Answer:
[tex]\frac{x}{5y} -lnxy = K[/tex]
Step-by-step explanation:
Given the differential equation
[tex]9x(x+5y )y' = 9y(x -5y )\\x(x+5y )\frac{dy}{dx} = y(x -5y)\\\frac{dy}{dx} = \frac{y(x -5y)}{x(x+5y )} .\\let\ y = vx\\\frac{dy}{dx} =v+ x\frac{dv}{dx} \\v+ x\frac{dv}{dx} = \frac{vx(x -5vx)}{x(x+5vx )} \\v+ x\frac{dv}{dx} = \frac{v(1 -5v)}{(1+5v )} \\x\frac{dv}{dx} = \frac{v(1 -5v)}{(1+5v )} - v\\x\frac{dv}{dx} = \frac{v(1 -5v)-v(1+5v)}{(1+5v )} \\x\frac{dv}{dx} = \frac{-10v^{2} }{1+5v} \\\frac{dx}{x} = \frac{ 1+5v}{-10v^{2}}dv\\[/tex]
[tex]\int\limits\frac{dx}{x} = \frac{-1}{10} \int\limits v^{-2} dv - \frac{1}{2}\int\limits \frac{dv}{v} \\lnx + C = \frac{1}{10v}-\frac{1}{2}lnv\\ since\ y =vx\\lnx+C = \frac{1}{10(\frac{y}{x} )}-\frac{1}{2}ln(\frac{y}{x} )\\lnx+C = \frac{x}{10y}-\frac{1}{2}ln(\frac{y}{x} )[/tex]
[tex]2lnx +2C = \frac{x}{5y} - ln \frac{y}{x} \\\frac{x}{5y} - ln \frac{y}{x} -2lnx = 2C\\\frac{x}{5y} -(ln \frac{y}{x} +2lnx) = 2C\\\frac{x}{5y} -(ln \frac{y}{x} +lnx^{2} ) = 2C\\\\\frac{x}{5y} -lnxy = 2C\\\frac{x}{5y} -lnxy = K\ where \ K = 2C[/tex]
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = Correct: Your answer is correct. (b) Find an expression for the number of cells after t hours. P(t) = Correct: Your answer is correct. (c) Find the number of cells after 8 hours. 973078528 Correct: Your answer is correct. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. hr
Answer:
The E. Coli will grow at a rate of approximately 800% an hour.
In right triangle PQR, What is tan P
Answer:
c. 3/4
Step-by-step explanation:
tan is opposite over adjacent and based off of the included information its 3/4
If the legs of a right triangle are 10 and 24, then the
hypotenuse is
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
If the difference between two numbers is 7 and their product is 137 what is the sum of squares if the numbers?
Answer:
323
Step-by-step explanation:
a-b= 7
ab= 137
a²+b²= ?
---------
Since (a-b)²= a²-2ab +b²
⇒ a²+b²= (a-b)² + 2ab= 7² + 2*137= 323
To express the polynomial 4a^3 + a^2 - 6a^5 + 2a^3 - 4a + 1 in standard form, which terms should be combined?
Answer:
Step-by-step explanation:
-6a^5+6a^3+a^2-4a+1
Answer:
4a^3 and 2a^3
Step-by-step explanation:
you always start by combining like terms
Does the equation Axequalsb have a solution for each b in set of real numbers RSuperscript 4? A. No, because A has a pivot position in every row. B. Yes, because the columns of A span set of real numbers RSuperscript 4. C. Yes, because A does not have a pivot position in every row. D. No, because the columns of A do not span set of real numbers R
Answer:
C. Yes, because A does not have a pivot position in every row.
Step-by-step explanation:
The pivot position in the matrix is determined by entries in non zero rows. The pivot position may be in the row or a column. By Invertible Matrix Theorem the equation Axequalsb has non trivial solution. A has fewer pivot positions therefore A is not invertible. Ax will map RSuperscript into real numbers for n times. A has pivot position if left parenthesis bold x right parenthesis.
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using
function notation?
