7
What is the solution to the inequality
below?
5x-10 ≥-3x + 14
A. x ≥-3
B. x≤-3
C. x ≥ 3
D. x ≤ 3

The critical path analysis reveals that the critical path consists of the following activities: 1-3-4-5-7. The total duration of the critical path is 15 and 2/6 units of time.

Critical path analysis is a project management technique used to determine the longest path of activities in a project schedule. It helps identify the sequence of activities that have the most significant impact on the overall project duration.
The given information provides the durations of various activities and their dependencies. By analyzing the information, we can determine the critical path.
Based on the given durations, the critical path consists of the activities 1-3-4-5-7. These activities have a total duration of 15 and 2/6 units of time.
To calculate the critical path duration, we add up the durations of the activities on the critical path. In this case, the durations are as follows: Activity 1-3 takes 2 and 1/6 units, activity 3-4 takes 1 and 2/6 units, activity 4-5 takes 4 and 4/6 units, and activity 5-7 takes 5 and 1/6 units. Summing these durations gives a total of 15 and 2/6 units.
The critical path represents the sequence of activities that must be completed within their estimated durations to ensure the project is completed in the shortest possible time. Any delay in activities along the critical path will directly impact the overall project duration.

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The mean, variance, and standard deviation of the distribution are respectively 33.8, 27.433, and 5.238 words.

The number of beans in some cocoa pond are 30, 28, 30, 35, 40, 25, 32, 36, 38 and 40. We need to calculate the mean, variance, and standard deviation of the distribution.

Mean: The sum of all numbers divided by the number of elements is called the mean.

Here n=10

Now we calculate the variance of the given data set

Variance: The variance is the average of the squared deviations from the mean.

Here n=10

Now we can find the standard deviation of the given data set

Standard deviation:

The square root of the variance is called the standard deviation.

Now n=10, So, the formula for the standard deviation is;

Therefore, the mean, variance, and standard deviation of the distribution are respectively 33.8, 27.433, and 5.238 words.

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Answer:

1. Chloe has more money.

2. Dylan does not have enough money to buy 3 bags of candy.

3. Mikayla could get 4 pennies, 2 nickels, 2 dimes, and 2 quarters back in change.

Step-by-step explanation:

Penny = 1 cent

Nickel = 5 cents

Dime = 10 cents

Quarter = 25 cents

1. Chloe has 2 quarters(50 cents) and 3 dimes(30 cents). 50 + 30 = 80 cents

Haru has 5 nickels(25 cents) and 4 dimes(40 cents). 25 + 40 = 65 cents

2. If each bag costs $350(oddly enough). Dylan would need $1,050 to buy 3 bags of candy. Instead he only has $10. This means he would need $1,040 more dollars.

3. $5 - 4.16 = 84 cents in return

quarter(25) + quarter(25) + dime(10) + dime(10) + nickel(5) + nickel(5) + penny(1) + penny(1) + penny(1) + penny(1) = 84 cents

By secant line formula, the slopes corresponding to the lines are listed below:

In this problem we have nine representations of lines, whose slopes must be determined. A line is represented by equations of the form:

y = m · x + b

Where:

According to analytic geometry, slope can be found by knowning the location of two points (initial, final) set on Cartesian plane and secant line formula:

m = (y₂ - y₁) / (x₂ - x₁)

Where:

Case 1: (x₁, y₁) = (0, - 3), (x₂, y₂) = (2, 1)

m = (2 - 0) / [1 - (- 3)]

m = 2 / 4

m = 1 / 2

Case 2: (x₁, y₁) = (- 3, 2), (x₂, y₂) = (1, - 3)

m = (- 3 - 2) / [1 - (- 3)]

m = - 5 / 4

Case 3: (x₁, y₁) = (- 3, - 4), (x₂, y₂) = (2, 3)

m = [3 - (- 4)] / [2 - (- 3)]

m = 7 / 5

Case 4: (x₁, y₁) = (0, 3), (x₂, y₂) = (3, - 3)

m = (- 3 - 3) / (3 - 0)

m = - 6 / 3

m = - 2

Case 5: (x₁, y₁) = (- 2, 1), (x₂, y₂) = (3, 2)

m = (2 - 1) / [3 - (- 2)]

m = 1 / 5

Case 6: (x₁, y₁) = (- 4, 3), (x₂, y₂) = (4, 1)

m = (1 - 3) / [4 - (- 4)]

m = - 2 / 8

m = - 1 / 4

Case 7: (x₁, y₁) = (2, - 4), (x₂, y₂) = (4, 2)

m = [2 - (- 4)] / (4 - 2)

m = 6 / 2

m = 3

Case 8: (x₁, y₁) = (- 4, - 1), (x₂, y₂) = (0, - 3)

m = [- 3 - (- 1)] / [0 - (- 4)]

m = - 2 / 4

m = - 1 / 2

Case 9: (x₁, y₁) = (- 2, 0), (x₂, y₂) = (4, 1)

m = (1 - 0) / [4 - (- 2)]

m = 1 / 6

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The inequality expression for the number of years when tree will be atleast 20 feets tall is x ≥14

The height of the tree after x years can be represented as a linear equation thus :

Number of years when the tree will be 20 feets tall :

The tree would be atleast 20 feets tall in 14 years x this can be expressed thus

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A small number of individuals could cause a widespread distribution of the disease.

