Put the following equation of a line into slope-intercept form, simplifying all fractions.
2x+4y=-20

all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

We can obtain the autonomous differential equation having all of the given properties as shown below:First of all, let's determine the equilibrium solutions:dy/dx = 0 at y = 0 and y = 3y' > 0 for 0 < y < 3For -∞ < y < 0 and 3 < y < ∞, dy/dx < 0This means y = 0 and y = 3 are stable equilibrium solutions. Let's take two constants a and b.a > 0, b > 0 (these are constants)An autonomous differential equation should have the following form:dy/dx = f(y)To get the desired properties, we can write the differential equation as shown below:dy/dx = a (y - 3) (y) (y - b)If y < 0, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If 0 < y < 3, y - 3 < 0, y - b < 0, and y > b. Therefore, all the three terms on the right-hand side are negative and hence dy/dx is positive.If y > 3, y - 3 > 0, y - b > 0, and y > b. Therefore, all the three terms on the right-hand side are positive and hence dy/dx is negative. Thus, this satisfies all the properties given. Therefore, the required autonomous differential equation is:dy/dx = a (y - 3) (y) (y - b).

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There is no success probability for which the first success is most likely to occur on the fourth attempt.

Assuming the success probability of an experiment is p and the number of trials until the first success occurs is denoted by X, X follows a geometric distribution with the probability mass function P(X=k) = (1-p)^(k-1) * p, where k is the number of trials until the first success occurs.

Given that the first success occurs on the 4th attempt, P(X=4) is maximum when p is maximum. To find the value of p, we need to maximize the function P(X=4), which can be represented by (1 - p)^(3) * p.

Differentiating this function with respect to p, we get d[P(X=4)]/dp = -3(1 - p)^(2) * p + (1 - p)^(3).

Equating the above equation to zero, we get -3(1 - p)^(2) * p + (1 - p)^(3) = 0, which further leads to (1 - p)^(2)[(1 - p) + 3p] = 0 and (1 - p)^(2)(1 + 2p) = 0.

Since (1 - p)^(2) > 0, the solution is given by: 1 + 2p = 0, which results in p = -1/2.

However, the probability of success cannot be negative. Therefore, p cannot be equal to -1/2. Hence, there is no success probability for which the first success is most likely to occur on the fourth attempt.

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Answer:33.41

Step-by-step explanation:

Answer:

33.41

Step-by-step explanation:

easiest way to do this is start by adding 21 and 12 which is 33

and the next and final step is to add .41 and 0 which is .41 and then you just add .41 to 33 which is 33.41 which is your answer

21 + 12 = 33

.41 + 0 = .41

33 + .41 = 33.41

hope this helps

Expected Value (E(x)):

E(x) = Σ(x * P(x))

E(x) = 1.20 + 4.00 + 3.00

E(x) = 8.20

Variance:

Variance = Σ([x - E(x)]^2 * P(x))

Variance = ([6 - 8.20]^2 * 0.20) + ([8 - 8.20]^2 * 0.50) + ([10 - 8.20]^2 * 0.30)

Variance = (4.84 * 0.20) + (0.04 * 0.50) + (1.96 * 0.30)

Variance = 0.968 + 0.020 + 0.588

Variance = 1.576

Standard Deviation:

Standard Deviation = √Variance

Standard Deviation = √1.576

Standard Deviation ≈ 1.25

Therefore, the calculations for the given discrete probability distribution are as follows:

Expected Value (E(x)) = 8.20

Variance = 1.576

Standard Deviation ≈ 1.25

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\(\longrightarrow\) This problem can be tackled by using distributive property of multiplication .

It states for any three numbers a,b and c

\(\green{ \underline { \boxed{ \sf{(a±b)\times c = a \times c±b\times c}}}}\)

Similarly,

\(\quad\)23 × 45

\(\longrightarrow\)(21+2) ×45

\(\longrightarrow\)21×45+2×45

\(\longrightarrow\)945 + 90

\(\longrightarrow\) 1035

It can also be done as-

\(\quad\)23 × 45

\(\longrightarrow\)(25-2) ×45

\(\longrightarrow\)25×45-2×45

\(\longrightarrow\)1125-90

\(\longrightarrow\) 1035

The radius of the circle with circumference 112\(\pi\) cm is given by 56 centimeters.

