Answer:
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
Step-by-step explanation:
Given that:
a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved.
The rate at which pure water is pumped into the tank is 4 gal/min
After stirring; the pure water is then pumped out at the same rate.
The objective is to determine the differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)
Taking the differential of:
[tex]\dfrac{dA}{dt}=R_{in}-R_{out}[/tex] ---- (1)
where ;
[tex]R_{in[/tex] = 0
[tex]R_{out} =\dfrac{A(t)}{400}*4[/tex]
[tex]R_{out} =\dfrac{A}{100}[/tex]
replacing them into (1) ; we have:
[tex]\dfrac{dA}{dt}=0 - \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}=- \dfrac{A}{100}[/tex]
[tex]\dfrac{dA}{dt}+ \dfrac{A}{100}=0[/tex]
A(0) = 70 (i.e the pounds of salt dissolved into the tank)
The differential equation for the amount of salt A(t) in the tank at time t > 0 is [tex]\frac{dA}{dt} + \frac{A}{100} = 0[/tex]
A (0)= 70
Given that,
Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/minThe Calculation is as follows:[tex]dA\div dt=R_{in}-R_{out}[/tex]
Rin=0
[tex]R_{out}=A(t)\div 400 \times (4)\\\\ =A\div 100[/tex]
so,
[tex]dA\div dt=R_{in}-R_{out}\\\\dA\div dt=0- A\div 100[/tex]
So,
[tex]dA\div dt +A\div 100=0[/tex]
A(0)=70
Find out more information about the Water here:brainly.com/question/4381433?referrer=searchResults
What is the value of x in the equation 3x - y = 18, when y= 27?
O 5
O 7
O45
O 63
Answer:
Step-by-step explanation:3x-y=18
y=27
Therefore 3x-(27)=18
3x=18+27..Nb when the 27 is now being added instead of subtracted.
3x=45
3x/3=45/3 Nb the 3 is now being divided instead of being multiplied.
Therefore X=15
What is the value of x?
Answer:
The answer is B.
Step-by-step explanation:
Given that the total angle in a triangle is 180°. So in order to find x, you have to subatract 95° and 57° from 180°
[tex]x + 95 + 57 = 180[/tex]
[tex]x = 180 - 95 - 57[/tex]
[tex]x = 28[/tex]
Use the DISTRIBUTIVE PROPERTY to simplify the expression. 4(3r - 8)
Answer:
12r-32
Step-by-step explanation:
Distribute the 4 between the different numbers.
3r * 4 = 12r and 8 * 4 = 32
So...you end up with 12r-32
Hi! I hope you're enjoying your day!
Let's recall that the Distributive Property states that
a(b+c)=ab+ac
Where
a, b, and c can be either constants (numbers like 4) or variables (letters like d)
Simplify:
4(3r-8)
4 times 3r is equal to 12r
12r- (4*8)
[tex]\boxed{\boxed{\bold{12r-32}}}[/tex]
Hope everything is clear.
If you have any questions, please comment.
#LearningIsFun
What is the value of (3-5)4(2) – 16+ 2?
-40
-16
24
56
Answer:
-30
Step-by-step explanation:
(3-5)4(2) – 16+ 2= -2*8-14= -16-14= -30
Tienes un triángulo equilátero con lados de 10cm, lo divides en dos partes de manera horizontal tal que el área de ambos figuras resultantes es igual, ¿cuánto vale la distancia del lado x?
Answer:
x = 10/√2 ≈ 7.07
Step-by-step explanation:
Comenzaremos por dividir el triángulo en dos partes y definir H, como en la figura adjunta.
Aplicando el teorema de Tales, sabemos que:
[tex]\dfrac{l/2}{H}=\dfrac{x/2}{h}\\\\\\\dfrac{l}{H}=\dfrac{x}{h}[/tex]
También sabemos que, dado que el tirángulo menor es la mitad que el triángulo mayor, la relación entre áreas es:
[tex]\dfrac{A}{A_x}=\dfrac{lH/2}{xh/2}=\dfrac{lH}{xh}=2[/tex]
Dado que formamos dos triángulos rectángulos, podemos despejar el valor de H como:
[tex](l/2)^2+H^2=l^2\\\\H^2=l^2-(l/2)^2=10^2-5^2=100-25=75\\\\H^2=\sqrt{75}[/tex]
Podemos entonces despejar x de la siguiente manera:
[tex]h=\dfrac{H}{l}\cdot x=\dfrac{lH}{2x}\\\\\\2x^2\dfrac{H}{l}=lH\\\\\\2x^2=l^2\\\\\\x=\dfrac{l}{\sqrt{2}}=\dfrac{10}{\sqrt{2}}\approx7.07[/tex]
Help asapa!! 30 poinst!!!