A researcher applying Watts's mathematical models to study the transmission of an airborne contagious disease can most reasonably assume that:

1. The disease transmission follows a network-based spread pattern.

In Watts's mathematical models, the focus is on network structures and the dynamics of spreading phenomena. Therefore, the researcher can reasonably assume that the transmission of the airborne contagious disease is influenced by the connections and interactions within a network. This implies that individuals are not randomly interacting but are part of a network where the disease can propagate along the links.

The spread of the disease is influenced by the characteristics of the network.

Watts's models highlight the importance of the network structure in determining the spread of contagion. Therefore, the researcher can reasonably assume that factors such as network connectivity, node centrality, clustering, and other network properties significantly influence the transmission dynamics of the airborne contagious disease. These characteristics can affect the speed, reach, and severity of the disease's spread within the network.

By considering these assumptions, the researcher can utilize Watts's mathematical models to gain insights into how an airborne contagious disease might spread through a network and inform strategies for disease control and prevention.

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Answer:

the most accurate argument is (C) The transportation and brokerage costs that Suriland's farmers would face if they sold their wheat outside Suriland could amount to almost a dollar per bushel.

Step-by-step explanation:

The cost of transportation and other logistics is being covered by the government that is why the government pay less than dollar per bushel.

so the price of the wheat would have to decrease at home so that the cost of the transportation can be covered by the government who are buying directly from the farmers.

Answer:

5 units

Step-by-step explanation:

The area of a sector is \(A=\frac{r^2\theta}{2}\) where \(r\) is the radius and \(\theta\) is the angle formed:

\(A=\frac{r^2\theta}{2}\\\\\frac{75\pi}{16} =\frac{r^2(\frac{3\pi}{8})}{2}\\\\150\pi=16r^2(\frac{3\pi}{8})\\\\150\pi=6\pi r^2\\\\25=r^2\\\\5=r\)

Therefore, the radius of the sector is 5 units

Answer:

4y - 8x = 24

Step-by-step explanation:

4y -8x = 24  Add 8x to both sides

4y = 8x + 24  Divide both sides by 4

y = 2x + 6  

This slope is 2 which would great a line parallel to y = 2x + 9

Desmos is a free program that can help you graph.  See the picture below.  You just type in the equation and it graphs it for you.  Cool

Answer:

1734.85

Step-by-step explanation:

Answer:

the correct answer is 1,734.85cm2

Step-by-step explanation:

i did the assignment and got it right

Answer:

The shadow cast by the tree is 80 meters long.

Step-by-step explanation:

Flagpole:

object/shadow

25/50 = 1/2

Tree:

object/shadow

40/x

Solve for x:

1/2 = 40/x

x = 80

The two planes will meet 6 hours after they start, i.e. at 3 pm.

Two planes leave at 9 am from airports that are 2700 miles apart and fly towards each other at a speed of 200 mph and 250 mph. At what time will they pass each other?

Let's assume the planes A and B leave the two airports that are 2700 miles apart at the same time. The speed of the first plane is 200 mph and the speed of the second plane is 250 mph. To find out the time at which they pass each other, we need to calculate the distance between them and divide it by the sum of their speeds.

Distance traveled by the first plane in time t1 is equal to 200t1.Distance traveled by the second plane in time t2 is equal to 250t2.The distance covered by the first plane and the second plane together will be 2700 miles.Time taken by both the planes to meet can be calculated as below:

t1 + t2 = 2700/(200+250) = 6 hoursAs both the planes start at 9 am, they will meet each other after 6 hours of their journey. Therefore, they will pass each other at 3 pm. This is the required answer. Explanation: So, the two planes will meet 6 hours after they start, i.e. at 3 pm.

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The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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The Garden B has 76.47% more data than Garden A.

Percentage is a way of expressing a number as a fraction of 100. It is a commonly used method to represent proportions, rates, and percentages in various fields such as finance, economics, and statistics.

Let's first find the actual values of Garden A's and Garden B's data:

For Garden A, we know that 75% of its data is equal to 12.75. We can use this information to set up an equation:

0.75x = 12.75

Solving for x, we get:

x = 12.75 / 0.75 = 17

Therefore, Garden A's total data is 17.