We know that the circumference of a circle with radius r is given by,

C = 2\(\pi\)r

Let the radius of the circle be r cm.

So the circumference of the circle is 2\(\pi\)r cm.

According to the question, the circumference is 112\(\pi\) cm. So,

2\(\pi\)r = 112\(\pi\)

2r = 112

r = 112/2

r = 56

Hence the radius of the circle is 56 centimeters.

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The number of miles for same rental costs are 300 miles.

Let the number of miles be x.

Firstly calculating the cost of Company a -

Total cost = One day cost + Number of miles × Cost per mile

Total cost = 110 + 0.70x

Calculating the cost of Company b -

Total cost = One day cost + Number of miles × Cost per mile

Total cost = 80 + 0.80x

Now, for the same rental cost, we will equate the two expressions. This will calculate the value of x.

110 + 0.70x = 80 + 0.80x

Rearranging the expression -

110 - 80 = 0.80x - 0.70x

Performing subtraction

30 = 0.10x

Shifting the values on other side of equation

x = 30/0.10

Performing division

x = 300

Hence, the rental cost for both companies will be same for 300 miles.

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Answer:

9996

Step-by-step explanation:

8. To find horsepower, all units need to be converted to the same units.Then, 1 hp = 745.7 watts1 Btu/hr = 0.293 watt500 ft-lbf/sec = 1.35581795 kW5,000 kJ/s = 5,000 kWSo, converting each to kW, we have:5,000 kW - 1.3558 kW - 12.4 x 0.293 kW = 4,631.44 kWNow convert this to hp. 4,631.44 kW = 4,631.44 / 745.7 hp = 6.21 hp to 3 significant figures. Therefore, the answer to the given problem is 6.21 hp to 3 significant figures.

9. we need to calculate the sum of all the given numbers and find the value to the correct significant digits.6.7832 + 1.234 + (2.8723 * 2.3) - 0.97268= 6.7832 + 1.234 + 6.61329 - 0.97268= 13.65881The given numbers have four significant figures (the ones with decimals), so the answer should also have four significant figures. Therefore, the value of the given expression to the correct significant digits is 13.66.10. Stefan-Boltzmann constant expressed in terms of cal/week.ft.mile. K².R².The Stefan-Boltzmann constant, also known as the Stefan constant, is given as σ = 5.670373(21) x 10^-8 W/(m²K^4).Here, the units are in watts per meter squared Kelvin to the fourth power.1 watt = 0.239006 calories/second 1 meter = 3.28084 feet1 week = 604800 seconds1 mile = 5280 feet1 R (Rankine temperature scale) = 1.8 K = 1.8°CThus, σ = 5.670373(21) x 10^-8 W/(m²K^4) can be written as:σ = (5.670373(21) x 10^-8 W)/(m²K^4) × 0.239006 cal/(s·W) × 604800 s/week × (ft/m)^2 × (mi/5280 ft)^2 × (°R/K)^4σ = 0.177134 cal/week·ft^2·mi·K^4·°R^4Hence, the Stefan-Boltzmann constant can be expressed in terms of cal/week·ft^2·mi·K^4·°R^4.

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For any value of inequality for t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

What is inequality?

In mathematics, an inequality is a statement that compares two quantities using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).

Let's start by calculating the total number of calories burned in each routine as a function of the number of minutes spent running:

Routine #1:

Total calories burned = 24 + 15.5t

Routine #2:

Total calories burned = 52 + 9.9t

To find the point where Routine #1 burns at most as many calories as Routine #2, we need to solve the inequality:

24 + 15.5t ≤ 52 + 9.9t

Simplifying this inequality, we get:

5.6t ≤ 28

Dividing both sides by 5.6, we get:

t ≤ 5

Therefore, for any value of t less than or equal to 5 minutes, Routine #1 will burn at most as many calories as Routine #2.

So the answer is: t ≤ 5.

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Answer:

The minimum number of faces a polyhedron can have is 4 faces.

Step-by-step explanation:

We know that a polyhedron is a shape surrounded by polygons. We also know that we need at least 3 sides to make a polygon. So, at the minimum a polyhedron can be made by using only triangular faces but in order to make a closed figure we need at least four triangular faces (which is a tetrahedron).