Fly) = -
f(x) = - 3x + 4
f(x) =
FCV) = -3y+ 4
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Step 1: Write it in slope-intercept form
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
Step 2: Replace y with f(x)
f(x) = -3x + 4
In math, function f(x) is equal to the variable y.
What is the radius of a sphere with a surface area of 100Ttcm??
10 cm
3 cm
5 cm
25 cm
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water? Answer: (round to 4 decimal places)
Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [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].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: time = 20 seconds
Step-by-step explanation:
h(t) = -16t² + 316t + 80
The shape of this graph is an upside parabola ∩.
It lands on the ground when height (h) = 0
Set the equation equal to zero, factor, and solve for t.
0 = -16t² + 316t + 80
0 = 4t² - 79t - 20 divided both sides by -4
0 = (4t + 1)(t - 20) factored the equation
t = -1/4 t = 20 Applied Zero Product Property and solved for t
Since we know time cannot be negative, disregard t = -1/4
The only valid solution is: t = 20
78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
Taylor Swift wants to know the proportion of her fans who listened to her new single ME! within the first hour of it being released. In order to estimate this, she takes a sample of 150 of her fans and asks them if they listened to the song in this time period. Of the 150 fans, 135 of them (90%) responded that they did listen to the song during this time period. What is the parameter and what is its value
Answer:
The parameter is the population proportion of fans who listened to her new single and has an estimated value of 90%.
Step-by-step explanation:
The parameter is a value that corresponds to a population, while an a value that corresponds to a sample is know as statistic.
She takes a sample to estimate, with a point estimate and probably with a confidence interval around this point estimate, the true proportion of fans who listened to her new single.
This is the paramater: the population proportion of fans who listened to her new single.
Its value comes from an estimation based on the sample proportion (point estimate).
The sample proportion is 90%, so we can estimate, as there is no bias, that the population proportion is also 90%.
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
Translate to an algebraic expression.
28 more than d
Answer: d + 28
Step-by-step explanation:
Answer:
d+28
Step-by-step explanation:
it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28
Help me please thank u
Answer:
160cm
74mm
3.6km is 3600m
Step-by-step explanation:
1. 6 x 100= 160cm
7.4cm x 10 =74mm
3.6 x 1000= 3600m
Kinda been stuck on this one, someone pls let me know
Answer:
255
Step-by-step explanation:
use calculator
Answer:
255
Step-by-step explanation:
∑ᵢ₌₁⁸ 2ⁱ⁻¹
Using brute force method:
S = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷
S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
S = 255
Using formula:
S = a₁ (1 − rⁿ) / (1 − r)
S = 1 (1 − 2⁸) / (1 − 2)
S = 255
Five-thirds divided by one-third =
Answer:
Step-by-step explanation: [tex]\frac{5}{3}[/tex]÷[tex]\frac{1}{3}[/tex] =
(Decimal: 0.555556)
parallelogram JKLM is shown on the coordinate plane below
Answer: c) K' = (6, 4) L' = (3, 3)
Step-by-step explanation:
The simplest way to find the coordinates is to rotate the graph 3 times.
Rotate 1 time to the left (counterclockwise) = 90°
Rotate 2 times to the left (counterclockwise) = 180°
Rotate 3 times to the left (counterclockwise) = 270°
see image for 3 times to the left = 270°
The two figures are similar. Write a proportion to find the missing measure. Then find the value of x.
Answer:
First option is the right choice.
Step-by-step explanation:
x/95 = 15/19
x = 75
Best Regards!
Answer:
Option A
Step-by-step explanation:
Triangle ABC and DEF are similar.
Taking proportion of their sides to find the value of the unknown.
=> x/15 = 95/19
Cross Multiplying
=> 19x = 1425
Dividing both sides by 9
=> x = 75
The graph of linear function f passes through the point (1, −9) and has a slope of −3.
Answer:
Equation of a line y = mx + c
m = slope
Using point (1,-9) and slope -3
y + 9 = -3(x - 1)
y + 9 = -3x + 3
y = -3x + 3 - 9
y = -3x - 6
Hope this helps.
To the right are the outcomes that are possible when a couple has three children. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there are exactly 0 girls.
