To gather data for a statistics project, a student asked 10 friends how many hours of sleep they got on the previous night. The data are shown in the following list.

The given first-order linear equation 4ydx (3√y-2x)dy = 0. The general solution to the given equation is:

2y^(3/2) - x^2y + 2y^2 + C = 0

where C is an arbitrary constant.

To solve the given first-order linear equation:

4y dx + (3√y - 2x) dy = 0

We can rearrange it to the standard form of a linear equation:

(3√y - 2x) dy + 4y dx = 0

Now, let's separate the variables and integrate both sides:

∫ (3√y - 2x) dy + ∫ 4y dx = 0

∫ (3√y dy - 2xy dy) + ∫ 4y dx = 0

Integrating each term separately:

∫ 3√y dy - ∫ 2xy dy + ∫ 4y dx = 0

We use the power rule for integration:

∫ 3y^(1/2) dy - ∫ 2xy dy + ∫ 4y dx = 0

Integrating:

2y^(3/2) - x^2y + 2y^2 + C = 0

where C is the constant of integration.

So, the general solution to the given equation is:

2y^(3/2) - x^2y + 2y^2 + C = 0

where C is an arbitrary constant.

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Answer:

5

Step-by-step explanation:

√

3

x

+

10

=

x

To remove the radical on the left side of the equation, square both sides of the equation.

√

3

x

+

10

2

=

x

2

Simplify each side of the equation.

Tap for more steps...

3

x

+

10

=

x

2

Solve for  

x

.

Tap for more steps...

x

=

5

,

−

2

Exclude the solutions that do not make  

x

=

√

3

x

+

10

true.

x

=

5

Answer:

5x+1

5x^2+6

Step-by-step explanation:

The value of the input of the function, f(x) = (-1/3)·x + 7, that would result an output of 2/3 is; x = 19

An input value is a value that is put into a function, upon which the rule or definition of the function is applied to produce an output.

The possible function in the question, obtained from a similar question on the site is; f(x) = (-1/3)·x + 7

The two column table, from the question can be presented as follows;

x    \({}\)      f(x)

-3  \({}\)       8

-1\({}\)         22/3

1 \({}\)         20/3

3\({}\)         6

The required output based on the value of the input, obtained from the similar question is; 2/3

The function in the question indicates that the required input can be obtained as follows;

f(x) = (-1/3)·x + 7 = 2/3

Therefore;

(-1/3)·x = 2/3 - 7 = -19/3

x = -19/3/(-1/3) = 19

The input value that would give an output of 2/3 is; x = 19

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Answer: ima try

Step-by-step explanation: how i always do it is the second number (-2) you start for the mid point (0,0) if its -2 go down 2 if it 2 go up 2 if its 0 stay there then you go to the first number(2/3) from where you landed thats now the new start point then you go (x,y) in this equation its (2/3) so go up 2 right three but watch out for the negatives. so if it was -2/3 you would go down 2 then right 3

i hoped this helped its hard to explain but I tried

The company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.

To maximize the sales, the company needs to determine how many units of each type of electric hedge trimmers it should produce, subject to the constraints of manufacturing time and packaging capacity. Let x be the number of cord-type trimmers and y be the number of cordless trimmers that the company produces per day.

Since the cord-type trimmer requires 2 hours to make and the cordless model requires 4 hours, the total manufacturing time can be expressed as:

2x + 4y ≤ 800

Similarly, the packaging department can package only 300 trimmers per day, which means:

x + y ≤ 300

We also know that the company sells the cord-type model for $22.50 and the cordless model for $45.00, so the total sales can be expressed as:

total sales = 22.50x + 45.00y

To maximize the total sales subject to the above constraints, we can use linear programming. Solving the above equations using the graphical method, we get the feasible region bounded by the lines 2x + 4y = 800 and x + y = 300. The corners of this feasible region are (0, 300), (200, 100), and (400, 0).

