activity b has a duration of 12 days and an earliest finish (ef) of 22 days. if b's latest start (ls) is 15 days, this must mean that b's slack (in days) is

Answer:

Option B is the best way to write the underlined parts of sentences 2 and 3.

Sentence 2: They have a special finish that helps.

Sentence 3: The finish helps the swimmer glide through the water.

Option B provides a clear and concise way to connect the two sentences and convey the idea that the special finish of the swimsuits helps the swimmer glide through the water. It avoids any ambiguity or redundancy in the language.

The Converse of the Angle Bisector Theorem states that if a point is in the same plane as an angle and divides the angle into two congruent angles, then it lies on the angle's bisector.

The fact that the converse states that the point must be in the same plane as the angle implies that if the point is not in the same plane as the angle, then it cannot divide the angle into two congruent angles, and thus cannot lie on the angle's bisector.

The Angle Bisector Theorem states that if a ray bisects an angle of a triangle, then it divides the opposite side into segments that are proportional to the other two sides of the triangle. The converse of this theorem states that if a point on the interior of a triangle divides one side of the triangle into two segments that are proportional to the other two sides, then the point lies on the bisector of the angle opposite the divided side.

To understand why this implies that the point must be in the same plane as the angle, we need to consider the definition of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions.

It is determined by any three non-collinear points in space. In the context of a triangle, the three vertices of the triangle are non-collinear points that determine a plane.

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Answer:

$40y - $3g

Step-by-step explanation:

it wouldn't be c because the 3 and 40 are on the wrong side. and it wouldn't be a because the y and g are on the wrong number. you should realise that the variables y and g need to go to the corresponding amount and $40 is how much she get by mowing lawns (y) and $3 is how much gasoline costs to take away from her total amount. so its now between b and d. it is d because you are subtracting 3 from 40 because that how much she spent and it takes away from her total.

Option D : $40y − $3g  is correct.

We have the following information about Alicia -

For every yard she mows, she earns $40

She spends part of this money on gasoline which costs $3

We have to find expression for the amount of money that Alicia earns in a day.

An equation of the form ax + by + c=0, where a, b are the coefficients of x and y and are non -zero and all a, b, and c are real in nature.

Let the amount of money she earns in a day = x

Number of yards she mows in a day = y

Money earned on mowing ' y ' yards in a day = $40 y

Number of gallons of gasoline she buys = g

Amount spent in gasoline in a day = $3 g

Total money earned  = Money earned - money spent on gasoline

x = $40y - $3g

Hence, Option D is correct

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Answer:

(4.6, 4)

Step-by-step explanation:

Given the coordinates (3,2) and (7, 7) partitioned between 3:2

M(X,Y) = [(ax1+bx2/a+b, ay1+by2/a+b)]

X = 3(3)+2(7)/3+2

X = 9+14/5

X = 23/5

X = 4.6

Similarly;

Y = 3(2) + 2(7)/3+2

Y = 6+14/5

Y = 20/5

Y = 4

Hence the required coordinate is (4.6, 4)

The sum of the first 7 terms of the following series is 52

'A geometric sequence is a sequence where every term has a constant ratio to its preceding term. A geometric sequence with the first term a and the common ratio r and has a finite number of terms.'

According to the given problem,

Sequence = 32,40,50

Let the common ratio be r,

Let the first term of the sequence be a,

⇒ a × r = second term

⇒ 32 × r = 40

⇒ r = 40/32

⇒ r = 5/4

We know,

Sum of n number of terms in a geometric sequence can be represented by,

sn=a(1-\(r^{7}\))/1-r

⇒ \(s_{7}\) =32(1 - (5/4)\(^{7}\)/1 - 5/4

⇒ \(s_{7}\) = 32 (1 - (5/4)\(^{7}\)/3/5

⇒ \(s_{7}\) = 5*32(1 - (5/4)\(^{7}\))/3

⇒ \(s_{7}\) = 160(0.972)/3

⇒ \(s_{7}\) = 156/3

=52

Hence, we can conclude, the sum of the first 7 terms of the geometric sequence is 52

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From the two column proof below, we have seen it is proven that m∠A = m∠C