Answer:
The answer is option B
Step-by-step explanation:
I cant exactly explain it cus i dont remember but i know i got it right lol
but here goes
after she proves that AD is congruent to the other sides, all she has left to prove is ∠A≅∠B and AB≅BC.
'Tis how you get thine answer
(╯°□°）╯
Answer:
Option 1
Step-by-step explanation:
ABCD is a parallelogram, Julie wants to prove that ABCD is also a square.
Remember that a parallelogram has opposite sides equal.
So,
AB ≅ CD
AD ≅ BC
The 4 triangles are congruent. The bases of the triangles are vertically opposite to each other and are congruent. We can use the definition of a parallelogram to prove AB ≅ BC.
simplify the following algebraic expression. 3/4(1/2x-12)+4/5
Answer:
Step-by-step explanation:
(3/8)x - 9 + 4/5
40(3/8x - 9 + 4/5)
15x - 360 + 32
15x - 328
Answer:
3/8 x - 7 1/5
Step-by-step explanation:
3/4 (1/2 x - 12) + 4/5
3/8 x - 8 + 4/5
15/40 x - 8 x 32/40
15/40 x - 7 8/40
15/40 x - 7 1/5
3/8 x - 7 1/5
What is 10 times larger than the 7 in this number 16372
Answer:
700
Step-by-step explanation:
I am slightly confused by your wording, but Im assuming you mean the expanded form.
In the base ten system, the second to last digit is the tens place. Therefore, the 7 represents 7*10 = 70
10 times larger than 70 is 700
What is the measure of angle 1 in the diagram below?*
D
18°
A
B
120°
E
Answer:
123
Step-by-step explanation:
If LM = 41 – 2x and NP = 7x + 5, find LM.
The outside temperature at 6:00 was 75º F. The temperature dropped 0.8ºF for the next 4 hours.What was the outside temperature after 4 hours?
Answer:
71.8° F
Step-by-step explanation:
Given 75° and 4 times 0.8° drop = 3.2°, so the temperature is 75° - 3.2°
= 71.8° F
Evaluate 3|-5| -2|-2|
Answer:
11
Step-by-step explanation:
absolute value is always a positive number so
3|-5| -2|-2| =
3 * 5 -2*2
follow PEMDAS
15 -4 = 11
What is the volume of a cylinder with base radius 2 and height 5?
Answer:
20 pi (sign)
Step-by-step explanation:
khan answer trust me bro
Determine whether the integral is convergent or divergent. 1 59 1 − x2 dx 0 convergent divergent Correct: Your answer is correct. If it is convergent, evaluate it. (If the quantity diverges, enter DIVERGES
Complete Question
The complete question is shown on the first uploaded image
Answer:
it is convergent and the solution is [tex]= \frac{33 \pi }{2}[/tex]
Step-by-step explanation:
From the question we are given
[tex]\int\limits^1_0 {\frac{33}{\sqrt{1-x^2} } } \, dx[/tex]
When integrated
[tex]= 33 sin^{-1} x \left | \ 1} \atop {0}} \right.[/tex]
[tex]= 33[ \frac{\pi }{2} - 0][/tex]
[tex]= \frac{33 \pi }{2}[/tex]
This implies that the integral converges
There were 500 goats and geese on a farm. If I see 1,468 legs, how many of each are on the farm? Pls help now
Answer:
734
Step-by-step explanation:
divide 1468 by 2
Answer:
234 goats266 geeseStep-by-step explanation:
Let x represent the number of goats. The 500-x is the number of geese. The total number of legs is ...
4x +2(500 -x) = 1468
2x +1000 = 1468 . . . . . . . eliminate parentheses
2x = 468 . . . . . . . . . . .subtract 1000
x = 234 . . . . . . . . .number of goats
(500 -x) = 266 . . number of geese
Which are perfect cubes? Check all that apply. 64 x16 8x3 27x4 81x6 125x9
Answer:
A,C,F
Step-by-step explanation: I took the test :)
The expression 64 is perfect cube of 3.
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
We have to determine, which to the following is perfect cube.
According to the question,
A perfect cube is an integer that is equal to some other integer raised to the third power.
To obtain the perfect cubes of the expression, it can be determined in following steps.
The given expression is 64.
To convert it into perfect square written in small factor parts.