Answer:
12.5% probability that when a couple has three children, there are exactly 0 girls.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
b for boy, g for girl
g - g - g
g - g - b
g - b - g
g - b - b
b - g - g
b - g - b
b - b - g
b - b - b
8 outcomes, one of which (b - b - b) with exactly 0 girls.
So
1/8 = 0.125
12.5% probability that when a couple has three children, there are exactly 0 girls.
The probability that when a couple has three children, there are exactly 0 girls is 12.5%
Calculation of the probability:Here we assume b for boy, g for girl
Now the probability conditions are
g - g - g
g - g - b
g - b - g
g - b - b
b - g - g
b - g - b
b - b - g
b - b - b
There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.
So
[tex]= 1\div 8[/tex]
= 0.125
Learn more about probability here: https://brainly.com/question/24613748
A rotary cutter has a radius of 4 centimeters. The hole in the middle of
the cutter has a radius of 0.5 centimeter. What is the area of one side of
the cutter?
10 of 11 QUESTIONS
3.577 cm
15.757 cm?
1671 cm2
13.571 cm2
Answer:
15.757 im not sure but i came up with that one.
Step-by-step explanation:
Which of the following is equivalent 8-3x>2(3x-5)
Answer:
2 >x
Step-by-step explanation:
8-3x>2(3x-5)
distribute
8-3x>6x-10
Add 3x to each side
8+3x-3x>6x+3x -10
8 > 9x-10
Add 10 to each side
8+10 > 9x -10+10
18 > 9x
Divide by 9
18/9 > 9x/9
2 >x
Answer:
[tex]x < 2[/tex]
hope this helps you
brainliest appreciated
good luck! have a nice day!
Step-by-step explanation:
[tex]8 - 3x > 2(3x - 5) \\ 8 - 3x > 6x - 10 \\ 8 + 10 > 3x +6 x \\ 18 > 9x \\ \frac{18}{9} > \frac{9x}{9} \\ 2 > x[/tex]
Please answer this correctly without making mistakes as my work is due today
Answer:
2
Step-by-step explanation:
Arranging them in ascending order we have the scores as;
[tex]2, 3, 3, 4, 4, 6, 8, 9, 9, 9[/tex]
The median is the average of the 5th and 6th scores.
[tex] \frac{4 + 6}{2} \\ \frac{10}{2} \\ 5[/tex]
The new set of scores become
[tex]2,3,3,4,6,8,9,9,9,9[/tex]
The median is;
[tex] \frac{6 + 8}{2} \\ \frac{14}{2} \\ 7[/tex]
The difference is
[tex]7 - 5 = 2[/tex]
Hope it helps! Vote for brainliest!
the ratio of men to women in a village is 12: 25. if there are 120men, (a)how many women are there ?, (b) what is the total number of men to women
Answer:
a) 250 women
b) 370 in total
Step-by-step explanation:
Men : Women
12 : 25
120 : 250
a) If there are 120 men that means 12 was multiplied 10 times to get 120 so to get the amount for women we multiply 25 ten times which will give 250.
b) the sum will be 120 + 250 = 370
Which best compares the slope and y-intercepts of the linear functions f and g where f= 1/3 x + 3 and g is shown in the table? X =0,1,2,3 and g(x) =3,6,9,12
Answer:
different slope same intercept
Step-by-step explanation:
g(x)= 3x+3
this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for
Please answer this correctly
Answer:
The mode would not change
Step-by-step explanation:
Mode is the frequency of 1 number. In this case, the mode is 3. If we add 8, the frequency of 3 would not change; there would still be 4 3's, and 3 would still have the most of itself.
find the mean of x,2x,3x,4x,5
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{TotalNumberOfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
whats the the answer -x/3 = 2
Answer:
-6
Step-by-step explanation:
-x/3=2
Multiply both sides by 3:
-x=6
Divide both sides by -1:
x=-6
Hope this helps!
A problem requires finding the distance traveled in miles. Which would not be a reasonable answer? Justify your response. A. minus10 B. 1.8 C. 10 and one half D. 50
Answer:
A. minus 10,
Step-by-step explanation:
The distance travelled must be positive.
Therefore minus 10 would not be a reasonable answer.