The two column proof to show that ∠A = ∠C is as follows:

Statement 1: ∠A and ∠B are complementary

Reason 1: Given

Statement 2: ∠C and ∠B are complementary

Reason 2: Given

Statement 3: m∠A  + m∠B = 90°

Reason 3: Definition of Complementary Angles

Statement 4: m∠C  + m∠B = 90°

Reason 4: Definition of Complementary Angles

Statement 5: m∠A  + m∠B = m∠C  + m∠B

Reason 5: Substitution Property of Equality

Statement 6: m∠A = m∠C

Reason 6: Subtraction Property of equality

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Answer:

Step-by-step explanation:

Monday x 2 = Tuesday

Tuesday - 6 = Wednesday

Lets say

Monday = m

Tuesday = t

Wednesday = w

m = m

2m = t

2m - 6 = w

Combine like terms: 5m - 6 = 19

Add 6 to both sides

5m = 25

Divide both sides by 5

m = 5

Plug it in the equations.

Monday = 5

Tuesday =  10

Wednesday = 4

Answer:

5x - 6 = 19

Step-by-step explanation:

Answer: 6.6ft

Step-by-step explanation:

The required greatest common factor among the values 30 and 80 is 2 x 5. Option A is correct.

Given that,
Among the option, it is to be determined which of the option consist of the greatest common factor (GCF) of 30 and 80.

The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.

Here,
30 and 80
30 = 2×3×5
80 = 2×2×2×5
The greatest common factor is given 2×5.

Thus,  the required greatest common factor among the values 30 and 80 is 2 x 5. Option A is correct.

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Therefore ,there are 158,184,000 ways to create a license plate in this system.

A selection from a group of separate items is called a combination in mathematics, and the order in which the elements are chosen is irrelevant (unlike permutations). An apple and a pear, an apple and an orange, or a pear and an orange are three combinations of two fruits that can be chosen from a set of three fruits, such as an apple, an orange, and a pear. Formally speaking, a set S's k-combination is a subset of S's k unique components. Two combinations are therefore equal if and only if they have the same elements in both combinations.

According to the counting principle, the total number of ways to obtain a license plate is calculated by multiplying the number of times each of these events might occur together.

The first number (the digits 1 through 9) can be obtained in nine different ways.

There are 26 methods to obtain the first letter. There are 26 ways to obtain the following letter (repetition is acceptable).

There are 26 methods to get the third letter, 10 ways to get the next number (zero is acceptable), and 10 ways to get the following number with repetitions.

How many ways are there to get the next number? 10 ways\s.

Thus ,total options for obtaining a license plate:

9 x 26 x 26 x 26 x 10 x 10=158184000

Therefore ,there are 158,184,000 ways to create a license plate in this system.

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Answer:

\(\Huge \boxed{{x=56\°}}\)

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

Create an equation.

64 + x + 60 = 180

Solve for x.

Add the numbers.

x + 124 = 180

Subtract 124 from both sides.

x + 124 - 124 = 180 - 124

x = 56

Answer:

56°

Step-by-step explanation:

Why?

Therefore, x is 56°

Answer: $123

Step-by-step explanation:

$20.50/3 (weeks) = 6.83333333333

$6.83333333333 x 18 (weeks) = $123

Answer:

Step-by-step explanation:

18 weeks = 6 * 3

                = 6 * 20.5

                 = $ 123

Answer:

A. 7

Step-by-step explanation:

We already know that 8+4 = 12, So now we have to find out how to make the equation equal 12.

2×6= 12, we have to find out what x will be in order to make the equation true.

2(7-1) = 2(6) = 12. Substitute the 7 for x.

x = 7

Answer:

125.

Given:

Step-by-step explanation:

As given in the question that the ratio is already given,

therefore,

1. The ratio of tourist of to locals

the ratio of tourist to local is 4:5

\(\frac{tourist}{locals}\)=\(\frac{4}{5}\)

2. Attendance of locals at the opening

here are 100 tourist at the opening

\(\frac{100}{locals} =\frac{4}{5}\)

locals= 125

locals are 125 in attendance.