Therefore, 64 written as,
[tex]= 64\\\\= 2 \times 2 \times 2 \times 2 \times 2 \times 2 \\\\= (2)^{3} \times (2)^{3}\\\\= (2\times 2)^{3}\\\\=( 4)^{3}[/tex]
The expression 64 is perfect cube of 3.
The given expression is 16x.
To convert it into perfect square written in small factor parts.
Then,
16x can be written as,
[tex]= 16x \\\\= 2\times 2\times 2\times 2\times x\\\\= 2x.(2)^{3}\\[/tex]
The expression 16x is not perfect cube.
The given expression is [tex]8x^{3][/tex].
To convert it into perfect square written in small factor parts.
Then,
[tex]8x^{3}[/tex] can be written as,
[tex]= 8x^{3}\\\\= 2 \times 2 \times 2 \times x^{3}\\\\= (2)^3 \times {x^{3}}\\\\= (2x)^{3}[/tex]
The expression [tex]8x^{3][/tex] is the perfect cube of [tex](2x)^{3}[/tex].
The given expression is [tex]27x^{4}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]27x^{4}[/tex] can be written as,
[tex]= 27x^{4}\\\\= 3 \times3 \times3 \times x^{4}\\\\= (3)^{3} \times x \times x^{3}\\\\= x \times (3x)^3[/tex]
The expression [tex]27x^{4}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]81x^6[/tex] can be written as,
[tex]= 81x^{6}\\\\= 3 \times3 \times3 \times3 \times x^{6}\\\\= 3.(3)^{3} \times x^{3} \times x^{3}\\\\= 3 \times ( 3x^{2}) ^{3}[/tex]
The expression [tex]81x^{6}[/tex] is not a perfect cube.
The given expression is [tex]81x^{6}[/tex]
To convert it into perfect square written in small factor parts.
Then,
[tex]125x^{9}[/tex] can be written as,
[tex]=125x^{9}\\\\= 5 \times 5 \times 5 \times x^{3} \times x^{3} \times x^{3}\\\\= (5x^{3})^{3}[/tex]
The expression [tex]12x^{9}[/tex] is perfect square of [tex](5x^{3})^{3}[/tex]
To know more about perfect square click the link given below.
https://brainly.com/question/16780291
is it possible for a triangle to have the side lengths of 3, 8, and 13
Answer:
No
Step-by-step explanation:
The longest side of a triangle must be less than the sum of the shorter two sides.
3 + 8 = 11. 13 is not less than 11. So it is not possible for a triangle to have these sides.
Students at an agricultural station conducted a study to compare geneticallymodified (GM) corn with regular corn. Each of 33 plots of land was divided intotwo half-plots; one half-plot was randomly selected to be planted with the GMcorn, and the other half-plot was planted with the regular corn.The table shows summary statistics for the yields, in bushels per acre, and thedifference in yield (GM minus regular) for each plot.MeanStandardDeviation n Minimum Q1 Median Q3 MaximumGM 125.018 13.623 33 107.4 111.9 127.5 138.0 144.0Regular 120.482 10.321 33 102.9 111.0 119.4 129.0 133.5Difference 4.536 6.444 33 –2.1 –0.9 3.0 6.0 20.1(a) Explain why the yields from one type of corn are not independent of the yields from the other type of corn.(b) Based on the summary statistics, would it be more likely to obtain a yield of 123 or more bushels per acre from a plot of GM corn or a plot of regular corn? Justify your answer.
Answer:
Step-by-step explanation:
The given data is represented in the attachment.
a) Explain why yields from one type of corn are not independent of the yields from the other type of corn.
Yields from one type of corn are not independent of the yields from the other type of corn because, as the corns are planted in two similar plots, they could compete during watering process, even the amount of nutrients shared and the type of air. This means one corn may get more nutrients than the other. Therefore, they are not independent (they are dependent).
b) Based on the summary statistics, GM is expected to more likely obtain yield greater than 123, because 123 is greater than mean for regular corn but less than mean for GM corn.
Thus,
P(yield>123|GM)>0.5; and P(yield>123|Regular)<0.5
Express the following number in scientific notation. 46,000,000 = _____ 4.6000 x 10 7 4.6 x 10 7 4.600 x 10 7 0.460 x 10 6
Answer:
4.6 x 10^7
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
(2k2 - 8k + k4) - (7k+8k^2-5k^4) simplify each difference. write the final answer in standard form. identify the leading coefficient and the constant. show all work
Answer:
-7k-8k^2+5k^4
Step-by-step explanation:
A _ _ _ _ _ of a circle is a segment that begins and ends on the circle; a segment whose endpoints are on the circle. It does not have to pass through the center.
