Answer:
[tex]A(t)=250-230e^{-\frac{t}{50} }[/tex]
Step-by-step explanation:
A(t) is the amount of salt in the tank at time t.
dA / dt = rate of salt flowing into the tank - rate of salt going out of the tank
dA / dt = (1 g/L)*(5 L/min) - (A(t)/250 g/L) * (5L/min)
dA / dt = 5 g/min - (A(t) / 50) g/min
[tex]\frac{dA}{dt}+\frac{A(t)}{50} = 5\\\\The\ integrating\ factor(IF)= e^{\int\limits \frac{1}{50}dt }=e^{\frac{t}{50} }\\\\Multiplying\ through\ by\ the\ I.F:\\\\\frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} } = 5*e^{\frac{t}{50} }\\\\Integrating \ both \ sides:\\\\\int\limits[ \frac{dA}{dt}*e^{\frac{t}{50} }+\frac{A(t)}{50}*e^{\frac{t}{50} }] dt=\int\limits 5e^{\frac{t}{50} } dt\\\\A(t)e^{\frac{t}{50} } =\int\limits 5e^{\frac{t}{50} } dt\\\\[/tex]
[tex]A(t)e^{\frac{t}{50} } =250e^{\frac{t}{50} }+C\\\\A(t)=250+Ce^{-\frac{t}{50} }\\\\But\ A(0) = 20\\\\20=250+Ce^{-\frac{0}{50} }\\\\C+250=20\\\\C=-230\\\\A(t)=250-230e^{-\frac{t}{50} }[/tex]
The soccer players are in motion as they run up and down the field in the tournament at the end of the video to score a goal. One of the soccer players applied 50N of force to the right on the 2.5kg ball which encounters 3.5N of friction as it rolled across the field into the goal. Which of the following is the net force and direction of motion of the soccer ball as it rolls along the field?
................................................
Solve 3(x + 1) = −2(x − 1) − 4
-1
1
-3
5
Answer:
x = -1
Step-by-step explanation:
3(x + 1) = -2(x - 1 ) - 4
use the distributive property to get rid of the parentheses. on -2 and -1 they cancel each other out so it becomes + 2. now you have:
3x + 3 = -2x + 2 - 4 (+2 and -4 are like terms so they become -2. so technically its 3x + 3 = -2x -2)
get +3 on the other side by subtracting it from itself and then subtracting it from -2 so it becomes -5.
3x = -2x - 5
get -2x on the other side by adding 2x to itself then adding 2x to 3x so it becomes 5x
5x = -5
divide 5 from -5 and you get x = -1
6(x+2)=5(x+7) please help me is urgent
Answer:
x=23
Step-by-step explanation:
6(x+2)=5(x+7)
6x+12=5x+35
6x-5x=35-12
x=23
-1 - 4x
1
1
4x
?
- 4x
42
-1
Answer:
I don't understand
Step-by-step explanation:
a recipe calls for 1/3 cup of milk for each 1/4 cups of water how many cups of water are needed for each cup of milk.
Answer:
3/4??
Step-by-step explanation:
Please help me I’ll give you a thanks :-)
Answer:
I love algebra anyways
The ans is in the picture with the steps how i got it
(hope this helps can i plz have brainlist :D hehe)
Step-by-step explanation:
What are two combinations that equal EXACTLY $30?
Answer:
6 Cheese burgers 11 fries
4 Cheese Burgers 9 fries
Step-by-step explanation:
Answer:
2 cheese burgers($6),12 fries ($24)
6 cheeseburgers($18), 6 fries($12)
what is the percent of change from 100 to 41, please help!! :(
Answer:
59% decrease
Step-by-step explanation:
PLEASE PLEASE HELP PLEASEEEEEEEEEEEEEEE
Answer:
Six less than five times a number is less than fourteen
Step-by-step explanation:
I had the same question on my homework haha
E/2=3 please help ASAP
Answer:
E= 6
Step-by-step explanation:
6/2 = 3
hope this helped!
Answer:
As per as the given equation
E/2=3
E=3*2
E=6
In the triangle below, the measure of angle A = 52°. Find the measure of angle C.
Answer:
128°
Step-by-step explanation:
180-52=128
Answer this question as soon as possible please. Thanks!
Step-by-step explanation:
36/6 or it is just 6 depends on if you need it as a fraction or not
(tan^(2)x)/(secx)=secx-cosx how do i verify the identity
Answer:
sec x − cos x = sin x tan x? First convert all terms into sinx and cosx. Second apply fraction sum rules to the LHS. and replace secx with 1 cosx. The LHS, secx − cosx becomes 1 cosx − cosx. The RHS, sinxtanx becomes sinx sinx cosx or sin2x cosx.
Step-by-step explanation:
pls help me on this........
Answer:
9x+9
it the 3rd one
If f(x) = 6x – 4, what is f(x) when x = 8?
0.16
[tex]f(8)=6\cdot8-4=48-4=44[/tex]
Answer:
substitute x therefore 6*8=48
48-4=44
Pls help me I don't understand
Answer: 0
Step-by-step explanation:
the answer is 0
=================================================
Explanation:
Think of z as having 1 zebra
2z means we have 2 zebras
If we started with 2z, and subtracted off 2z, then we're left with 0 zebras. We write this as 0z or just 0 since 0 times anything is 0.
---------
As another example:
Let's say we wanted to simplify 5z - 2z
Well that's the same as saying "5 zebras take away 2 zebras". We'd be left with 3 zebras because 5-2 = 3
Since 5-2 = 3, this leads to 5z-2z = 3z. The difference is that I tacked 'z's onto each number.
