Answer:
m=-63 b=825
Step-by-step explanation:
To get m, make sure you use rise over run. y2-y1 over x2-x1
Answer:
m (slope) = -63
b (y-intercept) = 825
Step-by-step explanation:
I had the same question.
The initial mass of a certain species of fish is million tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of /yr. However, commercial fishing removes fish mass at a constant rate of million tons per year. When will all the fish be gone? If the fishing rate is changed so that the mass of fish remains constant, what should that rate be?
The question is incomplete. Here is the complete question.
The initial mass of a certain species of fish is 7 millions tons. The mass of fish, if left alone, would increase at a rate proportional to the mass, with a proportionality constant of 2/yr. However, comercial fishing removes fish mass at a rate of 15 million tons per year.
(a) When will all fish be gone?
(b) If the fishing rate is changed so that the mass of fish remains constant, what should the rate be?
Answer: (a) t = 1.35 years.
(b) Rate = 14,000,000
Step-by-step explanation:
(a) Initial mass is [tex]m_{0}[/tex] = 7,000,000
Rate of increase and comercial fishing gives an equation of growth:
[tex]\frac{dm}{dt}=2m-15,000,000[/tex]
m' - 2m = - 15,000,000
This is an ordinary linear equation (ODE) of first order, of type:
y' + a(x)y = f(x)
where a(x) and f(x) are continuous.
To solve this type of linear equation, first calculate integrating factor, using:
[tex]u(x) = e^{\int\limits {a(x)} \, dx }[/tex]
In our case,
[tex]u(t) = e^{\int\limits {-2} \, dt }[/tex]
Solving:
[tex]u(t) = e^{-2t }[/tex]
The general solution of a ODE can be written as
[tex]y=\frac{1}{e^{u(x)}}[\int\ {u(x).f(x)} \, dx + c][/tex]
In our case:
[tex]m=\frac{1}{e^{-2t}}[\int\ {-2t.(-15)} \, dt + c][/tex]
Solving:
[tex]m=\frac{1}{e^{-2t}}[\frac{15}{2}e^{-2t}+c ][/tex]
To find constant c, use initial condition, i.e., m(0)=7,000,000:
[tex]7,000,000=\frac{1}{e^{-2.0}}[\frac{15}{2}e^{-2.0}+c ][/tex]
[tex]c=-500,000[/tex]
Then for the fish growth, general equation is:
[tex]m=7500,000-500,000e^{2t}[/tex]
When the fish is gone, means m = 0, then:
[tex]7500,000-500,000e^{2t}=0[/tex]
[tex]500,000e^{2t}=7500,000[/tex]
[tex]e^{2t}=15[/tex]
[tex]ln(e^{2t})=ln(15)[/tex]
[tex]t=\frac{ln(15)}{2}[/tex]
t = 1.35
It will take 1.35 years for the fish to be gone.
(b) For the mass to be constant, rate of growth must be zero:
[tex]\frac{dm}{dt}=0[/tex]
Suppose the changed fishing rate is k:
[tex]2m_{0}-k=0[/tex]
[tex]-k=-2.7,000,000[/tex]
k = 14,000,000
To remain constant, rate must be 14,000,000.
Answer:I think it’s 40 sorry if it’s wrong :/
Step-by-step explanation:
To solve the equation y – 4 = 9 for y, what operation must be applied to both sides in order to isolate the variable y?
Answer:
[tex]y-4=9[/tex]
The opposite of subtraction is addition, so you would have to add 4 to both sides:
[tex]y-4+4=9+4[/tex]
[tex]y=13[/tex]
The value of the y for the equation,y – 4 = 9 will be y=13 and e have to apply the subtraction operation must be applied to both sides in order to isolate the variable y.
What are arithmetic operations?The subject of arithmetic operations includes the study of numbers and their operations, which are important to all other branches of mathematics. These systems' fundamental operations are addition, subtraction, multiplication, and division.
It is given that the equation is,y – 4 = 9.
We have to solve the equation y – 4 = 9 and find the operation that must be applied to both sides in order to isolate the variable y.
