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.
A business has seven locations to choose from and wishes to rank only the top three locations. How many different ways can this be done?
Answer: 210
Step-by-step explanation:
Given: total locations = 7
Number of locations wishes to rank = 3
If order of selection matters, then the number of permutations of r things from n= [tex]\dfrac{n!}{(n-r)!}[/tex]
The number of ways to rank 3 locations out of 7 [tex]=\dfrac{7!}{(7-3)!}=7\times6\times5=210[/tex]
Hence, the number of different ways required = 210
Help me please math is a pain...
Answer:
D
Step-by-step explanation:
The degree of 10 moves the decimal. As we are multiplying, move the decimal 5 places to right.
Pls mark me brainliest
Answer:
Answer is D (750,000)
Step-by-step explanation:
Basically you do 10^5 = 10 x 10 x 10 x 10 x 10 to get 100,000 then you multiply by 7.25 lol
how do i solve intervals
An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than allowed by environmental regulations. They measure water temperatures at the cooling system input and the cooling system output for several different days in several different seasons. A list containing these measurements is below:
Sample Input Temp (deg F) Output Temp (deg F)
1 57.6 65.1
2 68.9 74.4
3 68.1 74.7
4 47.7 55.4
5 48.1 51
6 67.2 71.9
7 69.9 79.2
8 48.1 57.2
9 35 41.4
10 56 61
11 44.3 50.8
12 65 70.5
13 48.3 56.9
14 54.9 61.7
15 60.4 67.3
Do a statistical analysis on this data to determine if the temperature change between the input and output of the cooling system is different than 6 degrees.
1. What does your analysis indicate?
a. The cooling system changes the temperature of the water by an amount different than 6 degrees.
b. The cooling system changes the temperature of the water by 6 degrees.
2. What is the P-Value associated with your decision above?
a. 0.001
b. 0.026
c. 0.049
d. 0.070
e. 0.110
f. 0.131
g. 0.148
h. 0.201
i. 0.278
j. 0.289
Answer:
1
The correct option is b
2
The correct option is h
Step-by-step explanation:
From the question we are told that
The sample size is n = 15
The difference in population proportion is [tex]d = 6[/tex]
Generally the sample mean of the input temperature is
[tex]\= x_1 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_1 = \frac{57.6 + 68.9 + \cdots +60.4 }{15}[/tex]
=> [tex]\= x_1 = 62.57 [/tex]
Generally the sample mean of the output temperature is
[tex]\= x_2 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x_2 = \frac{65.1 + 74.4 + \cdots +67.3 }{15}[/tex]
=> [tex]\= x_2 = 55.97 [/tex]
Generally the difference of the sample mean of the input temperature and that of the output temperature is
[tex]\= d = \= x_1 - \= x_2[/tex]
=> [tex]\= d = 62.57 -55.97[/tex]
=> [tex]\= d = 6.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]s_d = \sqrt{\frac{\sum(d_1 - \= d )^2}{n} }[/tex]
=> [tex]s_d = \sqrt{\frac{([57.6- 65.1]- 6.6)^2+ ([68.9 - 74.4]- 6.6)^2 + \cdots + ([60.4 - 67.3]- 6.6)^2 }{15} }[/tex]
=> [tex]s_d = 1.732 [/tex
Generally the test statistics is mathematically represented as
[tex]t = \frac{ d - \= d }{ \frac{s_d}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 6-6.6 }{ \frac{1.732}{\sqrt{15} } }[/tex]
=> [tex]t = 1.3417[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 15 - 1[/tex]
=> [tex]df = 14[/tex]
Generally the probability of t obtained from the t - distribution table at a degree of freedom of [tex]df = 14[/tex] is
[tex]P(t >1.3417 ) = 0.10052569[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 1.3417)[/tex]
=> [tex]p-value = 2 * 0.10052569[/tex]
=> [tex]p-value = 0.201 [/tex]
From the values obtained we see that [tex]p-value > \alpha[/tex] hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
The cooling system changes the temperature of the water by 6 degrees.
11. Given a polynomial P(x) = x³-4x²-5x is one of the zeroes.
a) Factorise P(x) completely
b) Sketch the graph of P(x)
C)Find the domain and range.
