Answer:
1 for both slope and rate of change
Step-by-step explanation:
Slope is another word for the rate of change of y with respect to x.
Suppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows into the second lake, and then water from the second lake flows further downstream. The in and out flow from each lake is 500 liters per hour. The first lake contains 100 thousand liters of water and the second lake contains 200 thousand liters of water. A truck with 500 kg of toxic substances crashes into the first lake. Assume that the water is being continually mixed perfectly by the stream.
a. Find the concentration of toxic substances as a function of time in both lakes.
b. When will the concentration in the first lake be below 0.001 kg per liter?
c. When will the concentration in the second lake be maximal?
Answer:
a. For the first lake;
c = (m·t - 0.005·m·t²)/100000
For the second tank, we have;
c = m·t/200 - m·t²/80000
b. t ≈ 1.00505 hours
c. 200 hours
Step-by-step explanation:
The flow rate of water in and out of the lakes = 500 liters/hour
The volume of water in the first lake = 100 thousand liters
The volume of water in the second lake = 200 thousand liters
The mass of toxic substances that entered into the first lake = 500 kg
The concentration of toxic substance in the first lake = m₁/(100000)
Therefore, we have;
The quantity of fresh water supplied at t hours = 500 × t
The change
The change in the mass of the toxic substance with time is given as follows
dm/dt = (m - m/100000 × 500 × t)/100000
c = (m·t - 0.005·m·t²)/100000
For the second tank, we have;
c = m/100000 × 500 × t - (m/100000 × 500 × t)/200000 × 500 × t
Using an online tool, we have;
c = m·t/200 - m·t²/80000
b. When c < 0.001 kg per liter, we have m < 0.001 × 100000, which gives m < 100
Substituting gives;
0.001 = (100·t - 0.005·100·t²)/100000, solving with an online tool, gives;
t ≈ 1.00505 hours
c. For maximum concentration, we have;
c = m·t/200 - m·t²/80000
m/200000 = m·t/200 - m·t²/80000
1/200000 = t/200 - t²/80000
dc/dt = d(t/200 - t²/80000)/dt = 0
Solving with an online tool gives t = 200 hours
who's good at math? i need help ASAP. *don't mind the red numbers, i think they're wrong*
Answer:
Seems like someone answered them, because the red writing is right, but here's the answers with explanation
Step-by-step explanation:
The vertex is the point at which the graph changes direction as we go from left to right. Maximum means the graph is changing direction and going down, so the f(x)-values start becoming smaller. So the graph reached its maximum/highest point and dropped.Minimum means the graph is changing direction and going up, so the f(x)-values start becoming bigger. So the graph reached its minimum/lowest point and started risingNow the answers:Vertex is (-1,0) because if you look at the numbers for f(x) they go, 4 then 1, then 0, but instead of getting smaller they start getting bigger, so it changes as this point and goes up so minimumvertex is (3,44), when you look at f(x) it goes 143, then 88, then 55, then 44, then it changes and starts getting bigger so minimumvertex is (-4,-5) but this one is different from the first two. f(x) starts with -17 then -9, then -5, then it sort of stops and stays there, then -5 then drops and gets smaller. So it changes at x=-4 so use this point, immediately before the change and it is maximumVertex is (21,500) because f(x) was getting bigger but then it changes and goes down and becomes smaller, so it is maximumvertex is (1.5,6) the point immediately before the change, and we see f(x) was getting smaller going down, but it changes and goes up and gets bigger so it is minimumvertex is (0.5,5) because it was getting big then changed and started getting smaller so maximumQuestion 16
7 pts
16. The ratio of the number of girls to the number of
boys in art in 7 to 4. There are 60 boys in art. How
many girls are in art? (6.4B)
Answer:
105 girls
Step-by-step explanation:
girls : boys
7 : 4
Let total number of people in art be (7 + 4)x.
4x = 60
x = 15
no. of girls = 7x = 7 x 15 = 105
This is a question on ratios and proportions. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Jackson had $53 in his account. He bought a video game. He now has -$12 in his
account. How much was the video game?
Answer:
$65
Step-by-step explanation:
Add 53 and 12 together to see how much it costed.
A plastic ball with a volume of 19.7
cm3 has a mass of 15.8 g. Would this
ball sink or float in a container of
gasoline (density of gasoline is 0.66-
0.69 g/cm3).
Answer:
as the density of the plastic ball is greater than the density of the gasoline it sinks
Step-by-step explanation:
D = 15.8 / 19.7
D = 0.80 g / c ^ 3
0.8> (0.66-0.69)
The density of the plastic ball is greater than the density of gasoline, the ball would sink in a container of gasoline.