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125 is the attendance of locals

The ratio of tourists to locals is 4:5

Tourists / Locals = 4 / 5

There are 100 tourists at the opening of the new museum

100 / locals = 4/5

locals = 500/4

locals = 125

The attendance of locals is 125.

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Answer:

7x-7=14

7x=14+7

7x=21

x=21/7

x=3

Step-by-step explanation:

Hope it helps you

Answer: Side Angle Side

Answer:

B.

She can rotate triangle DEF 180and then compare the angles and sides. She will see that the triangles are congruent by the Side Angle Side theorem.

Step-by-step explanation:

The dog's running speed of 5 km/hr can be converted to approximately 3.125 mi/hr by multiplying it by the conversion factor of 1 mi/1.6 km. Rounding to the nearest thousandth, the dog can run at about 3.125 mi/hr.

To convert the dog's running speed from kilometers per hour (km/hr) to miles per hour (mi/hr), we need to use the conversion factor of 1.6 km = 1 mi.First, we can convert the dog's speed from km/hr to mi/hr by multiplying it by the conversion factor: 5 km/hr * (1 mi/1.6 km) = 3.125 mi/hr.

However, we need to round the answer to the nearest thousandth (three decimal places). Since the digit after the thousandth place is 5, we round up the thousandth place to obtain the final answer.

Therefore, the dog can run at approximately 3.125 mi/hr.

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Answer:

x= - 20

y= 6

Step-by-step explanation:

2x + 5y = -10

-2x + y = 46

if u solve it

it is 6y= 36 so y =6

and substitute y value into the equation:

-2x+ 6 = 46

-2x= 40

so x= -20

Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.

Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4.  So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.

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The equation that describes this situation is:

105 = 7l

Let's break down the given information:

Mu walks laps to raise money for charity.

For each lap Mu walks, her sponsors will donate $7.

Mu has walked l laps.

The total amount raised by Mu is $105.

To write an equation to describe this situation, let's use the variables:

l represents the number of laps Mu has walked.

$7 represents the amount donated for each lap.

The equation can be written as follows:

Total amount raised = Amount donated per lap × Number of laps

$105 = $7 × l

Therefore, the equation that describes this situation is:

105 = 7l

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Answer:

multiply 4 times x and 3

Step-by-step explanation:

this is because the first step needed to solve is to expand it into 4x+12=12, so that u can solve it from here:

4x+12 =12

4x=12-12

4x=0

x=0/4

x=0

hope this helps :)

Answer: c. subtract three from both sides of the equation

Step-by-step explanation: you want to get the variable by itself. To do this reverse the subtraction or addition. In your case change the addition to subtraction.

Frederick Taylor's theory is known as "scientific management," which aimed to improve workplace productivity by emphasizing efficiency and standardization.

Here are some pros and cons of his theory:

Pros:

1. Increased productivity and efficiency: Taylor's approach helped companies streamline their processes and make better use of their resources. This led to increased productivity and efficiency, which can lead to greater profits and growth.

2. Improved worker skills: By breaking down work into smaller tasks and optimizing them, Taylor's method allowed workers to learn new skills and become more specialized in their work. This can lead to a sense of mastery and increased job satisfaction.

3. Clear division of labor: Taylor's method led to a clear division of labor, which allowed companies to better organize their workers and maximize their output. This also helped to reduce conflict and confusion in the workplace.

Cons:

1. Dehumanization of workers: Taylor's approach viewed workers as mere cogs in a machine rather than as human beings. This led to a lack of respect and dignity for workers, which can lead to low morale and high turnover rates.

2. Lack of creativity and innovation: Taylor's method emphasized standardization and efficiency over creativity and innovation.

3. Potential for abuse: Taylor's approach can be abused by employers who are more concerned with profit than with worker welfare.

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The statement for all possible combinations of truth values for its variables. This can help identify patterns and simplify the expression.

To simplify a complicated expression in formal logic, you can use various techniques such as logical equivalences, truth tables, and laws of logic. The goal is to reduce the expression to its simplest form, making it easier to analyze and understand.

