Consider the system of differential equations
dx/dt= x+ y=1
dy/dt =1- x^2 +y^2
Required:
Sketch the x-nullcline, where solutions must travel vertically. Identify the regions in the plane where solutions will move toward the right, and where solutions move toward the right.
Answer:
Step-by-step explanation:
Given that:
the differential equations:
[tex]\dfrac{dx}{dt}= x+y = 1 \\ \\ \dfrac{dy}{dt}= 1-x^2+y^2[/tex]
For x-nullcline;
[tex]\implies \dfrac{dx}{dt} =0 \\ \\ \implies x+y-1[/tex]
From the image attached below, the sketch of the x-nullcline was carefully drawn and the regions were identified.
So, x-increases at the time when [tex]\dfrac{dx}{dt}>0[/tex]
[tex]\implies x+y -1 >0[/tex]
Thus, the solution move towards the right for x+y>1
Determine if the given value of the variable is the solution of the equation . write yes or no .
please i need help i will mark u brill
Answer:
no, b does not equal 5 in that equation
Step-by-step explanation:
if you solve for x, this is how it would look:
65/b + 8 x 4 = 20
65/b + 32 = 20
65/b = 20 - 32
65/b = -12
65 = -12b
-12b = 65
b = -65/12 (or -5 5/12)
Two student council representatives are chosen at random from a group of 7 girls and 3 boys. Let G be the random variable denoting the number of girls chosen. What is E[G]
This question is incomplete, the complete question is;
Two student council representatives are chosen at random from a group of 7 girls and 3 boys. Let G be the random variable denoting the number of girls chosen.
a) What is E[G] or range of G
b) Give the distribution over the random variable G
Answer:
a) E[G] is [ 0, 1 , 2 ]
b)
the distribution over the random variable G.
x P(x)
0 0.0667
1 0.4667
2 0.4667
Step-by-step explanation:
Given the data in the question;
Number to be chosen is 2
from 7 girls and 3 boys
a) range of G
number of girls can be; [ 0, 1 , 2 ]
Therefore, E[G] is [ 0, 1 , 2 ]
b) he distribution over the random variable G.
Distribution of the random variable G is Hypergeometric;
so
with P( G=g ) = P( getting g girls from 7 and 2-g boys from 3)
= (([tex]^7C_g[/tex]) × ([tex]^3C_{2-g[/tex])) / [tex]^{10}C_2[/tex]
now since, the range of G is [ 0, 1 , 2 ]
P( G=0 ) = (([tex]^7C_0[/tex]) × ([tex]^3C_{2[/tex])) / [tex]^{10}C_2[/tex]
= [(7!/(0!(7-0)!)) × (3!/(2!(3-2)!))] / (10!/(2!(10-2)!))
= [1 × 3] / 45 = 3/45 = 0.0667
P( G=1 ) = (([tex]^7C_1[/tex]) × ([tex]^3C_{1[/tex])) / [tex]^{10}C_2[/tex]
= [(7!/(1!(7-1)!)) × (3!/(1!(3-1)!))] / (10!/(2!(10-2)!))
= [ 7 × 3 ] / 45 = 21/45 = 0.4667
P( G=2 ) = (([tex]^7C_2[/tex]) × ([tex]^3C_{0[/tex])) / [tex]^{10}C_2[/tex]
= [(7!/(2!(7-2)!)) × (3!/(0!(3-0)!))] / (10!/(2!(10-2)!))
= [ 21 × 1 ] / 45 = 21/45 = 0.4667
Therefore, the distribution over the random variable G.
x P(x)
0 0.0667
1 0.4667
2 0.4667
What is the answer to this question
Answer:
3
Step-by-step explanation:
NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Answer:
A person jumping on a trampoline
In planning a Thanksgiving vacation, you want to rent a car for a week and travel the Pacific Highway from San Francisco to San Diego. You want to return to San Francisco via Las Vegas, Death Valley, and Yosemite National Park. This trip covers approximately 1,500 miles. You plan to return the car with a full tank of gasoline. You are considering two options advertised by Hertz:
Toyota Camry, 40 mpg highway, costs $448.27 plus taxes and fees, totaling $533.65.
Toyota Prius Hybrid, 49 mpg highway, costs $610.58 plus taxes and fees, totaling $772.88.
In both cases, you must purchase gasoline, which costs $4.00 per gallon in California.
Camry: Total gasoline cost is?
Answer:
The gas cost for the Camry will be $ 150.
Step-by-step explanation:
Since in planning a Thanksgiving vacation, you want to rent a car for a week and travel the Pacific Highway from San Francisco to San Diego, and you want to return to San Francisco via Las Vegas, Death Valley, and Yosemite National Park, and this trip covers approximately 1,500 miles, and you plan to return the car with a full tank of gasoline and are considering two options advertised by Hertz:
Toyota Camry, 40 mpg highway, costs $ 448.27 plus taxes and fees, totaling $ 533.65.