Martha earns $15 per hour for babysitting. The parents always giver her a $5 tip.
What is the slope of this situation?
Enter the correct answer in the box.
? Dollars per hour
Answer:
$3.25 multiplied by the hour
Step-by-step explanation:
The slope of the situation if, Martha earns $15 per hour for babysitting, The parents always give her a $5 tip is $15 per hour.
What is the slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively.
Given:
Martha earns $15 per hour for babysitting,
The parents always give her a $5 tip,
The equation for the total money earned by Martha can be written as shown below,
The total money earned = Money per hour for babysitting × number of hours + tip
Assume the total money earned is y, the number of hours is x,
y = 15x + 5
As you can see, the above equation is in slope intercept form,
Slope = $15 per hour
To know more about the slope:
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A survey was conducted from 1000 people about what fruit they like the most. By looking at the graph how many people enjoyed grapes and bananas
Answer:
200 to 70
Step-by-step explanation:
well if it were 100 it would be 20 people to 7 so scale it up by 10 and you get 200 to 70 people
ni p*t* idea pibe :)
Find the sum of 4.5 x 10^-1and the quotient of 7x10^-4 and 8x10^-3
Answer:
4.5=9+8=10 cause we subbed
8+9=17
Step-by-step explanation:
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 250 pounds is Group of answer choices 0.9505 0.9772 0.0228 0.4505 0.0495
Answer:
0.0228
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
This means that [tex]\mu = 200, \sigma = 25[/tex]
The probability of a player weighing more than 250 pounds is
This is 1 subtracted by the pvalue of Z when X = 250. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{250 - 200}{25}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
The probability of a player weighing more than 250 pounds is 0.0228
Find the value of x. The angles are in the picture! Please quick I will give Brainliest!
Answer:
x = 50
Step-by-step explanation:
The interior angles of a Pentagon adds up to 540.
90 + 125 + 125 + 2x + 2x = 540
340 + 4x = 540
4x = 200
x = 50
Consider a class with 30 students. Compute the probability that at least two of them have their birthdays on the same day. (For simplicity, ignore the leap year.) (b) How many students should be in class in order to have this probability above 0.5
Answer:
0.7063
Step-by-step explanation:
Given that:
Number of students = 30
Number of days in a year = 365
P(atleast 2 people share same birthday) = 1 - p(none share same Birthday)
p(none share same Birthday) =
(365! / (365 - 30)!) * 1/365^30
(365! / 335!) * 1/365^30
365! ÷ (335! * 365^30)
= 0.2936837
P(atleast 2 people share same birthday) :
1 - 0.2936837
= 0.7063163
= 0.7063 * 100%
= 70.63%
Solve for x.
Please help!
Which of the following is a rational number?
square root of 79, square root of 80, square root of 81, square root of 82
Which point is on the graph of the function y=8x+4y
Group of answer choices
(-6,4)
(-2, -3)
(0, 4)
(6, 4)
At a hockey game, a vendor sold a combined total of 148 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
If the number of sodas sold was three times the number of hot dogs sold then the number of sodas sold is 78 and the number of hot dogs sold is 26.
What is equation?Equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It is of many types like linear equation, quadratic equation, cubic equation, etc.
here, we have,
The total number of hot dogs and sodas sold is 104 and the number of sodas sold was 3 times the number of hot dogs sold.
We have to form an equation first.
let the number of hot dogs sold be x.
Number of sodas will be 3x.
According to question :
x+3x=104
4x=104
x=26
Put the value of x in 3x to get the number of sodas sold.
=3x
=3*26
=78
Hence If the number of sodas sold was three times the number of hot dogs sold then the number of sodas sold is 78 and the number of hot dogs sold is 26.
Learn more about equation at
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HELP ME WITH THIS IM DESPERATE!
Answer:
The anwser is 213.465 m2
Step-by-step explanation:
Yes uh get it i guess
Answer:
I got 114
Step-by-step explanation:
Formula for a triangle is bh1/2
(12)(19)(1/2)
228(1/2)
= 114
Hope that helps ig
Manuel is preparing to run in a race. He has developed a training program in which he increases his running distance each day. If he continues to follow the same pattern, what distance will he run on the fifth day.
Day 1 -- 1 mile
Day 2 -- 2 miles
Day 3 -- 4 miles
Day 4 -- 7 miles
A.) 8 miles
B.) 9 miles
C.) 11 miles
D.) 14 miles
Answer:
c
Step-by-step explanation:
c)11 miles
the day and the miles on that day add together to make the miles for the next day so 4+7=11
If R is the midpoint of PS with PR=6x+16 and RS=-26 then find PS
Answer:
PS = 116
Step-by-step explanation:
Given:
PR = 6x + 16
RS = 12x - 26
Required:
Find PS
Solution:
Since R is the midpoint of PS, therefore,
PR = RS
6x + 16 = 12x - 26
Collect like terms
6x - 12x = -16 - 26
-6x = -42
Divide both sides by -6
x = -42/-6
x = 7
✔️PS = PR + RS (segment addition postulate)
PS = 6x + 16 + 12x - 26
Plug in the value of x
PS = 6(7) + 16 + 12(7) - 26
PS = 42 + 16 + 84 - 26
PS = 116
If 3/4 pounds of Fudge coast $6. 75, how much does 1 pound cost. Write as an equation.