Given that a plastic ball with a volume of 19.7 cm³ has a mass of 15.8 g.
We need to check if the ball sink or float in a container of gasoline if the density of gasoline is 0.69 g/cm³.
To determine whether the plastic ball would sink or float in a container of gasoline, we need to compare the density of the ball with the density of gasoline.
Density is defined as the mass of an object divided by its volume. In this case, the density of the plastic ball can be calculated as:
Density of ball = Mass of ball / Volume of ball
Given that the mass of the ball is 15.8 g and the volume is 19.7 cm³, we can calculate the density of the ball:
Density of ball = 15.8 g / 19.7 cm³
Density of ball ≈ 0.8 g/cm³
Now, we can compare the density of the ball with the density of gasoline, which is stated to be between 0.66 g/cm³ and 0.69 g/cm³.
Since the density of the ball (0.8 g/cm³) is greater than the density range of gasoline (0.66-0.69 g/cm³), the ball would sink in a container of gasoline.
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Delta owns a D.C. 10 airplane that has seats for 318 people. The company flies this airplane only if there are at least 96 people on the plane. Write a compound inequality to show the possible number of people on a Delta flight. Let n represent the amount of people.
Answer: n greater than or equal to 96 or n is greater than or less than 318
Step-by-step explanation:
Brainliest plz
A recipe calls for 3 cups of flour to 4 cups of sugar. Find the unit rate of flour to cups of sugar.
Answer: 0.75 cups of flour to 1 cup of sugar.
Step-by-step explanation:
From the question, we are informed that a recipe calls for 3 cups of flour to 4 cups of sugar and told to calculate the unit rate.
It simply means what we need to calculate much of flour to one cup of sugar. This will be:
= 3/4 = 0.75
Therefore, the unit rate will be:
0.75 cups of flour to 1 cup of sugar.
Which statement is true about the equations –3x + 4y = 12 and 1 x - y = 1?
O The system of the equations has exactly one solution at (-8, 3).
O The system of the equations has exactly one solution at (-4, 3).
The system of the equations has no solution; the two lines are parallel.
O The system of the equations has an infinite number of solutions represented by either equation.
Answer:
None of these answers is trueStep-by-step explanation:
1x - y = 1 ⇒ x - 1 = y
-3x + 4y = 12
-3x + 4(x - 1) = 12
-3x + 4x - 4 = 12
x - 4 = 12
x = 16 ⇒ 16 - 1 = y ⇒ y = 15
Therefore the system of the equations has exactly one solution at (16,15)
Answer:
D- There are infinite solutions
Step-by-step explanation:
-3x + 4y= 12 is the same as 1/4x -1/3y = 1.
1/4x multiplied by 12 is 3x
-1/3y multiplied by 12 is -4y
To flip the negatives you multiply by -1 to get -3x + 4y+ 12 on both equations
4 friends are sharing a new pack of pencils. if there are 12 pencils in each pack how many will each friend get?
(I am lazy to answer this by myself so please help me)
Answer:
3
Step-by-step explanation:
3 times 4 equals 12
hope I got it right
Step-by-step explanation:
they would each get 4 pencils
PLS HELP I WILL GIVE YOU A GOOD BRAINLY SCORE!!!!!!!!
Answer:
I cannot see what the titles in the chart say, so cannot help.
Step-by-step explanation:
Let’s say the chart says this:
Total | Bob | George
5 dics 2 dics. 3 Discs
Unless they give you a total number, and an expression, you cannot solve for x.
What is the value of this expression below when z=8 and w=3
9z-8w
Answer:
Step-by-step explanation:
Putting values in the equation
9z - 8w
9(8) - 8(3)
72 - 24
= 48
Answer:
9z-8w=48
Step-by-step explanation:
9x8-8x3
72-24=48
From Mickey Grace to Everyone:
Grace is 4 years older than Elena. If Grace is 9
years old, how old is Elena? Grace is
Answer:5
Step-by-step explanation:
PLEASE HELP ME
Analia is a school district manager. Here are some details about two schools in her district for the last school year:
School A School B
Number of students 300030003000 400040004000
Number of teachers 190190190 380380380
Graduation rate 86\%86%86, percent 90\%90%90, percent
Budget per student \$10{,}500$10,500dollar sign, 10, comma, 500 \$10{,}000$10,000dollar sign, 10, comma, 000
% of students in sports club 62\%62%62, percent 68\%68%68, percent
Number of sports medals won 999 777
SAT average 120012001200 105010501050
SAT range (max-min) 900900900 700700700
Analia wants to know which school has higher academic achievements relative to the budget per student.