For Garden B, we know that 50% of its data is equal to 15. We can use this information to set up an equation:

0.5x = 15

Solving for x, we get:

x = 15 / 0.5 = 30

Therefore, Garden B's total data is 30.

Now, to find how much more percent Garden B has than Garden A, we can use the formula:

percent difference = |(Garden B - Garden A) / Garden A| * 100

Plugging in the values, we get:

percent difference = |(30 - 17) / 17| * 100 = 76.47%

Therefore, Garden B has 76.47% more data than Garden A.

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The distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

To find the distance between successive fourth roots of a complex number on the unit circle, we can use the concept of the angle between the roots. Let's proceed step by step:

The given complex number is √3/2 - 1/2i. This complex number lies on the unit circle because its magnitude is equal to 1.

1. Convert the given complex number to trigonometric form:

  √3/2 - 1/2i = cos(θ) + i*sin(θ)

  By comparing the real and imaginary parts, we can determine the angle θ:

  cos(θ) = √3/2

  sin(θ) = -1/2

  Using the unit circle, we can find that θ = 5π/6 (or 150 degrees). This angle represents the position of the given complex number on the unit circle.

2. Find the angle between successive fourth roots:

  Since we are interested in the fourth roots, we divide the angle θ by 4:

  θ/4 = (5π/6) / 4 = 5π/24

  This angle represents the angular distance between two successive fourth roots on the unit circle.

3. Calculate the distance between the two points:

  To find the distance, we multiply the angular distance by the radius of the unit circle (which is 1):

  Distance = (5π/24) * 1 = 5π/24

  Therefore, the distance between successive fourth roots of the complex number √3/2 - 1/2i on the unit circle is 5π/24 units.

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From the situation described in the problem, we have that:

a) The sinusoidal function that models the depth of the water is given by: D(t) = 2sin(π/6x) + 3.

b) After 4 hours, the depth is of 4.732 meters.

The sine function is defined as follows:

g(x) = a sin(bx+c)+d.

The coefficients are defined as follows:

For this problem, the minimum value is of 1 and the maximum value is of 5, having a difference of 4, hence the amplitude is found as follows:

2a = 4 -> a = 2.

A standard sine function with an amplitude of 2 varies between -2 and 2, while this varies between 1 and 5, meaning that it had a vertical shift up 3 units, and d = 3.

The period is of 12 hours, hence:

2π/B = 12

12B = 2π

B = π/6.

The function has no phase shift, hence c = 0 and the function is given by:

D(t) = 2sin(π/6x) + 3.

From point (4, 4.732) on the graph of the function, after 4 hours, the depth is of 4.732 meters.

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Answer:

x<2

Step-by-step explanation:

x- 2 <0

x < 2

Answer:

\(0<x<2\)

Step-by-step explanation:

Hi there!

\(x(x-2)<0\)

Set x(x-2) equal to 0:

\(x(x-2)=0\)

Solve for x by using the zero product property:

\(x(x-2)=0\)

\(x=0\) and \(x=2\)

Now, we know that for the inequality \(x(x-2)<0\), one of the following must be true:

1) \(0<x<2\)

2) \(x<0\) or \(x>2\)

To find out which one it is, 1) or 2), we can substitute a value into \(x(x-2)<0\) to see if the inequality is true.

For example, 1 takes place in between 0 and 2. If 1 satisfies \(x(x-2)<0\), then \(0<x<2\) must be true. If it does not, then \(x<0\) or \(x>2\) must be true:

\(1(1-2)<0\\1(-1)<0\\-1<0\)

This inequality is true. Thus, \(0<x<2\).

I hope this helps!

Answer:

b

Step-by-step explanation:

you have to rotate it 180 degrees clockwise to find the transition.

Answer:

\(x=65\)

Step-by-step explanation:

Area of a triangle is always 180 degrees...

In this triangle we have two values given, lets make an equation & solve it:

\(x+68+47=180\)

\(x+115=180\)

\(x=180-115\)

\(x=65\)

To check if you have the right answer, add all the angles to get 180:

\(68+47+65=180\)

Therefore, x = 65

I hope this help :)

\(\huge\bold{Given :}\)

Angle ABC = \(x\)

Angle BAC = 68°

Angle BCA = 47°

\(\huge\bold{To\:find :}\)

The measure of angle ABC \(''x"\).

\(\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}\)

\(\longrightarrow{\green{x\:=\:65°}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

We know that,

\(\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}\)

➪ ∠ ABC + ∠ BAC + ∠ BCA = 180°

➪ \(x\) + 68° + 47° = 180°

➪ \(x\) + 115° = 180°

➪ \(x\) = 180° - 115°

➪ \(x\) = 65°

Therefore, the measure of ∠ ABC is 65°.

Hence, the three angles of the triangle are 65°, 68° and 47° respectively.

