 105 people.
One hundred years later, the yearly attendance was 1.7 × 106 fans.
How many times greater was the attendance in 2002 than in 1902? Enter your answer in the box. helpppppp
Answer: 1902 had 357 people and 2002 had 180.2 people so, the answer would be
176.8
Step-by-step explanation: i hope this helps
plz tell me if its wrong so i can fix it
2.) Your parents drove 300 miles in 6 hours. At what speed (miles per hour) were they driving?
Answer:
50 mph
Step-by-step explanation:
300 / 6 = 50
you can check this by setting up the equation,
6 x 50 = 300
So with this being said, you can conclude that your parents are driving a 50 miles per hour.
6 is added to the square of a number
I assume you want the math statement.
Let n = a number
Let n^2 = the square of a number
Add means to use addition.
Answer: 6 + n^2
QUICKKKKK Someone plz answer number 2
Answer:
5 times the sun of 2x and 3y equals the difference of y to the second power and 2x cubed
TEST
1) ERROR ANALYSIS: Identify and correct the error in describing the transformation of the parent
function.
Sadly the question is incomplete, so we can not see the described transformation of the parent function, thus we can't see the error in that description.
What we can do is describe the transformation shown here.
Here we can see the parent function:
f(x) = x^2
This function opens upwards, so what we see in the graph is this function reflected across the horizontal axis (the x-axis). So the transformation is just a reflection across the x-axis.
(notice that it passes through (-1, -1) and (1, -1), so there is no dilation nor contraction)
For a general function f(x), a reflection across the x-axis is just:
g(x) = -f(x)
So here the transformed function is:
g(x) = - x^2
If you want to learn more, you can read:
https://brainly.com/question/14536884
You roll two dice. The first dice shows a ONE and the other dice rolls under the table and you cannot see it. Now, what is the probability that both dice show one?
how many faces does the dice have? I'm gonna assume it had six faces.
Answer:
1/6
Step-by-step explanation:
since the dice has one 1 on it and it cannot be seen
23.85 + 7.42 + 16.15
Answer:
47.42
Step-by-step explanation:
Try solving this way
23.85
+07.42
+16.16
=======
47.42