Toyota Prius Hybrid, 49 mpg highway, costs $ 610.58 plus taxes and fees, totaling $ 772.88.
In both cases, you must purchase gasoline, which costs $ 4.00 per gallon in California.
To determine the total cost of gasoline for the Camry, the following calculation must be performed:
(1,500 / 40) x 4 = X
37.5 x 4 = X
150 = X
Therefore, the gas cost for the Camry will be $ 150.
Expression represents five less a third of a number?
Answer:
[tex] \frac {1}{3}x - 5 [/tex]
Step-by-step explanation:
Let the unknown number be x.
Translating the word problem into an algebraic expression, we have;
[tex] \frac {1}{3}x - 5 [/tex]
Or
[tex] \frac {x}{3} - 5 [/tex]
Simplifying further, we have;
[tex] \frac {x}{3} = 5 [/tex]
Cross-multiplying, we have;
x = 15
Therefore, the above algebraic expression is five less a third of a number.
PLEASE HELP
2!/0!=
0
2
undefined
Answer:
2
Step-by-step explanation:
any expression divided by 1 remains the same
you can also calculate the factorial
The dot plot shows the favorite sport to play according to some middle school students chosen at random.
Which statement is true according to the information in the dot pot?
Answer choices
A. Exactly 2/5 of the students chose basketball, golf, and track as their favorite sport to play.
B. Exactly 15% of the students chose baseball as their favorite sport to play.
C. Less than 1/5 of the students chose soccer and hockey as their favorite sport to play.
D. More than 25% of the students chose football and tennis as their favorite sport to play
PLEASE ANSWER THE QUESTION. IF YOU DONT KNOW YOU DONT KNOW
Answer:
D. More than 25% of the students chose football and tennis as their favorite sport to play
Step-by-step explanation:
From the dot plot :
Sport __Number of students
Hockey = 4
Track = 2
Tennis = 3
Basketball = 12
Soccer = 6
Football = 10
Golf = 5
Baseball = 8
Total = (4+2+3+12+6+10+5+8) = 50
Students of basketball, golf and track = (12 + 5 + 2) = 19 ; 19 /50 =
Percentage that chose base ball = 8 /50 *100 = 16%
(soccer + hockey) = (6+4) = 10/50 = 1/5
Football + tennis = (10 + 3) = 13
13/50 = 0.26 * 100% = 26% (True)
8. Which of the following correctly multiplies f(x) x g(x) if f(x) = 3x-1 and g(x) = 2x + 1?
A) f(x) x g(x) = 6x2 + x + 1
B) f(x) x g(x) = 5x
C) f(x) x g(x) = 6x2 + x-1
D) f(x) x g(x) = 5x2 + x-1
Answer:
C) f(x) x g(x) = 6x2 + x-1
Step-by-step explanation:
Multiplication of functions:
Two multiply two polynomial functions, we apply the distributive property(multiply each two terms and add).
In this question, we have that:
[tex]f(x) = 3x - 1, g(x) = 2x + 1[/tex]
The multiplication is:
[tex]f(x) \times g(x) = (3x - 1)(2x+1) = 3x*2x + 3x*1 -1*2x -1*1 = 6x^2 + 3x - 2x - 1 = 6x^2 + x - 1[/tex]
The correct answer is given by option C.
A card is randomly selected from a deck of playing cards. Find the probability that it is a face card, given that a black card is drawn.
A. 3/13
B. 6/26
C. 26/52
D. 1/2
Answer 3/13
Step-by-step explanation:
There are 12 face cards, and 6 are black. Thus, the probability of choosing one would be 6/26, or 3/13
What percent of the cars passed through between 2pm and 2:59 pm
Answer:
Can you actually do your own work
Step-by-step explanation:
Do it yourself
What is the equation of a line that contains the point (6,-4) and has a slope of 3/4?
A. y-4 = 3/4 (x-6) B. y+ 4 = 3/4 (x-6) C. y- 6 = 3/4 (x-4) D. y-6 = 3/4 (x+4)
Answer:
B. y+ 4 = 3/4 (x-6)
Step-by-step explanation:
Given:
m = 3/4
Slope-intercept:
y - y1 = m(x - x1)
y + 4 = 3/4(x - 6)
Help QUICK PLS ITS DUE IN 30 MINS
Answer: false, true, true, and i don’t know the last one
Step-by-step explanation:
An aquarium is to be drained. The aquarium is shaped like a rectangular prism with length 25 in, width 19 in, and height 12 in. Suppose water is pumped out
of the aquarium at a rate of 475 in per minute. If the aquarium starts completely full, how many minutes does it take to empty the aquarium. ( NO LINKS)
9514 1404 393
Answer:
12 minutes
Step-by-step explanation:
The volume of the aquarium is ...
V = LWH
V = (25 in)(19 in)(12 in) = 5700 in³
The time required to empty it is given by ...
time = quantity/rate
time = (5700 in³)/(475 in³/min) = 12 min
It takes 12 minutes to empty the aquarium.