The following steps are to be taken to isolate the variable y.
y – 4 = 9
y-4+4=9+4
y=13
Thus, the value of the y in the equation, y - 4 = 9, will be 13, and in order to isolate the variable y, the subtraction operation must be done on both sides.
Learn more about the arithmetic operations here,
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What is the quotient? 457.6 divided by negative 286 –16 –1.6 1.6 16
Answer:
-1.6
Step-by-step explanation:
The quotient when 457.6 is divided by - 286 is - 1.6.
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
We know A number N divided by D with quotient Q and the remainder R can be written as,
N = DQ + R.
Given, The quotient when 457.6 is divided by - 286 is - 1.6.
learn more about quotient here :
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Determine the quail’s and pheasant’s speeds in miles per hour. Quail: 20yards in 2 1/2 minuts and pheasant’s : 200yards in 5/6 minuts.
In the sequence 1. 2. 3. 4. 1.2.3.4... the numbers 1.2.3.4
repeat indefinitely. What is the sum of the first 150 terms?
A. 300
B. 77
C 37
D.3
=============================================
Explanation:
The sequence {1,2,3,4,1,2,3,4...} has "1,2,3,4" repeat forever. We can say that the cycle is 4 terms before it restarts the pattern again. Because of this 4-cycle pattern, we know that 150/4 = 37.5 = 37 full cycles happen. The leftover part is of length 150-37*4 = 2.
In short we have 37 full cycles of {1,2,3,4} happening. The last leftover bit has {1,2} only
In the subsquence {1,2,3,4} its sum is 1+2+3+4 = 10. Having 37 copies of {1,2,3,4} leads to a sum of 37*10 = 370 so far.
Then we add on the last bit 1+2 = 3 to get 370+3 = 373.
Therefore, the sum of the first 150 terms is 373. I think your teacher made a typo when listing out the answer choices. Please double check to make sure.
2 squared+ 1 squared=?
Answer:
the answer is five(5).
is 16 less than 10 write that as a inequality
Answer:
16 < 10
Step-by-step explanation:
Less than = <
[tex]16 < 10[/tex]
By the way, this inequality is FASLE
12-21-3x5
What is the answer to this Order of operation question
Answer:
-24
Step-by-step explanation:
first multiply -3 and 5 to get -15
so it will be 12-21-15 then subtract 12-21 and you get -9
then do -9-15=24
hope this helps :)
1. Solve the equation: p + 15 = 51
a. p = 65
b. p = 46
C. p = 66
d. p = 36
Answer:
D. 36
Step-by-step explanation:
51-15= 36
The age of employees at a company is an example of _____.a. quantitative datab. label datac. time series datad. categorical data
Answer:
Quantitative data
Step-by-step explanation:
When we measure something, then we can quantify them. By also making a count, we are trying to quantify a particular entity.
Now in this case, we know that age is something we can quantify or measure. By nothing the difference between the year of birth and the present year, we can simply give the number of years or simply how
old a person is.
This clearly show that we have measured the count of that entity. This makes age an example of quantitative data
categorical data Step-by-step explanation:
Subtract 23.4 – 8.78 =_____
Answer:
14.62
Step-by-step explanation:
Answer:
14.62
Step-by-step explanation:
23.40
- 8.78
________
1 4 .6 2
For you to answer you need to place the commas correctly. The commas must be below each other to help you place the other numebrs correctly vertically. And after that you subtract and remember borrowing :)
HOPE IT HELPED
A line segment has the endpoints V(–3, –5) and W(16, –10). Find the coordinates of its midpoint M.
Answer:
(6.5, -7.5)
Step-by-step explanation:
Use the midpoint formula (x1 + x2) / 2 , (y1 + y2) / 2
Plug in the points:
(-3 + 16) / 2 , (-5 - 10) / 2
13/2 , -15/2
6.5, -7.5
So, the coordinates of midpoint M are (6.5, -7.5)
Use a stem-and-leaf plot to display the data, which represent the scores of a biology class on a midterm exam. Describe any patterns.