Now, we need to determine the values of x and y that maximize the total sales. We can evaluate the total sales at each of the corners of the feasible region and choose the corner that gives the maximum total sales.

At (0, 300), the total sales = 22.50x + 45.00y = 45.00 * 300 = $13,500.

At (200, 100), the total sales = 22.50x + 45.00y = 22.50 * 200 + 45.00 * 100 = $10,500.

At (400, 0), the total sales = 22.50x + 45.00y = 22.50 * 400 = $9,000.

Therefore, the company should produce 200 cord-type trimmers and 100 cordless trimmers per day to maximize its sales. The total sales will be $10,500.

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Answer:

Median=3, Mean=2.333

Step-by-step explanation:

The p-value is 0.0064

Given that a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. Let us first understand the t-test(a2:a31, b2:b31, 2, 3) formula:

t-test stands for student's t-test.

a2:a31 is the first range or dataset.

b2:b31 is the second range or dataset.

2 represents the type of test (i.e., two-sample equal variance).

3 represents the type of t-test (i.e., two-tailed).

Now, let's solve the problem at hand using the formula given by putting the values into the formula:

P-value = 0.0064

The p-value calculated using the t.test(a2:a31, b2:b31, 2, 3) formula is 0.0064.

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Answer:

No, IMPOSSIABLE

Step-by-step explanation:

According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. In you case 3+4=7.  7 is less than 8.

The statement using absolute value notation will be x - 78 ≤ 22.

The student will pass the test which scores 22 points for the number 78

Absolute values are any digit's value without taking the sign into an account. Therefore, all negative numbers will be regarded as positive for absolute value. The absolute value of -5, for instance, will be 5, whereas that of -7, will be 7.

In essence, the absolute value calculates the distance from zero. Putting an absolute value on something does not imply that they are the same number but that they are the same distance from 0.

Le the score of student be = x

Forming the absolute value notation -

This can be expressed as,

x - 78 ≤ 22.

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Answer: 36 pt = 21.6171 qt. There are 1.66535 pints in a quart.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

2 pints are in 1 quart

Answer: Cleo will be 64.

Step-by-step explanation:

38/2= 19

19-7= 12

Clara is 12

38-12= 26

38+26=64

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer:

20% and Rate

Step-by-step explanation:

percent is associated with "is" ex (18 is what)

base is associated with "of" ex( of 90)

Rate is (what percent)

you are missing the rate

P=B*R

18=90*R

18=90*R

18/90=(90*R)/90

0.2=R

0.2*100 =20%

On a postsynaptic membrane, the opening of K+ ion channel induces an IPSP (Inhibitory Postsynaptic Potential).

The potential changes in a neuron after the receptor and ion channel activation is called synaptic potential. This potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP).EPSP is a depolarizing potential that results from the opening of the Na+ ion channel. It causes a change in the potential of the neuron towards threshold level that may trigger an action potential.Ion channels and pumps in a postsynaptic neuron regulate the internal potential of the cell. In a typical postsynaptic cell, the resting potential (Vrest) is -70 mV, the threshold value is -55 mV, the reversal potential for Cl- ion (Ec) is -63 mV, the reversal potential for K+ ion (Ex) is -90 mV, and the reversal potential for Na+ ion (ENa) is 60 mV.The opening of Cl- ion channel leads to an inward flow of negative ions and thus results in hyperpolarization. The opening of K+ ion channel leads to an outward flow of K+ ions, and the membrane potential becomes more negative. Thus, it also results in hyperpolarization. The opening of a Na+ ion channel leads to inward flow of Na+ ions, which makes the cell more positive, and it is depolarization. Therefore, the opening of K+ ion channel leads to an IPSP, and it hyperpolarizes the neuron.

The postsynaptic potential can be either an Excitatory Postsynaptic Potential (EPSP) or an Inhibitory Postsynaptic Potential (IPSP). The opening of the K+ ion channel leads to an outward flow of K+ ions, which makes the cell more negative and hyperpolarizes it, leading to IPSP.