\(\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}\)

∠ ABC + ∠ BAC + ∠ BCA = 180°

✒ 65° + 68° + 47° = 180°

✒ 180° = 180°

✒ L. H. S. = R. H. S.

\(\boxed{Hence\:verified.}\)

(Note:- Kindly refer to the attached file.)

\(\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}\)

The equation of the line that contains the points (-11,7) and (-9,-5) is

y = -6x - 59.

To find the equation of a line that contains the given pair of points (-11,7) and (-9,-5), we can use the slope-intercept form of a linear equation,

y = mx + b, where m represents the slope of the line and b represents the y-intercept.

First, let's calculate the slope (m) using the formula: \(m=\frac{y_2-y_1}{x_2-x_1}\).

Substituting the values, we have: m = (-5 - 7) / (-9 - (-11)) = -12 / 2 = -6.

Now, we can choose one of the given points (let's use (-11,7)) and substitute it into the equation y = mx + b to solve for b.

Substituting the values, we get: 7 = -6(-11) + b.

Simplifying the equation, we have: 7 = 66 + b.

Solving for b, we get: b = -59.

Therefore, the equation of the line in slope-intercept form is: y = -6x - 59.

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Answer:

No

Step-by-step explanation:

x=(b-5)/c≠(5-b)/c

supposedly

b=6

c=1

x=6-5/1=1

x=5-6/1= -1

1≠ -1

Answer:

No

Step-by-step explanation:

x = b - 5 / L equal to - (5 - b) / L

Answer:

A

Step-by-step explanation:

geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. Option b is the geometric sequence with the common ratio of 2

Using laws of exponents, the expression is simplified to get: ²⁵/₆a⁹b¹⁰

Some of the laws of exponents are:

- When multiplying by like bases, keep the same bases and add exponents.

- When raising a base to a power of another, keep the same base and multiply by the exponent.

- If dividing by equal bases, keep the same base and subtract the denominator exponent from the numerator exponent.  

The expression we want to solve is given as:

(5ab)³/(30a⁻⁶b⁻⁷)

Using laws of exponents, the bracket is simplified to get:

¹²⁵/₃₀(a³b³ * a⁶b⁷)

This simplifies to get:

²⁵/₆a⁹b¹⁰

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The plane will reach an altitude of 21,000 feet approximately 29.2 minutes after lift off. Rounded to the nearest whole minute, the plane will be at an altitude of 21,000 feet 37 minutes after lift off.

To determine the number of minutes after lift off when the plane reaches an altitude of 21,000 feet, we need to solve the equation a = 21,000, where "a" represents the altitude in feet. By substituting the altitude value into the equation and solving for the variable, we can find the number of minutes.

The given equation represents the altitude "a" of the plane in feet, given by a = 3480 + 600t, where "t" represents the time in minutes after lift off. We need to find the number of minutes when the plane is at an altitude of 21,000 feet.

By substituting a = 21,000 into the equation, we have:

21,000 = 3480 + 600t

To isolate "t," we subtract 3480 from both sides:

21,000 - 3480 = 600t

Simplifying, we get:

17,520 = 600t

Dividing both sides by 600, we find:

t = 29.2

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Answer:

\(x^{2} < 1\)

Step-by-step explanation:

Answer:

\(x\) \(\leq\) 3

Step-by-step explanation:

Answerx

 x≤3

Step-by-step explanation:

2.(-3x-5) \(\geq\)-28

⇔-3x-5≥-1

⇔-3x≥-9

The division of 14 by 29 will gives 14/29 in reduced fractions

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the number is divided.

WE need to divide the number 14 by 29 to find the fraction form first.

14 divided by 29 means 14 ÷ 29

Therefore, 14/29 in reduced fractions

14/29 = 0.482758620 in decimal

Hence, The division of 14 by 29 will gives 14/29 in reduced fractions

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The complete question is;

Find 14 divided by 29. Input your answer as a reduced fraction.

Answer:

Step-by-step explanation:

Givens

Let the first piece be x

Let the second piece 4x

Let the third piece = 5x

Total length = 40 inches.

Equation

x + 4x + 5x = 40                Combine

Solution

10x = 40                             Divide by 10

10x/10 = 40/10        

x = 4

Answer

The smallest piece (x) = 4

The middle piece 4x  = 4*4 = 16

The largest piece 5x= 5 * 4 = 20

Answer:

the volume of the prism is 60 cubic meters (m³).

Step-by-step explanation:

We can calculate the volume of the rectangular prism by multiplying its length, width, and height.

Given:

Length = 3 m

Width = 4 m

Height = 5 m

The volume of the rectangular prism is:

Volume = length x width x height

Volume = 3 m x 4 m x 5 m

Volume = 60 m³

Therefore, the volume of the prism is 60 cubic meters (m³).