85
80
87
67
88
95
91
78
75
84
90
94
82
98
80
89
92
68
75
91
87
76
91
85
Determine the leaves in the stem-and-leaf plot below.
Key: 3|3 = 33
Exam Scores
6|
7|
8|
9|
*this is for statistics, any help is appreciated please*
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
85
80
87
67
88
95
91
78
75
84
90
94
82
98
80
89
92
68
75
91
87
76
91
85
STEM | LEAF
6 | 7 _ 8
7 | 5 _ 5 _ 6 _ 8
8 | 0_0_2_4_5_5_7_7_8_9
9 | 0_1_1_1_2_4_5_3
The statistics which could be obtained fro the data include; The range = (98 - 67) = 31
Number of observations = 24
Mode of data = 91 ( most occurring number)
Median = 50th percentile = 86
Mean = Σx / N
= Σx = 2028
Mean = 2028 / 24 = 84.5
-Removable discontinuity at 3, jump discontinuity at 5
Chris drove 693 miles in 11 hours.
At the same rate, how many miles would he drive in 13 hours?
Answer:
693/11. Cris is driving 63 mph.
Step-by-step explanation:
if you want to see how many miles he would go is 13 hours multipy 13 by 63 which is 819.
He would go 819 miles in 13 hours.
hope this helps.
Step-by-step explanation:
First find 1 hour=how many miles
-4 + 4x + 4 = -24 - 8x *
Answer: X= -2
Step-by-step explanation:
-4+4x+4=-24-8x
4x=-24-8x
12x=-24
X=-2
PLEASE HELP 100 POINTS PLEASE HELP 100 POINTS The ratio between the number of students (s) on a field trip and the number of teachers (t) on the field trip is 21/4. There are 84 students going on a field trip. How many teachers must go?
Answer:
16 teachers.
Step-by-step explanation:
84 / 21 = 4
4 * 4 = 16
Hope this helped. Please give brainly if its the best!
Answer:
[tex] \huge \colorbox{blue}{16 students}[/tex]
Step-by-step explanation:
we are given the ratio of students and teachers:
[tex] \displaystyle \: \frac{21}{4} [/tex]
which means if the number of students is 21 then the number of teachers should be 4
to find how many teachers should go if students 84 we have to divide 84 by [tex]21/4[/tex] :
[tex] \displaystyle \: 84 \div \frac{21}{4} [/tex]
simplify division:
[tex] = \displaystyle \: 84 \times \frac{4}{21} [/tex]
simplify multiplication:
[tex] = \displaystyle \: \cancel{ 84} \: ^{4} \times \frac{4}{ \cancel{21}} \\ = 4 \times 4 \\ = 16 [/tex]
Let L be the line with parametric equations x=2+t, y=1-t, z=1+3t.Let v=(1,2,0).Find vectors w1 and w2 such that v= w1 + w2, and such that w1 is parallel to L and w2 is perpendicular to L.
Answer:
w1 = (-1/11, 1/11, -3/11)
w2 = (12/11, 21/11, 3/11)
Step-by-step explanation:
Direction ratio of w1 = Direction ratio of L (because parallel) = K+(1, -1, 3)
Let <a,b,c> be direction ratio of w2.
Then, <a,b,c>. <1,-1,3> = 0
a-b+3c = 0
v = w1 + w2
(1, 2, 0) = k(1, -1, 3) + (a, b, c)
a + k = 1
b - K = 2
c - 3k = 0
Solving 4 equations, a = 12/11, b= 21/11, c = 3/11, k=-1/11
So, w1 = -1/11(1, -1 ,3) = (-1/11, 1/11, -3/11)
w2 = (12/11, 21/11, 3/11)
steps of 17/3 - 3/4x = 1/2x + 5
Answer:
Step-by-step explanation:
12(17/3 - 3/4x = 1/2x + 5)
68 - 9x = 6x + 60
-15x = -8
x = 8/15
portia has 72 postcards this is. 8 time as many as jonathan has how many postcards does jonathan have
A box contains colored poker chips. There are 100 red, 100 white, and 100 blue chips. Without looking, what is the minimum number of poker chips that must be drawn to be assured of getting 30 chips of one color?