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The x and y components of the total force exerted on this charge by the other two charges are 3.72 × 10⁻⁶ N and 8.87 × 10⁻⁶ N respectively. The magnitude of this force is 9.64 × 10⁻⁶ N. The direction of this force is 66.02° below the +x-axis.

The formula to calculate electric force is:

Electric force = (k*q1*q2)/r²

Where,k = Coulomb's constant = 9 × 10⁹ Nm²/C²

q1, q2 = Charges in Coulombs

r = Distance in meters

(a) The third charge q3 at (3.10, 3.95) experiences the force from q1 and q2.

Let's calculate the distance of q3 from q1 and q2.

Distance from q1 to q3 is = sqrt( (3.10-0)² + (3.95-0)² ) = 4.38 cm = 0.0438 m

Distance from q2 to q3 is = sqrt( (3.10-0)² + (3.95-3.95)² ) = 3.10 cm = 0.0310 m

Magnitude of electric force due to q1 = k*q1*q3/r1²Here, q1 = -3.20 nC and q3 = 5.00 nC

Thus, the electric force due to q1 = (9 × 10⁹) * (-3.20 × 10⁻⁹) * (5.00 × 10⁻⁹) / (0.0438)² = - 9.38 × 10⁻⁶ N ….. (i)

Here, r1 is the distance from q1 to q3.

Distance from q2 to q3 is = 3.10 cm = 0.0310 m.

Magnitude of electric force due to q2 = k*q2*q3/r2²Here, q2 = 1.60 nC and q3 = 5.00 nC

Thus, the electric force due to q2 = (9 × 10⁹) * (1.60 × 10⁻⁹) * (5.00 × 10⁻⁹) / (0.0310)² = 8.87 × 10⁻⁶ N ….. (ii)

Here, r2 is the distance from q2 to q3.

Total force in the x direction on q3 is: Fx = F1x + F2xFx = -F1 cos(θ1) + F2 cos(θ2)

Here, θ1 is the angle between r1 and the x-axis and θ2 is the angle between r2 and the x-axis

Let's calculate the angle θ1

tanθ1 = (3.95 - 0) / 3.10θ1 = tan⁻¹(3.95/3.10) = 51.04°

And the angle θ2

tanθ2 = (3.95 - 0) / 0θ2 = 90°

Now, the force in the x direction on q3:

Fx = - F1 cos(θ1) + F2 cos(θ2) = -(-9.38 × 10⁻⁶) cos(51.04) + 8.87 × 10⁻⁶ cos(90°) = 3.72 × 10⁻⁶ N

Total force in the y direction on q3: Fy = F1y + F2yFy = -F1 sin(θ1) + F2 sin(θ2)

Here, θ1 is the angle between r1 and the y-axis and θ2 is the angle between r2 and the y-axis. Let's calculate the angle θ1

tanθ1 = 0 / 3.10θ1 = tan⁻¹(0/3.10) = 0°

And the angle θ2

tanθ2 = 0 / 0θ2 = 90°

Now, the force in the y direction on q3:

Fy = - F1 sin(θ1) + F2 sin(θ2) = -(-9.38 × 10⁻⁶) sin(0°) + 8.87 × 10⁻⁶ sin(90°) = 8.87 × 10⁻⁶ N

Thus, the x and y components of the total force exerted on this charge by the other two charges are 3.72 × 10⁻⁶ N and 8.87 × 10⁻⁶ N respectively.

(b) The magnitude of this force = √(Fx² + Fy²) = √[(3.72 × 10⁻⁶)² + (8.87 × 10⁻⁶)²] = 9.64 × 10⁻⁶ N

The magnitude of this force is 9.64 × 10⁻⁶ N.

(c) Calculation of the direction of this force.

θ = tan⁻¹(Fy/Fx)θ = tan⁻¹(8.87 × 10⁻⁶ / 3.72 × 10⁻⁶) = 66.02°

The direction of this force is 66.02° below the +x-axis.