Answer:
Chord
Step-by-step explanation:
I believe the word you are looking for is a chord.
Complete the square to make a perfect square trinomial. Write the result as a binomial square. q2−23q
Answer:
[tex]\left(q-\dfrac{23}{2}\right)^2[/tex]
Step-by-step explanation:
Given the expression: [tex]q^2-23q[/tex]
To complete the square, we follow these steps:
Step 1: Identify the coefficient of q
Coefficient of q=-23
Step 2: Divide the coefficient of q by 2
[tex]=-\dfrac{23}{2}[/tex]
Step 3: Square your result from step 2 and add it to the equation
This gives us: [tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2[/tex]
We have now completed the square.
Step 4: Write the result as a binomial square.
To write it as a binomial square, pick the variable and add the term in the bracket.
Therefore:
[tex]q^2-23q+\left(-\dfrac{23}{2}\right)^2=\left(q-\dfrac{23}{2}\right)^2[/tex]
The perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
The given expression is [tex]q^2-23q[/tex].
It is required to write the given expression as a perfect square polynomial or trinomial.
We will use the identity [tex](a+b)^2=a^2+2ab+b^2[/tex].
So, the first term from the given expression will be [tex]a=q[/tex].
To find the second term b, divide the 2nd term of the given expression by 2,
[tex]b=\dfrac{-23}{2}[/tex]
So, the given expression can be written in the perfect square form as,
[tex]a^2+2ab+b^2=q^2-23q+(\dfrac{-23}{2})^2\\=(q-\dfrac{23}{2})(q-\dfrac{23}{2})\\=(q-\dfrac{23}{2})^2[/tex]
Therefore, the perfect square form of the given expression will be [tex](q-\dfrac{23}{2})^2[/tex].
For more details, refer to the link:
https://brainly.com/question/18875994
Función inversa f(x) = 7/x -9
Answer:
F-1(x)=7/(x+9)
Step-by-step explanation:
Change F(x) to y so y=7/x -9
Swap variables x=7/y -9
Solve x+9=7/y
7/(x+9)=y
Then change y to F inverse
F-1(x)=7/(x+9)
Thats ur inverse!!!
Answer:
(x+9)/7
Step-by-step explanation:
Let f(x) = y;
y =7/x - 9
y + 9 = 7x
x = (y + 9)/7
Substitute x for y and X = f^{-1}(x)
f^{-1}(x) =(x+9)/7 this is the inverse of f(x)
what is the probability of choosing an even number from the set of numbers 1,2,3,4,5,6,7,8,9,10
Answer:
the probability of getting an even numbers out of this set is 1/2
Step-by-step explanation:
The set of numbers are: 10
1,2,3,4,5,6,7,8,9,10
Even Numbers: 5
2,4,6,8,10
Probability = [tex]\frac{NumberOfFavourableOutcomes}{TotalNumberOfOutcomes}[/tex]
P = [tex]\frac{Even Numbers}{Total Numbers}[/tex]
P = [tex]\frac{5}{10}[/tex]
P = [tex]\frac{1}{2}[/tex]
So, the probability of getting an even numbers out of this set is 1/2
Answer:
The probability of this set of numbers is 1/2.
Step-by-step explanation:
Probability is the odds of an event happening. It is expressed by writing it as a fraction, decimal, or a percent.
The formula for probability is the number of favorable outcomes divided by the total number of outcomes. In this case, we have odd and even numbers. The even numbers in this set are 2, 4, 6, 8, and 10.
These are the favorable outcomes.
Since there are 5 even numbers, there are 5 favorable outcomes.
There are total of 10 outcomes. Therefore P(Even number)= 5/10.
Don't forget to always simplify. You can divide the numerator and denominator by 5. 5 divided 5 is 1 and 10 divided by 5 is 2.
Therefore, the probability of choosing an even number from this set of numbers is 1/2.
I hope this helps, and I hope you enjoy the rest of your day!
Suppose that each customer asks to sample a food item with probability 1/4, independently of all other customers. The service time for a customer who samples a food item is an exponential random variable with parameter 1/5. i. What is the expected number of minutes until you reach the front of the line
Answer:
An approximately 2 minutes is expected to reach the front of the line
Step-by-step explanation:
Expected value of minutes =
(1/4)^(1/5) + (1 - 1/4)^(1/5)
= (1/4)^0.2 + (3/4)^0.2
= 0.7579 + 0.9441
= 1.702.