Answer:
draw all 100 of two colors to be assured
Step-by-step explanation:
if wrong plz tell me i can help on other things if wrong
10.) A meat shop sold 4 1/6 pounds of sausage and 4 times as much burger as sausages. How
many pounds of burgers were sold?
For every $2 Pam saves, her brother saves $7. If Pam has $20 in her account how much does her brother have?
Answer:
70
Step-by-step explanation:
I need help I don’t understand it at all
Answer:
Correct Answer Is 3160 Maybe
Step-by-step explanation:
Answer:
3160
Step-by-step explanation:
3.16*10^3
=31.6*10^2
=316*10
=3160
f(x)=-4xto the power of 2 what is the range
Answer:
(-infinity, 0]
Step-by-step explanation:
I'm assuming you meant f(x) = -4x^2. If so, the graph is that of a parabola that opens down and has vertex at (0, 0). In other words, f(x) is always zero or below zero.
Thus the range is (-infinity, 0]
(6h + 8) - (3h + 2) = 15
PLEASE HELP I ALSO NEED TO SHOW WORK
Answer:
[tex]h=3[/tex]
Step-by-step explanation:
So we have the equation:
[tex](6h+8)-(3h+2)=15[/tex]
First, let's distribute the negative:
[tex](6h+8)+(-3h-2)=15[/tex]
Combine like terms:
[tex](6h-3h)+(8-2)=15[/tex]
Subtract or add:
[tex]3h+6=15[/tex]
Subtract 6 from both sides:
[tex]3h=9[/tex]
Divide both sides by 3:
[tex]h=3[/tex]
And we're done!
Answer:
h=3
Step-by-step explanation:
1 Remove parentheses.
6h+8-3h-2=156h+8−3h−2=15
2 Simplify 6h+8-3h-26h+8−3h−2 to 3h+63h+6.
3h+6=153h+6=15
3 Subtract 66 from both sides.
3h=15-63h=15−6
4 Simplify 15-615−6 to 99.
3h=93h=9
5 Divide both sides by 33.
h=\frac{9}{3}h=
3
9
What is 8.3-2.57 I really need this answer fast thanks
Answer: 5.73
Step-by-step explanation:
What is the vertex of f(x) = |x + 8| – 3?
Answer:
(-8,-3)
Step-by-step explanation:
This question is similar to the vertex form of a quadratic equation, so you can think of this equation like f(x) = (x-h)+k. Using this equation, you can determine the vertex (h,k) of |x+8|-3, which is (-8,-3).
Step-by-step explanation:
Its B
edge 2021 :))
The Fairy Tale Spectacular is coming to town. Admission to the fair costs $32.50 and each ride costs $0.80. You have $50 to spend at the Fairy Tale Spectacular including admission. What is the maximum number of rides you can enjoy?
Answer:
21 rides
Step-by-step explanation:
let x = number of rides you can ride
32.50 + 0.80x [tex]\leq[/tex] 50
subtract 32.50 from both sides
0.8x [tex]\leq[/tex] 17.5
divide the left and right by 0.8
x [tex]\leq[/tex] 21.875
this means you can ride 21 times, because you can't ride a ride unless you can afford the whole cost
how to check; 32.50 + 0.8(21) is 49.30 and 80 cents more would go over your 50 dollar spending limit
In a run-off election between two candidates, a total of 25,200 votes were cast. If 300 voters had switched
from the winner to the loser, the loser would have won by 200 votes. How many votes did each candidate
actually receive?
Step-by-step explanation:
yikes that's hard GG bro
Answer:
The winner received 12,800 votes and the loser received 12,400.
Step-by-step explanation:
Divided the votes in half, then took 100 votes from the winner, defined W, and added 100 to the loser, defined L to give the Loser a lead of 200. Then switch 300 votes from the losers number to the winner. You'll end up with 12,800 and 12,400 and you can check by switching 300 voters from winner (12,800) to loser (12,400) to make the loser win by 200 votes. 12,800 and 12,400 also add up to 25,200.