Answer:
thats some tuff
Step-by-step explanation:
Answer:
Step-by-step explanation:
P(x)=x³-4x²-5x=x(x²-4x-5)
=x(x²-5x+x-5)
=x[x(x-5)+1(x-5)]
=x(x-5)(x+1)
domain (-∞,∞)
range: (-∞,∞)
Cost of bowling if it is $3 per game and $5 for shoes. Find the linear equation.
Answer:
y=3x+5
Step-by-step explanation:
Depending on how many games he has played that number where the x is. So let’s say he plays two games so what you’re going to do is plug the two in for the X so then it would be 2×3 which is 6 then you would do 6+5 because you still have the 5 left and it says to add.
That should be right and follow me if this helps.
-14+6b +7-2b=1+5b what is answer?~PLEASE SHOW WORK 45 POINTS
Answer:
b=-8
Step-by-step explanation:
Sorry I don't have time to show work right now and write it down but this is the answer.
Answer:
b=8
Step-by-step explanation:
1.1 Pull out like factors :
-8 - b = -1 • (b + 8)
Solving a Single Variable Equation
2.1 Solve : -b-8 = 0
Add 8 to both sides of the equation :
-b = 8
Multiply both sides of the equation by (-1) : b = -8
Multiply 2 3/4 x 1 1/3. Write your answer in simplest form
so , bro to multripy fractions , you have to convert the mixed fraction into unlike fractions . so lets get started.
2 3/4 * 1 1/3
= 12 / 4 * 4/3
now multiply normally
= 48 / 12
divide this by 4/4 to get simplest for
= 12 / 3 divided by 3/3
= 4/1
Step-by-step explanation:
2+2 this is for that one guy that answered my question he needs some more points and answers so imma help him out
I think it’s a boy honestly Idk
Answer:
I need more too lol the answer is 4
What is (1 x 10(5) + (3 x 10(3) + (7 x 10(2) in standard form?
A. 1,030,700
B. 1,037,000 I. C. 103,700
D. 1,370
03 = 1000
8. 10-5 = 1/100,000 = 0.00001
9. 109 = 1,000,000,000
10. 1 X 10-2 = 1/100Answer:
1. 100 = 102
2. 10,000,000 = 107
3. 1 / 10,000 = 10-4
4. one million = 106
5. 1 / 10,000,000 = 10-7
6. one ten millionth = 10-7
7. 1 = 0.01
Step-by-step explanation:
PLEASE HELP These equations represent different possibilities for a waiter earning $11.25 for waiting on one table for one hour. The constant is the hourly rate and the coefficient represents the fraction of the bill, b, the customers left as a tip. Which equation correctly represents the hourly rate and tip for a bill of $30.00?
A. 5.00 + 1/6 b = 11.25
B. 5.25 +1/3 b = 11.25
C. 5.25 + 1/5 b = 11.25
D. 6.00 + 1/8 b = 11.25
Answer:
C
Step-by-step explanation:
Just took test n got it right
Answer:
C. 5.25 + 1/5 b = 11.25
Step-by-step explanation:
Please help me be right! Ordered pairs
Answer:
the answer is C
Step-by-step explanation:
both the ordered pair satisfy the equation
Need help with both 7 and 8
PLEASE HELP!!! I DON’T KNOW THISSS
Jenny has only 3 1/2 cups of flour in her house. She needs 1 5/8 cups for a brownie recipe. Her sister Jody needs 1 3/4 cup flour for her cookie recipe. Will there be enough flour for both recipes?
Answer:
yes, she will still have 1/8 of a cup left
Step-by-step explanation:
you have to convert all the fractions to have the same denominator.
to do that you need improper fractions
3 1/2= 7/2
1 5/8= 13/8
1 3/4= 7/4
with this information, you need to find a common number between 2, 8, and 4. the largest number that they all fit into is 8.
so 7/2 becomes 28/8
13/8 stays the same
and 7/4 becomes 14/8
add 13/8 and 14/8 and subtract from 28/8
you get 1/8, which means you have enough flower for both recipes!