≈ 2 minutes
Let x stand for the number of minutes spent waiting in line for a rollercoaster at an amusement park. 81 people are sampled at a time. The sample mean is 18 minutes and the sample standard deviation is 0.5 minutes. What is the standard deviation of the population?
Answer:
The standard deviation of the population is 4.5 minutes.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation of the population [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question:
[tex]s = 0.5, n = 81[/tex]
So
[tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = \frac{\sigma}{\sqrt{81}}[/tex]
[tex]\sigma = 9*0.5 = 4.5[/tex]
The standard deviation of the population is 4.5 minutes.
1. Determine a rule that could be used to explain how the volume of a
Cylinder or cone is affected when the radius is multiplied by a positive
number.
Answer:
See explanation
Step-by-step explanation:
Solution:-
- We will use the basic formulas for calculating the volumes of two solid bodies.
- The volume of a cylinder ( V_l ) is represented by:
[tex]V_c = \pi *r^2*h[/tex]
- Similarly, the volume of cone ( V_c ) is represented by:
[tex]V_c = \frac{1}{3}*\pi *r^2 * h[/tex]
Where,
r : The radius of cylinder / radius of circular base of the cone
h : The height of the cylinder / cone
- We will investigate the correlation between the volume of each of the two bodies wit the radius ( r ). We will assume that the height of cylinder/cone as a constant.
- We will represent a proportionality of Volume ( V ) with respect to ( r ):
[tex]V = C*r^2[/tex]
Where,
C: The constant of proportionality
- Hence the proportional relation is expressed as:
V∝ r^2
- The volume ( V ) is proportional to the square of the radius. Now we will see the effect of multiplying the radius ( r ) with a positive number ( a ) on the volume of either of the two bodies:
[tex]V = C*(a*r)^2\\\\V = C*a^2*r^2[/tex]
- Hence, we see a general rule frm above relation that multiplying the result by square of the multiple ( a^2 ) will give us the equivalent result as multiplying a multiple ( a ) with radius ( r ).
- Hence, the relations for each of the two bodies becomes:
[tex]V = (\frac{1}{3} \pi *r^2*h)*a^2[/tex]
&
[tex]V = ( \pi *r^2*h)*a^2[/tex]
Find the five-number summary for the data.
{238, 213, 223, 212, 225, 233, 230, 239, 223, 207, 219,
217, 234, 204, 212, 242}
A. 204, 212.5, 223, 233.5, 242
B. 204, 212, 223, 233, 239
OC. 204, 212, 219, 233, 242
OD. 207, 212, 223, 234, 239
Answer:
The correct option is A. 204, 212.5, 223, 233.5, 242.
Step-by-step explanation:
The five number summary of a data set is:
Minimum First Quartile Median Third Quartile Maximum.The data provided, in ascending order is:
S = {204 , 207 , 212 , 212 , 213 , 217 , 219 , 223 , 223 , 225 , 230 , 233 , 234 , 238 , 239 , 242}
There are a total of 16 values in the data set.
The minimum value is,
Minimum = 204
The first quartile is the median value of the first half of the data.
The first half of the data is:
S₁ = {204 , 207 , 212 , 212 , 213 , 217 , 219 , 223 }
The median for even number of observations is the mean of the middle two values.
[tex]\text{Q}_{1}=\frac{4^{th}+5^{th}}{2}=\frac{212+213}{2}=212.5[/tex]
The first quartile is 212.5.
The median for even number of observations is the mean of the middle two values.
[tex]\text{Median}=\frac{8^{th}+9^{th}}{2}=\frac{223+223}{2}=223[/tex]
The median of the data is 223.
The third quartile is the median value of the second half of the data.
The first half of the data is:
S₂ = {223 , 225 , 230 , 233 , 234 , 238 , 239 , 242}
The median for even number of observations is the mean of the middle two values.
[tex]\text{Q}_{3}=\frac{12^{th}+13^{th}}{2}=\frac{233+234}{2}=233.5[/tex]
The third quartile is 233.5.
The maximum value is,
Maximum = 242
10+10+10-10+10+10+10
Answer:
60
Step-by-step explanation:
=> 10+10+10-10+10+10+10+10
=> 30-10+40
=> 20+40
=> 60
Answer:
60
Step-by-step explanation:
10+10+10-10+10+10+10
Write this number in expanded notation 2,930,365
Answer:
2,000,000+900,000+30,000+300+60+5
Step-by-step explanation:
hope this helps and Please Rate brainliest!!!