Express 35 1/3 in simplest radical form.

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

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

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)

Answer:

Can you actually do your own work

Step-by-step explanation:

Do it yourself

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.

Answer:

3

Step-by-step explanation:

11:59 AM is midday not midnight

Answer:

Decision Rule; Reject H₀ if t > 1.708

Step-by-step explanation:

Given the data in the question;

sample size n = 26

sample mean x' = 4.9

Variance = 0.81

standard deviation σ = √variance = √0.81 = 0.9

level of significance ∝ = 0.05

Claim;

Null hypothesis             H₀ : μ = 4.6

Alternative hypothesis H₁ : μ > 4.6

Test Statistics;

Right tailed test

Now, decision rule for rejecting H₀;

degree of freedom df = n - 1 = 26 - 1 = 25

so, Right tailed test { > in H₁ }

Hence, Critical Value = [tex]t_{\alpha ,df[/tex] = [tex]t_{0.05, 25[/tex] = 1.708

Decision Rule; Reject H₀ if t > 1.708

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.

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)

Answer:

erm i think 5

Step-by-step explanation:

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.

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.

Answer:

67,600

Step-by-step explanation:

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.

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

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.

Answer:

the answer is A

Step-by-step explanation:

Answer:

A person jumping on a trampoline

Answer:

C. Mushrooms

Step-by-step explanation:

Mushrooms are known to be decomposers, they break down nutrients.

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.

Answer:

1/2 x -10 ≥ 0

Step-by-step explanation:

We know that a square root must have an answer that is greater that or equal to zero.  The result of a square root cannot be negative. What is inside the square root must be greater than or equal to zero.  To find the domain we solve that equation to determine the value of x.

1/2 x -10 ≥ 0

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

Answer:

The first skier goes at a speed of 11 kilometers per hour, while the second does it at a speed of 18 kilometers per hour.

Step-by-step explanation:

Given that two skiers are 43.5 kilometers apart and head towards each other, and they meet in 1.5 hours, if the second skier is 7 kilometers per hour faster the other, to find the speed of each skier the following calculation must be performed:

43.5 / 1.5 = 29

29 - 7 = 22

2/22 = 11

11 x 1.5 + 18 x 1.5 = X

43.5 = X

Thus, the first skier goes at a speed of 11 kilometers per hour, while the second does it at a speed of 18 kilometers per hour.

Answer: 1/3

Step-by-step explanation:

Each friend gets 1/3

1/3 / 9 = 3

Answer:

2

Step-by-step explanation:

any expression divided by 1 remains the same

you can also calculate the factorial

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)

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