Answer:
[tex]YES.[/tex]
Step-by-step explanation:
[tex]if \: 1 \frac{5}{8} + 1 \frac{3}{4} = 3.375 \\ and \\ 3 \frac{1}{2} = \: 3.5 \\ then \: 3.5 > 3.375[/tex]
What is the product?
please help ??? Thanks
Answer:
Each y- value is determined by adding 4
Step-by-step explanation:
what is 3.14 x 11 x2
Answer:jurrhthrhth
Step-by-step explanation:hdhdbbdfh
Answer:
69.08
Step-by-step explanation:
I hope this helped!
what is 1423 divided bye 789
Answer:
1.8
Step-by-step explanation:
Answer:
use calculator
Step-by-step explanation:
search calculator on google
least common denominator of 7/2 and1/2
help wil give brainly if right
Answer:
I think it B as well as the other person I just learned this so I'm not the best at it
Mr. Martin bought a microwave that was originally priced at $225. Using a coupon, he received a 30% discount on the microwave. What is the total price Mr. Martin will pay at the register if there is a 6% sales tax. Round your answer to the nearest cent if necessary.
Answer: 125 I think
Step-by-step explanation:
Simplify the expression and enter your answer below.
(191/99
Answer:
the correct answer is 1 92/99
Which statement is true?
Answer:a
Step-by-step explanation:because the number equals the letter.
Find the domain and the range of each relation. Use the vertical
Line test to determine whether each graph is the graph of a function.
Answer:
29) x> or equal to 0 and y= all real number
30) x= all real y> or equal to 0
There are 40 players on Bill's football team, 2/5 of the players walk to practice and 1/4 of the players ride with their parents. The remaining players ride the bus. How many students ride the bus?
Answer:
22 students.
Step-by-step explanation:
There are a total of 40 players on the football team. 2/5 walk, 1/4 ride with their parents, and the rest ride the bus. To solve, I'm going to be using fractions to find out how many students ride the bus.
1/4 of 40 or 40/4 is equal to 10.
So we know 10 players ride with their parents.
2/5 of 40 or 40/5 is equal to 8.
Cool, 8 students walk to practice.
Now the rest ride the bus. Let's use addition to find the total amount of players that dont use the bus and subtract it from the total amount of players.
10+8=18
40-18=22.
22 students/players ride the bus to football practice.
Plz solve for brainlistMarlene runs 4 km in 30 min. At this rate,
can Marlene run 6 km in 45 min?
Complete the following calculation an
d
explanation. Use the Communication
Checklist.
Answer:
comparing rates.. use the formula d = r * t where d= distance , r = rate or speed and t = time ofc. :)
Step-by-step explanation:
we know the distance and the time but not the rate.. find that r ....
d/t = r 4/30 = r = 0.13333333333 this is in Km per minute, b/c the 4 is Km and the 30 is in minutes. Units are not to important other than keeping track of what they are.
Now we can answer the question can Marlene run 6 Km in 45 mins. b/c we know her rate , or speed, so at her rate of 0.133333333 Km/min and using that d = r * t formula what is her distance in 45 minutes.. so multiply 45 * 0.133333= 6 so she runs exactly 6 Km in 45 minutes.. so the math answer is yes
2.5 puzzle time Which month has 28 days
Answer:
February has 28 days on every year except a leap year, but all months have at least 28 days.
Step-by-step explanation:
Answer:
February is the answer
Step-by-step explanation: hope this helps.
Dylan makes $336 for 32 hours of work, and Angela makes $420 for 42 hours of work.
1] How much do Dylan and Angela each make per hour?
2] Is Dylan’s wage for 25 hours proportional to Amber’s wage for 42 hours? Why or why not?
Answer:
Step-by-step explanation:
1 . Dylan : $336/32 hrs = 10.50/ hr Angela : $420/42hrs = $ 10.00/hr
2. No because $ 10.50x25 262.50 where ambers is 15 420 there unit rate is different.
What’s the rule it’s algebra 1
Answer:
An algebraic rule is a mathematical expression that relates two variables and is written in the form of an equation. There are many constant algebraic rules, such as area = length x width. You can also create your own rule when given a set of variables
Step-by-step explanation:
Is 4:5 equivalent to 8:10 as radios?