1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Choose 2 answers:
(Choice A)
A
SAT average divided by budget per student
(Choice B)
B
Graduation rate divided by budget per student
(Choice C)
C
Number of sports medals won divided by budget per student
(Choice D)
D
Graduation rate divided by number of sports medals won
2) Determine which school has higher academic achievements relative to the budget per student, according to the two definitions. Did you get the same result for both definitions?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Yes. According to both definitions, School A has higher academic achievements relative to the budget per student.
(Choice B)
B
Yes. According to both definitions, School B has higher academic achievements relative to the budget per student.
(Choice C)
C
No. The definitions have opposite results.
The two different quantities to measure which school has higher academic performance are:
Graduation rate / Budget per studentSAT average / Budget per studentHow to illustrate the information?The parameters which could be used to measure academic achievement are the graduation rate of each school he SAT average of each school.
Therefore, defining the quantity to measure academic achievement relative to budget per student could be expressed as the graduation rate divided by the budget per student. It can also be the SAT average divided by the Budget per student.
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Answer:
SAT average/budget per student and graduation rate/budget per student----No, the definitions have opposite results
Step-by-step explanation:
khan
ANSWER THIS CORRECTLY AND I WILL 5 STAR U AND GIVE U POINTS AND THANK YOU
IF NOT ME AND MY CLASS WILL REPORT YOU FOR WRONG ASNWERS AND GIVE U ONE STAR
HELP ME OUT PLS :))
HAPPY THANKSGIVING ALL!
Answer:
C
Step-by-step explanation:
given:
m= -2 and (3, -1)
point-slope form: y-y1= m(x-x1)
y - (-1) = -2(x-3)
y + 1 = -2(x-3)
Answer:
C.
Step-by-step explanation:
A.) y - 1 = -2(x - 3)
y - 1 = -2x + 6
y = -2x + 6 + 1
y = -2x + 7
B.) y - 1 = -2(x + 3)
y - 1 = -2x - 6
y = -2x - 6 + 1
y = -2x - 5
C.) y + 1 = -2(x - 3)
y + 1 = -2x + 6
y = -2x + 6 - 1
y = -2x + 5
D.) y + 1 = -2(x + 3)
y + 1 = -2x - 6
y = -2x - 6 - 1
y = -2x - 7
Determine the correlation:
How much you study vs. The grade you get on your test
A- positive correlation
B- negative correlation
C- no correlation
Landon is building new bookshelves for his bookstore's new mystery section. Each shelf can hold 34 books. There are 1,265 mystery books. How many shelves will he need to build?
Answer:
37.2 = 38
Step-by-step explanation:
After divideing 1265 by 34, you will get 37.2. As you cannot have books not in bookshelves, you will have to round up and have 38 bookshelves.
A rug has a length to width ratio of 5:3 and the area of the rug is 135 sq. ft. What are the dimensions of the rug?
Answer:
Length = 15 and Width = 9
Step-by-step explanation:
5:3 = 135
make 5, 5x and 3, 3x so that would be 5x*3x = 135
when you times two x's that makes x²
making 15x² = 135
Divide 15 on both sides making 135 now 9
so x² = 9
with a squared x you used a square root
√9 = 3
so x is equal to 3
then put those into 5x, 5(3) and 3x, 3(3)
thus making 15 sq. ft and 9 sq. ft
Please help 30 points
Answer (see photo below):
I hope this helps!
Answer:
Step-by-step explanation:
First, we find the formula. Since we have a slope and only one point we can use the Slope Form, which is "y - y1 = m(x - x1)". Now to find The Slope Intercept Form.
Formula = y - y1 = m(x - x1)
Slope = 3/4 or 0.75
Point = (2,-3)
y - y1 = m(x - x1)
y - (-3) = 3/4(x - 2)
y + 3 = 3/4x - 1.5
y = 3/4x - 1.5 - 3
y = 3/4x - 4.5
Graph is shown below.
------------------------
|
V
5% of 60 is what number?
a . 6
b . 5
c . 3
d . 60
Answer: The answer is 3
Step-by-step explanation:
Does anyone know the answer to this?
Answer:
<ABD is 73 ...work below
Step-by-step explanation:
5x + 18 + 4x +5 = 122
9x + 23 = 122
9x = 99
x = 11
no since we got x...