Here are some steps you can follow to simplify the statement "s":

1. Identify the logical operators: Look for logical operators like AND (∧), OR (∨), and NOT (¬) in the expression. These operators help connect different parts of the statement.

2. Apply logical equivalences: Use logical equivalences to transform the expression into an equivalent, but simpler form. For example, you can use De Morgan's laws to convert negations of conjunctions or disjunctions.

3. Simplify using truth tables: Construct a truth table for the expression to determine the truth values of the statement for all possible combinations of truth values for its variables. This can help identify patterns and simplify the expression.

4. Use laws of logic: Apply laws of logic such as the distributive law, commutative law, or associative law to simplify the expression further. These laws allow you to rearrange the terms or combine similar terms.

5. Keep simplifying: Repeat the steps above until you cannot simplify the expression any further. This ensures that you have reached the simplest form of the expression.

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Answer:

757.08 is your answer

Step-by-step explanation:

Hope this helped!

Sorry for not answering sooner :(

Answer:

75.

Step-by-step explanation:

The mean = (78 + 64 + 74 + 92 + 67) / 5

                 = 375 / 5

                 = 75.

Answer:A.75

Step-by-step explanation:

i did it in class

If A is a square matrix:

\(A^2\) = 13 18

         22 31

To do the matrix multiplication, we multiply the first row of A by the first column of A, and then the first row of A by the second column of A. We repeat the process for the second row of A and collect the results in a new 2x2 matrix, which is \(A^2\).

To find A^2, we need to multiply matrix A by itself.

A = 2 3

      4 5

\(A^2 = AA = (2 3)(2 3) + (4 5)(3 4)= (2x2 + 3x4) (2x3 + 3x5) + (4x3 + 5x4) (4x3 + 5x5)\)

\(A^2\) = 13 18

       22 31

Therefore, \(A^2\) = 13 18

                            22 31

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To sketch the region enclosed by the curves y = x^3 - 4x and y = 12x and determine the appropriate method of integration. By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

The curves intersect when x^3 - 4x = 12x. Simplifying this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, which gives us x = 0 and x = ±4 as the intersection points.

To determine whether to integrate with respect to x or y, we can observe that the region is vertically bounded by the curves. Therefore, we'll integrate with respect to x.

To find the area of the region, we'll integrate the difference of the upper and lower curves within the given bounds, from x = -4 to x = 4.

Now, for a more detailed explanation:

First, let's analyze the curves individually. The curve y = x^3 - 4x represents a cubic function, and y = 12x represents a linear function. By plotting these curves on a graph, we can observe that they intersect at three points: (0, 0), (-4, -48), and (4, 48).

To determine the enclosed region, we need to find the x-values at which the curves intersect. Setting the two equations equal to each other, we have x^3 - 4x = 12x. Rearranging this equation, we get x^3 - 16x = 0. Factoring out x, we have x(x^2 - 16) = 0, giving us x = 0 and x = ±4 as the x-values of intersection.

Since the region is vertically bounded by the curves, we'll integrate with respect to x. To find the area, we'll integrate the difference between the upper curve (y = 12x) and the lower curve (y = x^3 - 4x) within the bounds from x = -4 to x = 4.

By evaluating the definite integral ∫[-4 to 4] (12x - (x^3 - 4x)) dx, we can calculate the area of the region enclosed by the given curves.

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Answer: C

Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.

On solving the provided question, we can say that Length of the wooden strip required to frame the photograph= Perimeter of the photograph = 106 cm

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

The length of the photograph = 32cm

The breadth of the photograph = 2 lcm

Length of the wooden strip required to frame the photograph= Perimeter of

the photograph

= 2 x (length + breadth)

= 2 x (32 +21)cm

= 2 53cm

= 106cm

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Sample Space (S) = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

To illustrate all possible outcomes of tossing a dime 3 times, we can create a tree diagram. We'll represent a Head as "H" and a Tail as "T".

Here's the tree diagram:

         H

      /     \

  H       T

 /  \    /  \

H    T  H    T

         T

      /     \

  H       T

 /  \    /  \

H    T  H    T

Using the tree diagram, we can write out the sample space as a set of all possible outcomes:

Sample Space (S) = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

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