Answer:

Step-by-step explanation:

492

The  function that models y in terms of x is y=0.804x

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

m=4.02-0/5-0

m=4.02/5 = 0.804

Now let us find y intercept

0=0.804(0)+b

b=0

Hence, the  function that models y in terms of x is y=0.804x

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If a clock shows the hour hand between 6 and 7 and the minute hand at 10. It means : D.50 minutes after 6, E. 6:50

Each of the section time of an analog clock is 5 minutes. Since the hour hand is between 6 and 7 and the minute hand is on 10 ,  it implies that :

5 minutes × 10 minutes

= 50 minutes after 6

Or

6: 50minutes

Therefore the correct option is D and E.

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a) The domain of the function f(x, y) = 6x²yT¹-4y² is determined by the condition T¹-4y² ≥ 0. The domain can be expressed as -√(T¹/4) ≤ y ≤ √(T¹/4). A sketch of the function requires more information about T¹ and any constraints on x.

b) To find the limit of the function as (x, y) approaches (0, 0), we substitute the values into the function and find that f(0, 0) = 0. However, to determine the existence of the limit, further analysis along different paths approaching (0, 0) is required. Without additional information, we cannot conclusively determine the limit.

a) To find the domain of the function f(x, y) = 6x²yT¹-4y², we need to determine the values of x and y for which the function is defined.

From the given function, we can see that the only restriction is on the term T¹-4y², which implies that the function is undefined when the expression T¹-4y² is negative, as we can't take the square root of a negative number.

Setting T¹-4y² ≥ 0, we solve for y:

T¹-4y² ≥ 0

4y² ≤ T¹

y² ≤ T¹/4

Taking the square root of both sides, we get:

|y| ≤ √(T¹/4)

So the domain of the function f(x, y) is given by:

Domain: -√(T¹/4) ≤ y ≤ √(T¹/4)

To provide a sketch, we would need additional information about the value of T¹ and any other constraints on x. Without that information, it's not possible to accurately sketch the function.

b) To find the limit of the function lim(x,y) → (0,0) f(x, y), we need to evaluate the function as the variables x and y approach zero.

Substituting x = 0 and y = 0 into the function f(x, y), we get:

f(0, 0) = 6(0)²(0)T¹-4(0)² = 0

The function evaluates to zero at (0, 0), which suggests that the limit might exist. However, to determine if the limit exists, we need to analyze the behavior of the function as we approach (0, 0) from different directions.

By examining various paths approaching (0, 0), if we find that the function f(x, y) approaches different values or diverges, then the limit does not exist.

Without further information or constraints on the function, we cannot definitively determine the limit. Additional analysis of the behavior of the function along different paths approaching (0, 0) would be required.

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The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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The main conclusion that Keisha can make is that m is equal to 7 based on the given information.

Based on the given information, Keisha's teacher tells her that p is equal to 0 and that A is equal to m while B is equal to 7. We can infer that m is equal to 7 since A is equal to m. Additionally, the information given about p being equal to 0 is irrelevant to the conclusion that Keisha can make.

Therefore, the conclusion that Keisha can make is that m is equal to 7.
To summarize:
- p = 0
- A = m
- B = 7

From this, we can conclude that m = 7.
In this case, we don't need to use the values of n and q, since the conclusion can be made solely based on the given values of p, A, and B.


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Answer:

25X48=1200 buttons in all

1200 divided by 15 = 80

She needs to buy 80 bags which totals 1200 buttons

Step-by-step explanation:

By definitions of line segment and midpoint, we find that \(\overline{TU} \cong \overline {UV}\).