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Answer: please find the attached files

Step-by-step explanation:

A unit circle formula and special triangle of 45, 30 and 60 degrees can be used to solve the problem.

Please find the attached files for the solution

Answer:

Step-by-step explanation:

0 is the answer

Answer:

the answer would be 4/10 but the simplified version would be 2/5.

Step-by-step explanation:

add up how many bows you have, that will be the denominator. Then, the numerator is the number of purple bows. and if your going to simplify it divide the numerator and denominator by 2.

Answer:

fraction wise(4/10 chance)

percent wise:(40% chance)

Step-by-step explanation:

(There are 2 options) First add all of the bows then see how many purple bows there are. Since there are 4 bows it would be 4/10 or 40%.

Answer:

10.4476119402

Step-by-step explanation:

If you want a reasonable answer it would be 10.44 or 10.4!

M(x) is continuous on (-∞, -5/2) ∪ (5/2, ∞).

f(x)=  M(x) = (x - 4)/(4x² - 25). Here, we need to determine the intervals where the given function is continuous.

To determine where the given function is continuous, we need to consider the denominator of the given function.

The denominator is 4x² - 25. Therefore, the denominator is zero when 4x² - 25 = 0 ⇒ 4x² = 25 ⇒ x² = 25/4 ⇒ x = ±5/2. Thus, the given function M(x) is discontinuous at x = -5/2 and x = 5/2.

These values divide the number line into three intervals. Check the continuity of the function M(x) in these intervals.

Therefore, the given function M(x) is continuous on (-∞, -5/2) ∪ (5/2, ∞).Hence, the answer is M(x) is continuous on (-∞, -5/2) ∪ (5/2, ∞).

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Answer:

C

Step-by-step explanation:

\(x^2 +8+x^2+8+x^2+6x-3+x^2+6x-3\)

\(x^2+x^2+x^2+x^2=4x^2\)

\(6x+6x=12x\)

\(8+8-3-3=10\)

Ans: \(4x^2+12x+10\)

Answer:

(B)25

Step-by-step explanation:

If Lines DE and AB intersect at point C; and

\(\angle ACE =(2x+2)^\circ\\\angle ECB=(5x+3)^\circ\)

From the attached diagram, we can see that Angles ACE and ECB are supplementary angles by the linear postulate.

Therefore:

\(\angle ACE +\angle ECB=180^\circ\\(2x+2)^\circ+(5x+3)^\circ=180^\circ\\2x+5x+2+3=180\\7x+5=180\\7x=175\\$Divide both sides by 7\\x=25\)

The correct answer is B.

Answer:

B. 25

Step-by-step explanation: This is the correct answer on Edge 2021, just took the quiz. Hope this helps ^-^.

R6500 in the ratio of 3:4:6 is equal to R1,500, R2,000 and R3,000.

Given the following data:

To divide R6500 in the ratio of 3:4:6​:

In this exercise, you're required to divide the total amount of money in the ratio of 3:4:6. Thus, we would solve as follows:

For a ratio of 3:

\(Amount=\frac{3}{13} \times 6500\\\\Amount=\frac{19500}{13}\)

Amount = R1,500.

For a ratio of 4:

\(Amount=\frac{4}{13} \times 6500\\\\Amount=\frac{26000}{13}\)

Amount = R2,000.

For a ratio of 6:

\(Amount=\frac{6}{13} \times 6500\\\\Amount=\frac{39000}{13}\)

Amount = R3,000.

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Answer:747/1000

Step-by-step explanation:

Answer:

747/1000

Step-by-step explanation:

Answer

Option 1 is correct.

The graph could easily be the graph of a linear function.

Explanation

The points (2, 5) and (8, 5) can be seen to lie on the same line of y = 5

So, we can conclude that the graph could be a simple linear function, or a curve that passes this point twice.

So, option A is the only correct option here.

Hope this Helps!!!

Answer:

72.00 =105.6

Step-by-step explanation:

i searched it up