WILL GIVE BRAINLIEST!!! No LINKS or REPORT!!!
The formula is:
V= (3.14)π⋅ (radius)r^2⋅(height)h/3
(^2 is a exponent)
How to solve:
π ·2^2· 9/3= 37.69911
(Round to the nearest tenth)
37.7Solve: -3x = 15 you can get the brainiest
I NEED HELP UNDER 5 MINUTES BEST ANSWER GETS BAINLESS hits 96 must play 3 minutes of commercials for every 30 minutes of music played. how many minutes of commercials must be played for 210 minutes of music?
Answer:
21
Step-by-step explanation:
so the relationship is that the music is ten times the commercials so, divide 210 by 30 and times that number by 3 210/30= 7, 7'3=21
Answer:
21 minutes of commercials
Step-by-step explanation:
If Hits 96 must play 3 minutes of commercials for every 30 minutes of music played, than the ratio of minutes of commercials to minutes of music is 3:30=1:10.
If 210 minutes of music is played, we can model the situation with the equation [tex]\frac{1}{10} =\frac{x}{210}[/tex]
We can use cross multiply to simplify the equation to [tex]10x=210[/tex]
Dividing each side by 10, we get [tex]x=21[/tex]
So, if 210 minutes of music is played, 21 minutes of commercials is played.
What is the measure of op С : 429 180°
Answer:
90
Step-by-step explanation:
the angles that are on the opposite side are same
LEARNED THIS IN FOURTH GRADE
I'm still in fourth grade
my math teacher taught us this separately.
I go to School for the Highly Gifted in Grand Prairie, Texas
Which pair of events is dependent?
O A. You get a head and a tail in two coin tosses with two different coins.
O B.
You get a head and a tail in two coin tosses using the same coin twice.
O C. You pick two
numbered billiard balls from a bag of balls one after the other without replacement.
O D. You draw two red cards one after the other with replacement.
Answer:
It's option C
Step-by-step explanation:
C. You pick two numbered billiard balls from a bag of balls one after the other without replacement.
How many possible passwords can be made for a website that requires passwords to consist of 3 digits followed by 2 letters? (Note that each digit or letter is allowed to be repeated.)
Answer:
67,600
Step-by-step explanation:
someone please help me answer this!!
Answer:
c = 2.2m is the answer.
Step-by-step explanation:
a = 1m
b = 2m
c = ?
According to the Pythagorean theorem,
a² + b² = c²
1² + 2² = c²
1 + 4 = c²
c² = 5
c = 2.2m
∴ the slide is 2.2m long.
the ratio of hamburgers to hot dogs at the picnic is 25:10. If there are 100 hamburgers how many lunch itemd are there altogether?
Answer:
140 lunch items
Step-by-step explanation:
The unit ratio is 5:2
So if we take that and multiply it by 20 we get 100:40. 100+40 is 140
Answer:
140
Step-by-step explanation:
well if there is 25 hamburgers to 10 hot dogs, than 25 times four is 100 and 10 times four is 40 so 140 but i dont know if i did it right
Question 2 of 10
What is the solution to this equation?
x - 16 = -8
A. x= 8
B. x = -8
C. x = 24
D. x= -24
What time is 11: 59 AM is it midday or midnight?
11:59 AM is midday not midnight
HELP PLEASE
A bus that seats 50 people was rented by a local club. As the bus fills with people, the price of each seat is lowered. What type of
trend would this be?
A) Positive
B) Negative
C)No trend
Answer: B) Negative
Step-by-step explanation:
Answer:
B) Negative
Step-by-step explanation:
The question states that as the number of people increases, the price of each seat decreases. Therefore this is a negative trend, because the increase in one variable leads to the decrease in the other variable.
Hope this helped!
please help quickly!!!!!!!!!!!!!!!!!!!!!!
Answer:
erm i think 5
Step-by-step explanation:
Find the lateral area of a cylinder
whose radius is 5 cm and whose
height is 10 cm.
Round to the nearest whole number.
[? ] cm2
Answer:
314 cm^2
Step-by-step explanation:
(=^w^=)
A= 2*pi*r*h
A=2*pi*5*10
A=314.16 cm^2
Step-by-step explanation:
2×5×10=
10×10= 100 cm²
=100 cm²
Find the value of x in the triangle shown below.
a.164
b.2
c.6
d.80
Answer:Answer:
Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex]by using Pythagoras law:h²=p²+b²
10²=x²+8²
x=√36=6 units.
the point (3, 4) is plotted on the coordinate plane below.
What are the coordinates of the point after a 90° counterclockwise rotation about the origin followed by a translation 4 units to the left?
A.
(-1, 4)
B.
(-4, 3)
C.
(0, 3)
D.
(-8, 3)
NO LINKS
Answer:
D) (-8, 3)
Step-by-step explanation:
90° counterclockwise brings point to (-4, 3)
translation 4 units to left brings point to (-8, 3)