In this problem we find a line segments partitioned in four parts by using midpoints, each of them are listed below:

A point within a line segment is a midpoint if and only if it partitions the line segment into two parts of equal length. If point U is the midpoint of line segment SW, then SU = UW. If point T is the midpoint of SU, then ST = TU and if point V is the midpoint of UW, then UV = VW. Finally, we get the following result by algebraic handling:

SU = UW

ST + TU = UV + VW

2 · TU = 2 · UV

TU = UV

\(\overline{TU} \cong \overline {UV}\)

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Answer:

Step-by-step explanation:

y = a(x - p)² + q  - the vertex form of an equation of a parabola with a vertex (p, q)

(-2, 5)  ⇒  p = -2,   q = 5

y = a(x + 2)² + 5   - the vertex form of an equation of the parabola with vertex (-2, 5)

y-intercept of -27 means x=0,  y=-27

-27 = a(0 + 2)² + 5

-27 -5 = a(2)² + 5 -5

-32 = 4a

  a = -8

The equation of the parabola in vertex form that has a vertex (-2, 5) and y-intercept of -27:

                              f(x) = -8(x + 2)² + 5

The correct alternative hypothesis is H1: pL> pH.

We test whether the proportion of children in the low-income group who drew the nickel too large is greater than the proportion of children in the high-income group who drew the nickel too large.

Proportion of children in the low-income group (denoted pL) who also drew a nickel. large is greater than the proportion of the high-income group (indicated by pH) that attracted nickel too large, we test at the 0.1 significance level.

a) First, we need to identify the correct alternative hypothesis. The alternative hypothesis in this case should be:

H1: PL > pH

This hypothesis states that the proportion of children in the low-income group who drew oversized nickels would be greater than the proportion of children in the high-incomegroup who drew oversized nickels.

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Answer:

17

Step-by-step explanation:

Well you have to get x by itself so....

subtract 8 from both sides

25 -8 = 17 there is your answer

Hey there!

x + 8 = 25

SUBTRACT 8 to BOTH SIDES

x + 8 - 8 = 25 - 8

SIMPLIFY IT!

x = 25 - 8

x = 17

Therefore, the answer should be: x = 17

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 49.5 dollars

Step-by-step explanation: the original price is 330, but the sale takes 15 percent off

so we turn 15% into a decimal so we can multiply 330 and 15%

we get 0.15 × 330 = 49.5

Answer:

B=100

Step-by-step explanation:

The given circle is

Consider the triangle AOB, Using the triangle sum property, we get

AOB+AOB+BOA=180

Substitute ABO=55 and BAO=45 we get

AOB+55+45=180

AOB+100=180

AOB+100-100=180-100

AOB=80

Here AOB and AOC are supplementary angles

The sum of the supplementary angles is 180 degrees.

AOB+AOC=180

Substitute AOB=80 we get

80+AOC=180

80+ AOC-80=180-80

AOC=100

Now consider the Central angle AOC  and intercepted arc AC.

mAOC=mAC

Substitute m AOC=100 and mAC=b we get

100=b

Hence the value of b is 100 degrees.

Answer:

Step-by-step explanation:Price per pound of strawberries is $-0.31635 and blueberries is $0.6836.

Explanation :

Given data ;

Weight of strawberries required for dessert = 212 lb

Weight of blueberries required for dessert = 112 lb

Total cost spent = $9.50

Let,

Cost of blueberries per pound =x

Cost of strawberries per pound = (x-1)

We know that,

Cost of blueberries for overall weight + Cost of strawberries for overall weight = Total cost spent on fruits.

x(112) + (x-1)212 = 9.50

112x + 212x – 212 = 9.50

324x = 221.5

X = 221.5/324

X = $0.6836

So, (x-1) = $-0.31635

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Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

Given that ;

Ben is making a dessert that requires 212 lbs of strawberries and 112 lbs of blueberries. Strawberries cost $1 less per pound than blueberries. Ben spent a total of $9.50 on the fruit.

So according to the question get the price per pound of each type of fruit;

Let ' x ' be the price per pound of strawberries and ' y ' be the price per pound of blueberries.

By assuming the following equations;

212x - 112y = 1 → ( I )

212x + 112y = 9.5 → ( II )

By solving above equations ( I ) ( II ) we get;

424x = 10.5

      x = 10.5/424

      x = 0.02476

224y = 8.5

      y = 8.5/224

      y = 0.03794

Price per pound of strawberries is $0.02476 and the price per pound of blueberries is $0.03794

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Answer:

x=15

Step-by-step explanation:

5x+17+36=128

5x+53=128

5x=75

x=15

Answer:

x-intercept is also known as y=0

Answer:

The answer is 43.52 you're welcome