5(11) + 18
73
I Tried 140 And 80. Those answer were incorrect. Right Answer gets 5 stars and a branliest. THANK YOU SO MUCH!!
Answer:
a 60
Step-by-step explanation:
Answer:
The Answer Is 60 I Had This Test Already.
Step-by-step explanation:
Find the inverse of the function y = x2 – 12.
Answer:
y = √ x+12(square root of x+12)
Step-by-step explanation:
x = y^2 - 12
x+12 = y^2
y^2 = x+12
y = √ x+12
Answer:
Question 1. Find the inverse of the function y = x2 – 12.
B. y=+/- sqrt x+12 end sqrt
Question2. Find the inverse of the function y=2x2+2
D. y= +/- sqrt 1/2x-1 end sqrt
1. The sum of a number and ten.
Answer:
x+10
Step-by-step explanation:
sum = addition (+)
number = variable because we don't know what the number is yet (x)
ten=ten
So by this we can get x+10
Which equation can be used to find 75 percent of 200?
Answer:
The first equation
Step-by-step explanation:
Answer:
150
Step-by-step explanation:
75 percent *200 =
(75:100)*200 =
(75*200):100 =
15000:100 = 150
Now we have: 75 percent of 200 = 150
Question: What is 75 percent of 200?
Percentage solution with steps:
Step 1: Our output value is 200.
Step 2: We represent the unknown value with x.
Step 3: From step 1 above,200=100%
Step 4: Similarly, x=75%.
Step 5: This results in a pair of simple equations:
$200=100%(1).
x=75%(2).
Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
200/x = 100% / 75%
Step 7: Again, the reciprocal of both sides gives
x/200 = 75/100
Therefore, 75% of 200 is 150
after 3 hours ernie had traveled at 195 miles if he travels at a constant speed how far will he have traveled after 5 hours
Answer:
325
Step-by-step explanation:
195/3=65
5*65=325
can someone help me ASAP please
Answer:
46 degrees
Step-by-step explanation:
Answer:
[tex]x = 46[/tex]
Step-by-step explanation:
First I identified that 2 of side lengths are the same, being 5. Then 88° is inbetween them, so I now know that both missing angles will be equal. This works with all triangles, if 2 sides equal the same then 2 angles will be equal.
So now we know a triangles angles always add up to be 180, so now we just subtract and divide.
[tex]180 - 88 = 92[/tex]
So now we know the sum of both missing angles so we can just divide the value in half because both angles are the same.
[tex]92 \div 2 = 46[/tex]
Now we know x=46°
Help please I’m so bad at these
Answer:
23/24
Step-by-step explanation:
I used my calculator, but find the greatest common factor which is 24 and convert and multiply to get 23/24.
Pure copper was mixed with a 10% copper alloy to produce an alloy thát was 25% copper. How much of the pure copper and how much 10% alloy were used to produce 36 kg of 25% alloy?
Answer:
6kg pure copper and 30 kg 10% copper was mixed to give 36kg of 25% alloy
Step-by-step explanation:
Here, we want to produce 36 kg of 25% alloy
Let the Pure copper be x kg while 10% alloy be y kg
Pure copper is simply 100% copper
Thus;
x + y = 36 •••••(i)
Then;
100% of x + 10% of y = 25% of 36
= x + 0.1y = 9 •••••• ii)
From i x = 36-y
from ii, x = 9-0.1y
Equate both x
36-y = 9-0.1y
36-9 = 0.1y + y
0.9y = 27
y = 27/0.9
y = 30
x = 36-y
x = 36-30
x = 6 kg
The ratio on a key board of number keys to letter keys is 3:15. If a manufacturer produced 156 letter keys,then how many keys would need to be produced?
Answer: Approximately 31 number keys.
Step-by-step explanation: Ratio is a comparison between two values.
Ratio for number keys to letter keys is [tex]\frac{3}{15}[/tex], which means each 3 group of number keys is equivalent to 15 letter keys.
The producer will need
[tex]\frac{3}{15} =\frac{x}{156}[/tex]
[tex]x=\frac{3.156}{15}[/tex]
x = 31
The manufacturer will need to be produced 31 keys.
please help (picture provided shows question)
Answer:
They need to sell 3 tees, and incurred $60.
Step-by-step explanation:
What is the revenue equation? R = 20x, where x is the # of tees sold.
What is the cost equation? C = 5x + 45, where x is the # of tees sold.
Set those two equations equal, we get:
20x = 5x + 45, 15x = 45, x = 3.
3*5 + 45 = 60.